TSTP Solution File: FLD017-3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD017-3 : 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 : n025.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 10:37:28 EDT 2023

% Result   : Unsatisfiable 4.67s 2.21s
% Output   : CNFRefutation 4.67s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   58 (  20 unt;  14 typ;   0 def)
%            Number of atoms       :   90 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   96 (  50   ~;  46   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   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    :   10 (  10 usr;   6 con; 0-2 aty)
%            Number of variables   :   51 (;  51   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ sum > product > less_or_equal > defined > multiply > add > #nlpp > multiplicative_inverse > additive_inverse > x > multiplicative_identity > c > b > 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(x,type,
    x: $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(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(c,type,
    c: $i ).

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

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_253,axiom,
    sum(additive_identity,a,x),
    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(f_73,axiom,
    ! [X] :
      ( sum(additive_identity,X,X)
      | ~ defined(X) ),
    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_83,axiom,
    ! [Y,X,Z] :
      ( sum(Y,X,Z)
      | ~ sum(X,Y,Z) ),
    file(unknown,unknown) ).

tff(f_250,axiom,
    defined(b),
    file(unknown,unknown) ).

tff(f_254,axiom,
    sum(a,b,c),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [W,U,Z,X,Y,V] :
      ( sum(X,V,W)
      | ~ sum(X,Y,U)
      | ~ sum(Y,Z,V)
      | ~ sum(U,Z,W) ),
    file(unknown,unknown) ).

tff(f_256,axiom,
    ~ sum(x,b,c),
    file(unknown,unknown) ).

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

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_133,plain,
    ! [Y_65] :
      ( ~ defined(Y_65)
      | less_or_equal(Y_65,Y_65) ),
    inference(factorization,[status(thm),theory(equality)],[c_46]) ).

tff(c_62,plain,
    sum(additive_identity,a,x),
    inference(cnfTransformation,[status(thm)],[f_253]) ).

tff(c_209,plain,
    ! [V_119,X_116,Y_118,Z_117,U_115] :
      ( ~ sum(Y_118,Z_117,V_119)
      | ~ sum(X_116,Z_117,U_115)
      | ~ less_or_equal(X_116,Y_118)
      | less_or_equal(U_115,V_119) ),
    inference(cnfTransformation,[status(thm)],[f_233]) ).

tff(c_517,plain,
    ! [X_150,U_151] :
      ( ~ sum(X_150,a,U_151)
      | ~ less_or_equal(X_150,additive_identity)
      | less_or_equal(U_151,x) ),
    inference(resolution,[status(thm)],[c_62,c_209]) ).

tff(c_558,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(x,x) ),
    inference(resolution,[status(thm)],[c_62,c_517]) ).

tff(c_641,plain,
    ~ less_or_equal(additive_identity,additive_identity),
    inference(splitLeft,[status(thm)],[c_558]) ).

tff(c_647,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_133,c_641]) ).

tff(c_654,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_28,c_647]) ).

tff(c_656,plain,
    less_or_equal(additive_identity,additive_identity),
    inference(splitRight,[status(thm)],[c_558]) ).

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

tff(c_1268,plain,
    ! [X_193,X_194,U_195] :
      ( ~ sum(X_193,X_194,U_195)
      | ~ less_or_equal(X_193,additive_identity)
      | less_or_equal(U_195,X_194)
      | ~ defined(X_194) ),
    inference(resolution,[status(thm)],[c_6,c_209]) ).

tff(c_1340,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(x,a)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_62,c_1268]) ).

tff(c_1404,plain,
    less_or_equal(x,a),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_656,c_1340]) ).

tff(c_540,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,x)
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_6,c_517]) ).

tff(c_557,plain,
    ( ~ less_or_equal(additive_identity,additive_identity)
    | less_or_equal(a,x) ),
    inference(demodulation,[status(thm),theory(equality)],[c_54,c_540]) ).

tff(c_708,plain,
    less_or_equal(a,x),
    inference(demodulation,[status(thm),theory(equality)],[c_656,c_557]) ).

