TSTP Solution File: LCL854-1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% 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 : n015.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 10:49:10 EDT 2023
% Result : Unsatisfiable 5.02s 2.22s
% Output : CNFRefutation 5.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 88
% Syntax : Number of formulae : 91 ( 5 unt; 86 typ; 0 def)
% Number of atoms : 5 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 138 ( 72 >; 66 *; 0 +; 0 <<)
% Number of predicates : 36 ( 35 usr; 1 prp; 0-4 aty)
% Number of functors : 51 ( 51 usr; 14 con; 0-5 aty)
% Number of variables : 0 (; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_lessequals > c_Wellfounded_Oaccp > c_Type_Otypings > c_Type_Otyping > c_List_Olistsp > hBOOL > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Oring__1__no__zero__divisors > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_OrderedGroup_Osemigroup__add > class_OrderedGroup_Opordered__comm__monoid__add > class_OrderedGroup_Opordered__ab__semigroup__add__imp__le > class_OrderedGroup_Opordered__ab__semigroup__add > class_OrderedGroup_Opordered__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ocomm__monoid__add > class_OrderedGroup_Ocancel__semigroup__add > class_OrderedGroup_Ocancel__ab__semigroup__add > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > c_List_Ofoldr > c_List_Ofoldl > c_Type_Otype_Otype__rec > c_Type_Otype_Otype__case > c_Type_Osko__Type__Xvar__app__types__1__1 > c_Type_Osko__Type__Xvar__app__typesE__1__1 > c_Type_Osko__Type__Xtyping__elims__2__1 > c_Type_Osko__Type__Xlist__app__typeE__1__1 > c_Type_Osko__Type__Xlist__app__typeD__1__1 > c_Type_Oshift > c_Type_Osko__Type__Xtyping__elims__3__2 > c_Type_Osko__Type__Xtyping__elims__3__1 > c_Predicate_Oconversep > c_Power_Opower__class_Opower > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubst > tc_fun > hAPP > c_Type_Osko__Type__Xabs__typeE__1__2 > c_Type_Osko__Type__Xabs__typeE__1__1 > c_Transitive__Closure_Ortranclp > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Osko__Lambda__Xbeta__cases__2__1 > c_Lambda_Olift > #nlpp > c_fequal > c_Type_Otype_Otype__size > c_Type_Otype_OAtom > c_Type_Osko__Type__Xtype__induct__1__1 > c_Suc > c_List_Olist_ONil > c_Lambda_OdB_OdB__size > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oplus__class_Oplus > c_HOL_Oone__class_Oone > v_ta____ > v_s____ > v_ea____ > v_U____ > v_Ta____ > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > t_a > c_Type_Otype_OFun > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(class_Orderings_Olinorder,type,
class_Orderings_Olinorder: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add,type,
class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).
tff(class_Int_Onumber__ring,type,
class_Int_Onumber__ring: $i > $o ).
tff(c_List_Olist_ONil,type,
c_List_Olist_ONil: $i > $i ).
tff(c_Type_Osko__Type__Xtyping__elims__3__2,type,
c_Type_Osko__Type__Xtyping__elims__3__2: ( $i * $i * $i ) > $i ).
tff(c_fequal,type,
c_fequal: $i > $i ).
tff(c_Type_Osko__Type__Xtype__induct__1__1,type,
c_Type_Osko__Type__Xtype__induct__1__1: $i > $i ).
tff(c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(tc_Type_Otype,type,
tc_Type_Otype: $i ).
tff(c_Type_Osko__Type__Xvar__app__typesE__1__1,type,
c_Type_Osko__Type__Xvar__app__typesE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oring__1__no__zero__divisors,type,
class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Osemiring__0,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
tff(c_Nat_Osemiring__1__class_Oof__nat,type,
c_Nat_Osemiring__1__class_Oof__nat: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__semigroup__add,type,
class_OrderedGroup_Oab__semigroup__add: $i > $o ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i ).
