TSTP Solution File: SET064-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET064-6 : 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 : n006.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 10:55:47 EDT 2023

% Result   : Unsatisfiable 6.52s 2.49s
% Output   : CNFRefutation 6.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   75 (  10 unt;  48 typ;   0 def)
%            Number of atoms       :   49 (  13 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   46 (  24   ~;  22   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   65 (  39   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   39 (  39 usr;   9 con; 0-3 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ homomorphism > compatible > subclass > member > single_valued_class > operation > one_to_one > inductive > function > restrict > range > not_homomorphism2 > not_homomorphism1 > domain > unordered_pair > union > symmetric_difference > ordered_pair > not_subclass_element > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > regular > range_of > power_class > inverse > flip > first > domain_of > diagonalise > complement > cantor > z > universal_class > successor_relation > subset_relation > omega > null_class > identity_relation > element_relation > choice

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(not_homomorphism2,type,
    not_homomorphism2: ( $i * $i * $i ) > $i ).

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

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

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

tff(not_homomorphism1,type,
    not_homomorphism1: ( $i * $i * $i ) > $i ).

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

tff(f_645,axiom,
    z != null_class,
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(f_647,axiom,
    ~ member(not_subclass_element(z,null_class),z),
    file(unknown,unknown) ).

tff(f_470,axiom,
    ! [X] :
      ( ( X = null_class )
      | member(regular(X),X) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

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

tff(c_184,plain,
    z != null_class,
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_469,plain,
    ! [X_243,Y_244] :
      ( subclass(X_243,Y_244)
      | member(not_subclass_element(X_243,Y_244),X_243) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_186,plain,
    ~ member(not_subclass_element(z,null_class),z),
    inference(cnfTransformation,[status(thm)],[f_647]) ).

tff(c_489,plain,
    subclass(z,null_class),
    inference(resolution,[status(thm)],[c_469,c_186]) ).

tff(c_132,plain,
    ! [X_131] :
      ( member(regular(X_131),X_131)
      | ( null_class = X_131 ) ),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

tff(c_792,plain,
    ! [U_285,Y_286,X_287] :
      ( member(U_285,Y_286)
      | ~ member(U_285,X_287)
      | ~ subclass(X_287,Y_286) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_827,plain,
    ! [X_131,Y_286] :
      ( member(regular(X_131),Y_286)
      | ~ subclass(X_131,Y_286)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_132,c_792]) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_1647,plain,
    ! [X_377,Y_378] :
      ( member(regular(X_377),Y_378)
      | ~ subclass(X_377,Y_378)
      | ( null_class = X_377 ) ),
    inference(resolution,[status(thm)],[c_132,c_792]) ).

tff(c_237,plain,
    ! [Z_201,X_202] :
      ( ~ member(Z_201,X_202)
      | ~ member(Z_201,complement(X_202)) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_246,plain,
    ! [X_202] :
      ( ~ member(regular(complement(X_202)),X_202)
      | ( complement(X_202) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_237]) ).

tff(c_1701,plain,
    ! [Y_379] :
      ( ~ subclass(complement(Y_379),Y_379)
      | ( complement(Y_379) = null_class ) ),
    inference(resolution,[status(thm)],[c_1647,c_246]) ).

tff(c_1723,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[c_8,c_1701]) ).

tff(c_48,plain,
    ! [Z_55,X_56] :
      ( ~ member(Z_55,X_56)
      | ~ member(Z_55,complement(X_56)) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_1813,plain,
    ! [Z_381] :
      ( ~ member(Z_381,universal_class)
      | ~ member(Z_381,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1723,c_48]) ).

tff(c_1817,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ~ subclass(X_131,universal_class)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_827,c_1813]) ).

tff(c_2047,plain,
    ! [X_399] :
      ( ~ member(regular(X_399),null_class)
      | ( null_class = X_399 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1817]) ).

tff(c_2062,plain,
    ! [X_400] :
      ( ~ subclass(X_400,null_class)
      | ( null_class = X_400 ) ),
    inference(resolution,[status(thm)],[c_827,c_2047]) ).

tff(c_2065,plain,
    z = null_class,
    inference(resolution,[status(thm)],[c_489,c_2062]) ).

tff(c_2081,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_184,c_2065]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET064-6 : 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 : n006.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 16:05:58 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.52/2.49  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.52/2.50  
% 6.52/2.50  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.77/2.53  
% 6.77/2.53  Inference rules
% 6.77/2.53  ----------------------
% 6.77/2.53  #Ref     : 0
% 6.77/2.53  #Sup     : 441
% 6.77/2.53  #Fact    : 0
% 6.77/2.53  #Define  : 0
% 6.77/2.53  #Split   : 14
% 6.77/2.53  #Chain   : 0
% 6.77/2.53  #Close   : 0
% 6.77/2.53  
% 6.77/2.53  Ordering : KBO
% 6.77/2.53  
% 6.77/2.53  Simplification rules
% 6.77/2.53  ----------------------
% 6.77/2.53  #Subsume      : 52
% 6.77/2.53  #Demod        : 63
% 6.77/2.53  #Tautology    : 79
% 6.77/2.53  #SimpNegUnit  : 5
% 6.77/2.53  #BackRed      : 3
% 6.77/2.53  
% 6.77/2.53  #Partial instantiations: 0
% 6.77/2.53  #Strategies tried      : 1
% 6.77/2.53  
% 6.77/2.53  Timing (in seconds)
% 6.77/2.53  ----------------------
% 6.77/2.53  Preprocessing        : 0.69
% 6.77/2.53  Parsing              : 0.36
% 6.77/2.53  CNF conversion       : 0.05
% 6.77/2.53  Main loop            : 0.77
% 6.77/2.53  Inferencing          : 0.26
% 6.77/2.53  Reduction            : 0.23
% 6.77/2.53  Demodulation         : 0.16
% 6.77/2.53  BG Simplification    : 0.05
% 6.77/2.53  Subsumption          : 0.18
% 6.77/2.53  Abstraction          : 0.03
% 6.77/2.53  MUC search           : 0.00
% 6.77/2.53  Cooper               : 0.00
% 6.77/2.53  Total                : 1.51
% 6.77/2.53  Index Insertion      : 0.00
% 6.77/2.53  Index Deletion       : 0.00
% 6.77/2.54  Index Matching       : 0.00
% 6.77/2.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------