TSTP Solution File: FLD065-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : FLD065-1 : 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/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 : n005.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 10:37:40 EDT 2023

% Result   : Unsatisfiable 267.01s 245.13s
% Output   : CNFRefutation 267.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   80 (  22 unt;  10 typ;   0 def)
%            Number of atoms       :  153 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  174 (  91   ~;  83   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   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   :   82 (;  82   !;   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_236,axiom,
    defined(a),
    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_131,axiom,
    ! [X] :
      ( defined(additive_inverse(X))
      | ~ defined(X) ),
    file(unknown,unknown) ).

tff(f_126,axiom,
    defined(additive_identity),
    file(unknown,unknown) ).

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

tff(f_199,axiom,
    ! [X,Y] :
      ( equalish(X,Y)
      | ~ equalish(Y,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_231,axiom,
    ! [Y,Z,X] :
      ( less_or_equal(Y,Z)
      | ~ less_or_equal(X,Z)
      | ~ equalish(X,Y) ),
    file(unknown,unknown) ).

tff(f_237,axiom,
    less_or_equal(additive_inverse(a),additive_identity),
    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(f_181,axiom,
    ! [X,Z,Y] :
      ( less_or_equal(add(X,Z),add(Y,Z))
      | ~ defined(Z)
      | ~ less_or_equal(X,Y) ),
    file(unknown,unknown) ).

tff(f_75,axiom,
    ! [X,Y] :
      ( equalish(add(X,Y),add(Y,X))
      | ~ defined(X)
      | ~ defined(Y) ),
    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(c_56,plain,
    defined(a),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

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_161,plain,
    ! [X_29] :
      ( ~ defined(X_29)
      | less_or_equal(X_29,X_29) ),
    inference(factorization,[status(thm),theory(equality)],[c_36]) ).

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

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

tff(c_84,plain,
    ! [X_61] :
      ( ~ defined(X_61)
      | equalish(add(X_61,additive_inverse(X_61)),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_87,plain,
    ! [X_61] :
      ( equalish(additive_identity,add(X_61,additive_inverse(X_61)))
      | ~ defined(X_61) ),
    inference(resolution,[status(thm)],[c_84,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_94,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_334,plain,
    ! [X_92,X_93] :
      ( ~ equalish(X_92,add(additive_identity,X_93))
      | equalish(X_92,X_93)
      | ~ defined(X_93) ),
    inference(resolution,[status(thm)],[c_4,c_94]) ).

tff(c_338,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity))
    | ~ defined(additive_identity) ),
    inference(resolution,[status(thm)],[c_87,c_334]) ).

tff(c_356,plain,
    ( equalish(additive_identity,additive_inverse(additive_identity))
    | ~ defined(additive_inverse(additive_identity)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_338]) ).

tff(c_361,plain,
    ~ defined(additive_inverse(additive_identity)),
    inference(splitLeft,[status(thm)],[c_356]) ).

tff(c_381,plain,
    ~ defined(additive_identity),
    inference(resolution,[status(thm)],[c_24,c_361]) ).

tff(c_385,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_381]) ).

tff(c_386,plain,
    equalish(additive_identity,additive_inverse(additive_identity)),
    inference(splitRight,[status(thm)],[c_356]) ).

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_459,plain,
    ! [X_100] :
      ( ~ equalish(X_100,additive_identity)
      | equalish(X_100,additive_inverse(additive_identity)) ),
    inference(resolution,[status(thm)],[c_386,c_46]) ).

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_288752,plain,
    ! [X_1708,Z_1709] :
      ( ~ less_or_equal(X_1708,Z_1709)
      | less_or_equal(additive_inverse(additive_identity),Z_1709)
      | ~ equalish(X_1708,additive_identity) ),
    inference(resolution,[status(thm)],[c_459,c_52]) ).

tff(c_291208,plain,
    ! [X_1714] :
      ( less_or_equal(additive_inverse(additive_identity),X_1714)
      | ~ equalish(X_1714,additive_identity)
      | ~ defined(X_1714) ),
    inference(resolution,[status(thm)],[c_161,c_288752]) ).

tff(c_396,plain,
    equalish(additive_inverse(additive_identity),additive_identity),
    inference(resolution,[status(thm)],[c_386,c_44]) ).

