TSTP Solution File: LCL755-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : LCL755-1 : 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/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n008.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 10:48:54 EDT 2023

% Result   : Unsatisfiable 13.27s 4.06s
% Output   : CNFRefutation 13.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   68
% Syntax   : Number of formulae    :   73 (   6 unt;  65 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 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   82 (  61   >;  21   *;   0   +;   0  <<)
%            Number of predicates  :   48 (  47 usr;   1 prp; 0-3 aty)
%            Number of functors    :   18 (  18 usr;   4 con; 0-3 aty)
%            Number of variables   :    6 (;   6   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ c_lessequals > c_HOL_Oord__class_Oless > c_Lambda_Obeta > class_Ring__and__Field_Ozero__neq__one > class_Ring__and__Field_Osemiring > class_Ring__and__Field_Oring__no__zero__divisors > class_Ring__and__Field_Oring > class_Ring__and__Field_Opordered__semiring > class_Ring__and__Field_Opordered__ring > class_Ring__and__Field_Opordered__cancel__semiring > class_Ring__and__Field_Oordered__semiring__strict > class_Ring__and__Field_Oordered__semiring > 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_Omult__mono1 > class_Ring__and__Field_Omult__mono > 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__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__mult > 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_Int_Onumber__ring > class_Divides_Osemiring__div > class_Divides_Oring__div > c_InductTermi_OIT > c_Orderings_Oord__class_Omin > c_Orderings_Oord__class_Omax > c_Lambda_Osubst > c_HOL_Otimes__class_Otimes > c_HOL_Oplus__class_Oplus > c_HOL_Ominus__class_Ominus > c_Divides_Odiv__class_Omod > c_Lambda_Olift > c_Lambda_OdB_OApp > #nlpp > c_Suc > c_Lambda_OdB_OVar > c_Lambda_OdB_OAbs > c_HOL_Ozero__class_Ozero > c_HOL_Oone__class_Oone > v_ra > v_ja > v_ia > 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_OrderedGroup_Opordered__ab__semigroup__add,type,
    class_OrderedGroup_Opordered__ab__semigroup__add: $i > $o ).

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

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_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_Oordered__semiring,type,
    class_Ring__and__Field_Oordered__semiring: $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(class_OrderedGroup_Oab__semigroup__add,type,
    class_OrderedGroup_Oab__semigroup__add: $i > $o ).

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(class_Ring__and__Field_Ozero__neq__one,type,
    class_Ring__and__Field_Ozero__neq__one: $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(v_ra,type,
    v_ra: $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_Orderings_Oord__class_Omin,type,
    c_Orderings_Oord__class_Omin: ( $i * $i * $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_Divides_Oring__div,type,
    class_Divides_Oring__div: $i > $o ).

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(tc_nat,type,
    tc_nat: $i ).

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

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

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

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

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

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(class_Ring__and__Field_Oordered__semiring__strict,type,
    class_Ring__and__Field_Oordered__semiring__strict: $i > $o ).

tff(class_Ring__and__Field_Opordered__cancel__semiring,type,
    class_Ring__and__Field_Opordered__cancel__semiring: $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_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(class_Ring__and__Field_Omult__mono1,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

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

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

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

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

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

tff(class_Ring__and__Field_Opordered__semiring,type,
    class_Ring__and__Field_Opordered__semiring: $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_Oordered__semidom,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

tff(f_4729,axiom,
    ! [V_i,V_j] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i),V_j)),
    file(unknown,unknown) ).

tff(f_4676,axiom,
    ! [V_r] :
      ( c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r))
      | ~ c_InductTermi_OIT(V_r) ),
    file(unknown,unknown) ).

tff(f_4731,axiom,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    file(unknown,unknown) ).

tff(c_1448,plain,
    ! [V_i_2115,V_j_2116] : c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(V_i_2115),V_j_2116)),
    inference(cnfTransformation,[status(thm)],[f_4729]) ).

tff(c_1420,plain,
    ! [V_r_2090] :
      ( ~ c_InductTermi_OIT(V_r_2090)
      | c_InductTermi_OIT(c_Lambda_OdB_OAbs(V_r_2090)) ),
    inference(cnfTransformation,[status(thm)],[f_4676]) ).

tff(c_1450,plain,
    ~ c_InductTermi_OIT(c_Lambda_OdB_OAbs(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja)))),
    inference(cnfTransformation,[status(thm)],[f_4731]) ).

tff(c_4531,plain,
    ~ c_InductTermi_OIT(c_Lambda_Osubst(v_ra,c_Lambda_OdB_OVar(c_Suc(v_ia)),c_Suc(v_ja))),
    inference(resolution,[status(thm)],[c_1420,c_1450]) ).

tff(c_4535,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1448,c_4531]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : LCL755-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.18/0.35  % Computer : n008.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Thu Aug  3 14:19:18 EDT 2023
% 0.18/0.35  % CPUTime  : 
% 13.27/4.06  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.27/4.06  
% 13.27/4.06  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.43/4.09  
% 13.43/4.09  Inference rules
% 13.43/4.09  ----------------------
% 13.43/4.09  #Ref     : 5
% 13.43/4.09  #Sup     : 570
% 13.43/4.09  #Fact    : 2
% 13.43/4.09  #Define  : 0
% 13.43/4.09  #Split   : 0
% 13.43/4.09  #Chain   : 0
% 13.43/4.09  #Close   : 0
% 13.43/4.09  
% 13.43/4.09  Ordering : KBO
% 13.43/4.09  
% 13.43/4.09  Simplification rules
% 13.43/4.09  ----------------------
% 13.43/4.09  #Subsume      : 167
% 13.43/4.09  #Demod        : 498
% 13.43/4.09  #Tautology    : 534
% 13.43/4.09  #SimpNegUnit  : 4
% 13.43/4.09  #BackRed      : 0
% 13.43/4.09  
% 13.43/4.09  #Partial instantiations: 0
% 13.43/4.09  #Strategies tried      : 1
% 13.43/4.09  
% 13.43/4.09  Timing (in seconds)
% 13.43/4.09  ----------------------
% 13.43/4.09  Preprocessing        : 1.50
% 13.43/4.09  Parsing              : 0.85
% 13.43/4.09  CNF conversion       : 0.13
% 13.43/4.09  Main loop            : 1.53
% 13.43/4.09  Inferencing          : 0.25
% 13.43/4.09  Reduction            : 0.69
% 13.43/4.09  Demodulation         : 0.47
% 13.43/4.09  BG Simplification    : 0.14
% 13.43/4.09  Subsumption          : 0.38
% 13.43/4.09  Abstraction          : 0.04
% 13.43/4.09  MUC search           : 0.00
% 13.43/4.09  Cooper               : 0.00
% 13.43/4.09  Total                : 3.07
% 13.43/4.09  Index Insertion      : 0.00
% 13.43/4.09  Index Deletion       : 0.00
% 13.43/4.09  Index Matching       : 0.00
% 13.43/4.09  BG Taut test         : 0.00
%------------------------------------------------------------------------------