TSTP Solution File: LCL773-1 by Beagle---0.9.51
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : LCL773-1 : 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 : n018.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 10:48:58 EDT 2023
% Result : Unsatisfiable 17.00s 5.38s
% Output : CNFRefutation 17.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 100
% Syntax : Number of formulae : 105 ( 6 unt; 97 typ; 0 def)
% Number of atoms : 10 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 131 ( 92 >; 39 *; 0 +; 0 <<)
% Number of predicates : 64 ( 63 usr; 1 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 5 con; 0-3 aty)
% Number of variables : 6 (; 6 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ c_lessequals > c_Ring__and__Field_Odvd__class_Odvd > c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osgn__if > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring__0 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring__1__no__zero__divisors > 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__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > 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_Ono__zero__divisors > class_Ring__and__Field_Omult__zero > class_Ring__and__Field_Omult__mono1 > class_Ring__and__Field_Omult__mono > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ofield > class_Ring__and__Field_Odvd > class_Ring__and__Field_Odivision__ring > class_Ring__and__Field_Odivision__by__zero > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Ring__and__Field_Ocomm__ring__1 > class_Ring__and__Field_Ocomm__ring > class_Power_Opower > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > class_Orderings_Obot > class_OrderedGroup_Opordered__comm__monoid__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__ab__group__add > class_OrderedGroup_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__add > 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__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Lattices_Oboolean__algebra > class_Int_Onumber__ring > c_InductTermi_OIT > c_Power_Opower__class_Opower > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_List_Oreplicate > c_List_Odrop > c_Lambda_Osubstn > c_Lambda_Osubst > c_Lambda_Oliftn > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_HOL_Oinverse__class_Odivide > c_Nitpick_Onat__gcd > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Olift > c_Lambda_OdB_OApp > c_HOL_Ouminus__class_Ouminus > c_HOL_Osgn__class_Osgn > c_HOL_Oinverse__class_Oinverse > #nlpp > c_nat_Onat__size > c_Suc > c_String_Ochar_Ochar__size > c_Orderings_Obot__class_Obot > c_Lambda_OdB_OdB__size > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_r > v_i > tc_nat > tc_String_Ochar > tc_Lambda_OdB
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(class_OrderedGroup_Oab__semigroup__idem__mult,type,
class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).
tff(c_Lambda_Olift,type,
c_Lambda_Olift: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oordered__ab__group__add,type,
class_OrderedGroup_Oordered__ab__group__add: $i > $o ).
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_HOL_Oord__class_Oless,type,
c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).
tff(c_Nat_Osize__class_Osize,type,
c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).
tff(c_Lambda_Oliftn,type,
c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).
tff(c_InductTermi_OIT,type,
c_InductTermi_OIT: $i > $o ).
tff(c_HOL_Oinverse__class_Oinverse,type,
c_HOL_Oinverse__class_Oinverse: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring,type,
class_Ring__and__Field_Oordered__semiring: $i > $o ).
tff(class_Ring__and__Field_Osemiring,type,
class_Ring__and__Field_Osemiring: $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_Ocomm__semiring,type,
class_Ring__and__Field_Ocomm__semiring: $i > $o ).
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_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(v_i,type,
v_i: $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_Lambda_Obeta,type,
c_Lambda_Obeta: ( $i * $i ) > $o ).
tff(class_Orderings_Oorder,type,
class_Orderings_Oorder: $i > $o ).
tff(class_Orderings_Opreorder,type,
class_Orderings_Opreorder: $i > $o ).
tff(class_OrderedGroup_Oab__semigroup__mult,type,
class_OrderedGroup_Oab__semigroup__mult: $i > $o ).
tff(c_HOL_Oinverse__class_Odivide,type,
c_HOL_Oinverse__class_Odivide: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Odivision__by__zero,type,
class_Ring__and__Field_Odivision__by__zero: $i > $o ).