tff(c_403,plain,
    ! [Z_49] :
      ( ~ less_or_equal(additive_inverse(additive_identity),Z_49)
      | less_or_equal(additive_identity,Z_49) ),
    inference(resolution,[status(thm)],[c_396,c_52]) ).

tff(c_291393,plain,
    ! [X_1717] :
      ( less_or_equal(additive_identity,X_1717)
      | ~ equalish(X_1717,additive_identity)
      | ~ defined(X_1717) ),
    inference(resolution,[status(thm)],[c_291208,c_403]) ).

tff(c_58,plain,
    less_or_equal(additive_inverse(a),additive_identity),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_121,plain,
    ! [Y_73,X_74] :
      ( ~ less_or_equal(Y_73,X_74)
      | ~ less_or_equal(X_74,Y_73)
      | equalish(X_74,Y_73) ),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_124,plain,
    ( ~ less_or_equal(additive_identity,additive_inverse(a))
    | equalish(additive_identity,additive_inverse(a)) ),
    inference(resolution,[status(thm)],[c_58,c_121]) ).

tff(c_125,plain,
    ~ less_or_equal(additive_identity,additive_inverse(a)),
    inference(splitLeft,[status(thm)],[c_124]) ).

tff(c_291559,plain,
    ( ~ equalish(additive_inverse(a),additive_identity)
    | ~ defined(additive_inverse(a)) ),
    inference(resolution,[status(thm)],[c_291393,c_125]) ).

tff(c_291567,plain,
    ~ defined(additive_inverse(a)),
    inference(splitLeft,[status(thm)],[c_291559]) ).

tff(c_291570,plain,
    ~ defined(a),
    inference(resolution,[status(thm)],[c_24,c_291567]) ).

tff(c_291574,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_291570]) ).

tff(c_291576,plain,
    defined(additive_inverse(a)),
    inference(splitRight,[status(thm)],[c_291559]) ).

tff(c_38,plain,
    ! [X_31,Y_33,Z_32] :
      ( ~ less_or_equal(X_31,Y_33)
      | ~ defined(Z_32)
      | less_or_equal(add(X_31,Z_32),add(Y_33,Z_32)) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_422,plain,
    ! [Y_97,X_98] :
      ( ~ defined(Y_97)
      | ~ defined(X_98)
      | equalish(add(X_98,Y_97),add(Y_97,X_98)) ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_3888,plain,
    ! [X_211,Y_212,Z_213] :
      ( ~ less_or_equal(add(X_211,Y_212),Z_213)
      | less_or_equal(add(Y_212,X_211),Z_213)
      | ~ defined(Y_212)
      | ~ defined(X_211) ),
    inference(resolution,[status(thm)],[c_422,c_52]) ).

tff(c_281534,plain,
    ! [Z_1638,X_1639,Y_1640] :
      ( less_or_equal(add(Z_1638,X_1639),add(Y_1640,Z_1638))
      | ~ defined(X_1639)
      | ~ less_or_equal(X_1639,Y_1640)
      | ~ defined(Z_1638) ),
    inference(resolution,[status(thm)],[c_38,c_3888]) ).

tff(c_6,plain,
    ! [X_5] :
      ( ~ defined(X_5)
      | equalish(add(X_5,additive_inverse(X_5)),additive_identity) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_126,plain,
    ! [X_75,Y_76,Z_77] :
      ( ~ equalish(X_75,Y_76)
      | ~ less_or_equal(X_75,Z_77)
      | less_or_equal(Y_76,Z_77) ),
    inference(cnfTransformation,[status(thm)],[f_231]) ).

tff(c_142,plain,
    ! [X_5,Z_77] :
      ( ~ less_or_equal(add(X_5,additive_inverse(X_5)),Z_77)
      | less_or_equal(additive_identity,Z_77)
      | ~ defined(X_5) ),
    inference(resolution,[status(thm)],[c_6,c_126]) ).

tff(c_574121,plain,
    ! [Y_2735,Z_2736] :
      ( less_or_equal(additive_identity,add(Y_2735,Z_2736))
      | ~ defined(additive_inverse(Z_2736))
      | ~ less_or_equal(additive_inverse(Z_2736),Y_2735)
      | ~ defined(Z_2736) ),
    inference(resolution,[status(thm)],[c_281534,c_142]) ).

tff(c_574807,plain,
    ( less_or_equal(additive_identity,add(additive_identity,a))
    | ~ defined(additive_inverse(a))
    | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_58,c_574121]) ).

