TSTP Solution File: SET096-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET096-6 : 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 : n002.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 7.22s 2.63s
% Output   : CNFRefutation 7.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   59
% Syntax   : Number of formulae    :   84 (  14 unt;  49 typ;   0 def)
%            Number of atoms       :   66 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   54 (  23   ~;  31   |;   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   :   38 (;  38   !;   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_648,axiom,
    singleton(y) != x,
    file(unknown,unknown) ).

tff(f_644,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_646,axiom,
    x != null_class,
    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_123,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | ( U = X )
      | ( U = Y ) ),
    file(unknown,unknown) ).

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

tff(f_66,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(c_188,plain,
    singleton(y) != x,
    inference(cnfTransformation,[status(thm)],[f_648]) ).

tff(c_184,plain,
    subclass(x,singleton(y)),
    inference(cnfTransformation,[status(thm)],[f_644]) ).

tff(c_444,plain,
    ! [Y_248,X_249] :
      ( ( Y_248 = X_249 )
      | ~ subclass(Y_248,X_249)
      | ~ subclass(X_249,Y_248) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_466,plain,
    ( ( singleton(y) = x )
    | ~ subclass(singleton(y),x) ),
    inference(resolution,[status(thm)],[c_184,c_444]) ).

tff(c_483,plain,
    ~ subclass(singleton(y),x),
    inference(negUnitSimplification,[status(thm)],[c_188,c_466]) ).

tff(c_186,plain,
    x != null_class,
    inference(cnfTransformation,[status(thm)],[f_646]) ).

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

tff(c_743,plain,
    ! [U_280,Y_281,X_282] :
      ( member(U_280,Y_281)
      | ~ member(U_280,X_282)
      | ~ subclass(X_282,Y_281) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_1525,plain,
    ! [X_363,Y_364] :
      ( member(regular(X_363),Y_364)
      | ~ subclass(X_363,Y_364)
      | ( null_class = X_363 ) ),
    inference(resolution,[status(thm)],[c_132,c_743]) ).

tff(c_24,plain,
    ! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_606,plain,
    ! [Y_262,U_263,X_264] :
      ( ( Y_262 = U_263 )
      | ( X_264 = U_263 )
      | ~ member(U_263,unordered_pair(X_264,Y_262)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_627,plain,
    ! [X_24,U_263] :
      ( ( X_24 = U_263 )
      | ( X_24 = U_263 )
      | ~ member(U_263,singleton(X_24)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_606]) ).

tff(c_2341,plain,
    ! [X_408,X_409] :
      ( ( regular(X_408) = X_409 )
      | ~ subclass(X_408,singleton(X_409))
      | ( null_class = X_408 ) ),
    inference(resolution,[status(thm)],[c_1525,c_627]) ).

tff(c_2352,plain,
    ( ( regular(x) = y )
    | ( x = null_class ) ),
    inference(resolution,[status(thm)],[c_184,c_2341]) ).

tff(c_2361,plain,
    regular(x) = y,
    inference(negUnitSimplification,[status(thm)],[c_186,c_2352]) ).

tff(c_2389,plain,
    ( member(y,x)
    | ( x = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2361,c_132]) ).

tff(c_2396,plain,
    member(y,x),
    inference(negUnitSimplification,[status(thm)],[c_186,c_2389]) ).

tff(c_4,plain,
    ! [X_4,Y_5] :
      ( subclass(X_4,Y_5)
      | member(not_subclass_element(X_4,Y_5),X_4) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_662,plain,
    ! [X_271,U_272] :
      ( ( X_271 = U_272 )
      | ( X_271 = U_272 )
      | ~ member(U_272,singleton(X_271)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_606]) ).

tff(c_2676,plain,
    ! [X_442,Y_443] :
      ( ( not_subclass_element(singleton(X_442),Y_443) = X_442 )
      | subclass(singleton(X_442),Y_443) ),
    inference(resolution,[status(thm)],[c_4,c_662]) ).

tff(c_2711,plain,
    not_subclass_element(singleton(y),x) = y,
    inference(resolution,[status(thm)],[c_2676,c_483]) ).

tff(c_6,plain,
    ! [X_6,Y_7] :
      ( subclass(X_6,Y_7)
      | ~ member(not_subclass_element(X_6,Y_7),Y_7) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_2722,plain,
    ( subclass(singleton(y),x)
    | ~ member(y,x) ),
    inference(superposition,[status(thm),theory(equality)],[c_2711,c_6]) ).

tff(c_2729,plain,
    subclass(singleton(y),x),
    inference(demodulation,[status(thm),theory(equality)],[c_2396,c_2722]) ).

tff(c_2731,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_483,c_2729]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET096-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12  % 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
% 0.11/0.33  % Computer : n002.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu Aug  3 16:31:01 EDT 2023
% 0.11/0.34  % CPUTime  : 
% 7.22/2.63  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.48/2.63  
% 7.48/2.63  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.58/2.66  
% 7.58/2.66  Inference rules
% 7.58/2.66  ----------------------
% 7.58/2.66  #Ref     : 0
% 7.58/2.66  #Sup     : 603
% 7.58/2.66  #Fact    : 0
% 7.58/2.66  #Define  : 0
% 7.58/2.66  #Split   : 24
% 7.58/2.66  #Chain   : 0
% 7.58/2.66  #Close   : 0
% 7.58/2.66  
% 7.58/2.66  Ordering : KBO
% 7.58/2.66  
% 7.58/2.66  Simplification rules
% 7.58/2.66  ----------------------
% 7.58/2.66  #Subsume      : 72
% 7.58/2.66  #Demod        : 88
% 7.58/2.66  #Tautology    : 107
% 7.58/2.66  #SimpNegUnit  : 13
% 7.58/2.66  #BackRed      : 9
% 7.58/2.66  
% 7.58/2.66  #Partial instantiations: 0
% 7.58/2.66  #Strategies tried      : 1
% 7.58/2.66  
% 7.58/2.66  Timing (in seconds)
% 7.58/2.66  ----------------------
% 7.58/2.67  Preprocessing        : 0.68
% 7.58/2.67  Parsing              : 0.35
% 7.58/2.67  CNF conversion       : 0.05
% 7.58/2.67  Main loop            : 0.93
% 7.58/2.67  Inferencing          : 0.32
% 7.58/2.67  Reduction            : 0.30
% 7.58/2.67  Demodulation         : 0.21
% 7.58/2.67  BG Simplification    : 0.05
% 7.58/2.67  Subsumption          : 0.19
% 7.58/2.67  Abstraction          : 0.03
% 7.58/2.67  MUC search           : 0.00
% 7.58/2.67  Cooper               : 0.00
% 7.58/2.67  Total                : 1.66
% 7.58/2.67  Index Insertion      : 0.00
% 7.58/2.67  Index Deletion       : 0.00
% 7.58/2.67  Index Matching       : 0.00
% 7.58/2.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------