TSTP Solution File: SWV317-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV317-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Aug 22 11:03:41 EDT 2023
% Result : Unsatisfiable 39.48s 21.06s
% Output : CNFRefutation 39.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 366
% Syntax : Number of formulae : 373 ( 9 unt; 362 typ; 0 def)
% Number of atoms : 13 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 707 ( 300 >; 407 *; 0 +; 0 <<)
% Number of predicates : 88 ( 86 usr; 1 prp; 0-3 aty)
% Number of functors : 276 ( 276 usr; 62 con; 0-18 aty)
% Number of variables : 5 (; 5 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > c_in > c_List_Oop_Amem > c_Divides_Oop_Advd > c_Wellfounded__Recursion_Owf > c_Wellfounded__Recursion_Oacyclic > c_Relation_Otrans > c_Parity_Oeven > c_List_Onull > c_List_Odistinct > c_IntDef_Oneg > c_IntDef_Oiszero > c_Infinite__Set_Oatmost__one > class_Wellfounded__Recursion_Owellorder > class_Ring__and__Field_Osemiring__1__cancel > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0__cancel > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__1 > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__comm__semiring > class_Ring__and__Field_Opordered__comm__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Opordered__cancel__comm__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > class_Ring__and__Field_Oordered__field > class_Ring__and__Field_Oordered__comm__semiring__strict > class_Ring__and__Field_Olordered__ring > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1__cancel > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring__0__cancel > class_Ring__and__Field_Ocomm__semiring__0 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Ring__and__Field_Oaxclass__no__zero__divisors > class_Ring__and__Field_Oaxclass__abs__if > class_Ring__and__Field_Oaxclass__0__neq__1 > class_Power_Orecpower > class_Parity_Oeven__odd > class_Orderings_Oorder > class_Orderings_Oord > class_Orderings_Olinorder > class_OrderedGroup_Osemigroup__mult > class_OrderedGroup_Osemigroup__add > class_OrderedGroup_Opordered__cancel__ab__semigroup__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Oordered__cancel__ab__semigroup__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Olordered__ab__group__meet > class_OrderedGroup_Olordered__ab__group__join > class_OrderedGroup_Olordered__ab__group__abs > class_OrderedGroup_Olordered__ab__group > class_OrderedGroup_Ocomm__monoid__mult > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Numeral_Onumber__ring > class_Numeral_Onumber > class_Nat_Opower > class_LOrder_Omeet__semilorder > class_LOrder_Olorder > class_LOrder_Ojoin__semilorder > class_HOL_Ozero > class_HOL_Otimes > class_HOL_Oplus > class_HOL_Oone > class_HOL_Ominus > class_HOL_Oinverse > class_Finite__Set_Ofinite > class_Divides_Odiv > c_List_Onibble_Onibble__rec > c_List_Onibble_Onibble__case > c_Main_Orel__compE__3 > c_Main_Orel__compE__2 > c_Main_Orel__compE__1 > c_Relation_Orel__comp > c_Main_OuprodE__2 > c_Main_OuprodE__1 > c_Main_Olistrel__Cons2__2 > c_Main_Olistrel__Cons2__1 > c_Main_Olistrel__Cons1__2 > c_Main_Olistrel__Cons1__1 > c_Main_OdprodE__4 > c_Main_OdprodE__3 > c_Main_OdprodE__2 > c_Main_OdprodE__1 > c_Main_OImageE__1 > c_Wellfounded__Relations_Olex__prod > c_Sum__Type_OPlus > c_Relation_OImage > c_Public_Okeymode_Okeymode__rec > c_Public_Okeymode_Okeymode__case > c_Pair > c_Numeral_Obit_Obit__rec > c_Numeral_Obit_Obit__case > c_Map_Omap__of > c_Main_OusumE__2 > c_Main_OusumE__1 > c_Main_OdsumE__4 > c_Main_OdsumE__3 > c_Main_OdsumE__2 > c_Main_OdsumE__1 > c_Main_OconverseE__2 > c_Main_OconverseE__1 > c_Main_ORangeE__1 > c_Main_OPlusE__2 > c_Main_OPlusE__1 > c_Main_ODomainE__1 > c_List_Ozip > c_List_Olist__update > c_Extraction_Osumbool_Osumbool__rec > c_Extraction_Osumbool_Osumbool__case > c_Datatype__Universe_Ousum > c_Datatype__Universe_Ouprod > c_Datatype__Universe_Ontrunc > c_Datatype__Universe_Odsum > c_Datatype__Universe_Odprod > c_Datatype__Universe_OScons > v_sko__usf > c_union > c_times > c_snd > c_plus > c_minus > c_inter > c_insert > c_fst > c_divide > c_div > c_append > c_Sum__Type_OInr > c_Sum__Type_OInl > c_SetInterval_OgreaterThanLessThan > c_SetInterval_OgreaterThanAtMost > c_SetInterval_OatLeastLessThan > c_SetInterval_OatLeastAtMost > c_Relation_Oconverse > c_Relation_ORange > c_Relation_ODomain > c_Orderings_Omin > c_Orderings_Omax > c_Nat_Opower > c_Main_Osurj__pair__2 > c_Main_Osurj__pair__1 > c_Main_OsubsetI__1 > c_Main_Oin__listsI__1 > c_Main_OdiagE__1 > c_Main_OUnion__iff__1 > c_Main_OUnionE__1 > c_Main_OMin__gr__iff__1 > c_Main_OMin__ge__iff__1 > c_Main_OMax__less__iff__1 > c_Main_OMax__le__iff__1 > c_Main_OInter__iff__1 > c_Main_OInterI__1 > c_List_Otake > c_List_Osublist > c_List_Oset__Cons > c_List_Orotate > c_List_Oreplicate > c_List_Oremove1 > c_List_Onth > c_List_Olist__inter > c_List_Olist_OCons > c_List_Olexn > c_List_Oitrev > c_List_Odrop > c_LOrder_Omeet > c_LOrder_Ojoin > c_Event_Oevent_OSays > c_Equiv__Relations_Oquotient > c_Divides_Oop_Amod > c_Datatype__Universe_ONumb > c_Datatype__Universe_OLeaf > c_Datatype__Universe_OIn1 > c_Datatype__Universe_OIn0 > c_Datatype__Universe_OAtom > c_Datatype_Ounit_Ounit__rec > c_Datatype_Ounit_Ounit__case > v_sko__uhi > tc_sum > tc_prod > tc_fun > tc_Datatype__Universe_Onode > c_uminus > c_Union > c_Transitive__Closure_Otrancl > c_Transitive__Closure_Ortrancl > c_Set_Ocontents > c_SetInterval_OlessThan > c_SetInterval_OgreaterThan > c_SetInterval_OatMost > c_SetInterval_OatLeast > c_Relation_Odiag > c_Public_OpublicKey > c_Pow > c_OrderedGroup_Opprt > c_OrderedGroup_Onprt > c_Numeral_Onumber__of > c_Numeral_Obin__mult > c_Numeral_Obin__add > c_Numeral_OBit > c_Nat_Osize > c_NatArith_Oof__nat > c_Message_Omsg_OMPair > c_Message_Omsg_OCrypt > c_Message_OHPair > c_Main_Ozmod__eq__0D__dest__1 > c_Main_Onot__Some__eq__1 > c_Main_Onot__None__eq__1 > c_Main_Omod__eq__0D__dest__1 > c_Main_Olexord__Nil__left__2 > c_Main_Olexord__Nil__left__1 > c_Main_Ofinite__Union__1 > c_Main_Oempty__Union__conv__1 > c_Main_Oconcat__eq__Nil__conv__1 > c_Main_Oall__not__in__conv__1 > c_Main_OUnion__empty__conv__1 > c_Main_ONil__eq__concat__conv__1 > c_Main_OInter__UNIV__conv__2__1 > c_Main_OInter__UNIV__conv__1__1 > c_Main_OIdE__1 > c_List_Oupt > c_List_Otl > c_List_Oset > c_List_Orotate1 > c_List_Orev > c_List_Oremdups > c_List_Olistset > c_List_Olists > c_List_Olistrel > c_List_Olexord > c_List_Olex > c_List_Olenlex > c_List_Olast > c_List_Ohd > c_List_Oconcat > c_List_Ochar_OChar > c_List_Obutlast > c_Inter > c_IntDiv_Oadjust > c_IntDef_Oof__int > c_HOL_Oinverse > c_HOL_Oabs > c_Fun_Oid > c_Finite__Set_Ocard > c_Finite__Set_OMin > c_Finite__Set_OMax > c_Event_Oknows > c_Event_Oevent_ONotes > c_Event_Oevent_OGets > c_Datatype_Othe > c_Datatype_Ooption_OSome > c_Datatype_Oo2s > c_Binomial_Obinomial > #nlpp > tc_set > tc_List_Olist > tc_Datatype_Ooption > c_Suc > c_Public_OshrK > c_Numeral_Obin__succ > c_Numeral_Obin__pred > c_Numeral_Obin__minus > c_Message_Osynth > c_Message_Oparts > c_Message_Omsg_ONumber > c_Message_Omsg_ONonce > c_Message_Omsg_OKey > c_Message_Omsg_OHash > c_Message_Omsg_OAgent > c_Message_OkeysFor > c_Message_OinvKey > c_Message_Oanalz > c_Message_Oagent_OFriend > c_IntDiv_OposDivAlg > c_IntDiv_OnegateSnd > c_IntDiv_OnegDivAlg > c_IntDef_Onat > c_IntDef_Oint > c_IntDef_ORep__Integ > c_IntDef_OAbs__Integ > c_GCD_Ogcd > c_Event_Oused > c_Event_OinitState > v_evs3 > v_NB > v_NA > v_KAB > v_B > v_Aa > v_A > tc_nat > tc_bool > tc_Public_Okeymode > tc_Product__Type_Ounit > tc_Numeral_Obit > tc_Message_Omsg > tc_Message_Oagent > tc_List_Onibble > tc_List_Ochar > tc_IntDef_Oint > tc_Extraction_Osumbool > tc_Event_Oevent > c_emptyset > c_Wellfounded__Relations_Oless__than > c_UNIV > c_Relation_OId > c_Public_Okeymode_OSignature > c_Public_Okeymode_OEncryption > c_Product__Type_OUnity > c_OtwayRees_Ootway > c_Numeral_Obit_OB1 > c_Numeral_Obit_OB0 > c_Numeral_OPls > c_Numeral_OMin > c_Message_OsymKeys > c_Message_Oagent_OSpy > c_Message_Oagent_OServer > c_List_Onibble_ONibbleF > c_List_Onibble_ONibbleE > c_List_Onibble_ONibbleD > c_List_Onibble_ONibbleC > c_List_Onibble_ONibbleB > c_List_Onibble_ONibbleA > c_List_Onibble_ONibble9 > c_List_Onibble_ONibble8 > c_List_Onibble_ONibble7 > c_List_Onibble_ONibble6 > c_List_Onibble_ONibble5 > c_List_Onibble_ONibble4 > c_List_Onibble_ONibble3 > c_List_Onibble_ONibble2 > c_List_Onibble_ONibble1 > c_List_Onibble_ONibble0 > c_List_Olist_ONil > c_IntDef_Ointrel > c_IntDef_ONats > c_IntDef_OInts > c_IntDef_OInteg > c_Finite__Set_OFinites > c_Extraction_Osumbool_ORight > c_Extraction_Osumbool_OLeft > c_Event_Obad > c_Datatype_Ooption_ONone > c_1 > c_0
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_HOL_Ozero,type,
class_HOL_Ozero: $i > $o ).
tff(c_List_Olist__inter,type,
c_List_Olist__inter: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibble8,type,
c_List_Onibble_ONibble8: $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(c_List_Olistset,type,
c_List_Olistset: ( $i * $i ) > $i ).
tff(c_Numeral_Obit_OB1,type,
c_Numeral_Obit_OB1: $i ).
