TSTP Solution File: SWV240-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV240-1 : 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 : n006.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 11:03:17 EDT 2023
% Result : Unsatisfiable 43.51s 21.25s
% Output : CNFRefutation 43.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 224
% Syntax : Number of formulae : 235 ( 7 unt; 218 typ; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 427 ( 196 >; 231 *; 0 +; 0 <<)
% Number of predicates : 82 ( 81 usr; 1 prp; 0-3 aty)
% Number of functors : 137 ( 137 usr; 22 con; 0-6 aty)
% Number of variables : 31 (; 31 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_less > c_in > c_Divides_Oop_Advd > c_Wellfounded__Recursion_Owf > c_Wellfounded__Recursion_Oacyclic > c_Relation_Otrans > c_List_Odistinct > 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_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_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_Datatype__Universe_Ousum > c_Datatype__Universe_Ouprod > c_Datatype__Universe_Odsum > c_Datatype__Universe_Odprod > c_Datatype__Universe_OScons > c_union > c_times > c_plus > c_minus > c_inter > c_insert > 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_Main_OsubsetI__1 > c_Main_Oin__listsI__1 > c_Main_OdiagE__1 > c_Main_OUnionE__1 > c_Main_OInterI__1 > c_List_Olist_OCons > 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 > tc_sum > tc_prod > tc_fun > tc_Datatype__Universe_Onode > c_uminus > c_Union > c_Transitive__Closure_Otrancl > c_Transitive__Closure_Ortrancl > c_SetInterval_OlessThan > c_SetInterval_OgreaterThan > c_SetInterval_OatMost > c_SetInterval_OatLeast > c_Relation_Odiag > c_Pow > c_Nat_Osize > c_Message_Omsg_OMPair > c_Message_Omsg_OCrypt > c_Main_Ozmod__eq__0D__dest__1 > c_Main_Onot__Some__eq__iff1__1 > c_Main_Onot__None__eq__iff1__1 > c_Main_Omod__eq__0D__dest__1 > c_Main_Ofinite__Union__1 > c_Main_OIdE__1 > c_List_Oset > c_List_Orev > c_List_Oremdups > c_List_Olists > c_List_Olistrel > c_List_Olex > c_List_Olenlex > c_List_Ochar_OChar > c_Inter > c_Datatype_Ooption_OSome > c_Datatype_Oo2s > #nlpp > tc_set > tc_List_Olist > tc_Datatype_Ooption > c_Suc > 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_OinvKey > c_Message_Oanalz > c_Message_Oagent_OFriend > c_IntDef_Oint > c_GCD_Ogcd > v_H > v_G > tc_nat > tc_bool > tc_Product__Type_Ounit > tc_Message_Omsg > tc_IntDef_Oint > c_emptyset > c_Wellfounded__Relations_Oless__than > c_UNIV > c_Relation_OId > c_Numeral_Obit_OB1 > c_Numeral_Obit_OB0 > c_Message_Oagent_OSpy > c_Message_Oagent_OServer > c_List_Olist_ONil > 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(class_Ring__and__Field_Ocomm__semiring__0,type,
class_Ring__and__Field_Ocomm__semiring__0: $i > $o ).
tff(c_Numeral_Obit_OB1,type,
c_Numeral_Obit_OB1: $i ).
tff(c_Datatype_Ooption_ONone,type,
c_Datatype_Ooption_ONone: $i ).
tff(c_Message_Omsg_OMPair,type,
c_Message_Omsg_OMPair: ( $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_Main_Onot__Some__eq__iff1__1,type,
c_Main_Onot__Some__eq__iff1__1: ( $i * $i ) > $i ).
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(class_HOL_Otimes,type,
class_HOL_Otimes: $i > $o ).
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(v_G,type,
v_G: $i ).
tff(c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
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_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(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_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_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_Main_OPlusE__1,type,
c_Main_OPlusE__1: ( $i * $i * $i * $i ) > $i ).
tff(tc_Datatype_Ooption,type,
tc_Datatype_Ooption: $i > $i ).
tff(class_OrderedGroup_Olordered__ab__group__abs,type,
class_OrderedGroup_Olordered__ab__group__abs: $i > $o ).
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(class_Wellfounded__Recursion_Owellorder,type,
class_Wellfounded__Recursion_Owellorder: $i > $o ).
tff(c_Message_Oagent_OSpy,type,
c_Message_Oagent_OSpy: $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(c_Relation_ORange,type,
c_Relation_ORange: ( $i * $i * $i ) > $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(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_Main_Ozmod__eq__0D__dest__1,type,
c_Main_Ozmod__eq__0D__dest__1: ( $i * $i ) > $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_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_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(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_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_Oremdups,type,
c_List_Oremdups: ( $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_UNIV,type,
c_UNIV: $i ).
tff(class_Ring__and__Field_Ocomm__ring__1,type,
class_Ring__and__Field_Ocomm__ring__1: $i > $o ).
tff(class_Ring__and__Field_Ofield,type,
class_Ring__and__Field_Ofield: $i > $o ).
