TSTP Solution File: CAT006-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : CAT006-1 : TPTP v8.1.2. Released v1.0.0.
% 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 10:34:36 EDT 2023

% Result   : Unsatisfiable 4.14s 2.07s
% Output   : CNFRefutation 4.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   41 (  15 unt;   8 typ;   0 def)
%            Number of atoms       :   64 (  12 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   64 (  33   ~;  31   |;   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  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   44 (;  44   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ product > defined > identity_map > compose > #nlpp > domain > codomain > h > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(h,type,
    h: $i ).

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

tff(product,type,
    product: ( $i * $i * $i ) > $o ).

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

tff(defined,type,
    defined: ( $i * $i ) > $o ).

tff(identity_map,type,
    identity_map: $i > $o ).

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

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

tff(f_176,axiom,
    codomain(a) != h,
    file(unknown,unknown) ).

tff(f_144,axiom,
    ! [X] : product(codomain(X),X,X),
    file(unknown,unknown) ).

tff(f_173,axiom,
    defined(h,a),
    file(unknown,unknown) ).

tff(f_98,axiom,
    ! [Y,Z,Yz,X] :
      ( ~ product(Y,Z,Yz)
      | ~ defined(X,Yz)
      | defined(X,Y) ),
    file(unknown,unknown) ).

tff(f_174,axiom,
    identity_map(h),
    file(unknown,unknown) ).

tff(f_153,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | ~ identity_map(X)
      | product(X,Y,Y) ),
    file(unknown,unknown) ).

tff(f_136,axiom,
    ! [X] : identity_map(codomain(X)),
    file(unknown,unknown) ).

tff(f_53,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | product(X,Y,compose(X,Y)) ),
    file(unknown,unknown) ).

tff(f_161,axiom,
    ! [X,Y] :
      ( ~ defined(X,Y)
      | ~ identity_map(Y)
      | product(X,Y,X) ),
    file(unknown,unknown) ).

tff(f_170,axiom,
    ! [X,Y,Z,W] :
      ( ~ product(X,Y,Z)
      | ~ product(X,Y,W)
      | ( Z = W ) ),
    file(unknown,unknown) ).

tff(c_42,plain,
    codomain(a) != h,
    inference(cnfTransformation,[status(thm)],[f_176]) ).

tff(c_30,plain,
    ! [X_44] : product(codomain(X_44),X_44,X_44),
    inference(cnfTransformation,[status(thm)],[f_144]) ).

tff(c_38,plain,
    defined(h,a),
    inference(cnfTransformation,[status(thm)],[f_173]) ).

tff(c_119,plain,
    ! [X_74,Y_75,Yz_76,Z_77] :
      ( defined(X_74,Y_75)
      | ~ defined(X_74,Yz_76)
      | ~ product(Y_75,Z_77,Yz_76) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_830,plain,
    ! [Y_127,Z_128] :
      ( defined(h,Y_127)
      | ~ product(Y_127,Z_128,a) ),
    inference(resolution,[status(thm)],[c_38,c_119]) ).

tff(c_852,plain,
    defined(h,codomain(a)),
    inference(resolution,[status(thm)],[c_30,c_830]) ).

tff(c_40,plain,
    identity_map(h),
    inference(cnfTransformation,[status(thm)],[f_174]) ).

tff(c_32,plain,
    ! [X_45,Y_46] :
      ( product(X_45,Y_46,Y_46)
      | ~ identity_map(X_45)
      | ~ defined(X_45,Y_46) ),
    inference(cnfTransformation,[status(thm)],[f_153]) ).

tff(c_22,plain,
    ! [X_40] : identity_map(codomain(X_40)),
    inference(cnfTransformation,[status(thm)],[f_136]) ).

tff(c_2,plain,
    ! [X_1,Y_2] :
      ( product(X_1,Y_2,compose(X_1,Y_2))
      | ~ defined(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_34,plain,
    ! [X_47,Y_48] :
      ( product(X_47,Y_48,X_47)
      | ~ identity_map(Y_48)
      | ~ defined(X_47,Y_48) ),
    inference(cnfTransformation,[status(thm)],[f_161]) ).

tff(c_75,plain,
    ! [Z_68,W_69,X_70,Y_71] :
      ( ( Z_68 = W_69 )
      | ~ product(X_70,Y_71,W_69)
      | ~ product(X_70,Y_71,Z_68) ),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_1663,plain,
    ! [Z_168,X_169,Y_170] :
      ( ( Z_168 = X_169 )
      | ~ product(X_169,Y_170,Z_168)
      | ~ identity_map(Y_170)
      | ~ defined(X_169,Y_170) ),
    inference(resolution,[status(thm)],[c_34,c_75]) ).