tff(c_575118,plain,
    less_or_equal(additive_identity,add(additive_identity,a)),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_291576,c_574807]) ).

tff(c_67,plain,
    ! [X_55] :
      ( ~ defined(X_55)
      | equalish(add(additive_identity,X_55),X_55) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_70,plain,
    ! [X_55] :
      ( equalish(X_55,add(additive_identity,X_55))
      | ~ defined(X_55) ),
    inference(resolution,[status(thm)],[c_67,c_44]) ).

tff(c_271352,plain,
    ! [X_1547,Z_1548] :
      ( ~ less_or_equal(X_1547,Z_1548)
      | less_or_equal(add(additive_identity,X_1547),Z_1548)
      | ~ defined(X_1547) ),
    inference(resolution,[status(thm)],[c_70,c_126]) ).

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_271512,plain,
    ! [X_26,X_1547,Z_1548] :
      ( ~ less_or_equal(X_26,add(additive_identity,X_1547))
      | less_or_equal(X_26,Z_1548)
      | ~ less_or_equal(X_1547,Z_1548)
      | ~ defined(X_1547) ),
    inference(resolution,[status(thm)],[c_271352,c_34]) ).

tff(c_575126,plain,
    ! [Z_1548] :
      ( less_or_equal(additive_identity,Z_1548)
      | ~ less_or_equal(a,Z_1548)
      | ~ defined(a) ),
    inference(resolution,[status(thm)],[c_575118,c_271512]) ).

tff(c_576270,plain,
    ! [Z_2738] :
      ( less_or_equal(additive_identity,Z_2738)
      | ~ less_or_equal(a,Z_2738) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_575126]) ).

tff(c_60,plain,
    ~ less_or_equal(additive_identity,a),
    inference(cnfTransformation,[status(thm)],[f_239]) ).

tff(c_576812,plain,
    ~ less_or_equal(a,a),
    inference(resolution,[status(thm)],[c_576270,c_60]) ).

tff(c_576839,plain,
    ~ defined(a),
    inference(resolution,[status(thm)],[c_161,c_576812]) ).

tff(c_576866,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_576839]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : FLD065-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % 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
% 0.15/0.37  % Computer : n005.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 19:59:26 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 267.01/245.13  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 267.01/245.14  
% 267.01/245.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 267.01/245.19  
% 267.01/245.19  Inference rules
% 267.01/245.19  ----------------------
% 267.01/245.19  #Ref     : 0
% 267.01/245.19  #Sup     : 128297
% 267.01/245.19  #Fact    : 38
% 267.01/245.19  #Define  : 0
% 267.01/245.19  #Split   : 55
% 267.01/245.19  #Chain   : 0
% 267.01/245.19  #Close   : 0
% 267.01/245.19  
% 267.01/245.19  Ordering : KBO
% 267.01/245.19  
% 267.01/245.19  Simplification rules
% 267.01/245.19  ----------------------
% 267.01/245.19  #Subsume      : 36435
% 267.01/245.19  #Demod        : 69958
% 267.01/245.19  #Tautology    : 17824
% 267.01/245.19  #SimpNegUnit  : 3820
% 267.01/245.19  #BackRed      : 0
% 267.01/245.19  
% 267.01/245.19  #Partial instantiations: 0
% 267.01/245.19  #Strategies tried      : 1
% 267.01/245.19  
% 267.01/245.19  Timing (in seconds)
% 267.01/245.19  ----------------------
% 267.01/245.19  Preprocessing        : 0.52
% 267.01/245.19  Parsing              : 0.29
% 267.01/245.19  CNF conversion       : 0.03
% 267.01/245.19  Main loop            : 243.49
% 267.01/245.19  Inferencing          : 16.29
% 267.01/245.19  Reduction            : 119.66
% 267.01/245.19  Demodulation         : 98.40
% 267.01/245.19  BG Simplification    : 0.50
% 267.01/245.19  Subsumption          : 88.31
% 267.01/245.19  Abstraction          : 1.00
% 267.01/245.19  MUC search           : 0.00
% 267.01/245.19  Cooper               : 0.00
% 267.01/245.19  Total                : 244.08
% 267.01/245.19  Index Insertion      : 0.00
% 267.01/245.19  Index Deletion       : 0.00
% 267.01/245.19  Index Matching       : 0.00
% 267.01/245.19  BG Taut test         : 0.00
%------------------------------------------------------------------------------