TSTP Solution File: FLD032-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD032-1 : 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 : n012.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 102.59s 88.18s
% Output   : CNFRefutation 102.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   64 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :  125 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  138 (  67   ~;  71   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   11 (   7   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   70 (;  70   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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(equalish,type,
    equalish: ( $i * $i ) > $o ).

tff(f_238,axiom,
    ~ equalish(a,additive_identity),
    file(unknown,unknown) ).

tff(f_241,axiom,
    ~ equalish(a,multiplicative_identity),
    file(unknown,unknown) ).

tff(f_236,axiom,
    defined(a),
    file(unknown,unknown) ).

tff(f_147,axiom,
    ! [X] :
      ( defined(multiplicative_inverse(X))
      | ~ defined(X)
      | equalish(X,additive_identity) ),
    file(unknown,unknown) ).

tff(f_173,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
      | less_or_equal(Y,X)
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

tff(f_239,axiom,
    equalish(multiplicative_inverse(a),multiplicative_identity),
    file(unknown,unknown) ).

tff(f_231,axiom,
    ! [Y,Z,X] :
      ( less_or_equal(Y,Z)
      | ~ less_or_equal(X,Z)
      | ~ equalish(X,Y) ),
    file(unknown,unknown) ).

tff(f_199,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,X) ),
    file(unknown,unknown) ).

tff(f_207,axiom,
    ! [X,Z,Y] :
      ( equalish(X,Z)
      | ~ equalish(X,Y)
      | ~ equalish(Y,Z) ),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X] :
      ( equalish(multiply(multiplicative_identity,X),X)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_223,axiom,
    ! [X,Z,Y] :
      ( equalish(multiply(X,Z),multiply(Y,Z))
      | ~ defined(Z)
      | ~ equalish(X,Y) ),
    file(unknown,unknown) ).

tff(f_106,axiom,
    ! [X,Y] :
      ( equalish(multiply(X,Y),multiply(Y,X))
      | ~ defined(X)
      | ~ defined(Y) ),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ! [X] :
      ( equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity)
      | ~ defined(X)
      | equalish(X,additive_identity) ),
    file(unknown,unknown) ).

tff(c_58,plain,
    ~ equalish(a,additive_identity),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

tff(c_62,plain,
    ~ equalish(a,multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_241]) ).

tff(c_56,plain,
    defined(a),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_30,plain,
    ! [X_23] :
      ( equalish(X_23,additive_identity)
      | ~ defined(X_23)
      | defined(multiplicative_inverse(X_23)) ),
    inference(cnfTransformation,[status(thm)],[f_147]) ).

tff(c_36,plain,
    ! [Y_30,X_29] :
      ( ~ defined(Y_30)
      | ~ defined(X_29)
      | less_or_equal(Y_30,X_29)
      | less_or_equal(X_29,Y_30) ),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_255,plain,
    ! [Y_83] :
      ( ~ defined(Y_83)
      | less_or_equal(Y_83,Y_83) ),
    inference(factorization,[status(thm),theory(equality)],[c_36]) ).

tff(c_60,plain,
    equalish(multiplicative_inverse(a),multiplicative_identity),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_105,plain,
    ! [X_71,Y_72,Z_73] :
      ( ~ equalish(X_71,Y_72)
      | ~ less_or_equal(X_71,Z_73)
      | less_or_equal(Y_72,Z_73) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_132,plain,
    ! [Z_73] :
      ( ~ less_or_equal(multiplicative_inverse(a),Z_73)
      | less_or_equal(multiplicative_identity,Z_73) ),
    inference(resolution,[status(thm)],[c_60,c_105]) ).

tff(c_264,plain,
    ( less_or_equal(multiplicative_identity,multiplicative_inverse(a))
    | ~ defined(multiplicative_inverse(a)) ),
    inference(resolution,[status(thm)],[c_255,c_132]) ).

tff(c_267,plain,
    ~ defined(multiplicative_inverse(a)),
    inference(splitLeft,[status(thm)],[c_264]) ).

tff(c_270,plain,
    ( equalish(a,additive_identity)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_30,c_267]) ).

tff(c_273,plain,
    equalish(a,additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_270]) ).

tff(c_275,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_58,c_273]) ).

tff(c_277,plain,
    defined(multiplicative_inverse(a)),
    inference(splitRight,[status(thm)],[c_264]) ).