tff(t_a,type,
t_a: $i ).
tff(class_Ring__and__Field_Omult__zero,type,
class_Ring__and__Field_Omult__zero: $i > $o ).
tff(class_OrderedGroup_Olordered__ab__group__add,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
tff(c_List_Ofoldl,type,
c_List_Ofoldl: ( $i * $i * $i * $i * $i ) > $i ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(c_List_Olistsp,type,
c_List_Olistsp: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeD__1__1,type,
c_Type_Osko__Type__Xlist__app__typeD__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Lambda_Osubst,type,
c_Lambda_Osubst: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ono__zero__divisors,type,
class_Ring__and__Field_Ono__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_Type_Osko__Type__Xvar__app__types__1__1,type,
c_Type_Osko__Type__Xvar__app__types__1__1: ( $i * $i * $i * $i ) > $i ).
tff(c_Type_Otype_OAtom,type,
c_Type_Otype_OAtom: $i > $i ).
tff(c_ListOrder_Ostep1,type,
c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).
tff(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: ( $i * $i * $i ) > $i ).
tff(c_Type_Osko__Type__Xtyping__elims__2__1,type,
c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).
tff(c_List_Ofoldr,type,
c_List_Ofoldr: ( $i * $i * $i * $i * $i ) > $i ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: $i > $i ).
tff(class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,type,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le: $i > $o ).
tff(c_Lambda_OdB_OVar,type,
c_Lambda_OdB_OVar: $i > $i ).
tff(c_Type_Oshift,type,
c_Type_Oshift: ( $i * $i * $i * $i ) > $i ).
tff(c_Type_Otyping,type,
c_Type_Otyping: ( $i * $i * $i ) > $o ).
tff(c_Suc,type,
c_Suc: $i > $i ).
tff(c_Lambda_OdB_OAbs,type,
c_Lambda_OdB_OAbs: $i > $i ).
tff(class_OrderedGroup_Ocancel__semigroup__add,type,
class_OrderedGroup_Ocancel__semigroup__add: $i > $o ).
tff(c_lessequals,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(c_Type_Osko__Type__Xlist__app__typeE__1__1,type,
c_Type_Osko__Type__Xlist__app__typeE__1__1: ( $i * $i * $i * $i ) > $i ).
tff(tc_nat,type,
tc_nat: $i ).
tff(class_OrderedGroup_Ocomm__monoid__add,type,
class_OrderedGroup_Ocomm__monoid__add: $i > $o ).
tff(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(v_ta____,type,
v_ta____: $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(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: $i ).
tff(tc_bool,type,
tc_bool: $i ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_Type_Otypings,type,
c_Type_Otypings: ( $i * $i * $i ) > $o ).
tff(v_Ta____,type,
v_Ta____: $i ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(v_U____,type,
v_U____: $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(class_OrderedGroup_Osemigroup__add,type,
class_OrderedGroup_Osemigroup__add: $i > $o ).
tff(c_HOL_Ozero__class_Ozero,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
tff(c_HOL_Oone__class_Oone,type,
c_HOL_Oone__class_Oone: $i > $i ).
tff(class_OrderedGroup_Omonoid__mult,type,
class_OrderedGroup_Omonoid__mult: $i > $o ).
tff(c_Type_Otype_Otype__rec,type,
c_Type_Otype_Otype__rec: ( $i * $i * $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(hAPP,type,
hAPP: ( $i * $i ) > $i ).
tff(c_Type_Otype_Otype__case,type,
c_Type_Otype_Otype__case: ( $i * $i * $i * $i ) > $i ).
tff(c_Wellfounded_Oaccp,type,
c_Wellfounded_Oaccp: ( $i * $i * $i ) > $o ).
tff(c_Type_Otype_OFun,type,
c_Type_Otype_OFun: $i ).
tff(v_ea____,type,
v_ea____: $i ).
tff(c_Type_Osko__Type__Xabs__typeE__1__2,type,
c_Type_Osko__Type__Xabs__typeE__1__2: ( $i * $i ) > $i ).
tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).
tff(hBOOL,type,
hBOOL: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(c_Transitive__Closure_Ortranclp,type,
c_Transitive__Closure_Ortranclp: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_Type_Osko__Type__Xabs__typeE__1__1,type,
c_Type_Osko__Type__Xabs__typeE__1__1: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Type_Osko__Type__Xtyping__elims__3__1,type,
c_Type_Osko__Type__Xtyping__elims__3__1: ( $i * $i * $i ) > $i ).
tff(c_Type_Otype_Otype__size,type,
c_Type_Otype_Otype__size: $i > $i ).
tff(c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $i ).
tff(c_Predicate_Oconversep,type,
c_Predicate_Oconversep: ( $i * $i * $i ) > $i ).
tff(c_Lambda_Obeta,type,
c_Lambda_Obeta: $i ).
tff(class_Ring__and__Field_Osemiring__1,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
tff(class_Ring__and__Field_Oordered__semidom,type,
class_Ring__and__Field_Oordered__semidom: $i > $o ).
tff(v_s____,type,
v_s____: $i ).
tff(f_1481,axiom,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file(unknown,unknown) ).
tff(f_1459,axiom,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
file(unknown,unknown) ).
tff(c_536,plain,
~ c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(cnfTransformation,[status(thm)],[f_1481]) ).
tff(c_524,plain,
c_Type_Otyping(v_ea____,v_s____,hAPP(hAPP(c_Type_Otype_OFun,v_Ta____),v_U____)),
inference(cnfTransformation,[status(thm)],[f_1459]) ).
tff(c_593,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_536,c_524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : LCL854-1 : TPTP v8.1.2. Released v4.1.0.
% 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
% 0.13/0.36 % Computer : n015.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 3 13:49:14 EDT 2023
% 0.13/0.36 % CPUTime :
% 5.02/2.22 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.02/2.22
% 5.02/2.22 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/2.24
% 5.02/2.24 Inference rules
% 5.02/2.24 ----------------------
% 5.02/2.25 #Ref : 0
% 5.02/2.25 #Sup : 0
% 5.02/2.25 #Fact : 0
% 5.02/2.25 #Define : 0
% 5.02/2.25 #Split : 0
% 5.02/2.25 #Chain : 0
% 5.02/2.25 #Close : 0
% 5.02/2.25
% 5.02/2.25 Ordering : KBO
% 5.02/2.25
% 5.02/2.25 Simplification rules
% 5.02/2.25 ----------------------
% 5.02/2.25 #Subsume : 295
% 5.02/2.25 #Demod : 0
% 5.02/2.25 #Tautology : 0
% 5.02/2.25 #SimpNegUnit : 1
% 5.02/2.25 #BackRed : 0
% 5.02/2.25
% 5.02/2.25 #Partial instantiations: 0
% 5.02/2.25 #Strategies tried : 1
% 5.02/2.25
% 5.02/2.25 Timing (in seconds)
% 5.02/2.25 ----------------------
% 5.02/2.25 Preprocessing : 1.05
% 5.02/2.25 Parsing : 0.57
% 5.02/2.25 CNF conversion : 0.08
% 5.02/2.25 Main loop : 0.12
% 5.02/2.25 Inferencing : 0.00
% 5.02/2.25 Reduction : 0.06
% 5.02/2.25 Demodulation : 0.04
% 5.02/2.25 BG Simplification : 0.08
% 5.02/2.25 Subsumption : 0.04
% 5.02/2.25 Abstraction : 0.02
% 5.02/2.25 MUC search : 0.00
% 5.02/2.25 Cooper : 0.00
% 5.02/2.25 Total : 1.22
% 5.02/2.25 Index Insertion : 0.00
% 5.02/2.25 Index Deletion : 0.00
% 5.02/2.25 Index Matching : 0.00
% 5.02/2.25 BG Taut test : 0.00
%------------------------------------------------------------------------------