tff(c_1952,plain,
    ! [X_181,Y_182] :
      ( ( compose(X_181,Y_182) = X_181 )
      | ~ identity_map(Y_182)
      | ~ defined(X_181,Y_182) ),
    inference(resolution,[status(thm)],[c_2,c_1663]) ).

tff(c_1973,plain,
    ( ( compose(h,codomain(a)) = h )
    | ~ identity_map(codomain(a)) ),
    inference(resolution,[status(thm)],[c_852,c_1952]) ).

tff(c_2008,plain,
    compose(h,codomain(a)) = h,
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1973]) ).

tff(c_2033,plain,
    ( product(h,codomain(a),h)
    | ~ defined(h,codomain(a)) ),
    inference(superposition,[status(thm),theory(equality)],[c_2008,c_2]) ).

tff(c_2041,plain,
    product(h,codomain(a),h),
    inference(demodulation,[status(thm),theory(equality)],[c_852,c_2033]) ).

tff(c_36,plain,
    ! [Z_51,W_52,X_49,Y_50] :
      ( ( Z_51 = W_52 )
      | ~ product(X_49,Y_50,W_52)
      | ~ product(X_49,Y_50,Z_51) ),
    inference(cnfTransformation,[status(thm)],[f_170]) ).

tff(c_2230,plain,
    ! [Z_187] :
      ( ( h = Z_187 )
      | ~ product(h,codomain(a),Z_187) ),
    inference(resolution,[status(thm)],[c_2041,c_36]) ).

tff(c_2237,plain,
    ( ( codomain(a) = h )
    | ~ identity_map(h)
    | ~ defined(h,codomain(a)) ),
    inference(resolution,[status(thm)],[c_32,c_2230]) ).

tff(c_2250,plain,
    codomain(a) = h,
    inference(demodulation,[status(thm),theory(equality)],[c_852,c_40,c_2237]) ).

tff(c_2252,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_42,c_2250]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : CAT006-1 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.13  % 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 : n012.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 17:42:52 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.14/2.07  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.14/2.08  
% 4.14/2.08  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.14/2.11  
% 4.14/2.11  Inference rules
% 4.14/2.11  ----------------------
% 4.14/2.11  #Ref     : 0
% 4.14/2.11  #Sup     : 494
% 4.14/2.11  #Fact    : 0
% 4.14/2.11  #Define  : 0
% 4.14/2.11  #Split   : 1
% 4.14/2.11  #Chain   : 0
% 4.14/2.11  #Close   : 0
% 4.14/2.11  
% 4.14/2.11  Ordering : KBO
% 4.14/2.11  
% 4.14/2.11  Simplification rules
% 4.14/2.11  ----------------------
% 4.14/2.11  #Subsume      : 22
% 4.14/2.11  #Demod        : 452
% 4.14/2.11  #Tautology    : 275
% 4.14/2.11  #SimpNegUnit  : 1
% 4.14/2.11  #BackRed      : 5
% 4.14/2.11  
% 4.14/2.11  #Partial instantiations: 0
% 4.14/2.11  #Strategies tried      : 1
% 4.14/2.11  
% 4.14/2.11  Timing (in seconds)
% 4.14/2.11  ----------------------
% 4.14/2.11  Preprocessing        : 0.43
% 4.14/2.11  Parsing              : 0.24
% 4.14/2.11  CNF conversion       : 0.02
% 4.14/2.11  Main loop            : 0.65
% 4.14/2.11  Inferencing          : 0.24
% 4.14/2.11  Reduction            : 0.20
% 4.14/2.11  Demodulation         : 0.14
% 4.14/2.11  BG Simplification    : 0.03
% 4.14/2.11  Subsumption          : 0.14
% 4.14/2.11  Abstraction          : 0.03
% 4.14/2.11  MUC search           : 0.00
% 4.14/2.11  Cooper               : 0.00
% 4.14/2.11  Total                : 1.13
% 4.14/2.11  Index Insertion      : 0.00
% 4.14/2.11  Index Deletion       : 0.00
% 4.14/2.11  Index Matching       : 0.00
% 4.14/2.11  BG Taut test         : 0.00
%------------------------------------------------------------------------------