TSTP Solution File: FLD071-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD071-2 : 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/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 : n028.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 10:37:42 EDT 2023

% Result   : Unsatisfiable 6.34s 2.50s
% Output   : CNFRefutation 6.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   91 (  36 unt;  12 typ;   0 def)
%            Number of atoms       :  143 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  135 (  71   ~;  64   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :   62 (;  62   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_or_equal > equalish > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > u > multiplicative_identity > b > 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(u,type,
    u: $i ).

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

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

tff(b,type,
    b: $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_243,axiom,
    ~ less_or_equal(additive_identity,u),
    file(unknown,unknown) ).

tff(f_238,axiom,
    defined(u),
    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_241,axiom,
    equalish(multiply(a,b),u),
    file(unknown,unknown) ).

tff(f_199,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,X) ),
    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_126,axiom,
    defined(additive_identity),
    file(unknown,unknown) ).

tff(f_240,axiom,
    less_or_equal(additive_identity,b),
    file(unknown,unknown) ).

tff(f_163,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(X,Z)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,Z) ),
    file(unknown,unknown) ).

tff(f_239,axiom,
    less_or_equal(additive_identity,a),
    file(unknown,unknown) ).

tff(f_189,axiom,
    ! [Y,Z] :
      ( less_or_equal(additive_identity,multiply(Y,Z))
      | ~ less_or_equal(additive_identity,Y)
      | ~ less_or_equal(additive_identity,Z) ),
    file(unknown,unknown) ).

tff(f_131,axiom,
    ! [X] :
      ( defined(additive_inverse(X))
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X] :
      ( equalish(add(X,additive_inverse(X)),additive_identity)
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X] :
      ( equalish(add(additive_identity,X),X)
      | ~ defined(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_155,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ less_or_equal(X,Y)
      | ~ less_or_equal(Y,X) ),
    file(unknown,unknown) ).

tff(c_68,plain,
    ~ less_or_equal(additive_identity,u),
    inference(cnfTransformation,[status(thm)],[f_243]) ).

tff(c_60,plain,
    defined(u),
    inference(cnfTransformation,[status(thm)],[f_238]) ).

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_396,plain,
    ! [Y_30] :
      ( ~ defined(Y_30)
      | less_or_equal(Y_30,Y_30) ),
    inference(factorization,[status(thm),theory(equality)],[c_36]) ).

tff(c_66,plain,
    equalish(multiply(a,b),u),
    inference(cnfTransformation,[status(thm)],[f_241]) ).

tff(c_71,plain,
    ! [Y_53,X_54] :
      ( ~ equalish(Y_53,X_54)
      | equalish(X_54,Y_53) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_76,plain,
    equalish(u,multiply(a,b)),
    inference(resolution,[status(thm)],[c_66,c_71]) ).

tff(c_158,plain,
    ! [X_70,Y_71,Z_72] :
      ( ~ equalish(X_70,Y_71)
      | ~ less_or_equal(X_70,Z_72)
      | less_or_equal(Y_71,Z_72) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_183,plain,
    ! [Z_72] :
      ( ~ less_or_equal(u,Z_72)
      | less_or_equal(multiply(a,b),Z_72) ),
    inference(resolution,[status(thm)],[c_76,c_158]) ).

tff(c_22,plain,
    defined(additive_identity),
    inference(cnfTransformation,[status(thm)],[f_126]) ).

tff(c_274,plain,
    ! [Y_83,X_84] :
      ( ~ defined(Y_83)
      | ~ defined(X_84)
      | less_or_equal(Y_83,X_84)
      | less_or_equal(X_84,Y_83) ),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_64,plain,
    less_or_equal(additive_identity,b),
    inference(cnfTransformation,[status(thm)],[f_240]) ).

tff(c_211,plain,
    ! [Y_75,Z_76,X_77] :
      ( ~ less_or_equal(Y_75,Z_76)
      | ~ less_or_equal(X_77,Y_75)
      | less_or_equal(X_77,Z_76) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_219,plain,
    ! [X_79] :
      ( ~ less_or_equal(X_79,additive_identity)
      | less_or_equal(X_79,b) ),
    inference(resolution,[status(thm)],[c_64,c_211]) ).

tff(c_184,plain,
    ! [Z_72] :
      ( ~ less_or_equal(multiply(a,b),Z_72)
      | less_or_equal(u,Z_72) ),
    inference(resolution,[status(thm)],[c_66,c_158]) ).

tff(c_227,plain,
    ( less_or_equal(u,b)
    | ~ less_or_equal(multiply(a,b),additive_identity) ),
    inference(resolution,[status(thm)],[c_219,c_184]) ).

tff(c_241,plain,
    ~ less_or_equal(multiply(a,b),additive_identity),
    inference(splitLeft,[status(thm)],[c_227]) ).