tff(c_112,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_10,plain,
    ! [X_16,Y_15,Z_17] :
      ( ~ sum(X_16,Y_15,Z_17)
      | sum(Y_15,X_16,Z_17) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_118,plain,
    ! [X_96,Y_95] :
      ( sum(X_96,additive_identity,Y_95)
      | ~ less_or_equal(Y_95,X_96)
      | ~ less_or_equal(X_96,Y_95) ),
    inference(resolution,[status(thm)],[c_112,c_10]) ).

tff(c_56,plain,
    defined(b),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_64,plain,
    sum(a,b,c),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_442,plain,
    ! [Y_142,X_145,Z_141,V_143,W_146,U_144] :
      ( ~ sum(U_144,Z_141,W_146)
      | ~ sum(Y_142,Z_141,V_143)
      | ~ sum(X_145,Y_142,U_144)
      | sum(X_145,V_143,W_146) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_892,plain,
    ! [Y_181,V_182,X_183] :
      ( ~ sum(Y_181,b,V_182)
      | ~ sum(X_183,Y_181,a)
      | sum(X_183,V_182,c) ),
    inference(resolution,[status(thm)],[c_64,c_442]) ).

tff(c_907,plain,
    ! [X_183] :
      ( ~ sum(X_183,additive_identity,a)
      | sum(X_183,b,c)
      | ~ defined(b) ),
    inference(resolution,[status(thm)],[c_6,c_892]) ).

tff(c_1591,plain,
    ! [X_203] :
      ( ~ sum(X_203,additive_identity,a)
      | sum(X_203,b,c) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_907]) ).

tff(c_66,plain,
    ~ sum(x,b,c),
    inference(cnfTransformation,[status(thm)],[f_256]) ).

tff(c_1624,plain,
    ~ sum(x,additive_identity,a),
    inference(resolution,[status(thm)],[c_1591,c_66]) ).

tff(c_1627,plain,
    ( ~ less_or_equal(a,x)
    | ~ less_or_equal(x,a) ),
    inference(resolution,[status(thm)],[c_118,c_1624]) ).

tff(c_1631,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1404,c_708,c_1627]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : FLD017-3 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.13/0.13  % 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
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 20:11:05 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.67/2.21  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.67/2.21  
% 4.67/2.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.67/2.25  
% 4.67/2.25  Inference rules
% 4.67/2.25  ----------------------
% 4.67/2.25  #Ref     : 0
% 4.67/2.25  #Sup     : 366
% 4.67/2.25  #Fact    : 2
% 4.67/2.25  #Define  : 0
% 4.67/2.25  #Split   : 10
% 4.67/2.25  #Chain   : 0
% 4.67/2.25  #Close   : 0
% 4.67/2.25  
% 4.67/2.25  Ordering : KBO
% 4.67/2.25  
% 4.67/2.25  Simplification rules
% 4.67/2.25  ----------------------
% 4.67/2.25  #Subsume      : 54
% 4.67/2.25  #Demod        : 159
% 4.67/2.25  #Tautology    : 55
% 4.67/2.25  #SimpNegUnit  : 2
% 4.67/2.25  #BackRed      : 0
% 4.67/2.25  
% 4.67/2.25  #Partial instantiations: 0
% 4.67/2.25  #Strategies tried      : 1
% 4.67/2.25  
% 4.67/2.25  Timing (in seconds)
% 4.67/2.25  ----------------------
% 4.67/2.25  Preprocessing        : 0.49
% 4.67/2.25  Parsing              : 0.27
% 4.67/2.25  CNF conversion       : 0.03
% 4.67/2.25  Main loop            : 0.69
% 4.67/2.25  Inferencing          : 0.25
% 4.67/2.25  Reduction            : 0.19
% 4.67/2.25  Demodulation         : 0.13
% 4.67/2.25  BG Simplification    : 0.03
% 4.67/2.25  Subsumption          : 0.17
% 4.67/2.25  Abstraction          : 0.02
% 4.67/2.25  MUC search           : 0.00
% 4.67/2.25  Cooper               : 0.00
% 4.67/2.25  Total                : 1.24
% 4.67/2.25  Index Insertion      : 0.00
% 4.67/2.25  Index Deletion       : 0.00
% 4.67/2.25  Index Matching       : 0.00
% 4.67/2.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------