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_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(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_Datatype__Universe_OIn1,type,
c_Datatype__Universe_OIn1: ( $i * $i * $i ) > $i ).
tff(class_HOL_Oone,type,
class_HOL_Oone: $i > $o ).
tff(class_Ring__and__Field_Oaxclass__0__neq__1,type,
class_Ring__and__Field_Oaxclass__0__neq__1: $i > $o ).
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_SetInterval_OatLeastLessThan,type,
c_SetInterval_OatLeastLessThan: ( $i * $i * $i ) > $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_Main_OInterI__1,type,
c_Main_OInterI__1: ( $i * $i * $i ) > $i ).
tff(tc_fun,type,
tc_fun: ( $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(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_List_Olenlex,type,
c_List_Olenlex: ( $i * $i ) > $i ).
tff(tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
tff(class_OrderedGroup_Osemigroup__mult,type,
class_OrderedGroup_Osemigroup__mult: $i > $o ).
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_GCD_Ogcd,type,
c_GCD_Ogcd: $i > $i ).
tff(c_Message_Oparts,type,
c_Message_Oparts: $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_Ochar_OChar,type,
c_List_Ochar_OChar: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
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_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_plus,type,
c_plus: ( $i * $i * $i ) > $i ).
tff(c_Relation_OImage,type,
c_Relation_OImage: ( $i * $i * $i * $i ) > $i ).
tff(v_H,type,
v_H: $i ).
tff(c_Main_Ofinite__Union__1,type,
c_Main_Ofinite__Union__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_uminus,type,
c_uminus: ( $i * $i ) > $i ).
tff(c_Finite__Set_OFinites,type,
c_Finite__Set_OFinites: $i ).
tff(c_SetInterval_OatLeastAtMost,type,
c_SetInterval_OatLeastAtMost: ( $i * $i * $i ) > $i ).
tff(c_Extraction_Osumbool_OLeft,type,
c_Extraction_Osumbool_OLeft: $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_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(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(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_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_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_Wellfounded__Relations_Oless__than,type,
c_Wellfounded__Relations_Oless__than: $i ).
tff(c_Divides_Oop_Amod,type,
c_Divides_Oop_Amod: ( $i * $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_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_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(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_insert,type,
c_insert: ( $i * $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(class_Ring__and__Field_Ocomm__semiring__1__cancel,type,
class_Ring__and__Field_Ocomm__semiring__1__cancel: $i > $o ).
tff(c_Relation_OId,type,
c_Relation_OId: $i ).
tff(c_Transitive__Closure_Otrancl,type,
c_Transitive__Closure_Otrancl: ( $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(c_Extraction_Osumbool_ORight,type,
c_Extraction_Osumbool_ORight: $i ).
tff(c_Main_Onot__None__eq__iff1__1,type,
c_Main_Onot__None__eq__iff1__1: ( $i * $i ) > $i ).
tff(c_Sum__Type_OInr,type,
c_Sum__Type_OInr: ( $i * $i * $i ) > $i ).
tff(f_539,axiom,
! [V_A,V_B,T_a] :
( c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_A,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_6396,axiom,
! [V_X,V_H] :
( ~ c_in(V_X,V_H,tc_Message_Omsg)
| c_in(V_X,c_Message_Oanalz(V_H),tc_Message_Omsg) ),
file(unknown,unknown) ).
tff(f_544,axiom,
! [V_A,V_B,T_a] :
( ~ c_in(c_Main_OsubsetI__1(V_A,V_B,T_a),V_B,T_a)
| c_lessequals(V_A,V_B,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_554,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file(unknown,unknown) ).
tff(f_6506,axiom,
! [V_H,V_H_H,V_G,V_G_H] :
( ~ c_lessequals(c_Message_Oanalz(V_H),c_Message_Oanalz(V_H_H),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(V_G),c_Message_Oanalz(V_G_H),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(c_union(V_G,V_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(V_G_H,V_H_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)) ),
file(unknown,unknown) ).
tff(f_6513,axiom,
~ c_lessequals(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Oanalz(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
file(unknown,unknown) ).
tff(c_218,plain,
! [V_A_367,V_B_368,T_a_369] :
( c_lessequals(V_A_367,V_B_368,tc_set(T_a_369))
| c_in(c_Main_OsubsetI__1(V_A_367,V_B_368,T_a_369),V_A_367,T_a_369) ),
inference(cnfTransformation,[status(thm)],[f_539]) ).
tff(c_2754,plain,
! [V_X_1948,V_H_1949] :
( c_in(V_X_1948,c_Message_Oanalz(V_H_1949),tc_Message_Omsg)
| ~ c_in(V_X_1948,V_H_1949,tc_Message_Omsg) ),
inference(cnfTransformation,[status(thm)],[f_6396]) ).
