TSTP Solution File: SET851-1 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SET851-1 : 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 : n013.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 10:57:12 EDT 2023
% Result : Unsatisfiable 36.45s 15.62s
% Output : CNFRefutation 36.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 220
% Syntax : Number of formulae : 252 ( 26 unt; 208 typ; 0 def)
% Number of atoms : 71 ( 12 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 27 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 422 ( 187 >; 235 *; 0 +; 0 <<)
% Number of predicates : 83 ( 81 usr; 1 prp; 0-3 aty)
% Number of functors : 127 ( 127 usr; 21 con; 0-6 aty)
% Number of variables : 42 (; 42 !; 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_Zorn_OUnion__lemma0__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_Zorn_Osucc > 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_Zorn_OTFin > 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_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_IntDef_Oint > c_GCD_Ogcd > v_x > v_m > v_S > tc_nat > tc_bool > tc_Product__Type_Ounit > tc_IntDef_Oint > t_a > c_emptyset > c_Wellfounded__Relations_Oless__than > c_UNIV > c_Relation_OId > c_Numeral_Obit_OB1 > c_Numeral_Obit_OB0 > 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(v_x,type,
v_x: $i ).
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(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(v_S,type,
v_S: $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(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(c_Zorn_Osucc,type,
c_Zorn_Osucc: ( $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(t_a,type,
t_a: $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(c_Zorn_OTFin,type,
c_Zorn_OTFin: ( $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_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_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_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_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(c_Zorn_OUnion__lemma0__1,type,
c_Zorn_OUnion__lemma0__1: ( $i * $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(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(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(v_m,type,
v_m: $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(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(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(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_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(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_1507,axiom,
! [V_A,T_a] : c_lessequals(V_A,V_A,tc_set(T_a)),
file(unknown,unknown) ).
tff(f_1726,axiom,
! [T_1] : class_Orderings_Oorder(tc_set(T_1)),
file(unknown,unknown) ).
tff(f_1316,axiom,
! [T_a,V_x] :
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ),
file(unknown,unknown) ).
tff(f_1456,axiom,
! [V_A,V_B,T_a] :
( ~ c_less(V_A,V_B,tc_set(T_a))
| ~ c_lessequals(V_B,V_A,tc_set(T_a)) ),
file(unknown,unknown) ).
tff(f_6312,axiom,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
file(unknown,unknown) ).
tff(f_6303,axiom,
! [V_x,V_y,T_a,V_S] :
( ~ c_lessequals(V_x,V_y,tc_set(tc_set(T_a)))
| c_lessequals(V_x,c_Zorn_Osucc(V_S,V_y,T_a),tc_set(tc_set(T_a))) ),
file(unknown,unknown) ).
tff(f_6309,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_6305,axiom,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_6322,axiom,
! [V_U] :
( c_lessequals(c_Zorn_Osucc(v_S,V_U,t_a),v_m,tc_set(tc_set(t_a)))
| ( V_U = v_m )
| ~ c_lessequals(V_U,v_m,tc_set(tc_set(t_a)))
| ~ c_in(V_U,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
file(unknown,unknown) ).
tff(f_6307,axiom,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file(unknown,unknown) ).
tff(f_1505,axiom,
! [V_B,V_A,T_a] :
( ~ c_lessequals(V_B,V_A,tc_set(T_a))
| ~ c_lessequals(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file(unknown,unknown) ).
tff(f_1468,axiom,
! [V_A,V_B,T_a] :
( ~ c_lessequals(V_A,V_B,tc_set(T_a))
| c_less(V_A,V_B,tc_set(T_a))
| ( V_A = V_B ) ),
file(unknown,unknown) ).
tff(c_620,plain,
! [V_A_933,T_a_934] : c_lessequals(V_A_933,V_A_933,tc_set(T_a_934)),
inference(cnfTransformation,[status(thm)],[f_1507]) ).
tff(c_894,plain,
! [T_1_997] : class_Orderings_Oorder(tc_set(T_1_997)),
inference(cnfTransformation,[status(thm)],[f_1726]) ).
tff(c_532,plain,
! [V_x_789,T_a_788] :
( c_lessequals(V_x_789,V_x_789,T_a_788)
| ~ class_Orderings_Oorder(T_a_788) ),
inference(cnfTransformation,[status(thm)],[f_1316]) ).
tff(c_17049,plain,
! [V_B_3057,V_A_3058,T_a_3059] :
( ~ c_lessequals(V_B_3057,V_A_3058,tc_set(T_a_3059))
| ~ c_less(V_A_3058,V_B_3057,tc_set(T_a_3059)) ),
inference(cnfTransformation,[status(thm)],[f_1456]) ).
tff(c_17053,plain,
! [V_x_789,T_a_3059] :
( ~ c_less(V_x_789,V_x_789,tc_set(T_a_3059))
| ~ class_Orderings_Oorder(tc_set(T_a_3059)) ),
inference(resolution,[status(thm)],[c_532,c_17049]) ).
tff(c_17062,plain,
! [V_x_789,T_a_3059] : ~ c_less(V_x_789,V_x_789,tc_set(T_a_3059)),
inference(demodulation,[status(thm),theory(equality)],[c_894,c_17053]) ).
tff(c_2732,plain,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnfTransformation,[status(thm)],[f_6312]) ).
tff(c_18177,plain,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_2732]) ).
tff(c_18964,plain,
! [V_x_3405,V_S_3406,V_y_3407,T_a_3408] :
( c_lessequals(V_x_3405,c_Zorn_Osucc(V_S_3406,V_y_3407,T_a_3408),tc_set(tc_set(T_a_3408)))
| ~ c_lessequals(V_x_3405,V_y_3407,tc_set(tc_set(T_a_3408))) ),
inference(cnfTransformation,[status(thm)],[f_6303]) ).
