TSTP Solution File: SET071-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET071-7 : 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 : n027.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 10:55:49 EDT 2023

% Result   : Unsatisfiable 6.18s 2.45s
% Output   : CNFRefutation 6.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   59
% Syntax   : Number of formulae    :   90 (  25 unt;  49 typ;   0 def)
%            Number of atoms       :   62 (  36 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   37 (  16   ~;  21   |;   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  :   65 (  39   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;  10 con; 0-3 aty)
%            Number of variables   :   35 (;  35   !;   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 > y > x > 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(x,type,
    x: $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(y,type,
    y: $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(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_762,axiom,
    ~ member(x,universal_class),
    file(unknown,unknown) ).

tff(f_72,axiom,
    ! [X] : subclass(X,universal_class),
    file(unknown,unknown) ).

tff(f_744,axiom,
    ! [X,Y] : ( unordered_pair(X,Y) = unordered_pair(Y,X) ),
    file(unknown,unknown) ).

tff(f_758,axiom,
    ! [X,Y] :
      ( member(X,universal_class)
      | ( unordered_pair(X,Y) = singleton(Y) ) ),
    file(unknown,unknown) ).

tff(f_764,axiom,
    ~ member(y,universal_class),
    file(unknown,unknown) ).

tff(f_760,axiom,
    unordered_pair(x,y) != null_class,
    file(unknown,unknown) ).

tff(f_471,axiom,
    ! [X] :
      ( ( X = null_class )
      | member(regular(X),X) ),
    file(unknown,unknown) ).

tff(f_124,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_103,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | ( U = X )
      | ( U = Y ) ),
    file(unknown,unknown) ).

tff(f_58,axiom,
    ! [X,Y,U] :
      ( ~ subclass(X,Y)
      | ~ member(U,X)
      | member(U,Y) ),
    file(unknown,unknown) ).

tff(c_228,plain,
    ~ member(x,universal_class),
    inference(cnfTransformation,[status(thm)],[f_762]) ).

tff(c_8,plain,
    ! [X_8] : subclass(X_8,universal_class),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_216,plain,
    ! [Y_212,X_211] : ( unordered_pair(Y_212,X_211) = unordered_pair(X_211,Y_212) ),
    inference(cnfTransformation,[status(thm)],[f_744]) ).

tff(c_593,plain,
    ! [X_291,Y_292] :
      ( ( unordered_pair(X_291,Y_292) = singleton(Y_292) )
      | member(X_291,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_758]) ).

tff(c_649,plain,
    ! [Y_293] : ( unordered_pair(x,Y_293) = singleton(Y_293) ),
    inference(resolution,[status(thm)],[c_593,c_228]) ).

tff(c_781,plain,
    ! [X_297] : ( unordered_pair(X_297,x) = singleton(X_297) ),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_649]) ).

tff(c_230,plain,
    ~ member(y,universal_class),
    inference(cnfTransformation,[status(thm)],[f_764]) ).

tff(c_645,plain,
    ! [Y_292] : ( unordered_pair(y,Y_292) = singleton(Y_292) ),
    inference(resolution,[status(thm)],[c_593,c_230]) ).

tff(c_788,plain,
    singleton(y) = singleton(x),
    inference(superposition,[status(thm),theory(equality)],[c_781,c_645]) ).

tff(c_644,plain,
    ! [Y_292] : ( unordered_pair(x,Y_292) = singleton(Y_292) ),
    inference(resolution,[status(thm)],[c_593,c_228]) ).

tff(c_226,plain,
    unordered_pair(x,y) != null_class,
    inference(cnfTransformation,[status(thm)],[f_760]) ).

tff(c_648,plain,
    singleton(y) != null_class,
    inference(demodulation,[status(thm),theory(equality)],[c_644,c_226]) ).

tff(c_855,plain,
    singleton(x) != null_class,
    inference(demodulation,[status(thm),theory(equality)],[c_788,c_648]) ).

tff(c_132,plain,
    ! [X_131] :
      ( member(regular(X_131),X_131)
      | ( null_class = X_131 ) ),
    inference(cnfTransformation,[status(thm)],[f_471]) ).

tff(c_24,plain,
    ! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_124]) ).

tff(c_1625,plain,
    ! [Y_344,U_345,X_346] :
      ( ( Y_344 = U_345 )
      | ( X_346 = U_345 )
      | ~ member(U_345,unordered_pair(X_346,Y_344)) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_1893,plain,
    ! [X_361,U_362] :
      ( ( X_361 = U_362 )
      | ( X_361 = U_362 )
      | ~ member(U_362,singleton(X_361)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_1625]) ).

