TSTP Solution File: FLD039-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD039-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n010.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 10:37:34 EDT 2023

% Result   : Unsatisfiable 4.88s 2.14s
% Output   : CNFRefutation 4.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   50 (  19 unt;  11 typ;   0 def)
%            Number of atoms       :   78 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   85 (  46   ~;  39   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   34 (;  34   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > multiplicative_identity > additive_identity > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

tff(f_159,axiom,
    defined(additive_identity),
    file(unknown,unknown) ).

tff(f_222,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

tff(f_204,axiom,
    ! [X,Y] :
      ( sum(additive_identity,X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(f_246,axiom,
    ~ sum(additive_identity,additive_identity,multiplicative_identity),
    file(unknown,unknown) ).

tff(f_173,axiom,
    defined(multiplicative_identity),
    file(unknown,unknown) ).

tff(f_73,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_252,axiom,
    sum(additive_identity,multiplicative_identity,additive_identity),
    file(unknown,unknown) ).

tff(f_233,axiom,
    ! [U,Z,X,Y,V] :
      ( less_or_equal(U,V)
      | ~ less_or_equal(X,Y)
      | ~ sum(X,Z,U)
      | ~ sum(Y,Z,V) ),
    file(unknown,unknown) ).

tff(c_28,plain,
    defined(additive_identity),
    inference(cnfTransformation,[status(thm)],[f_159]) ).

tff(c_46,plain,
    ! [Y_65,X_64] :
      ( ~ defined(Y_65)
      | ~ defined(X_64)
      | less_or_equal(Y_65,X_64)
      | less_or_equal(X_64,Y_65) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_863,plain,
    ! [Y_65] :
      ( ~ defined(Y_65)
      | less_or_equal(Y_65,Y_65) ),
    inference(factorization,[status(thm),theory(equality)],[c_46]) ).

tff(c_97,plain,
    ! [Y_95,X_96] :
      ( ~ less_or_equal(Y_95,X_96)
      | ~ less_or_equal(X_96,Y_95)
      | sum(additive_identity,X_96,Y_95) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_52,plain,
    ~ sum(additive_identity,additive_identity,multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_246]) ).

tff(c_107,plain,
    ( ~ less_or_equal(multiplicative_identity,additive_identity)
    | ~ less_or_equal(additive_identity,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_97,c_52]) ).

tff(c_109,plain,
    ~ less_or_equal(additive_identity,multiplicative_identity),
    inference(splitLeft,[status(thm)],[c_107]) ).

tff(c_34,plain,
    defined(multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_127,plain,
    ! [Y_65] :
      ( ~ defined(Y_65)
      | less_or_equal(Y_65,Y_65) ),
    inference(factorization,[status(thm),theory(equality)],[c_46]) ).

tff(c_6,plain,
    ! [X_13] :
      ( ~ defined(X_13)
      | sum(additive_identity,X_13,X_13) ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_58,plain,
    sum(additive_identity,multiplicative_identity,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_214,plain,
    ! [V_123,Z_121,Y_122,U_119,X_120] :
      ( ~ sum(Y_122,Z_121,V_123)
      | ~ sum(X_120,Z_121,U_119)
      | ~ less_or_equal(X_120,Y_122)
      | less_or_equal(U_119,V_123) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_245,plain,
    ! [X_124,U_125] :
      ( ~ sum(X_124,multiplicative_identity,U_125)
      | ~ less_or_equal(X_124,additive_identity)
      | less_or_equal(U_125,additive_identity) ),
    inference(resolution,[status(thm)],[c_58,c_214]) ).

tff(c_265,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(multiplicative_identity,additive_identity)
    | ~ defined(multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_6,c_245]) ).

tff(c_281,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(multiplicative_identity,additive_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_265]) ).

tff(c_283,plain,
    ~ less_or_equal(additive_identity,additive_identity),
    inference(splitLeft,[status(thm)],[c_281]) ).

tff(c_286,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_127,c_283]) ).

tff(c_292,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_286]) ).

tff(c_294,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(splitRight,[status(thm)],[c_281]) ).

