TSTP Solution File: LCL858-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL858-1 : 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 : n017.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 10:49:11 EDT 2023

% Result   : Unsatisfiable 9.07s 3.22s
% Output   : CNFRefutation 9.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   51
% Syntax   : Number of formulae    :   56 (   6 unt;  48 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 :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   90 (  39   >;  51   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   9 con; 0-5 aty)
%            Number of variables   :    2 (;   2   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_Type_Otyping > c_List_Olistsp > c_Wellfounded_OwfP > hBOOL > class_Lattices_Oupper__semilattice > class_Lattices_Olower__semilattice > class_Lattices_Olattice > class_Lattices_Odistrib__lattice > c_Predicate_Opred__comp > c_List_Ofoldl > c_Type_Oshift > c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 > c_Predicate_Oconversep > c_List_Olist_OCons > c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 > c_Lattices_Oupper__semilattice__class_Osup > c_Lattices_Olower__semilattice__class_Oinf > c_Lambda_Osubst > c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 > c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 > c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 > v_sko__Wellfounded__Xaccp__Xinducts__1 > v_sko__Wellfounded__Xaccp__Xinduct__1 > tc_fun > hAPP > c_Wellfounded_Oaccp > c_Type_Otype_OFun > c_Transitive__Closure_Otranclp > c_Transitive__Closure_Ortranclp > c_ListOrder_Ostep1 > c_Lambda_Olift > #nlpp > tc_List_Olist > c_fequal > c_List_Olist_ONil > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > v_t > tc_nat > tc_bool > tc_Type_Otype > tc_Lambda_OdB > t_a > c_Lambda_OdB_OApp > c_Lambda_Obeta > c_InductTermi_OIT

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1,type,
    c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1: ( $i * $i * $i ) > $i ).

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

tff(v_sko__Wellfounded__Xaccp__Xinducts__1,type,
    v_sko__Wellfounded__Xaccp__Xinducts__1: ( $i * $i ) > $i ).

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

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

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

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

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

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

tff(c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1,type,
    c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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_Lambda_Osubst,type,
    c_Lambda_Osubst: ( $i * $i * $i ) > $i ).

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

tff(v_sko__Wellfounded__Xaccp__Xinduct__1,type,
    v_sko__Wellfounded__Xaccp__Xinduct__1: ( $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_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(tc_List_Olist,type,
    tc_List_Olist: $i > $i ).

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

tff(tc_nat,type,
    tc_nat: $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(c_Lambda_OdB_OApp,type,
    c_Lambda_OdB_OApp: $i ).

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

tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1,type,
    c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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

tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1,type,
    c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1: ( $i * $i * $i ) > $i ).

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

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

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

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

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

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

tff(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1,type,
    c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1: ( $i * $i * $i ) > $i ).

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

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

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

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

tff(f_994,axiom,
    hBOOL(hAPP(c_InductTermi_OIT,v_t)),
    file(unknown,unknown) ).

tff(f_806,axiom,
    ! [V_t] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t))
      | ~ hBOOL(hAPP(c_InductTermi_OIT,V_t)) ),
    file(unknown,unknown) ).

tff(f_996,axiom,
    ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
    file(unknown,unknown) ).

tff(c_378,plain,
    hBOOL(hAPP(c_InductTermi_OIT,v_t)),
    inference(cnfTransformation,[status(thm)],[f_994]) ).

tff(c_5161,plain,
    ! [V_t_950] :
      ( ~ hBOOL(hAPP(c_InductTermi_OIT,V_t_950))
      | hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),V_t_950)) ),
    inference(cnfTransformation,[status(thm)],[f_806]) ).

tff(c_380,plain,
    ~ hBOOL(hAPP(c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB),v_t)),
    inference(cnfTransformation,[status(thm)],[f_996]) ).

tff(c_5167,plain,
    ~ hBOOL(hAPP(c_InductTermi_OIT,v_t)),
    inference(resolution,[status(thm)],[c_5161,c_380]) ).

tff(c_5172,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_378,c_5167]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL858-1 : 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 : n017.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 13:33:21 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 9.07/3.22  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.07/3.22  
% 9.07/3.22  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.07/3.25  
% 9.07/3.25  Inference rules
% 9.07/3.25  ----------------------
% 9.07/3.25  #Ref     : 8
% 9.07/3.25  #Sup     : 1039
% 9.07/3.25  #Fact    : 0
% 9.07/3.25  #Define  : 0
% 9.07/3.25  #Split   : 0
% 9.07/3.25  #Chain   : 0
% 9.07/3.25  #Close   : 0
% 9.07/3.25  
% 9.07/3.25  Ordering : KBO
% 9.07/3.25  
% 9.07/3.25  Simplification rules
% 9.07/3.25  ----------------------
% 9.07/3.25  #Subsume      : 66
% 9.07/3.25  #Demod        : 1435
% 9.07/3.25  #Tautology    : 864
% 9.07/3.25  #SimpNegUnit  : 0
% 9.07/3.25  #BackRed      : 0
% 9.07/3.25  
% 9.07/3.25  #Partial instantiations: 0
% 9.07/3.25  #Strategies tried      : 1
% 9.07/3.25  
% 9.07/3.25  Timing (in seconds)
% 9.07/3.25  ----------------------
% 9.07/3.25  Preprocessing        : 1.03
% 9.07/3.25  Parsing              : 0.56
% 9.07/3.25  CNF conversion       : 0.08
% 9.07/3.25  Main loop            : 1.03
% 9.07/3.25  Inferencing          : 0.32
% 9.07/3.25  Reduction            : 0.43
% 9.07/3.25  Demodulation         : 0.34
% 9.07/3.25  BG Simplification    : 0.07
% 9.07/3.25  Subsumption          : 0.17
% 9.07/3.25  Abstraction          : 0.05
% 9.07/3.25  MUC search           : 0.00
% 9.07/3.25  Cooper               : 0.00
% 9.07/3.25  Total                : 2.11
% 9.07/3.25  Index Insertion      : 0.00
% 9.07/3.25  Index Deletion       : 0.00
% 9.07/3.25  Index Matching       : 0.00
% 9.07/3.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------