TSTP Solution File: LCL848-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL848-1 : 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 36.64s 18.45s
% Output   : CNFRefutation 36.70s
% 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 :    5 (   2 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  167 (  85   >;  82   *;   0   +;   0  <<)
%            Number of predicates  :   44 (  43 usr;   1 prp; 0-4 aty)
%            Number of functors    :   54 (  54 usr;  12 con; 0-5 aty)
%            Number of variables   :    4 (;   4   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_lessequals > c_in > c_fequal > c_Type_Otyping > c_List_Olistsp > c_HOL_Oord__class_Oless > c_List_Olinorder__class_Osorted > 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_Oring__1 > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__idom > 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__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_Omonoid__mult > class_OrderedGroup_Omonoid__add > class_OrderedGroup_Olordered__ab__group__add > class_OrderedGroup_Ogroup__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_Oring__char__0 > class_Int_Onumber__ring > class_Int_Onumber > c_List_Olinorder__class_Oinsort__key > c_List_Ofoldl > c_Lambda_OdB_OdB__case > c_COMBC > c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1 > c_List_Omap > c_List_Olist__update > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Power_Opower__class_Opower > c_List_OtakeWhile > c_List_Otake > c_List_Osublist > c_List_Osplice > c_List_Oreplicate > c_List_Onth > c_List_Olist_Olist__size > c_List_Olist_OCons > c_List_Odrop > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_HOL_Ominus__class_Ominus > tc_fun > hAPP > c_Nat_Osize__class_Osize > c_Nat_Osemiring__1__class_Oof__nat > c_List_Oset > c_List_Orev > c_List_Olistsum > c_List_Olength__unique > c_List_Olast > c_List_Ohd > c_List_Obutlast > c_Int_Onumber__class_Onumber__of > #nlpp > tc_List_Olist > 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____ > tc_nat > tc_bool > tc_Lambda_OdB > tc_Int_Oint > t_a > c_Lambda_Osubst > c_Lambda_Olift > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(class_Int_Oring__char__0,type,
    class_Int_Oring__char__0: $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_List_Olist_Olist__size,type,
    c_List_Olist_Olist__size: ( $i * $i * $i ) > $i ).

tff(c_List_Olist_ONil,type,
    c_List_Olist_ONil: $i > $i ).

tff(c_HOL_Oord__class_Oless,type,
    c_HOL_Oord__class_Oless: ( $i * $i * $i ) > $o ).

tff(c_COMBC,type,
    c_COMBC: ( $i * $i * $i * $i * $i ) > $i ).

tff(c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1,type,
    c_List_Osko__List__XtakeWhile__eq__take__P__nth__1__1: ( $i * $i * $i * $i ) > $i ).

tff(c_List_Oappend,type,
    c_List_Oappend: ( $i * $i * $i ) > $i ).

tff(c_Nat_Osize__class_Osize,type,
    c_Nat_Osize__class_Osize: ( $i * $i ) > $i ).

tff(c_Lambda_OdB_OdB__case,type,
    c_Lambda_OdB_OdB__case: ( $i * $i * $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Ocancel__ab__semigroup__add,type,
    class_OrderedGroup_Ocancel__ab__semigroup__add: $i > $o ).

tff(c_Int_Onumber__class_Onumber__of,type,
    c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).

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_List_Orev,type,
    c_List_Orev: ( $i * $i ) > $i ).

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_List_Onth,type,
    c_List_Onth: ( $i * $i * $i ) > $i ).

tff(tc_Int_Oint,type,
    tc_Int_Oint: $i ).

tff(c_InductTermi_OIT,type,
    c_InductTermi_OIT: $i ).

tff(c_List_Obutlast,type,
    c_List_Obutlast: ( $i * $i ) > $i ).

tff(t_a,type,
    t_a: $i ).

tff(c_List_OtakeWhile,type,
    c_List_OtakeWhile: ( $i * $i * $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_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(class_Ring__and__Field_Ono__zero__divisors,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

tff(class_Int_Onumber,type,
    class_Int_Onumber: $i > $o ).

tff(class_Ring__and__Field_Ozero__neq__one,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

tff(c_ListOrder_Ostep1,type,
    c_ListOrder_Ostep1: ( $i * $i * $i * $i ) > $o ).

tff(c_List_Oreplicate,type,
    c_List_Oreplicate: ( $i * $i * $i ) > $i ).

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_List_Oset,type,
    c_List_Oset: ( $i * $i ) > $i ).

tff(c_Lambda_Osubst,type,
    c_Lambda_Osubst: $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_Otyping,type,
    c_Type_Otyping: ( $i * $i * $i ) > $o ).

tff(c_Suc,type,
    c_Suc: $i > $i ).

tff(c_List_Olinorder__class_Osorted,type,
    c_List_Olinorder__class_Osorted: ( $i * $i ) > $o ).

tff(tc_List_Olist,type,
    tc_List_Olist: $i > $i ).

tff(c_List_Olistsum,type,
    c_List_Olistsum: ( $i * $i ) > $i ).

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(c_in,type,
    c_in: ( $i * $i * $i ) > $o ).

tff(c_List_Olist__update,type,
    c_List_Olist__update: ( $i * $i * $i * $i ) > $i ).

