TSTP Solution File: LCL774-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL774-1 : 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 : n005.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 5.30s 2.34s
% Output   : CNFRefutation 5.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :   59
% Syntax   : Number of formulae    :   62 (   5 unt;  57 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 (   2 avg)
%            Maximal term depth    :    2 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   74 (  54   >;  20   *;   0   +;   0  <<)
%            Number of predicates  :   38 (  37 usr;   1 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;   3 con; 0-3 aty)
%            Number of variables   :    2 (;   2   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Osemiring__1 > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semidom > class_Ring__and__Field_Oordered__ring__strict > class_Ring__and__Field_Oordered__idom > 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_Oidom > class_Ring__and__Field_Ocomm__semiring__1 > class_Ring__and__Field_Ocomm__semiring > class_Orderings_Opreorder > class_Orderings_Oorder > class_Orderings_Olinorder > 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__group__add > 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__mult > class_OrderedGroup_Oab__semigroup__idem__mult > class_OrderedGroup_Oab__semigroup__add > class_OrderedGroup_Oab__group__add > class_Nat_Osemiring__char__0 > class_Int_Onumber__ring > c_InductTermi_OIT > 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_Nat_Osemiring__1__class_Oof__nat > c_Lambda_Osko__Lambda__Xbeta__cases__2__1 > c_Lambda_Olift > c_Lambda_OdB_OApp > c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1 > #nlpp > c_Suc > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1 > c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1 > v_r > v_i > tc_nat

%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_Orderings_Olinorder,type,
    class_Orderings_Olinorder: $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_Lambda_Oliftn,type,
    c_Lambda_Oliftn: ( $i * $i * $i ) > $i ).

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

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

tff(class_Ring__and__Field_Osemiring,type,
    class_Ring__and__Field_Osemiring: $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(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_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_Opordered__ring,type,
    class_Ring__and__Field_Opordered__ring: $i > $o ).

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

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

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_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_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(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_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_Lambda_Osubstn,type,
    c_Lambda_Osubstn: ( $i * $i * $i ) > $i ).

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_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_HOL_Otimes__class_Otimes,type,
    c_HOL_Otimes__class_Otimes: ( $i * $i * $i ) > $i ).

tff(c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xless__Suc__eq__0__disj__1__1: ( $i * $i ) > $i ).

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

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

tff(c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xgr0__conv__Suc__1__1: $i > $i ).

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

tff(c_Lambda_Osko__Lambda__Xbeta__cases__2__1,type,
    c_Lambda_Osko__Lambda__Xbeta__cases__2__1: ( $i * $i ) > $i ).

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

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_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1,type,
    c_ATP__Linkup_Osko__Nat__Xgr0__implies__Suc__1__1: $i > $i ).

tff(f_2072,axiom,
    ! [V_n] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n)),
    file(unknown,unknown) ).

tff(f_2100,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
    file(unknown,unknown) ).

tff(c_700,plain,
    ! [V_n_956] : c_InductTermi_OIT(c_Lambda_OdB_OVar(V_n_956)),
    inference(cnfTransformation,[status(thm)],[f_2072]) ).

tff(c_720,plain,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OVar(v_i)),
    inference(cnfTransformation,[status(thm)],[f_2100]) ).

tff(c_766,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_700,c_720]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL774-1 : 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
% 0.18/0.36  % Computer : n005.cluster.edu
% 0.18/0.36  % Model    : x86_64 x86_64
% 0.18/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.36  % Memory   : 8042.1875MB
% 0.18/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.36  % CPULimit : 300
% 0.18/0.36  % WCLimit  : 300
% 0.18/0.36  % DateTime : Thu Aug  3 13:53:42 EDT 2023
% 0.18/0.36  % CPUTime  : 
% 5.30/2.34  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.30/2.34  
% 5.30/2.34  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.30/2.37  
% 5.30/2.37  Inference rules
% 5.30/2.37  ----------------------
% 5.30/2.37  #Ref     : 0
% 5.30/2.37  #Sup     : 0
% 5.30/2.37  #Fact    : 0
% 5.30/2.37  #Define  : 0
% 5.30/2.37  #Split   : 0
% 5.30/2.37  #Chain   : 0
% 5.30/2.37  #Close   : 0
% 5.30/2.37  
% 5.30/2.37  Ordering : KBO
% 5.30/2.37  
% 5.30/2.37  Simplification rules
% 5.30/2.37  ----------------------
% 5.30/2.37  #Subsume      : 381
% 5.30/2.37  #Demod        : 1
% 5.30/2.37  #Tautology    : 0
% 5.30/2.37  #SimpNegUnit  : 0
% 5.30/2.37  #BackRed      : 0
% 5.30/2.37  
% 5.30/2.37  #Partial instantiations: 0
% 5.30/2.37  #Strategies tried      : 1
% 5.30/2.37  
% 5.30/2.37  Timing (in seconds)
% 5.30/2.37  ----------------------
% 5.30/2.37  Preprocessing        : 1.18
% 5.30/2.37  Parsing              : 0.65
% 5.30/2.37  CNF conversion       : 0.10
% 5.30/2.37  Main loop            : 0.12
% 5.30/2.37  Inferencing          : 0.00
% 5.30/2.37  Reduction            : 0.06
% 5.30/2.37  Demodulation         : 0.04
% 5.30/2.37  BG Simplification    : 0.09
% 5.30/2.37  Subsumption          : 0.04
% 5.30/2.37  Abstraction          : 0.02
% 5.30/2.37  MUC search           : 0.00
% 5.30/2.37  Cooper               : 0.00
% 5.30/2.37  Total                : 1.34
% 5.30/2.37  Index Insertion      : 0.00
% 5.30/2.38  Index Deletion       : 0.00
% 5.30/2.38  Index Matching       : 0.00
% 5.30/2.38  BG Taut test         : 0.00
%------------------------------------------------------------------------------