tff(c_Datatype_Ooption_ONone,type,
c_Datatype_Ooption_ONone: $i ).
tff(c_List_Onibble_ONibbleC,type,
c_List_Onibble_ONibbleC: $i ).
tff(c_Parity_Oeven,type,
c_Parity_Oeven: ( $i * $i ) > $o ).
tff(c_Message_Omsg_OMPair,type,
c_Message_Omsg_OMPair: ( $i * $i ) > $i ).
tff(c_Event_Oknows,type,
c_Event_Oknows: ( $i * $i ) > $i ).
tff(c_Message_Oagent_OFriend,type,
c_Message_Oagent_OFriend: $i > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(c_Main_OuprodE__1,type,
c_Main_OuprodE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Transitive__Closure_Ortrancl,type,
c_Transitive__Closure_Ortrancl: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(c_append,type,
c_append: ( $i * $i * $i ) > $i ).
tff(class_Finite__Set_Ofinite,type,
class_Finite__Set_Ofinite: $i > $o ).
tff(class_Ring__and__Field_Osemiring__1__cancel,type,
class_Ring__and__Field_Osemiring__1__cancel: $i > $o ).
tff(c_Datatype__Universe_OScons,type,
c_Datatype__Universe_OScons: ( $i * $i * $i * $i ) > $i ).
tff(class_HOL_Ominus,type,
class_HOL_Ominus: $i > $o ).
tff(c_Nat_Osize,type,
c_Nat_Osize: ( $i * $i ) > $i ).
tff(c_Wellfounded__Recursion_Oacyclic,type,
c_Wellfounded__Recursion_Oacyclic: ( $i * $i ) > $o ).
tff(c_Main_Orel__compE__2,type,
c_Main_Orel__compE__2: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Numeral_Obin__minus,type,
c_Numeral_Obin__minus: $i > $i ).
tff(class_HOL_Otimes,type,
class_HOL_Otimes: $i > $o ).
tff(c_Numeral_OBit,type,
c_Numeral_OBit: ( $i * $i ) > $i ).
tff(c_Public_Okeymode_OEncryption,type,
c_Public_Okeymode_OEncryption: $i ).
tff(c_Extraction_Osumbool_Osumbool__case,type,
c_Extraction_Osumbool_Osumbool__case: ( $i * $i * $i * $i ) > $i ).
tff(c_Datatype_Oo2s,type,
c_Datatype_Oo2s: ( $i * $i ) > $i ).
tff(c_Relation_Oconverse,type,
c_Relation_Oconverse: ( $i * $i * $i ) > $i ).
tff(c_SetInterval_OlessThan,type,
c_SetInterval_OlessThan: ( $i * $i ) > $i ).
tff(c_Main_OdsumE__1,type,
c_Main_OdsumE__1: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Odistinct,type,
c_List_Odistinct: ( $i * $i ) > $o ).
tff(class_Numeral_Onumber__ring,type,
class_Numeral_Onumber__ring: $i > $o ).
tff(c_Datatype__Universe_OAtom,type,
c_Datatype__Universe_OAtom: ( $i * $i * $i ) > $i ).
tff(c_Public_OshrK,type,
c_Public_OshrK: $i > $i ).
tff(class_Ring__and__Field_Opordered__comm__semiring,type,
class_Ring__and__Field_Opordered__comm__semiring: $i > $o ).
tff(c_Numeral_Onumber__of,type,
c_Numeral_Onumber__of: ( $i * $i ) > $i ).
tff(c_Public_Okeymode_Okeymode__rec,type,
c_Public_Okeymode_Okeymode__rec: ( $i * $i * $i * $i ) > $i ).
tff(c_Message_OkeysFor,type,
c_Message_OkeysFor: $i > $i ).
tff(c_Numeral_Obin__pred,type,
c_Numeral_Obin__pred: $i > $i ).
tff(c_divide,type,
c_divide: ( $i * $i * $i ) > $i ).
tff(c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
tff(c_IntDef_ORep__Integ,type,
c_IntDef_ORep__Integ: $i > $i ).
tff(c_IntDef_Oiszero,type,
c_IntDef_Oiszero: ( $i * $i ) > $o ).
tff(c_Datatype__Universe_OIn0,type,
c_Datatype__Universe_OIn0: ( $i * $i * $i ) > $i ).
tff(c_Datatype__Universe_OLeaf,type,
c_Datatype__Universe_OLeaf: ( $i * $i * $i ) > $i ).
tff(c_IntDef_Oneg,type,
c_IntDef_Oneg: ( $i * $i ) > $o ).
tff(c_Datatype__Universe_Odsum,type,
c_Datatype__Universe_Odsum: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_OdsumE__3,type,
c_Main_OdsumE__3: ( $i * $i * $i * $i ) > $i ).
tff(tc_set,type,
tc_set: $i > $i ).
tff(c_Sum__Type_OPlus,type,
c_Sum__Type_OPlus: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_OusumE__1,type,
c_Main_OusumE__1: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(c_minus,type,
c_minus: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $i > $o ).
tff(c_Main_Olistrel__Cons2__1,type,
c_Main_Olistrel__Cons2__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Relation_Otrans,type,
c_Relation_Otrans: ( $i * $i ) > $o ).
tff(c_Relation_Odiag,type,
c_Relation_Odiag: ( $i * $i ) > $i ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i ).
tff(c_Main_OdprodE__1,type,
c_Main_OdprodE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Onull,type,
c_List_Onull: ( $i * $i ) > $o ).
tff(class_Ring__and__Field_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
tff(c_OtwayRees_Ootway,type,
c_OtwayRees_Ootway: $i ).
tff(c_Datatype__Universe_Odprod,type,
c_Datatype__Universe_Odprod: ( $i * $i * $i * $i ) > $i ).
tff(c_IntDef_OAbs__Integ,type,
c_IntDef_OAbs__Integ: $i > $i ).
tff(tc_Extraction_Osumbool,type,
tc_Extraction_Osumbool: $i ).
tff(c_Main_OdprodE__4,type,
c_Main_OdprodE__4: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring,type,
class_Ring__and__Field_Oring: $i > $o ).
