TSTP Solution File: FLD032-3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD032-3 : 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 : n020.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 10:37:32 EDT 2023

% Result   : Unsatisfiable 5.02s 2.17s
% Output   : CNFRefutation 5.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   54 (  16 unt;  11 typ;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   92 (  45   ~;  47   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   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   :   56 (;  56   !;   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_254,axiom,
    ~ product(multiplicative_identity,a,multiplicative_identity),
    file(unknown,unknown) ).

tff(f_251,axiom,
    ~ sum(additive_identity,a,additive_identity),
    file(unknown,unknown) ).

tff(f_249,axiom,
    defined(a),
    file(unknown,unknown) ).

tff(f_117,axiom,
    ! [X] :
      ( product(multiplicative_inverse(X),X,multiplicative_identity)
      | sum(additive_identity,X,additive_identity)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_122,axiom,
    ! [Y,X,Z] :
      ( product(Y,X,Z)
      | ~ product(X,Y,Z) ),
    file(unknown,unknown) ).

tff(f_252,axiom,
    product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
    file(unknown,unknown) ).

tff(f_180,axiom,
    ! [X] :
      ( defined(multiplicative_inverse(X))
      | ~ defined(X)
      | sum(additive_identity,X,additive_identity) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X] :
      ( product(multiplicative_identity,X,X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_105,axiom,
    ! [W,U,Z,X,Y,V] :
      ( product(U,Z,W)
      | ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(X,V,W) ),
    file(unknown,unknown) ).

tff(f_94,axiom,
    ! [W,U,Z,X,Y,V] :
      ( product(X,V,W)
      | ~ product(X,Y,U)
      | ~ product(Y,Z,V)
      | ~ product(U,Z,W) ),
    file(unknown,unknown) ).

tff(c_60,plain,
    ~ product(multiplicative_identity,a,multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_56,plain,
    ~ sum(additive_identity,a,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_251]) ).

tff(c_54,plain,
    defined(a),
    inference(cnfTransformation,[status(thm)],[f_249]) ).

tff(c_147,plain,
    ! [X_104] :
      ( ~ defined(X_104)
      | sum(additive_identity,X_104,additive_identity)
      | product(multiplicative_inverse(X_104),X_104,multiplicative_identity) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_20,plain,
    ! [X_33,Y_32,Z_34] :
      ( ~ product(X_33,Y_32,Z_34)
      | product(Y_32,X_33,Z_34) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_150,plain,
    ! [X_104] :
      ( product(X_104,multiplicative_inverse(X_104),multiplicative_identity)
      | ~ defined(X_104)
      | sum(additive_identity,X_104,additive_identity) ),
    inference(resolution,[status(thm)],[c_147,c_20]) ).

tff(c_58,plain,
    product(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_66,plain,
    ! [X_80,Y_81,Z_82] :
      ( ~ product(X_80,Y_81,Z_82)
      | product(Y_81,X_80,Z_82) ),
    inference(cnfTransformation,[status(thm)],[f_122]) ).

tff(c_72,plain,
    product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
    inference(resolution,[status(thm)],[c_58,c_66]) ).

tff(c_36,plain,
    ! [X_54] :
      ( sum(additive_identity,X_54,additive_identity)
      | ~ defined(X_54)
      | defined(multiplicative_inverse(X_54)) ),
    inference(cnfTransformation,[status(thm)],[f_180]) ).

tff(c_16,plain,
    ! [X_30] :
      ( ~ defined(X_30)
      | product(multiplicative_identity,X_30,X_30) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_71,plain,
    ! [X_30] :
      ( product(X_30,multiplicative_identity,X_30)
      | ~ defined(X_30) ),
    inference(resolution,[status(thm)],[c_16,c_66]) ).

tff(c_490,plain,
    ! [U_152,W_154,Y_150,Z_151,X_153,V_155] :
      ( ~ product(X_153,V_155,W_154)
      | ~ product(Y_150,Z_151,V_155)
      | ~ product(X_153,Y_150,U_152)
      | product(U_152,Z_151,W_154) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_698,plain,
    ! [Y_180,Z_181,U_182] :
      ( ~ product(Y_180,Z_181,multiplicative_inverse(a))
      | ~ product(multiplicative_identity,Y_180,U_182)
      | product(U_182,Z_181,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_58,c_490]) ).

tff(c_705,plain,
    ! [U_182] :
      ( ~ product(multiplicative_identity,multiplicative_inverse(a),U_182)
      | product(U_182,multiplicative_identity,multiplicative_identity)
      | ~ defined(multiplicative_inverse(a)) ),
    inference(resolution,[status(thm)],[c_71,c_698]) ).

tff(c_707,plain,
    ~ defined(multiplicative_inverse(a)),
    inference(splitLeft,[status(thm)],[c_705]) ).

tff(c_735,plain,
    ( sum(additive_identity,a,additive_identity)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_36,c_707]) ).

tff(c_738,plain,
    sum(additive_identity,a,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_735]) ).

tff(c_740,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_56,c_738]) ).

tff(c_742,plain,
    defined(multiplicative_inverse(a)),
    inference(splitRight,[status(thm)],[c_705]) ).