tff(c_1929,plain,
    ! [X_366] :
      ( ( regular(singleton(X_366)) = X_366 )
      | ( singleton(X_366) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_1893]) ).

tff(c_1944,plain,
    ( ( regular(singleton(x)) = y )
    | ( singleton(y) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_788,c_1929]) ).

tff(c_1947,plain,
    ( ( regular(singleton(x)) = y )
    | ( singleton(x) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_788,c_1944]) ).

tff(c_1948,plain,
    regular(singleton(x)) = y,
    inference(negUnitSimplification,[status(thm)],[c_855,c_1947]) ).

tff(c_1925,plain,
    ! [X_361] :
      ( ( regular(singleton(X_361)) = X_361 )
      | ( singleton(X_361) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_1893]) ).

tff(c_1952,plain,
    ( ( y = x )
    | ( singleton(x) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1948,c_1925]) ).

tff(c_1964,plain,
    y = x,
    inference(negUnitSimplification,[status(thm)],[c_855,c_1952]) ).

tff(c_1958,plain,
    ( member(y,singleton(x))
    | ( singleton(x) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1948,c_132]) ).

tff(c_1966,plain,
    member(y,singleton(x)),
    inference(negUnitSimplification,[status(thm)],[c_855,c_1958]) ).

tff(c_2026,plain,
    member(x,singleton(x)),
    inference(demodulation,[status(thm),theory(equality)],[c_1964,c_1966]) ).

tff(c_2,plain,
    ! [U_3,Y_2,X_1] :
      ( member(U_3,Y_2)
      | ~ member(U_3,X_1)
      | ~ subclass(X_1,Y_2) ),
    inference(cnfTransformation,[status(thm)],[f_58]) ).

tff(c_2078,plain,
    ! [Y_374] :
      ( member(x,Y_374)
      | ~ subclass(singleton(x),Y_374) ),
    inference(resolution,[status(thm)],[c_2026,c_2]) ).

tff(c_2101,plain,
    member(x,universal_class),
    inference(resolution,[status(thm)],[c_8,c_2078]) ).

tff(c_2118,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_228,c_2101]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET071-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % 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
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 16:37:39 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 6.18/2.45  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.18/2.45  
% 6.18/2.45  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.54/2.48  
% 6.54/2.48  Inference rules
% 6.54/2.48  ----------------------
% 6.54/2.48  #Ref     : 0
% 6.54/2.48  #Sup     : 447
% 6.54/2.48  #Fact    : 0
% 6.54/2.48  #Define  : 0
% 6.54/2.48  #Split   : 6
% 6.54/2.48  #Chain   : 0
% 6.54/2.48  #Close   : 0
% 6.54/2.48  
% 6.54/2.48  Ordering : KBO
% 6.54/2.48  
% 6.54/2.48  Simplification rules
% 6.54/2.48  ----------------------
% 6.54/2.48  #Subsume      : 61
% 6.54/2.48  #Demod        : 122
% 6.54/2.48  #Tautology    : 187
% 6.54/2.48  #SimpNegUnit  : 22
% 6.54/2.48  #BackRed      : 16
% 6.54/2.48  
% 6.54/2.48  #Partial instantiations: 0
% 6.54/2.48  #Strategies tried      : 1
% 6.54/2.48  
% 6.54/2.48  Timing (in seconds)
% 6.54/2.48  ----------------------
% 6.54/2.49  Preprocessing        : 0.71
% 6.54/2.49  Parsing              : 0.36
% 6.57/2.49  CNF conversion       : 0.05
% 6.57/2.49  Main loop            : 0.71
% 6.57/2.49  Inferencing          : 0.24
% 6.57/2.49  Reduction            : 0.23
% 6.57/2.49  Demodulation         : 0.16
% 6.57/2.49  BG Simplification    : 0.05
% 6.57/2.49  Subsumption          : 0.14
% 6.57/2.49  Abstraction          : 0.03
% 6.57/2.49  MUC search           : 0.00
% 6.57/2.49  Cooper               : 0.00
% 6.57/2.49  Total                : 1.47
% 6.57/2.49  Index Insertion      : 0.00
% 6.57/2.49  Index Deletion       : 0.00
% 6.57/2.49  Index Matching       : 0.00
% 6.57/2.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------