TSTP Solution File: LCL854-1 by Beagle---0.9.51

View Problem - 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
%------------------------------------------------------------------------------