tff(c_356,plain,
    ! [Z_133,V_136,X_135,W_134,U_132,Y_137] :
      ( ~ product(U_132,Z_133,W_134)
      | ~ product(Y_137,Z_133,V_136)
      | ~ product(X_135,Y_137,U_132)
      | product(X_135,V_136,W_134) ),
    inference(cnfTransformation,[status(thm)],[f_94]) ).

tff(c_978,plain,
    ! [Y_203,V_204,X_205] :
      ( ~ product(Y_203,multiplicative_inverse(a),V_204)
      | ~ product(X_205,Y_203,multiplicative_identity)
      | product(X_205,V_204,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_58,c_356]) ).

tff(c_998,plain,
    ! [X_205] :
      ( ~ product(X_205,multiplicative_identity,multiplicative_identity)
      | product(X_205,multiplicative_inverse(a),multiplicative_identity)
      | ~ defined(multiplicative_inverse(a)) ),
    inference(resolution,[status(thm)],[c_16,c_978]) ).

tff(c_1054,plain,
    ! [X_208] :
      ( ~ product(X_208,multiplicative_identity,multiplicative_identity)
      | product(X_208,multiplicative_inverse(a),multiplicative_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_742,c_998]) ).

tff(c_1082,plain,
    ! [X_209] :
      ( product(multiplicative_inverse(a),X_209,multiplicative_identity)
      | ~ product(X_209,multiplicative_identity,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_1054,c_20]) ).

tff(c_380,plain,
    ! [Y_137,V_136,X_135] :
      ( ~ product(Y_137,multiplicative_inverse(a),V_136)
      | ~ product(X_135,Y_137,multiplicative_identity)
      | product(X_135,V_136,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_58,c_356]) ).

tff(c_1088,plain,
    ! [X_135] :
      ( ~ product(X_135,multiplicative_inverse(a),multiplicative_identity)
      | product(X_135,multiplicative_identity,multiplicative_identity)
      | ~ product(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_1082,c_380]) ).

tff(c_1117,plain,
    ! [X_210] :
      ( ~ product(X_210,multiplicative_inverse(a),multiplicative_identity)
      | product(X_210,multiplicative_identity,multiplicative_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_1088]) ).

tff(c_1135,plain,
    ( product(a,multiplicative_identity,multiplicative_identity)
    | ~ defined(a)
    | sum(additive_identity,a,additive_identity) ),
    inference(resolution,[status(thm)],[c_150,c_1117]) ).

tff(c_1152,plain,
    ( product(a,multiplicative_identity,multiplicative_identity)
    | sum(additive_identity,a,additive_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_1135]) ).

tff(c_1153,plain,
    product(a,multiplicative_identity,multiplicative_identity),
    inference(negUnitSimplification,[status(thm)],[c_56,c_1152]) ).

tff(c_1171,plain,
    product(multiplicative_identity,a,multiplicative_identity),
    inference(resolution,[status(thm)],[c_1153,c_20]) ).

tff(c_1181,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_60,c_1171]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : FLD032-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.14/0.15  % 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
% 0.15/0.37  % Computer : n020.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 19:58:07 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 5.02/2.17  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.02/2.17  
% 5.02/2.17  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.02/2.21  
% 5.02/2.21  Inference rules
% 5.02/2.21  ----------------------
% 5.02/2.21  #Ref     : 0
% 5.02/2.21  #Sup     : 266
% 5.02/2.21  #Fact    : 2
% 5.02/2.21  #Define  : 0
% 5.02/2.21  #Split   : 5
% 5.02/2.21  #Chain   : 0
% 5.02/2.21  #Close   : 0
% 5.02/2.21  
% 5.02/2.21  Ordering : KBO
% 5.02/2.21  
% 5.02/2.21  Simplification rules
% 5.02/2.21  ----------------------
% 5.02/2.21  #Subsume      : 45
% 5.02/2.21  #Demod        : 74
% 5.02/2.21  #Tautology    : 29
% 5.02/2.21  #SimpNegUnit  : 20
% 5.02/2.21  #BackRed      : 0
% 5.02/2.21  
% 5.02/2.21  #Partial instantiations: 0
% 5.02/2.21  #Strategies tried      : 1
% 5.02/2.21  
% 5.02/2.21  Timing (in seconds)
% 5.02/2.21  ----------------------
% 5.02/2.21  Preprocessing        : 0.50
% 5.02/2.21  Parsing              : 0.27
% 5.02/2.21  CNF conversion       : 0.03
% 5.02/2.21  Main loop            : 0.64
% 5.02/2.21  Inferencing          : 0.24
% 5.02/2.21  Reduction            : 0.15
% 5.02/2.21  Demodulation         : 0.10
% 5.02/2.21  BG Simplification    : 0.03
% 5.02/2.21  Subsumption          : 0.17
% 5.02/2.21  Abstraction          : 0.02
% 5.02/2.21  MUC search           : 0.00
% 5.02/2.21  Cooper               : 0.00
% 5.02/2.21  Total                : 1.20
% 5.02/2.21  Index Insertion      : 0.00
% 5.02/2.21  Index Deletion       : 0.00
% 5.02/2.21  Index Matching       : 0.00
% 5.02/2.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------