tff(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(c_IntDef_Ointrel,type,
c_IntDef_Ointrel: $i ).
tff(c_Infinite__Set_Oatmost__one,type,
c_Infinite__Set_Oatmost__one: ( $i * $i ) > $o ).
tff(c_List_Orev,type,
c_List_Orev: ( $i * $i ) > $i ).
tff(c_Main_OuprodE__2,type,
c_Main_OuprodE__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_emptyset,type,
c_emptyset: $i ).
tff(c_Event_OinitState,type,
c_Event_OinitState: $i > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_LOrder_Omeet,type,
c_LOrder_Omeet: ( $i * $i * $i ) > $i ).
tff(c_Main_OPlusE__1,type,
c_Main_OPlusE__1: ( $i * $i * $i * $i ) > $i ).
tff(tc_Datatype_Ooption,type,
tc_Datatype_Ooption: $i > $i ).
tff(c_List_Onth,type,
c_List_Onth: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibble6,type,
c_List_Onibble_ONibble6: $i ).
tff(c_Event_Obad,type,
c_Event_Obad: $i ).
tff(c_List_Onibble_ONibble1,type,
c_List_Onibble_ONibble1: $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
tff(c_Main_OMax__le__iff__1,type,
c_Main_OMax__le__iff__1: ( $i * $i * $i ) > $i ).
tff(c_Main_Oconcat__eq__Nil__conv__1,type,
c_Main_Oconcat__eq__Nil__conv__1: ( $i * $i ) > $i ).
tff(c_Datatype_Othe,type,
c_Datatype_Othe: ( $i * $i ) > $i ).
tff(tc_IntDef_Oint,type,
tc_IntDef_Oint: $i ).
tff(c_SetInterval_OatMost,type,
c_SetInterval_OatMost: ( $i * $i ) > $i ).
tff(c_Main_OdiagE__1,type,
c_Main_OdiagE__1: ( $i * $i * $i ) > $i ).
tff(c_Main_OMin__ge__iff__1,type,
c_Main_OMin__ge__iff__1: ( $i * $i * $i ) > $i ).
tff(c_Finite__Set_OMin,type,
c_Finite__Set_OMin: ( $i * $i ) > $i ).
tff(class_Wellfounded__Recursion_Owellorder,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
tff(c_List_Obutlast,type,
c_List_Obutlast: ( $i * $i ) > $i ).
tff(c_List_Oitrev,type,
c_List_Oitrev: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibbleB,type,
c_List_Onibble_ONibbleB: $i ).
tff(c_Map_Omap__of,type,
c_Map_Omap__of: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Onibble_Onibble__rec,type,
c_List_Onibble_Onibble__rec: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Message_Oagent_OSpy,type,
c_Message_Oagent_OSpy: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_List_Onibble_ONibbleA,type,
c_List_Onibble_ONibbleA: $i ).
tff(v_KAB,type,
v_KAB: $i ).
tff(c_Relation_ORange,type,
c_Relation_ORange: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibble2,type,
c_List_Onibble_ONibble2: $i ).
tff(c_List_Onibble_ONibbleD,type,
c_List_Onibble_ONibbleD: $i ).
tff(c_Main_OdsumE__2,type,
c_Main_OdsumE__2: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
tff(c_List_Oupt,type,
c_List_Oupt: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__field,type,
class_Ring__and__Field_Oordered__field: $i > $o ).
tff(class_Ring__and__Field_Opordered__ring,type,
class_Ring__and__Field_Opordered__ring: $i > $o ).
tff(c_SetInterval_OgreaterThan,type,
c_SetInterval_OgreaterThan: ( $i * $i ) > $i ).
tff(class_Divides_Odiv,type,
class_Divides_Odiv: $i > $o ).
tff(c_HOL_Oabs,type,
c_HOL_Oabs: ( $i * $i ) > $i ).
tff(c_Main_Ozmod__eq__0D__dest__1,type,
c_Main_Ozmod__eq__0D__dest__1: ( $i * $i ) > $i ).
tff(tc_Event_Oevent,type,
tc_Event_Oevent: $i ).
tff(c_Datatype_Ounit_Ounit__rec,type,
c_Datatype_Ounit_Ounit__rec: ( $i * $i * $i ) > $i ).
tff(c_IntDef_ONats,type,
c_IntDef_ONats: $i ).
tff(c_Pow,type,
c_Pow: ( $i * $i ) > $i ).
tff(c_Main_OusumE__2,type,
c_Main_OusumE__2: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Olists,type,
c_List_Olists: ( $i * $i ) > $i ).
tff(c_SetInterval_OgreaterThanAtMost,type,
c_SetInterval_OgreaterThanAtMost: ( $i * $i * $i ) > $i ).
tff(v_NA,type,
v_NA: $i ).
tff(c_Main_Oin__listsI__1,type,
c_Main_Oin__listsI__1: ( $i * $i * $i ) > $i ).
tff(c_0,type,
c_0: $i ).
tff(tc_prod,type,
tc_prod: ( $i * $i ) > $i ).
tff(v_NB,type,
v_NB: $i ).
tff(c_IntDiv_Oadjust,type,
c_IntDiv_Oadjust: ( $i * $i ) > $i ).
tff(c_List_Otl,type,
c_List_Otl: ( $i * $i ) > $i ).
tff(c_Datatype__Universe_ONumb,type,
c_Datatype__Universe_ONumb: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__cancel__comm__semiring,type,
class_Ring__and__Field_Opordered__cancel__comm__semiring: $i > $o ).
tff(c_Main_Orel__compE__1,type,
c_Main_Orel__compE__1: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Oreplicate,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(c_Main_OMin__gr__iff__1,type,
c_Main_OMin__gr__iff__1: ( $i * $i * $i ) > $i ).
tff(c_Numeral_Obit_OB0,type,
c_Numeral_Obit_OB0: $i ).
tff(c_Divides_Oop_Advd,type,
c_Divides_Oop_Advd: ( $i * $i * $i ) > $o ).