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(c_String_Ochar_Ochar__size,type,
c_String_Ochar_Ochar__size: $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(class_Ring__and__Field_Ozero__neq__one,type,
class_Ring__and__Field_Ozero__neq__one: $i > $o ).
tff(c_Orderings_Obot__class_Obot,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(c_Lambda_OdB_OApp,type,
c_Lambda_OdB_OApp: ( $i * $i ) > $i ).
tff(c_List_Oreplicate,type,
c_List_Oreplicate: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oordered__ring__strict,type,
class_Ring__and__Field_Oordered__ring__strict: $i > $o ).
tff(class_Lattices_Oboolean__algebra,type,
class_Lattices_Oboolean__algebra: $i > $o ).
tff(c_nat_Onat__size,type,
c_nat_Onat__size: $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_Orderings_Oord__class_Omin,type,
c_Orderings_Oord__class_Omin: ( $i * $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(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_Ring__and__Field_Oordered__idom,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
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(tc_nat,type,
tc_nat: $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(class_Power_Opower,type,
class_Power_Opower: $i > $o ).
tff(c_Orderings_Oord__class_Omax,type,
c_Orderings_Oord__class_Omax: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__no__zero__divisors,type,
class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).
tff(class_Ring__and__Field_Oidom,type,
class_Ring__and__Field_Oidom: $i > $o ).
tff(class_OrderedGroup_Omonoid__add,type,
class_OrderedGroup_Omonoid__add: $i > $o ).
tff(c_Nitpick_Onat__gcd,type,
c_Nitpick_Onat__gcd: ( $i * $i ) > $i ).
tff(c_Lambda_Osubstn,type,
c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Ocomm__ring,type,
class_Ring__and__Field_Ocomm__ring: $i > $o ).
tff(class_Ring__and__Field_Oordered__semiring__strict,type,
class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).
tff(v_r,type,
v_r: $i ).
tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
class_Ring__and__Field_Opordered__cancel__semiring: $i > $o ).
tff(class_Nat_Osemiring__char__0,type,
class_Nat_Osemiring__char__0: $i > $o ).
tff(c_HOL_Oplus__class_Oplus,type,
c_HOL_Oplus__class_Oplus: ( $i * $i * $i ) > $i ).
tff(c_Power_Opower__class_Opower,type,
c_Power_Opower__class_Opower: ( $i * $i * $i ) > $i ).
tff(c_HOL_Otimes__class_Otimes,type,
c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).
tff(tc_Lambda_OdB,type,
tc_Lambda_OdB: $i ).
tff(c_Ring__and__Field_Odvd__class_Odvd,type,
c_Ring__and__Field_Odvd__class_Odvd: ( $i * $i * $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(class_Ring__and__Field_Omult__mono1,type,
class_Ring__and__Field_Omult__mono1: $i > $o ).
tff(c_HOL_Osgn__class_Osgn,type,
c_HOL_Osgn__class_Osgn: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Oab__group__add,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
tff(c_List_Odrop,type,
c_List_Odrop: ( $i * $i * $i ) > $i ).
tff(class_Ring__and__Field_Oring__1,type,
class_Ring__and__Field_Oring__1: $i > $o ).
tff(class_Ring__and__Field_Osgn__if,type,
class_Ring__and__Field_Osgn__if: $i > $o ).
tff(class_Ring__and__Field_Odvd,type,
class_Ring__and__Field_Odvd: $i > $o ).
tff(c_HOL_Ouminus__class_Ouminus,type,
c_HOL_Ouminus__class_Ouminus: ( $i * $i ) > $i ).
tff(class_OrderedGroup_Ogroup__add,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
tff(class_Ring__and__Field_Omult__mono,type,
class_Ring__and__Field_Omult__mono: $i > $o ).
tff(class_Ring__and__Field_Ocomm__semiring__1,type,
class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).
tff(class_Ring__and__Field_Odivision__ring,type,
class_Ring__and__Field_Odivision__ring: $i > $o ).
tff(tc_String_Ochar,type,
tc_String_Ochar: $i ).
tff(class_Ring__and__Field_Opordered__semiring,type,
class_Ring__and__Field_Opordered__semiring: $i > $o ).
tff(class_OrderedGroup_Opordered__comm__monoid__add,type,
class_OrderedGroup_Opordered__comm__monoid__add: $i > $o ).