tff(c_770,plain,
    ! [X_167,X_168,U_169] :
      ( ~ sum(X_167,X_168,U_169)
      | ~ less_or_equal(X_167,additive_identity)
      | less_or_equal(U_169,X_168)
      | ~ defined(X_168) ),
    inference(resolution,[status(thm)],[c_6,c_214]) ).

tff(c_800,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(additive_identity,multiplicative_identity)
    | ~ defined(multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_58,c_770]) ).

tff(c_822,plain,
    less_or_equal(additive_identity,multiplicative_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_294,c_800]) ).

tff(c_824,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_109,c_822]) ).

tff(c_825,plain,
    ~ less_or_equal(multiplicative_identity,additive_identity),
    inference(splitRight,[status(thm)],[c_107]) ).

tff(c_1018,plain,
    ! [V_201,X_198,Z_199,Y_200,U_197] :
      ( ~ sum(Y_200,Z_199,V_201)
      | ~ sum(X_198,Z_199,U_197)
      | ~ less_or_equal(X_198,Y_200)
      | less_or_equal(U_197,V_201) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_1049,plain,
    ! [X_202,U_203] :
      ( ~ sum(X_202,multiplicative_identity,U_203)
      | ~ less_or_equal(X_202,additive_identity)
      | less_or_equal(U_203,additive_identity) ),
    inference(resolution,[status(thm)],[c_58,c_1018]) ).

tff(c_1069,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(multiplicative_identity,additive_identity)
    | ~ defined(multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_6,c_1049]) ).

tff(c_1085,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(multiplicative_identity,additive_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_1069]) ).

tff(c_1086,plain,
    ~ less_or_equal(additive_identity,additive_identity),
    inference(negUnitSimplification,[status(thm)],[c_825,c_1085]) ).

tff(c_1091,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_863,c_1086]) ).

tff(c_1097,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_1091]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : FLD039-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n010.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 19:36:13 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.88/2.14  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.88/2.15  
% 4.88/2.15  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.88/2.18  
% 4.88/2.18  Inference rules
% 4.88/2.18  ----------------------
% 4.88/2.18  #Ref     : 0
% 4.88/2.18  #Sup     : 221
% 4.88/2.18  #Fact    : 6
% 4.88/2.18  #Define  : 0
% 4.88/2.18  #Split   : 4
% 4.88/2.18  #Chain   : 0
% 4.88/2.18  #Close   : 0
% 4.88/2.18  
% 4.88/2.18  Ordering : KBO
% 4.88/2.18  
% 4.88/2.18  Simplification rules
% 4.88/2.18  ----------------------
% 4.88/2.18  #Subsume      : 57
% 4.88/2.18  #Demod        : 113
% 4.88/2.18  #Tautology    : 26
% 4.88/2.18  #SimpNegUnit  : 4
% 4.88/2.18  #BackRed      : 0
% 4.88/2.18  
% 4.88/2.18  #Partial instantiations: 0
% 4.88/2.18  #Strategies tried      : 1
% 4.88/2.18  
% 4.88/2.18  Timing (in seconds)
% 4.88/2.18  ----------------------
% 4.88/2.19  Preprocessing        : 0.50
% 4.88/2.19  Parsing              : 0.29
% 4.88/2.19  CNF conversion       : 0.03
% 4.88/2.19  Main loop            : 0.58
% 4.88/2.19  Inferencing          : 0.24
% 4.88/2.19  Reduction            : 0.13
% 4.88/2.19  Demodulation         : 0.09
% 4.88/2.19  BG Simplification    : 0.03
% 4.88/2.19  Subsumption          : 0.14
% 4.88/2.19  Abstraction          : 0.02
% 4.88/2.19  MUC search           : 0.00
% 4.88/2.19  Cooper               : 0.00
% 4.88/2.19  Total                : 1.13
% 4.88/2.19  Index Insertion      : 0.00
% 4.88/2.19  Index Deletion       : 0.00
% 4.88/2.19  Index Matching       : 0.00
% 4.88/2.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------