tff(c_1,type,
c_1: $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(c_Equiv__Relations_Oquotient,type,
c_Equiv__Relations_Oquotient: ( $i * $i * $i ) > $i ).
tff(c_Main_OdsumE__4,type,
c_Main_OdsumE__4: ( $i * $i * $i * $i ) > $i ).
tff(c_IntDef_OInts,type,
c_IntDef_OInts: $i ).
tff(class_OrderedGroup_Olordered__ab__group__meet,type,
class_OrderedGroup_Olordered__ab__group__meet: $i > $o ).
tff(c_List_Oset,type,
c_List_Oset: ( $i * $i ) > $i ).
tff(c_IntDef_Oint,type,
c_IntDef_Oint: $i > $i ).
tff(c_Main_Olistrel__Cons1__1,type,
c_Main_Olistrel__Cons1__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_evs3,type,
v_evs3: $i ).
tff(class_OrderedGroup_Olordered__ab__group__join,type,
class_OrderedGroup_Olordered__ab__group__join: $i > $o ).
tff(class_Ring__and__Field_Oaxclass__abs__if,type,
class_Ring__and__Field_Oaxclass__abs__if: $i > $o ).
tff(tc_Product__Type_Ounit,type,
tc_Product__Type_Ounit: $i ).
tff(c_Datatype__Universe_Ousum,type,
c_Datatype__Universe_Ousum: ( $i * $i * $i * $i ) > $i ).
tff(c_IntDiv_OposDivAlg,type,
c_IntDiv_OposDivAlg: $i > $i ).
tff(c_Datatype__Universe_Ontrunc,type,
c_Datatype__Universe_Ontrunc: ( $i * $i * $i * $i ) > $i ).
tff(tc_Message_Oagent,type,
tc_Message_Oagent: $i ).
tff(c_times,type,
c_times: ( $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_List_Oop_Amem,type,
c_List_Oop_Amem: ( $i * $i * $i ) > $o ).
tff(c_List_Oconcat,type,
c_List_Oconcat: ( $i * $i ) > $i ).
tff(c_List_Onibble_ONibble7,type,
c_List_Onibble_ONibble7: $i ).
tff(c_List_Oremdups,type,
c_List_Oremdups: ( $i * $i ) > $i ).
tff(c_Main_Osurj__pair__2,type,
c_Main_Osurj__pair__2: ( $i * $i * $i ) > $i ).
tff(c_Message_Osynth,type,
c_Message_Osynth: $i > $i ).
tff(c_Main_OIdE__1,type,
c_Main_OIdE__1: ( $i * $i ) > $i ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(class_Ring__and__Field_Oordered__comm__semiring__strict,type,
class_Ring__and__Field_Oordered__comm__semiring__strict: $i > $o ).
tff(c_Numeral_Obin__succ,type,
c_Numeral_Obin__succ: $i > $i ).
tff(c_List_Ozip,type,
c_List_Ozip: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_ONil__eq__concat__conv__1,type,
c_Main_ONil__eq__concat__conv__1: ( $i * $i ) > $i ).
tff(c_UNIV,type,
c_UNIV: $i ).
tff(v_Aa,type,
v_Aa: $i ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(c_Numeral_OMin,type,
c_Numeral_OMin: $i ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
tff(c_fst,type,
c_fst: ( $i * $i * $i ) > $i ).
tff(c_Public_Okeymode_Okeymode__case,type,
c_Public_Okeymode_Okeymode__case: ( $i * $i * $i * $i ) > $i ).
tff(class_Power_Orecpower,type,
class_Power_Orecpower: $i > $o ).
tff(c_Wellfounded__Relations_Olex__prod,type,
c_Wellfounded__Relations_Olex__prod: ( $i * $i * $i * $i ) > $i ).
tff(class_HOL_Oinverse,type,
class_HOL_Oinverse: $i > $o ).
tff(c_List_Onibble_ONibble0,type,
c_List_Onibble_ONibble0: $i ).
tff(c_Public_Okeymode_OSignature,type,
c_Public_Okeymode_OSignature: $i ).
tff(c_Message_Omsg_OAgent,type,
c_Message_Omsg_OAgent: $i > $i ).
tff(c_SetInterval_OatLeast,type,
c_SetInterval_OatLeast: ( $i * $i ) > $i ).
tff(tc_List_Olist,type,
tc_List_Olist: $i > $i ).
tff(class_Parity_Oeven__odd,type,
class_Parity_Oeven__odd: $i > $o ).
tff(c_List_Onibble_ONibble3,type,
c_List_Onibble_ONibble3: $i ).
tff(c_Message_OsymKeys,type,
c_Message_OsymKeys: $i ).
tff(class_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_Main_OsubsetI__1,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_in,type,
c_in: ( $i * $i * $i ) > $o ).
tff(class_Ring__and__Field_Oaxclass__no__zero__divisors,type,
class_Ring__and__Field_Oaxclass__no__zero__divisors: $i > $o ).
tff(c_List_Olexord,type,
c_List_Olexord: ( $i * $i ) > $i ).
tff(c_Datatype__Universe_OIn1,type,
c_Datatype__Universe_OIn1: ( $i * $i * $i ) > $i ).
tff(class_HOL_Oone,type,
class_HOL_Oone: $i > $o ).
tff(c_IntDiv_OnegateSnd,type,
c_IntDiv_OnegateSnd: $i > $i ).
tff(class_Ring__and__Field_Oaxclass__0__neq__1,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
tff(c_List_Olist__update,type,
c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_OdprodE__2,type,
c_Main_OdprodE__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(c_Union,type,
c_Union: ( $i * $i ) > $i ).
tff(c_Inter,type,
c_Inter: ( $i * $i ) > $i ).
tff(c_Datatype_Ooption_OSome,type,
c_Datatype_Ooption_OSome: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OHash,type,
c_Message_Omsg_OHash: $i > $i ).
tff(c_List_Oremove1,type,
c_List_Oremove1: ( $i * $i * $i ) > $i ).
