TSTP Solution File: SET096-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET096-7 : 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 : n003.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 10:55:57 EDT 2023

% Result   : Unsatisfiable 14.42s 4.56s
% Output   : CNFRefutation 14.42s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   59
% Syntax   : Number of formulae    :   76 (  10 unt;  51 typ;   0 def)
%            Number of atoms       :   46 (  18 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   42 (  21   ~;  21   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  41   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;  10 con; 0-3 aty)
%            Number of variables   :   24 (;  24   !;   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 > member_of1 > member_of > 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(member_of1,type,
    member_of1: $i > $i ).

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

tff(member_of,type,
    member_of: $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_939,axiom,
    x != null_class,
    file(unknown,unknown) ).

tff(f_936,axiom,
    ! [X,Y] :
      ( ~ member(X,Y)
      | subclass(singleton(X),Y) ),
    file(unknown,unknown) ).

tff(f_941,axiom,
    singleton(y) != x,
    file(unknown,unknown) ).

tff(f_937,axiom,
    subclass(x,singleton(y)),
    file(unknown,unknown) ).

tff(f_91,axiom,
    ! [X,Y] :
      ( ~ subclass(X,Y)
      | ~ subclass(Y,X)
      | ( X = Y ) ),
    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_842,axiom,
    ! [Y,X] :
      ( ~ member(Y,singleton(X))
      | ( Y = X ) ),
    file(unknown,unknown) ).

tff(c_282,plain,
    x != null_class,
    inference(cnfTransformation,[status(thm)],[f_939]) ).

tff(c_278,plain,
    ! [X_265,Y_266] :
      ( subclass(singleton(X_265),Y_266)
      | ~ member(X_265,Y_266) ),
    inference(cnfTransformation,[status(thm)],[f_936]) ).

tff(c_284,plain,
    singleton(y) != x,
    inference(cnfTransformation,[status(thm)],[f_941]) ).

tff(c_280,plain,
    subclass(x,singleton(y)),
    inference(cnfTransformation,[status(thm)],[f_937]) ).

tff(c_1129,plain,
    ! [Y_370,X_371] :
      ( ( Y_370 = X_371 )
      | ~ subclass(Y_370,X_371)
      | ~ subclass(X_371,Y_370) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_1151,plain,
    ( ( singleton(y) = x )
    | ~ subclass(singleton(y),x) ),
    inference(resolution,[status(thm)],[c_280,c_1129]) ).

tff(c_1170,plain,
    ~ subclass(singleton(y),x),
    inference(negUnitSimplification,[status(thm)],[c_284,c_1151]) ).

tff(c_1180,plain,
    ~ member(y,x),
    inference(resolution,[status(thm)],[c_278,c_1170]) ).

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

tff(c_2282,plain,
    ! [U_432,Y_433,X_434] :
      ( member(U_432,Y_433)
      | ~ member(U_432,X_434)
      | ~ subclass(X_434,Y_433) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_7789,plain,
    ! [X_715,Y_716] :
      ( member(regular(X_715),Y_716)
      | ~ subclass(X_715,Y_716)
      | ( null_class = X_715 ) ),
    inference(resolution,[status(thm)],[c_132,c_2282]) ).

tff(c_250,plain,
    ! [Y_245,X_246] :
      ( ( Y_245 = X_246 )
      | ~ member(Y_245,singleton(X_246)) ),
    inference(cnfTransformation,[status(thm)],[f_842]) ).

tff(c_15277,plain,
    ! [X_858,X_859] :
      ( ( regular(X_858) = X_859 )
      | ~ subclass(X_858,singleton(X_859))
      | ( null_class = X_858 ) ),
    inference(resolution,[status(thm)],[c_7789,c_250]) ).

tff(c_15341,plain,
    ( ( regular(x) = y )
    | ( x = null_class ) ),
    inference(resolution,[status(thm)],[c_280,c_15277]) ).

tff(c_15365,plain,
    regular(x) = y,
    inference(negUnitSimplification,[status(thm)],[c_282,c_15341]) ).

tff(c_15396,plain,
    ( member(y,x)
    | ( x = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_15365,c_132]) ).

tff(c_15415,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_282,c_1180,c_15396]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET096-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.14  % 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
% 0.14/0.36  % Computer : n003.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 16:32:53 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 14.42/4.56  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.42/4.56  
% 14.42/4.57  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.42/4.59  
% 14.42/4.59  Inference rules
% 14.42/4.59  ----------------------
% 14.42/4.59  #Ref     : 8
% 14.42/4.59  #Sup     : 3718
% 14.42/4.59  #Fact    : 6
% 14.42/4.59  #Define  : 0
% 14.42/4.59  #Split   : 47
% 14.42/4.59  #Chain   : 0
% 14.42/4.59  #Close   : 0
% 14.42/4.59  
% 14.42/4.59  Ordering : KBO
% 14.42/4.59  
% 14.42/4.59  Simplification rules
% 14.42/4.59  ----------------------
% 14.42/4.59  #Subsume      : 1072
% 14.42/4.59  #Demod        : 1099
% 14.42/4.59  #Tautology    : 982
% 14.42/4.59  #SimpNegUnit  : 295
% 14.42/4.59  #BackRed      : 68
% 14.42/4.59  
% 14.42/4.59  #Partial instantiations: 0
% 14.42/4.59  #Strategies tried      : 1
% 14.42/4.59  
% 14.42/4.59  Timing (in seconds)
% 14.42/4.59  ----------------------
% 14.42/4.60  Preprocessing        : 0.76
% 14.42/4.60  Parsing              : 0.36
% 14.42/4.60  CNF conversion       : 0.06
% 14.42/4.60  Main loop            : 2.78
% 14.42/4.60  Inferencing          : 0.74
% 14.42/4.60  Reduction            : 1.04
% 14.42/4.60  Demodulation         : 0.70
% 14.42/4.60  BG Simplification    : 0.08
% 14.42/4.60  Subsumption          : 0.66
% 14.42/4.60  Abstraction          : 0.07
% 14.42/4.60  MUC search           : 0.00
% 14.42/4.60  Cooper               : 0.00
% 14.42/4.60  Total                : 3.59
% 14.42/4.60  Index Insertion      : 0.00
% 14.42/4.60  Index Deletion       : 0.00
% 14.42/4.60  Index Matching       : 0.00
% 14.42/4.60  BG Taut test         : 0.00
%------------------------------------------------------------------------------