tff(c_65,plain,
    ! [Y_53,X_54] :
      ( ~ equalish(Y_53,X_54)
      | equalish(X_54,Y_53) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_71,plain,
    equalish(multiplicative_identity,multiplicative_inverse(a)),
    inference(resolution,[status(thm)],[c_60,c_65]) ).

tff(c_145,plain,
    ! [Y_76,Z_77,X_78] :
      ( ~ equalish(Y_76,Z_77)
      | ~ equalish(X_78,Y_76)
      | equalish(X_78,Z_77) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_173,plain,
    ! [X_79] :
      ( ~ equalish(X_79,multiplicative_inverse(a))
      | equalish(X_79,multiplicative_identity) ),
    inference(resolution,[status(thm)],[c_60,c_145]) ).

tff(c_191,plain,
    equalish(multiplicative_identity,multiplicative_identity),
    inference(resolution,[status(thm)],[c_71,c_173]) ).

tff(c_76,plain,
    ! [X_55] :
      ( ~ defined(X_55)
      | equalish(multiply(multiplicative_identity,X_55),X_55) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_44,plain,
    ! [Y_38,X_37] :
      ( ~ equalish(Y_38,X_37)
      | equalish(X_37,Y_38) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_79,plain,
    ! [X_55] :
      ( equalish(X_55,multiply(multiplicative_identity,X_55))
      | ~ defined(X_55) ),
    inference(resolution,[status(thm)],[c_76,c_44]) ).

tff(c_622,plain,
    ! [X_104,Y_105,Z_106] :
      ( ~ equalish(X_104,Y_105)
      | ~ defined(Z_106)
      | equalish(multiply(X_104,Z_106),multiply(Y_105,Z_106)) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_46,plain,
    ! [Y_41,Z_40,X_39] :
      ( ~ equalish(Y_41,Z_40)
      | ~ equalish(X_39,Y_41)
      | equalish(X_39,Z_40) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_7201,plain,
    ! [X_270,X_271,Z_272,Y_273] :
      ( ~ equalish(X_270,multiply(X_271,Z_272))
      | equalish(X_270,multiply(Y_273,Z_272))
      | ~ equalish(X_271,Y_273)
      | ~ defined(Z_272) ),
    inference(resolution,[status(thm)],[c_622,c_46]) ).

tff(c_7360,plain,
    ! [X_55,Y_273] :
      ( equalish(X_55,multiply(Y_273,X_55))
      | ~ equalish(multiplicative_identity,Y_273)
      | ~ defined(X_55) ),
    inference(resolution,[status(thm)],[c_79,c_7201]) ).

tff(c_3205,plain,
    ! [Y_191,Z_192,X_193] :
      ( equalish(multiply(Y_191,Z_192),multiply(X_193,Z_192))
      | ~ equalish(X_193,Y_191)
      | ~ defined(Z_192) ),
    inference(resolution,[status(thm)],[c_622,c_44]) ).

tff(c_41836,plain,
    ! [X_583,Y_584,Z_585,X_586] :
      ( ~ equalish(X_583,multiply(Y_584,Z_585))
      | equalish(X_583,multiply(X_586,Z_585))
      | ~ equalish(X_586,Y_584)
      | ~ defined(Z_585) ),
    inference(resolution,[status(thm)],[c_3205,c_46]) ).

tff(c_182869,plain,
    ! [X_1252,X_1253,Y_1254] :
      ( equalish(X_1252,multiply(X_1253,X_1252))
      | ~ equalish(X_1253,Y_1254)
      | ~ equalish(multiplicative_identity,Y_1254)
      | ~ defined(X_1252) ),
    inference(resolution,[status(thm)],[c_7360,c_41836]) ).

tff(c_184671,plain,
    ! [X_1252] :
      ( equalish(X_1252,multiply(multiplicative_inverse(a),X_1252))
      | ~ equalish(multiplicative_identity,multiplicative_identity)
      | ~ defined(X_1252) ),
    inference(resolution,[status(thm)],[c_60,c_182869]) ).

tff(c_186787,plain,
    ! [X_1255] :
      ( equalish(X_1255,multiply(multiplicative_inverse(a),X_1255))
      | ~ defined(X_1255) ),
    inference(demodulation,[status(thm),theory(equality)],[c_191,c_184671]) ).