tff(c_SetInterval_OatLeastLessThan,type,
c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $i ).
tff(c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: ( $i * $i ) > $i ).
tff(c_IntDef_OInteg,type,
c_IntDef_OInteg: $i ).
tff(class_OrderedGroup_Opordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__mult,type,
class_OrderedGroup_Ocomm__monoid__mult: $i > $o ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(c_Event_Oused,type,
c_Event_Oused: $i > $i ).
tff(c_Main_Orel__compE__3,type,
c_Main_Orel__compE__3: ( $i * $i * $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oordered__cancel__ab__semigroup__add,type,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add: $i > $o ).
tff(c_IntDef_Onat,type,
c_IntDef_Onat: $i > $i ).
tff(c_Main_OInterI__1,type,
c_Main_OInterI__1: ( $i * $i * $i ) > $i ).
tff(c_LOrder_Ojoin,type,
c_LOrder_Ojoin: ( $i * $i * $i ) > $i ).
tff(c_Main_Olexord__Nil__left__2,type,
c_Main_Olexord__Nil__left__2: ( $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $i * $i ) > $i ).
tff(c_IntDef_Oof__int,type,
c_IntDef_Oof__int: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_Orderings_Oord,type,
class_Orderings_Oord: $i > $o ).
tff(c_Numeral_Obin__mult,type,
c_Numeral_Obin__mult: ( $i * $i ) > $i ).
tff(c_Main_OUnion__iff__1,type,
c_Main_OUnion__iff__1: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__comm__ring,type,
class_Ring__and__Field_Opordered__comm__ring: $i > $o ).
tff(tc_bool,type,
tc_bool: $i ).
tff(c_Main_Olistrel__Cons1__2,type,
c_Main_Olistrel__Cons1__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_Binomial_Obinomial,type,
c_Binomial_Obinomial: ( $i * $i ) > $i ).
tff(c_List_Olenlex,type,
c_List_Olenlex: ( $i * $i ) > $i ).
tff(c_Numeral_Obit_Obit__rec,type,
c_Numeral_Obit_Obit__rec: ( $i * $i * $i * $i ) > $i ).
tff(tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
tff(c_Extraction_Osumbool_Osumbool__rec,type,
c_Extraction_Osumbool_Osumbool__rec: ( $i * $i * $i * $i ) > $i ).
tff(c_Finite__Set_OMax,type,
c_Finite__Set_OMax: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Osemigroup__mult,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
tff(c_List_Olexn,type,
c_List_Olexn: ( $i * $i * $i ) > $i ).
tff(c_Relation_Orel__comp,type,
c_Relation_Orel__comp: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group,type,
class_OrderedGroup_Olordered__ab__group: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(c_List_Orotate,type,
c_List_Orotate: ( $i * $i * $i ) > $i ).
tff(c_GCD_Ogcd,type,
c_GCD_Ogcd: $i > $i ).
tff(c_Main_OInter__UNIV__conv__2__1,type,
c_Main_OInter__UNIV__conv__2__1: ( $i * $i ) > $i ).
tff(c_Message_Oparts,type,
c_Message_Oparts: $i > $i ).
tff(c_HOL_Oinverse,type,
c_HOL_Oinverse: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(c_union,type,
c_union: ( $i * $i * $i ) > $i ).
tff(c_List_Osublist,type,
c_List_Osublist: ( $i * $i * $i ) > $i ).
tff(c_List_Ochar_OChar,type,
c_List_Ochar_OChar: ( $i * $i ) > $i ).
tff(tc_List_Onibble,type,
tc_List_Onibble: $i ).
tff(class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(c_div,type,
c_div: ( $i * $i * $i ) > $i ).
tff(c_Public_OpublicKey,type,
c_Public_OpublicKey: ( $i * $i ) > $i ).
tff(tc_Datatype__Universe_Onode,type,
tc_Datatype__Universe_Onode: ( $i * $i ) > $i ).
tff(c_less,type,
c_less: ( $i * $i * $i ) > $o ).
tff(c_Main_OPlusE__2,type,
c_Main_OPlusE__2: ( $i * $i * $i * $i ) > $i ).
tff(c_Nat_Opower,type,
c_Nat_Opower: ( $i * $i * $i ) > $i ).
tff(c_inter,type,
c_inter: ( $i * $i * $i ) > $i ).
tff(class_LOrder_Omeet__semilorder,type,
class_LOrder_Omeet__semilorder: $i > $o ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_Message_Omsg_OCrypt,type,
c_Message_Omsg_OCrypt: ( $i * $i ) > $i ).
tff(c_SetInterval_OgreaterThanLessThan,type,
c_SetInterval_OgreaterThanLessThan: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibble5,type,
c_List_Onibble_ONibble5: $i ).
tff(c_Numeral_Obin__add,type,
c_Numeral_Obin__add: ( $i * $i ) > $i ).
tff(c_Main_Oall__not__in__conv__1,type,
c_Main_Oall__not__in__conv__1: ( $i * $i ) > $i ).
tff(c_plus,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_Event_Oevent_ONotes,type,
c_Event_Oevent_ONotes: ( $i * $i ) > $i ).
tff(c_Relation_OImage,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(c_Orderings_Omax,type,
c_Orderings_Omax: ( $i * $i * $i ) > $i ).
tff(c_Message_OHPair,type,
c_Message_OHPair: ( $i * $i ) > $i ).
tff(c_Main_Ofinite__Union__1,type,
c_Main_Ofinite__Union__1: ( $i * $i ) > $i ).
tff(tc_Numeral_Obit,type,
tc_Numeral_Obit: $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(v_B,type,
v_B: $i ).
tff(c_Fun_Oid,type,
c_Fun_Oid: ( $i * $i ) > $i ).
tff(tc_Public_Okeymode,type,
tc_Public_Okeymode: $i ).
tff(c_List_Onibble_ONibbleE,type,
c_List_Onibble_ONibbleE: $i ).
tff(c_Main_OMax__less__iff__1,type,
c_Main_OMax__less__iff__1: ( $i * $i * $i ) > $i ).