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__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(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1,type,
    c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: ( $i * $i * $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_List_Osplice,type,
    c_List_Osplice: ( $i * $i * $i ) > $i ).

tff(c_List_Osublist,type,
    c_List_Osublist: ( $i * $i * $i ) > $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(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(c_fequal,type,
    c_fequal: ( $i * $i * $i ) > $o ).

tff(class_OrderedGroup_Omonoid__mult,type,
    class_OrderedGroup_Omonoid__mult: $i > $o ).

tff(c_List_Olinorder__class_Oinsort__key,type,
    c_List_Olinorder__class_Oinsort__key: ( $i * $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_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(c_List_Olist_OCons,type,
    c_List_Olist_OCons: ( $i * $i * $i ) > $i ).

tff(class_OrderedGroup_Ogroup__add,type,
    class_OrderedGroup_Ogroup__add: $i > $o ).

tff(hBOOL,type,
    hBOOL: $i > $o ).

tff(c_List_Ohd,type,
    c_List_Ohd: ( $i * $i ) > $i ).

tff(class_Ring__and__Field_Ocomm__semiring__1,type,
    class_Ring__and__Field_Ocomm__semiring__1: $i > $o ).

tff(c_List_Otake,type,
    c_List_Otake: ( $i * $i * $i ) > $i ).

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_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(c_Lambda_Obeta,type,
    c_Lambda_Obeta: $i ).

tff(c_List_Olast,type,
    c_List_Olast: ( $i * $i ) > $i ).

tff(c_Lambda_Olift,type,
    c_Lambda_Olift: $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(c_List_Olength__unique,type,
    c_List_Olength__unique: ( $i * $i ) > $i ).

tff(c_List_Omap,type,
    c_List_Omap: ( $i * $i * $i * $i ) > $i ).

tff(v_s____,type,
    v_s____: $i ).

tff(f_3739,axiom,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
    file(unknown,unknown) ).

tff(f_3628,axiom,
    ! [V_n,V_rs] :
      ( hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))
      | ~ c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB) ),
    file(unknown,unknown) ).

tff(f_3741,axiom,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    file(unknown,unknown) ).

tff(c_1316,plain,
    c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
    inference(cnfTransformation,[status(thm)],[f_3739]) ).

tff(c_1254,plain,
    ! [V_rs_1927,V_n_1926] :
      ( ~ c_List_Olistsp(c_InductTermi_OIT,V_rs_1927,tc_Lambda_OdB)
      | hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n_1926),V_rs_1927,tc_Lambda_OdB,tc_Lambda_OdB))) ),
    inference(cnfTransformation,[status(thm)],[f_3628]) ).

tff(c_1318,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
    inference(cnfTransformation,[status(thm)],[f_3741]) ).

tff(c_87505,plain,
    ~ c_List_Olistsp(c_InductTermi_OIT,c_List_Olist_OCons(hAPP(hAPP(c_Lambda_Olift,v_ta____),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),
    inference(resolution,[status(thm)],[c_1254,c_1318]) ).

tff(c_87512,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1316,c_87505]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL848-1 : 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
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 14:19:29 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 36.64/18.45  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.64/18.46  
% 36.64/18.46  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 36.70/18.48  
% 36.70/18.48  Inference rules
% 36.70/18.48  ----------------------
% 36.70/18.48  #Ref     : 46
% 36.70/18.48  #Sup     : 19876
% 36.70/18.48  #Fact    : 18
% 36.70/18.48  #Define  : 0
% 36.70/18.48  #Split   : 3
% 36.70/18.48  #Chain   : 0
% 36.70/18.48  #Close   : 0
% 36.70/18.48  
% 36.70/18.48  Ordering : KBO
% 36.70/18.48  
% 36.70/18.48  Simplification rules
% 36.70/18.48  ----------------------
% 36.70/18.48  #Subsume      : 7497
% 36.70/18.48  #Demod        : 7400
% 36.70/18.48  #Tautology    : 4670
% 36.70/18.48  #SimpNegUnit  : 708
% 36.70/18.48  #BackRed      : 0
% 36.70/18.48  
% 36.70/18.48  #Partial instantiations: 0
% 36.70/18.48  #Strategies tried      : 1
% 36.70/18.48  
% 36.70/18.48  Timing (in seconds)
% 36.70/18.48  ----------------------
% 36.70/18.49  Preprocessing        : 1.48
% 36.70/18.49  Parsing              : 0.82
% 36.70/18.49  CNF conversion       : 0.13
% 36.70/18.49  Main loop            : 15.94
% 36.70/18.49  Inferencing          : 2.52
% 36.70/18.49  Reduction            : 7.94
% 36.70/18.49  Demodulation         : 6.08
% 36.70/18.49  BG Simplification    : 0.24
% 36.70/18.49  Subsumption          : 4.44
% 36.70/18.49  Abstraction          : 0.22
% 36.70/18.49  MUC search           : 0.00
% 36.70/18.49  Cooper               : 0.00
% 36.70/18.49  Total                : 17.46
% 36.70/18.49  Index Insertion      : 0.00
% 36.70/18.49  Index Deletion       : 0.00
% 36.70/18.49  Index Matching       : 0.00
% 36.70/18.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------