tff(c_278,plain,
    ! [Y_84,X_85] :
      ( ~ defined(Y_84)
      | ~ defined(X_85)
      | equalish(multiply(X_85,Y_84),multiply(Y_84,X_85)) ),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_285,plain,
    ! [X_39,X_85,Y_84] :
      ( ~ equalish(X_39,multiply(X_85,Y_84))
      | equalish(X_39,multiply(Y_84,X_85))
      | ~ defined(Y_84)
      | ~ defined(X_85) ),
    inference(resolution,[status(thm)],[c_278,c_46]) ).

tff(c_186957,plain,
    ! [X_1255] :
      ( equalish(X_1255,multiply(X_1255,multiplicative_inverse(a)))
      | ~ defined(multiplicative_inverse(a))
      | ~ defined(X_1255) ),
    inference(resolution,[status(thm)],[c_186787,c_285]) ).

tff(c_194288,plain,
    ! [X_1272] :
      ( equalish(X_1272,multiply(X_1272,multiplicative_inverse(a)))
      | ~ defined(X_1272) ),
    inference(demodulation,[status(thm),theory(equality)],[c_277,c_186957]) ).

tff(c_325,plain,
    ! [X_88] :
      ( equalish(X_88,additive_identity)
      | ~ defined(X_88)
      | equalish(multiply(X_88,multiplicative_inverse(X_88)),multiplicative_identity) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_332,plain,
    ! [X_39,X_88] :
      ( ~ equalish(X_39,multiply(X_88,multiplicative_inverse(X_88)))
      | equalish(X_39,multiplicative_identity)
      | equalish(X_88,additive_identity)
      | ~ defined(X_88) ),
    inference(resolution,[status(thm)],[c_325,c_46]) ).

tff(c_194455,plain,
    ( equalish(a,multiplicative_identity)
    | equalish(a,additive_identity)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_194288,c_332]) ).

tff(c_194590,plain,
    ( equalish(a,multiplicative_identity)
    | equalish(a,additive_identity) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_194455]) ).

tff(c_194592,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_58,c_62,c_194590]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : FLD032-1 : 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 : n012.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 19:55:37 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 102.59/88.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 102.59/88.18  
% 102.59/88.18  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 102.59/88.22  
% 102.59/88.22  Inference rules
% 102.59/88.22  ----------------------
% 102.59/88.22  #Ref     : 0
% 102.59/88.22  #Sup     : 44853
% 102.59/88.22  #Fact    : 12
% 102.59/88.22  #Define  : 0
% 102.59/88.22  #Split   : 23
% 102.59/88.22  #Chain   : 0
% 102.59/88.22  #Close   : 0
% 102.59/88.22  
% 102.59/88.22  Ordering : KBO
% 102.59/88.22  
% 102.59/88.22  Simplification rules
% 102.59/88.22  ----------------------
% 102.59/88.22  #Subsume      : 9484
% 102.59/88.22  #Demod        : 21735
% 102.59/88.22  #Tautology    : 5903
% 102.59/88.22  #SimpNegUnit  : 612
% 102.59/88.22  #BackRed      : 0
% 102.59/88.22  
% 102.59/88.22  #Partial instantiations: 0
% 102.59/88.22  #Strategies tried      : 1
% 102.59/88.22  
% 102.59/88.22  Timing (in seconds)
% 102.59/88.22  ----------------------
% 102.59/88.22  Preprocessing        : 0.51
% 102.59/88.22  Parsing              : 0.27
% 102.59/88.22  CNF conversion       : 0.03
% 102.59/88.23  Main loop            : 86.59
% 102.59/88.23  Inferencing          : 6.97
% 102.59/88.23  Reduction            : 43.12
% 102.59/88.23  Demodulation         : 36.06
% 102.59/88.23  BG Simplification    : 0.22
% 102.59/88.23  Subsumption          : 29.29
% 102.59/88.23  Abstraction          : 0.37
% 102.59/88.23  MUC search           : 0.00
% 102.59/88.23  Cooper               : 0.00
% 102.59/88.23  Total                : 87.16
% 102.59/88.23  Index Insertion      : 0.00
% 102.59/88.23  Index Deletion       : 0.00
% 102.59/88.23  Index Matching       : 0.00
% 102.59/88.23  BG Taut test         : 0.00
%------------------------------------------------------------------------------