tff(c_245,plain,
    ~ less_or_equal(u,additive_identity),
    inference(resolution,[status(thm)],[c_183,c_241]) ).

tff(c_278,plain,
    ( ~ defined(u)
    | ~ defined(additive_identity)
    | less_or_equal(additive_identity,u) ),
    inference(resolution,[status(thm)],[c_274,c_245]) ).

tff(c_317,plain,
    less_or_equal(additive_identity,u),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_60,c_278]) ).

tff(c_319,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_68,c_317]) ).

tff(c_320,plain,
    less_or_equal(u,b),
    inference(splitRight,[status(thm)],[c_227]) ).

tff(c_34,plain,
    ! [Y_28,Z_27,X_26] :
      ( ~ less_or_equal(Y_28,Z_27)
      | ~ less_or_equal(X_26,Y_28)
      | less_or_equal(X_26,Z_27) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_483,plain,
    ! [X_92] :
      ( ~ less_or_equal(X_92,u)
      | less_or_equal(X_92,b) ),
    inference(resolution,[status(thm)],[c_320,c_34]) ).

tff(c_509,plain,
    ( less_or_equal(multiply(a,b),b)
    | ~ less_or_equal(u,u) ),
    inference(resolution,[status(thm)],[c_183,c_483]) ).

tff(c_855,plain,
    ~ less_or_equal(u,u),
    inference(splitLeft,[status(thm)],[c_509]) ).

tff(c_871,plain,
    ~ defined(u),
    inference(resolution,[status(thm)],[c_396,c_855]) ).

tff(c_880,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_60,c_871]) ).

tff(c_882,plain,
    less_or_equal(u,u),
    inference(splitRight,[status(thm)],[c_509]) ).

tff(c_321,plain,
    less_or_equal(multiply(a,b),additive_identity),
    inference(splitRight,[status(thm)],[c_227]) ).

tff(c_62,plain,
    less_or_equal(additive_identity,a),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_40,plain,
    ! [Z_35,Y_34] :
      ( ~ less_or_equal(additive_identity,Z_35)
      | ~ less_or_equal(additive_identity,Y_34)
      | less_or_equal(additive_identity,multiply(Y_34,Z_35)) ),
    inference(cnfTransformation,[status(thm)],[f_189]) ).

tff(c_24,plain,
    ! [X_20] :
      ( ~ defined(X_20)
      | defined(additive_inverse(X_20)) ),
    inference(cnfTransformation,[status(thm)],[f_131]) ).

tff(c_100,plain,
    ! [X_63] :
      ( ~ defined(X_63)
      | equalish(add(X_63,additive_inverse(X_63)),additive_identity) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

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_103,plain,
    ! [X_63] :
      ( equalish(additive_identity,add(X_63,additive_inverse(X_63)))
      | ~ defined(X_63) ),
    inference(resolution,[status(thm)],[c_100,c_44]) ).

tff(c_4,plain,
    ! [X_4] :
      ( ~ defined(X_4)
      | equalish(add(additive_identity,X_4),X_4) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_109,plain,
    ! [Y_66,Z_67,X_68] :
      ( ~ equalish(Y_66,Z_67)
      | ~ equalish(X_68,Y_66)
      | equalish(X_68,Z_67) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_1647,plain,
    ! [X_144,X_145] :
      ( ~ equalish(X_144,add(additive_identity,X_145))
      | equalish(X_144,X_145)
      | ~ defined(X_145) ),
    inference(resolution,[status(thm)],[c_4,c_109]) ).

tff(c_1667,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity))
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[c_103,c_1647]) ).

tff(c_1691,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1667]) ).

tff(c_1750,plain,
    ~ defined(additive_inverse(additive_identity)),
    inference(splitLeft,[status(thm)],[c_1691]) ).

tff(c_1770,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_24,c_1750]) ).

tff(c_1774,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1770]) ).

tff(c_1775,plain,
    equalish(additive_identity,additive_inverse(additive_identity)),
    inference(splitRight,[status(thm)],[c_1691]) ).

tff(c_52,plain,
    ! [X_50,Y_48,Z_49] :
      ( ~ equalish(X_50,Y_48)
      | ~ less_or_equal(X_50,Z_49)
      | less_or_equal(Y_48,Z_49) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_1878,plain,
    ! [Z_152] :
      ( ~ less_or_equal(additive_identity,Z_152)
      | less_or_equal(additive_inverse(additive_identity),Z_152) ),
    inference(resolution,[status(thm)],[c_1775,c_52]) ).

tff(c_334,plain,
    ! [X_26] :
      ( ~ less_or_equal(X_26,multiply(a,b))
      | less_or_equal(X_26,additive_identity) ),
    inference(resolution,[status(thm)],[c_321,c_34]) ).