tff(c_17482,plain,
! [V_A_3307,V_B_3308,T_a_3309] :
( c_lessequals(V_A_3307,V_B_3308,tc_set(T_a_3309))
| ~ c_in(c_Main_OsubsetI__1(V_A_3307,V_B_3308,T_a_3309),V_B_3308,T_a_3309) ),
inference(cnfTransformation,[status(thm)],[f_544]) ).
tff(c_42769,plain,
! [V_A_4820,V_H_4821] :
( c_lessequals(V_A_4820,c_Message_Oanalz(V_H_4821),tc_set(tc_Message_Omsg))
| ~ c_in(c_Main_OsubsetI__1(V_A_4820,c_Message_Oanalz(V_H_4821),tc_Message_Omsg),V_H_4821,tc_Message_Omsg) ),
inference(resolution,[status(thm)],[c_2754,c_17482]) ).
tff(c_42911,plain,
! [V_A_367] : c_lessequals(V_A_367,c_Message_Oanalz(V_A_367),tc_set(tc_Message_Omsg)),
inference(resolution,[status(thm)],[c_218,c_42769]) ).
tff(c_224,plain,
! [V_A_376,T_a_377] : c_lessequals(V_A_376,V_A_376,tc_set(T_a_377)),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_25992,plain,
! [V_G_4095,V_H_4096,V_G_H_4097,V_H_H_4098] :
( c_lessequals(c_Message_Oanalz(c_union(V_G_4095,V_H_4096,tc_Message_Omsg)),c_Message_Oanalz(c_union(V_G_H_4097,V_H_H_4098,tc_Message_Omsg)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(V_G_4095),c_Message_Oanalz(V_G_H_4097),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(V_H_4096),c_Message_Oanalz(V_H_H_4098),tc_set(tc_Message_Omsg)) ),
inference(cnfTransformation,[status(thm)],[f_6506]) ).
tff(c_2800,plain,
~ c_lessequals(c_Message_Oanalz(c_union(v_G,v_H,tc_Message_Omsg)),c_Message_Oanalz(c_union(c_Message_Oanalz(v_G),v_H,tc_Message_Omsg)),tc_set(tc_Message_Omsg)),
inference(cnfTransformation,[status(thm)],[f_6513]) ).
tff(c_25995,plain,
( ~ c_lessequals(c_Message_Oanalz(v_G),c_Message_Oanalz(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oanalz(v_H),tc_set(tc_Message_Omsg)) ),
inference(resolution,[status(thm)],[c_25992,c_2800]) ).
tff(c_26016,plain,
~ c_lessequals(c_Message_Oanalz(v_G),c_Message_Oanalz(c_Message_Oanalz(v_G)),tc_set(tc_Message_Omsg)),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_25995]) ).
tff(c_42926,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_42911,c_26016]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWV240-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % 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
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 23:04:58 EDT 2023
% 0.13/0.36 % CPUTime :
% 43.51/21.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 43.51/21.25
% 43.51/21.25 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.51/21.28
% 43.51/21.28 Inference rules
% 43.51/21.28 ----------------------
% 43.51/21.28 #Ref : 42
% 43.51/21.28 #Sup : 8904
% 43.51/21.28 #Fact : 2
% 43.51/21.28 #Define : 0
% 43.51/21.28 #Split : 17
% 43.51/21.28 #Chain : 0
% 43.51/21.28 #Close : 0
% 43.51/21.28
% 43.51/21.28 Ordering : KBO
% 43.51/21.28
% 43.51/21.28 Simplification rules
% 43.51/21.28 ----------------------
% 43.51/21.28 #Subsume : 2684
% 43.51/21.28 #Demod : 3645
% 43.51/21.28 #Tautology : 2347
% 43.51/21.28 #SimpNegUnit : 85
% 43.51/21.28 #BackRed : 151
% 43.51/21.28
% 43.51/21.28 #Partial instantiations: 0
% 43.51/21.28 #Strategies tried : 1
% 43.51/21.28
% 43.51/21.28 Timing (in seconds)
% 43.51/21.28 ----------------------
% 43.51/21.29 Preprocessing : 1.59
% 43.51/21.29 Parsing : 0.89
% 43.51/21.29 CNF conversion : 0.14
% 43.51/21.29 Main loop : 18.63
% 43.51/21.29 Inferencing : 4.35
% 43.51/21.29 Reduction : 6.81
% 43.51/21.29 Demodulation : 4.63
% 43.51/21.29 BG Simplification : 0.22
% 43.51/21.29 Subsumption : 5.97
% 43.51/21.29 Abstraction : 0.19
% 43.51/21.29 MUC search : 0.00
% 43.51/21.29 Cooper : 0.00
% 43.51/21.29 Total : 20.28
% 43.51/21.29 Index Insertion : 0.00
% 43.51/21.29 Index Deletion : 0.00
% 43.51/21.29 Index Matching : 0.00
% 43.51/21.29 BG Taut test : 0.00
%------------------------------------------------------------------------------