tff(c_2730,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_6309]) ).
tff(c_18978,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[c_18964,c_2730]) ).
tff(c_18989,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_18177,c_18978]) ).
tff(c_18990,plain,
c_lessequals(v_x,v_m,tc_set(tc_set(t_a))),
inference(splitRight,[status(thm)],[c_2732]) ).
tff(c_2726,plain,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_6305]) ).
tff(c_29291,plain,
! [V_U_4296] :
( ~ c_in(V_U_4296,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(V_U_4296,v_m,tc_set(tc_set(t_a)))
| ( v_m = V_U_4296 )
| c_lessequals(c_Zorn_Osucc(v_S,V_U_4296,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(cnfTransformation,[status(thm)],[f_6322]) ).
tff(c_2728,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnfTransformation,[status(thm)],[f_6307]) ).
tff(c_29304,plain,
( ~ c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m ) ),
inference(resolution,[status(thm)],[c_29291,c_2728]) ).
tff(c_29315,plain,
v_x = v_m,
inference(demodulation,[status(thm),theory(equality)],[c_18990,c_2726,c_29304]) ).
tff(c_618,plain,
! [V_B_930,V_A_931,T_a_932] :
( ( V_B_930 = V_A_931 )
| ~ c_lessequals(V_A_931,V_B_930,tc_set(T_a_932))
| ~ c_lessequals(V_B_930,V_A_931,tc_set(T_a_932)) ),
inference(cnfTransformation,[status(thm)],[f_1505]) ).
tff(c_19027,plain,
( ( v_x = v_m )
| ~ c_lessequals(v_m,v_x,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_18990,c_618]) ).
tff(c_19549,plain,
~ c_lessequals(v_m,v_x,tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_19027]) ).
tff(c_29322,plain,
~ c_lessequals(v_m,v_m,tc_set(tc_set(t_a))),
inference(demodulation,[status(thm),theory(equality)],[c_29315,c_19549]) ).
tff(c_29332,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_620,c_29322]) ).
tff(c_29333,plain,
v_x = v_m,
inference(splitRight,[status(thm)],[c_19027]) ).
tff(c_604,plain,
! [V_B_910,V_A_909,T_a_911] :
( ( V_B_910 = V_A_909 )
| c_less(V_A_909,V_B_910,tc_set(T_a_911))
| ~ c_lessequals(V_A_909,V_B_910,tc_set(T_a_911)) ),
inference(cnfTransformation,[status(thm)],[f_1468]) ).
tff(c_19028,plain,
( ( v_x = v_m )
| c_less(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_18990,c_604]) ).
tff(c_19548,plain,
c_less(v_x,v_m,tc_set(tc_set(t_a))),
inference(splitLeft,[status(thm)],[c_19028]) ).
tff(c_29335,plain,
c_less(v_m,v_m,tc_set(tc_set(t_a))),
inference(demodulation,[status(thm),theory(equality)],[c_29333,c_19548]) ).
tff(c_29343,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_17062,c_29335]) ).
tff(c_29344,plain,
v_x = v_m,
inference(splitRight,[status(thm)],[c_19028]) ).
tff(c_29349,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(demodulation,[status(thm),theory(equality)],[c_29344,c_2730]) ).
tff(c_29355,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_620,c_29349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET851-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu Aug 3 16:34:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 36.45/15.62 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.45/15.63
% 36.45/15.63 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.45/15.67
% 36.45/15.67 Inference rules
% 36.45/15.67 ----------------------
% 36.45/15.67 #Ref : 32
% 36.45/15.67 #Sup : 5787
% 36.45/15.67 #Fact : 0
% 36.45/15.67 #Define : 0
% 36.45/15.67 #Split : 19
% 36.45/15.67 #Chain : 0
% 36.45/15.67 #Close : 0
% 36.45/15.67
% 36.45/15.67 Ordering : KBO
% 36.45/15.67
% 36.45/15.67 Simplification rules
% 36.45/15.67 ----------------------
% 36.45/15.67 #Subsume : 2474
% 36.45/15.67 #Demod : 1989
% 36.45/15.67 #Tautology : 1689
% 36.45/15.67 #SimpNegUnit : 42
% 36.45/15.67 #BackRed : 132
% 36.45/15.67
% 36.45/15.67 #Partial instantiations: 0
% 36.45/15.67 #Strategies tried : 1
% 36.45/15.67
% 36.45/15.67 Timing (in seconds)
% 36.45/15.67 ----------------------
% 36.45/15.67 Preprocessing : 1.61
% 36.45/15.67 Parsing : 0.89
% 36.45/15.67 CNF conversion : 0.15
% 36.45/15.68 Main loop : 12.97
% 36.45/15.68 Inferencing : 3.14
% 36.45/15.68 Reduction : 5.05
% 36.45/15.68 Demodulation : 3.14
% 36.45/15.68 BG Simplification : 0.19
% 36.45/15.68 Subsumption : 3.58
% 36.45/15.68 Abstraction : 0.14
% 36.45/15.68 MUC search : 0.00
% 36.45/15.68 Cooper : 0.00
% 36.45/15.68 Total : 14.64
% 36.45/15.68 Index Insertion : 0.00
% 36.45/15.68 Index Deletion : 0.00
% 36.45/15.68 Index Matching : 0.00
% 36.45/15.68 BG Taut test : 0.00
%------------------------------------------------------------------------------