tff(c_HOL_Ominus__class_Ominus,type,
c_HOL_Ominus__class_Ominus: ( $i * $i * $i ) > $i ).
tff(class_Orderings_Obot,type,
class_Orderings_Obot: $i > $o ).
tff(class_OrderedGroup_Opordered__ab__group__add,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
tff(c_Lambda_OdB_OdB__size,type,
c_Lambda_OdB_OdB__size: $i > $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(f_8163,axiom,
c_InductTermi_OIT(v_r),
file(unknown,unknown) ).
tff(f_8144,axiom,
! [V_r,V_i,V_j] :
( c_InductTermi_OIT(c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j))
| ~ c_InductTermi_OIT(V_r) ),
file(unknown,unknown) ).
tff(f_8166,axiom,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
file(unknown,unknown) ).
tff(c_2132,plain,
c_InductTermi_OIT(v_r),
inference(cnfTransformation,[status(thm)],[f_8163]) ).
tff(c_3649,plain,
! [V_r_3270,V_i_3271,V_j_3272] :
( ~ c_InductTermi_OIT(V_r_3270)
| c_InductTermi_OIT(c_Lambda_Osubst(V_r_3270,c_Lambda_OdB_OVar(V_i_3271),V_j_3272)) ),
inference(cnfTransformation,[status(thm)],[f_8144]) ).
tff(c_2136,plain,
~ c_InductTermi_OIT(c_Lambda_Osubst(v_r,c_Lambda_OdB_OVar(v_i),c_HOL_Ozero__class_Ozero(tc_nat))),
inference(cnfTransformation,[status(thm)],[f_8166]) ).
tff(c_3652,plain,
~ c_InductTermi_OIT(v_r),
inference(resolution,[status(thm)],[c_3649,c_2136]) ).
tff(c_3664,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_2132,c_3652]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : LCL773-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15 % 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
% 0.15/0.37 % Computer : n018.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu Aug 3 13:39:35 EDT 2023
% 0.15/0.37 % CPUTime :
% 17.00/5.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.00/5.39
% 17.00/5.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.00/5.41
% 17.00/5.41 Inference rules
% 17.00/5.41 ----------------------
% 17.00/5.41 #Ref : 4
% 17.00/5.41 #Sup : 282
% 17.00/5.41 #Fact : 2
% 17.00/5.41 #Define : 0
% 17.00/5.41 #Split : 0
% 17.00/5.41 #Chain : 0
% 17.00/5.41 #Close : 0
% 17.00/5.41
% 17.00/5.41 Ordering : KBO
% 17.00/5.41
% 17.00/5.41 Simplification rules
% 17.00/5.41 ----------------------
% 17.00/5.41 #Subsume : 174
% 17.00/5.41 #Demod : 168
% 17.00/5.41 #Tautology : 279
% 17.00/5.41 #SimpNegUnit : 2
% 17.00/5.42 #BackRed : 0
% 17.00/5.42
% 17.00/5.42 #Partial instantiations: 0
% 17.00/5.42 #Strategies tried : 1
% 17.00/5.42
% 17.00/5.42 Timing (in seconds)
% 17.00/5.42 ----------------------
% 17.00/5.42 Preprocessing : 1.94
% 17.00/5.42 Parsing : 1.12
% 17.00/5.42 CNF conversion : 0.15
% 17.00/5.42 Main loop : 2.29
% 17.00/5.42 Inferencing : 0.20
% 17.00/5.42 Reduction : 1.13
% 17.00/5.42 Demodulation : 0.74
% 17.00/5.42 BG Simplification : 0.18
% 17.00/5.42 Subsumption : 0.62
% 17.00/5.42 Abstraction : 0.05
% 17.00/5.42 MUC search : 0.00
% 17.00/5.42 Cooper : 0.00
% 17.00/5.42 Total : 4.27
% 17.00/5.42 Index Insertion : 0.00
% 17.00/5.42 Index Deletion : 0.00
% 17.00/5.42 Index Matching : 0.00
% 17.00/5.42 BG Taut test : 0.00
%------------------------------------------------------------------------------