TSTP Solution File: ANA013-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ANA013-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n017.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 10:32:47 EDT 2023
% Result : Timeout 293.49s 261.00s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 330
% Syntax : Number of formulae : 341 ( 9 unt; 324 typ; 0 def)
% Number of atoms : 28 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 14 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 671 ( 278 >; 393 *; 0 +; 0 <<)
% Number of predicates : 87 ( 86 usr; 1 prp; 0-3 aty)
% Number of functors : 238 ( 238 usr; 46 con; 0-18 aty)
% Number of variables : 20 (; 20 !; 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_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 > 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_SetsAndFunctions_Oelt__set__times > c_SetsAndFunctions_Oelt__set__plus > 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_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 > 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_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_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_Datatype_Othe > c_Datatype_Ooption_OSome > c_Datatype_Oo2s > c_Binomial_Obinomial > #nlpp > v_x > v_f > tc_set > tc_List_Olist > tc_Datatype_Ooption > c_Suc > c_Numeral_Obin__succ > c_Numeral_Obin__pred > c_Numeral_Obin__minus > 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 > v_c > tc_nat > tc_bool > tc_Product__Type_Ounit > tc_Numeral_Obit > tc_List_Onibble > tc_List_Ochar > tc_IntDef_Oint > tc_Extraction_Osumbool > t_b > c_emptyset > c_Wellfounded__Relations_Oless__than > c_UNIV > c_Relation_OId > c_Product__Type_OUnity > c_Numeral_Obit_OB1 > c_Numeral_Obit_OB0 > c_Numeral_OPls > c_Numeral_OMin > 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_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(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_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(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(v_c,type,
v_c: $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_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_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(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_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(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_List_Onibble_ONibbleA,type,
c_List_Onibble_ONibbleA: $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(c_SetsAndFunctions_Oelt__set__plus,type,
c_SetsAndFunctions_Oelt__set__plus: ( $i * $i * $i ) > $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(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(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(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(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_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(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(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_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(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_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_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(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_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(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_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_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_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(c_Fun_Oid,type,
c_Fun_Oid: ( $i * $i ) > $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(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(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_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_Main_OInter__UNIV__conv__1__1,type,
c_Main_OInter__UNIV__conv__1__1: ( $i * $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(v_x,type,
v_x: $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(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(v_f,type,
v_f: $i > $i ).
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(t_b,type,
t_b: $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_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(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_SetsAndFunctions_Oelt__set__times,type,
c_SetsAndFunctions_Oelt__set__times: ( $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(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_15294,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file(unknown,unknown) ).
tff(f_13593,axiom,
! [T] :
( ~ class_Ring__and__Field_Oordered__idom(T)
| class_Orderings_Olinorder(T) ),
file(unknown,unknown) ).
tff(f_10723,axiom,
! [T_1] : class_Orderings_Oorder(tc_set(T_1)),
file(unknown,unknown) ).
tff(f_10313,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_9339,axiom,
! [T_a,V_x,V_y] :
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(c_SetInterval_OlessThan(V_x,T_a),c_SetInterval_OlessThan(V_y,T_a),tc_set(T_a))
| c_lessequals(V_x,V_y,T_a) ),
file(unknown,unknown) ).
tff(f_15293,axiom,
! [V_U] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),c_times(V_U,c_HOL_Oabs(v_f(v_x(V_U)),t_b),t_b),t_b),
file(unknown,unknown) ).
tff(c_5570,plain,
class_Ring__and__Field_Oordered__idom(t_b),
inference(cnfTransformation,[status(thm)],[f_15294]) ).
tff(c_8397,plain,
! [T_6085] :
( class_Orderings_Olinorder(T_6085)
| ~ class_Ring__and__Field_Oordered__idom(T_6085) ),
inference(cnfTransformation,[status(thm)],[f_13593]) ).
tff(c_8406,plain,
class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_5570,c_8397]) ).
tff(c_3740,plain,
! [T_1_4883] : class_Orderings_Oorder(tc_set(T_1_4883)),
inference(cnfTransformation,[status(thm)],[f_10723]) ).