tff(c_NatArith_Oof__nat,type,
c_NatArith_Oof__nat: ( $i * $i ) > $i ).
tff(c_List_Odrop,type,
c_List_Odrop: ( $i * $i * $i ) > $i ).
tff(c_uminus,type,
c_uminus: ( $i * $i ) > $i ).
tff(c_Finite__Set_OFinites,type,
c_Finite__Set_OFinites: $i ).
tff(tc_List_Ochar,type,
tc_List_Ochar: $i ).
tff(c_SetInterval_OatLeastAtMost,type,
c_SetInterval_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(c_snd,type,
c_snd: ( $i * $i * $i ) > $i ).
tff(c_Extraction_Osumbool_OLeft,type,
c_Extraction_Osumbool_OLeft: $i ).
tff(c_Main_Oempty__Union__conv__1,type,
c_Main_Oempty__Union__conv__1: ( $i * $i ) > $i ).
tff(c_Main_OconverseE__1,type,
c_Main_OconverseE__1: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__0__cancel,type,
class_Ring__and__Field_Ocomm__semiring__0__cancel: $i > $o ).
tff(c_Main_Onot__None__eq__1,type,
c_Main_Onot__None__eq__1: ( $i * $i ) > $i ).
tff(c_Message_Oagent_OServer,type,
c_Message_Oagent_OServer: $i ).
tff(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(c_List_Onibble_ONibble9,type,
c_List_Onibble_ONibble9: $i ).
tff(class_Ring__and__Field_Olordered__ring,type,
class_Ring__and__Field_Olordered__ring: $i > $o ).
tff(c_List_Olist_OCons,type,
c_List_Olist_OCons: ( $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibbleF,type,
c_List_Onibble_ONibbleF: $i ).
tff(class_LOrder_Ojoin__semilorder,type,
class_LOrder_Ojoin__semilorder: $i > $o ).
tff(c_Pair,type,
c_Pair: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Onibble_ONibble4,type,
c_List_Onibble_ONibble4: $i ).
tff(v_sko__usf,type,
v_sko__usf: ( $i * $i * $i ) > $i ).
tff(c_List_Olex,type,
c_List_Olex: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Osemiring__0__cancel,type,
class_Ring__and__Field_Osemiring__0__cancel: $i > $o ).
tff(c_Main_ORangeE__1,type,
c_Main_ORangeE__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_Onot__Some__eq__1,type,
c_Main_Onot__Some__eq__1: ( $i * $i ) > $i ).
tff(c_Main_OdprodE__3,type,
c_Main_OdprodE__3: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_HOL_Oplus,type,
class_HOL_Oplus: $i > $o ).
tff(c_List_Ohd,type,
c_List_Ohd: ( $i * $i ) > $i ).
tff(c_Datatype_Ounit_Ounit__case,type,
c_Datatype_Ounit_Ounit__case: ( $i * $i * $i ) > $i ).
tff(c_Event_Oevent_OGets,type,
c_Event_Oevent_OGets: ( $i * $i ) > $i ).
tff(c_Main_Olexord__Nil__left__1,type,
c_Main_Olexord__Nil__left__1: ( $i * $i ) > $i ).
tff(c_Wellfounded__Relations_Oless__than,type,
c_Wellfounded__Relations_Oless__than: $i ).
tff(c_OrderedGroup_Opprt,type,
c_OrderedGroup_Opprt: ( $i * $i ) > $i ).
tff(c_Divides_Oop_Amod,type,
c_Divides_Oop_Amod: ( $i * $i * $i ) > $i ).
tff(c_List_Orotate1,type,
c_List_Orotate1: ( $i * $i ) > $i ).
tff(c_Main_OconverseE__2,type,
c_Main_OconverseE__2: ( $i * $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_Message_OinvKey,type,
c_Message_OinvKey: $i > $i ).
tff(c_Main_OInter__UNIV__conv__1__1,type,
c_Main_OInter__UNIV__conv__1__1: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONonce,type,
c_Message_Omsg_ONonce: $i > $i ).
tff(class_Numeral_Onumber,type,
class_Numeral_Onumber: $i > $o ).
tff(c_List_Olistrel,type,
c_List_Olistrel: ( $i * $i ) > $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(c_IntDiv_OnegDivAlg,type,
c_IntDiv_OnegDivAlg: $i > $i ).
tff(c_List_Otake,type,
c_List_Otake: ( $i * $i * $i ) > $i ).
tff(c_Main_ODomainE__1,type,
c_Main_ODomainE__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_OUnionE__1,type,
c_Main_OUnionE__1: ( $i * $i * $i ) > $i ).
tff(c_Main_OImageE__1,type,
c_Main_OImageE__1: ( $i * $i * $i * $i * $i ) > $i ).
tff(v_A,type,
v_A: $i ).
tff(c_Product__Type_OUnity,type,
c_Product__Type_OUnity: $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Datatype__Universe_Ouprod,type,
c_Datatype__Universe_Ouprod: ( $i * $i * $i * $i ) > $i ).
tff(class_Nat_Opower,type,
class_Nat_Opower: $i > $o ).
tff(c_Numeral_OPls,type,
c_Numeral_OPls: $i ).
tff(c_Event_Oevent_OSays,type,
c_Event_Oevent_OSays: ( $i * $i * $i ) > $i ).
tff(c_Main_Osurj__pair__1,type,
c_Main_Osurj__pair__1: ( $i * $i * $i ) > $i ).
tff(c_insert,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(c_OrderedGroup_Onprt,type,
c_OrderedGroup_Onprt: ( $i * $i ) > $i ).
tff(c_Main_Omod__eq__0D__dest__1,type,
c_Main_Omod__eq__0D__dest__1: ( $i * $i ) > $i ).
tff(c_Message_Omsg_ONumber,type,
c_Message_Omsg_ONumber: $i > $i ).
tff(c_Main_Olistrel__Cons2__2,type,
c_Main_Olistrel__Cons2__2: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_List_Oset__Cons,type,
c_List_Oset__Cons: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__semiring__1__cancel,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
tff(c_Main_OInter__iff__1,type,
c_Main_OInter__iff__1: ( $i * $i * $i ) > $i ).