tff(c_1931,plain,
    ( less_or_equal(additive_inverse(additive_identity),additive_identity)
    | ~ less_or_equal(additive_identity,multiply(a,b)) ),
    inference(resolution,[status(thm)],[c_1878,c_334]) ).

tff(c_2905,plain,
    ~ less_or_equal(additive_identity,multiply(a,b)),
    inference(splitLeft,[status(thm)],[c_1931]) ).

tff(c_2911,plain,
    ( ~ less_or_equal(additive_identity,b)
    | ~ less_or_equal(additive_identity,a) ),
    inference(resolution,[status(thm)],[c_40,c_2905]) ).

tff(c_2919,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_64,c_2911]) ).

tff(c_2921,plain,
    less_or_equal(additive_identity,multiply(a,b)),
    inference(splitRight,[status(thm)],[c_1931]) ).

tff(c_32,plain,
    ! [Y_25,X_24] :
      ( ~ less_or_equal(Y_25,X_24)
      | ~ less_or_equal(X_24,Y_25)
      | equalish(X_24,Y_25) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_3047,plain,
    ( ~ less_or_equal(multiply(a,b),additive_identity)
    | equalish(multiply(a,b),additive_identity) ),
    inference(resolution,[status(thm)],[c_2921,c_32]) ).

tff(c_3061,plain,
    equalish(multiply(a,b),additive_identity),
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_3047]) ).

tff(c_3071,plain,
    equalish(additive_identity,multiply(a,b)),
    inference(resolution,[status(thm)],[c_3061,c_44]) ).

tff(c_135,plain,
    ! [X_68] :
      ( ~ equalish(X_68,multiply(a,b))
      | equalish(X_68,u) ),
    inference(resolution,[status(thm)],[c_66,c_109]) ).

tff(c_3082,plain,
    equalish(additive_identity,u),
    inference(resolution,[status(thm)],[c_3071,c_135]) ).

tff(c_3094,plain,
    equalish(u,additive_identity),
    inference(resolution,[status(thm)],[c_3082,c_44]) ).

tff(c_3197,plain,
    ! [Z_175] :
      ( ~ less_or_equal(u,Z_175)
      | less_or_equal(additive_identity,Z_175) ),
    inference(resolution,[status(thm)],[c_3094,c_52]) ).

tff(c_3238,plain,
    less_or_equal(additive_identity,u),
    inference(resolution,[status(thm)],[c_882,c_3197]) ).

tff(c_3296,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_68,c_3238]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : FLD071-2 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 20:16:24 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 6.34/2.50  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.34/2.51  
% 6.34/2.51  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.34/2.55  
% 6.34/2.55  Inference rules
% 6.34/2.55  ----------------------
% 6.34/2.55  #Ref     : 0
% 6.34/2.55  #Sup     : 668
% 6.34/2.55  #Fact    : 4
% 6.34/2.55  #Define  : 0
% 6.34/2.55  #Split   : 15
% 6.34/2.55  #Chain   : 0
% 6.34/2.55  #Close   : 0
% 6.34/2.55  
% 6.34/2.55  Ordering : KBO
% 6.34/2.55  
% 6.34/2.55  Simplification rules
% 6.34/2.55  ----------------------
% 6.34/2.55  #Subsume      : 82
% 6.34/2.55  #Demod        : 346
% 6.34/2.55  #Tautology    : 202
% 6.34/2.55  #SimpNegUnit  : 2
% 6.34/2.55  #BackRed      : 0
% 6.34/2.55  
% 6.34/2.55  #Partial instantiations: 0
% 6.34/2.55  #Strategies tried      : 1
% 6.34/2.55  
% 6.34/2.55  Timing (in seconds)
% 6.34/2.55  ----------------------
% 6.59/2.56  Preprocessing        : 0.50
% 6.59/2.56  Parsing              : 0.27
% 6.59/2.56  CNF conversion       : 0.03
% 6.59/2.56  Main loop            : 0.97
% 6.59/2.56  Inferencing          : 0.36
% 6.59/2.56  Reduction            : 0.27
% 6.59/2.56  Demodulation         : 0.18
% 6.59/2.56  BG Simplification    : 0.03
% 6.59/2.56  Subsumption          : 0.24
% 6.59/2.56  Abstraction          : 0.03
% 6.59/2.56  MUC search           : 0.00
% 6.59/2.56  Cooper               : 0.00
% 6.59/2.56  Total                : 1.53
% 6.59/2.56  Index Insertion      : 0.00
% 6.59/2.56  Index Deletion       : 0.00
% 6.59/2.56  Index Matching       : 0.00
% 6.59/2.56  BG Taut test         : 0.00
%------------------------------------------------------------------------------