TSTP Solution File: LCL789-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL789-1 : 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 : n001.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 10:49:01 EDT 2023

% Result   : Unsatisfiable 5.23s 2.23s
% Output   : CNFRefutation 5.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   85
% Syntax   : Number of formulae    :   90 (   8 unt;  82 typ;   0 def)
%            Number of atoms       :    8 (   2 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   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  :  145 (  58   >;  87   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-4 aty)
%            Number of functors    :   64 (  64 usr;  24 con; 0-5 aty)
%            Number of variables   :    0 (;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_ListOrder_Ostep1 > c_Wellfounded_Oaccp > c_Type_Otypings > c_Type_Otyping > c_List_Olistsp > hBOOL > class_Ring__and__Field_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_OrderedGroup_Osemigroup__add > 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_Int_Oring__char__0 > class_Int_Onumber__ring > c_Power_Opower_Opower > c_List_Osko__List__Xappend__eq__Cons__conv__1__1 > c_List_Osko__List__XCons__eq__append__conv__1__1 > 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__Xtypes__snocE__1__2 > c_Type_Osko__Type__Xlist__app__typeE__1__1 > c_Type_Osko__Type__Xlist__app__typeD__1__1 > c_Type_Oshift > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Type_Osko__Type__Xtyping__elims__3__2 > c_Type_Osko__Type__Xtyping__elims__3__1 > c_Predicate_Oconversep > c_List_Otake > c_List_Oreplicate > c_List_Olist_OCons > c_List_Oappend > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lambda_Osubst > hAPP > c_Transitive__Closure_Ortranclp > c_List_Orotate1 > c_List_Orev > c_List_Olistsum > c_List_Olast > c_List_Obutlast > c_Int_Onumber__class_Onumber__of > #nlpp > c_fequal > c_Type_Otype_OAtom > c_Type_Osko__Type__Xtype__induct__1__1 > c_List_Olist_ONil > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oplus__class_Oplus > v_ua______ > v_u____ > v_rs____ > v_n____ > v_ia______ > v_i____ > v_ea______ > v_e____ > v_as____ > v_a____ > v_Ts____ > v_T____ > v_T_Ha______ > v_T_H____ > v_T_H_H____ > tc_nat > tc_Type_Otype > tc_Lambda_OdB > tc_Int_Oint > t_a > c_Type_Otype_OFun > 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_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_List_Oappend,type,
    c_List_Oappend: ( $i * $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(c_Int_Onumber__class_Onumber__of,type,
    c_Int_Onumber__class_Onumber__of: ( $i * $i ) > $i ).

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

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

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

tff(v_T_Ha______,type,
    v_T_Ha______: $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(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(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(v_rs____,type,
    v_rs____: $i ).

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

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_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_Type_Osko__Type__Xtyping__elims__2__1,type,
    c_Type_Osko__Type__Xtyping__elims__2__1: ( $i * $i * $i * $i ) > $i ).

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

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

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

tff(c_Type_Osko__Type__Xtypes__snocE__1__2,type,
    c_Type_Osko__Type__Xtypes__snocE__1__2: ( $i * $i * $i * $i ) > $i ).

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

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(v_n____,type,
    v_n____: $i ).

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

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

tff(c_List_Olistsum,type,
    c_List_Olistsum: ( $i * $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_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(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(c_List_Osko__List__XCons__eq__append__conv__1__1,type,
    c_List_Osko__List__XCons__eq__append__conv__1__1: ( $i * $i * $i * $i * $i ) > $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(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_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(c_List_Osko__List__Xappend__eq__Cons__conv__1__1,type,
    c_List_Osko__List__Xappend__eq__Cons__conv__1__1: ( $i * $i * $i * $i * $i ) > $i ).

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(v_Ts____,type,
    v_Ts____: $i ).

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

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

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

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

tff(c_List_Orotate1,type,
    c_List_Orotate1: ( $i * $i ) > $i ).

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

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(v_as____,type,
    v_as____: $i ).

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

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

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

tff(c_Type_Osko__Type__Xtyping__elims__3__1,type,
    c_Type_Osko__Type__Xtyping__elims__3__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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

tff(f_1360,axiom,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    file(unknown,unknown) ).

tff(f_1359,axiom,
    v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
    file(unknown,unknown) ).

tff(f_1362,axiom,
    ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    file(unknown,unknown) ).

tff(c_598,plain,
    c_Type_Otyping(v_e____,v_u____,v_T____),
    inference(cnfTransformation,[status(thm)],[f_1360]) ).

tff(c_596,plain,
    hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)) = v_T____,
    inference(cnfTransformation,[status(thm)],[f_1359]) ).

tff(c_600,plain,
    ~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
    inference(cnfTransformation,[status(thm)],[f_1362]) ).

tff(c_643,plain,
    ~ c_Type_Otyping(v_e____,v_u____,v_T____),
    inference(demodulation,[status(thm),theory(equality)],[c_596,c_600]) ).

tff(c_645,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_598,c_643]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : LCL789-1 : 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
% 0.14/0.36  % Computer : n001.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 14:49:40 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 5.23/2.23  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.23/2.24  
% 5.23/2.24  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.23/2.26  
% 5.23/2.26  Inference rules
% 5.23/2.26  ----------------------
% 5.23/2.26  #Ref     : 0
% 5.23/2.26  #Sup     : 0
% 5.23/2.26  #Fact    : 0
% 5.23/2.26  #Define  : 0
% 5.23/2.26  #Split   : 0
% 5.23/2.26  #Chain   : 0
% 5.23/2.26  #Close   : 0
% 5.23/2.26  
% 5.23/2.26  Ordering : KBO
% 5.23/2.26  
% 5.23/2.26  Simplification rules
% 5.23/2.26  ----------------------
% 5.23/2.26  #Subsume      : 320
% 5.23/2.26  #Demod        : 2
% 5.23/2.26  #Tautology    : 0
% 5.23/2.26  #SimpNegUnit  : 0
% 5.23/2.26  #BackRed      : 0
% 5.23/2.26  
% 5.23/2.26  #Partial instantiations: 0
% 5.23/2.26  #Strategies tried      : 1
% 5.23/2.26  
% 5.23/2.26  Timing (in seconds)
% 5.23/2.26  ----------------------
% 5.23/2.27  Preprocessing        : 1.09
% 5.23/2.27  Parsing              : 0.58
% 5.23/2.27  CNF conversion       : 0.08
% 5.23/2.27  Main loop            : 0.10
% 5.23/2.27  Inferencing          : 0.00
% 5.23/2.27  Reduction            : 0.05
% 5.23/2.27  Demodulation         : 0.04
% 5.23/2.27  BG Simplification    : 0.08
% 5.23/2.27  Subsumption          : 0.04
% 5.23/2.27  Abstraction          : 0.02
% 5.23/2.27  MUC search           : 0.00
% 5.23/2.27  Cooper               : 0.00
% 5.23/2.27  Total                : 1.24
% 5.23/2.27  Index Insertion      : 0.00
% 5.23/2.27  Index Deletion       : 0.00
% 5.23/2.27  Index Matching       : 0.00
% 5.23/2.27  BG Taut test         : 0.00
%------------------------------------------------------------------------------