tff(c_Relation_OId,type,
c_Relation_OId: $i ).
tff(c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: ( $i * $i ) > $i ).
tff(c_Numeral_Obit_Obit__case,type,
c_Numeral_Obit_Obit__case: ( $i * $i * $i * $i ) > $i ).
tff(c_Main_OUnion__empty__conv__1,type,
c_Main_OUnion__empty__conv__1: ( $i * $i ) > $i ).
tff(c_List_Olast,type,
c_List_Olast: ( $i * $i ) > $i ).
tff(c_Message_Omsg_OKey,type,
c_Message_Omsg_OKey: $i > $i ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(tc_sum,type,
tc_sum: ( $i * $i ) > $i ).
tff(c_Relation_ODomain,type,
c_Relation_ODomain: ( $i * $i * $i ) > $i ).
tff(c_Sum__Type_OInl,type,
c_Sum__Type_OInl: ( $i * $i * $i ) > $i ).
tff(c_Wellfounded__Recursion_Owf,type,
c_Wellfounded__Recursion_Owf: ( $i * $i ) > $o ).
tff(class_LOrder_Olorder,type,
class_LOrder_Olorder: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(v_sko__uhi,type,
v_sko__uhi: ( $i * $i ) > $i ).
tff(c_Orderings_Omin,type,
c_Orderings_Omin: ( $i * $i * $i ) > $i ).
tff(c_Extraction_Osumbool_ORight,type,
c_Extraction_Osumbool_ORight: $i ).
tff(c_Set_Ocontents,type,
c_Set_Ocontents: ( $i * $i ) > $i ).
tff(c_List_Onibble_Onibble__case,type,
c_List_Onibble_Onibble__case: ( $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i * $i ) > $i ).
tff(c_Sum__Type_OInr,type,
c_Sum__Type_OInr: ( $i * $i * $i ) > $i ).
tff(f_15779,axiom,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
file(unknown,unknown) ).
tff(f_15795,axiom,
( ( c_Public_OshrK(v_A) = v_KAB )
| c_in(v_A,c_Event_Obad,tc_Message_Oagent) ),
file(unknown,unknown) ).
tff(f_15714,axiom,
! [V_A,V_evs] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A)),c_Event_Oused(V_evs),tc_Message_Omsg),
file(unknown,unknown) ).
tff(f_15776,axiom,
~ c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg),
file(unknown,unknown) ).
tff(c_5882,plain,
~ c_in(v_A,c_Event_Obad,tc_Message_Oagent),
inference(cnfTransformation,[status(thm)],[f_15779]) ).
tff(c_5890,plain,
( c_in(v_A,c_Event_Obad,tc_Message_Oagent)
| ( c_Public_OshrK(v_A) = v_KAB ) ),
inference(cnfTransformation,[status(thm)],[f_15795]) ).
tff(c_5891,plain,
c_Public_OshrK(v_A) = v_KAB,
inference(negUnitSimplification,[status(thm)],[c_5882,c_5890]) ).
tff(c_23076,plain,
! [V_A_7587,V_evs_7588] : c_in(c_Message_Omsg_OKey(c_Public_OshrK(V_A_7587)),c_Event_Oused(V_evs_7588),tc_Message_Omsg),
inference(cnfTransformation,[status(thm)],[f_15714]) ).
tff(c_23078,plain,
! [V_evs_7588] : c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(V_evs_7588),tc_Message_Omsg),
inference(superposition,[status(thm),theory(equality)],[c_5891,c_23076]) ).
tff(c_5878,plain,
~ c_in(c_Message_Omsg_OKey(v_KAB),c_Event_Oused(v_evs3),tc_Message_Omsg),
inference(cnfTransformation,[status(thm)],[f_15776]) ).
tff(c_23081,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_23078,c_5878]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWV317-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Thu Aug 3 22:53:06 EDT 2023
% 0.11/0.31 % CPUTime :
% 39.48/21.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.48/21.06
% 39.48/21.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.48/21.10
% 39.48/21.10 Inference rules
% 39.48/21.10 ----------------------
% 39.48/21.10 #Ref : 11
% 39.48/21.10 #Sup : 3819
% 39.48/21.10 #Fact : 0
% 39.48/21.10 #Define : 0
% 39.48/21.10 #Split : 0
% 39.48/21.10 #Chain : 0
% 39.48/21.10 #Close : 0
% 39.48/21.10
% 39.48/21.10 Ordering : KBO
% 39.48/21.10
% 39.48/21.10 Simplification rules
% 39.48/21.10 ----------------------
% 39.48/21.10 #Subsume : 2314
% 39.48/21.10 #Demod : 1168
% 39.48/21.10 #Tautology : 1582
% 39.48/21.10 #SimpNegUnit : 9
% 39.48/21.10 #BackRed : 2
% 39.48/21.10
% 39.48/21.10 #Partial instantiations: 0
% 39.48/21.10 #Strategies tried : 1
% 39.48/21.10
% 39.48/21.10 Timing (in seconds)
% 39.48/21.10 ----------------------
% 39.48/21.10 Preprocessing : 2.73
% 39.48/21.10 Parsing : 1.62
% 39.48/21.10 CNF conversion : 0.20
% 39.48/21.10 Main loop : 17.44
% 39.48/21.10 Inferencing : 2.44
% 39.48/21.10 Reduction : 8.51
% 39.48/21.10 Demodulation : 5.95
% 39.48/21.10 BG Simplification : 0.28
% 39.48/21.10 Subsumption : 4.22
% 39.48/21.10 Abstraction : 0.23
% 39.48/21.10 MUC search : 0.00
% 39.48/21.10 Cooper : 0.00
% 39.48/21.10 Total : 20.23
% 39.48/21.10 Index Insertion : 0.00
% 39.48/21.10 Index Deletion : 0.00
% 39.48/21.10 Index Matching : 0.00
% 39.48/21.10 BG Taut test : 0.00
%------------------------------------------------------------------------------