tff(c_3378,plain,
! [V_x_4675,T_a_4674] :
( c_lessequals(V_x_4675,V_x_4675,T_a_4674)
| ~ class_Orderings_Oorder(T_a_4674) ),
inference(cnfTransformation,[status(thm)],[f_10313]) ).
tff(c_159425,plain,
! [V_x_11078,V_y_11079,T_a_11080] :
( c_lessequals(V_x_11078,V_y_11079,T_a_11080)
| ~ c_lessequals(c_SetInterval_OlessThan(V_x_11078,T_a_11080),c_SetInterval_OlessThan(V_y_11079,T_a_11080),tc_set(T_a_11080))
| ~ class_Orderings_Olinorder(T_a_11080) ),
inference(cnfTransformation,[status(thm)],[f_9339]) ).
tff(c_159453,plain,
! [V_x_11078,T_a_11080] :
( c_lessequals(V_x_11078,V_x_11078,T_a_11080)
| ~ class_Orderings_Olinorder(T_a_11080)
| ~ class_Orderings_Oorder(tc_set(T_a_11080)) ),
inference(resolution,[status(thm)],[c_3378,c_159425]) ).
tff(c_159468,plain,
! [V_x_11078,T_a_11080] :
( c_lessequals(V_x_11078,V_x_11078,T_a_11080)
| ~ class_Orderings_Olinorder(T_a_11080) ),
inference(demodulation,[status(thm),theory(equality)],[c_3740,c_159453]) ).
tff(c_316837,plain,
! [V_U_13339] : ~ c_lessequals(c_times(c_HOL_Oabs(v_c,t_b),c_HOL_Oabs(v_f(v_x(V_U_13339)),t_b),t_b),c_times(V_U_13339,c_HOL_Oabs(v_f(v_x(V_U_13339)),t_b),t_b),t_b),
inference(cnfTransformation,[status(thm)],[f_15293]) ).
tff(c_316874,plain,
~ class_Orderings_Olinorder(t_b),
inference(resolution,[status(thm)],[c_159468,c_316837]) ).
tff(c_316926,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_8406,c_316874]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ANA013-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu Aug 3 14:58:51 EDT 2023
% 0.14/0.34 % CPUTime :
% 293.49/261.00 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 293.49/261.01
% 293.49/261.01 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 293.66/261.05
% 293.66/261.05 Inference rules
% 293.66/261.05 ----------------------
% 293.66/261.05 #Ref : 103
% 293.66/261.05 #Sup : 72912
% 293.66/261.05 #Fact : 9
% 293.66/261.05 #Define : 0
% 293.66/261.05 #Split : 36
% 293.66/261.05 #Chain : 0
% 293.66/261.05 #Close : 0
% 293.66/261.05
% 293.66/261.05 Ordering : KBO
% 293.66/261.05
% 293.66/261.05 Simplification rules
% 293.66/261.05 ----------------------
% 293.66/261.05 #Subsume : 30475
% 293.66/261.05 #Demod : 41422
% 293.66/261.05 #Tautology : 20036
% 293.66/261.05 #SimpNegUnit : 5173
% 293.66/261.05 #BackRed : 497
% 293.66/261.05
% 293.66/261.05 #Partial instantiations: 0
% 293.66/261.05 #Strategies tried : 1
% 293.66/261.05
% 293.66/261.05 Timing (in seconds)
% 293.66/261.05 ----------------------
% 293.66/261.05 Preprocessing : 2.58
% 293.66/261.05 Parsing : 1.53
% 293.66/261.05 CNF conversion : 0.18
% 293.66/261.05 Main loop : 257.32
% 293.66/261.05 Inferencing : 32.72
% 293.66/261.05 Reduction : 138.62
% 293.66/261.05 Demodulation : 109.17
% 293.66/261.05 BG Simplification : 0.53
% 293.66/261.05 Subsumption : 75.06
% 293.66/261.05 Abstraction : 1.07
% 293.66/261.05 MUC search : 0.00
% 293.66/261.05 Cooper : 0.00
% 293.66/261.05 Total : 259.97
% 293.66/261.05 Index Insertion : 0.00
% 293.66/261.05 Index Deletion : 0.00
% 293.66/261.05 Index Matching : 0.00
% 293.66/261.05 BG Taut test : 0.00
%------------------------------------------------------------------------------