TSTP Solution File: SET067-7 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET067-7 : 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/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 : n028.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 10:55:48 EDT 2023

% Result   : Unsatisfiable 8.94s 3.25s
% Output   : CNFRefutation 9.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   61
% Syntax   : Number of formulae    :   90 (  19 unt;  49 typ;   0 def)
%            Number of atoms       :   69 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   53 (  25   ~;  28   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   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   :   72 (;  72   !;   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_746,axiom,
    ~ subclass(singleton(x),unordered_pair(x,y)),
    file(unknown,unknown) ).

tff(f_62,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    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_151,axiom,
    ! [U,X,V,Y] :
      ( ~ member(U,X)
      | ~ member(V,Y)
      | member(ordered_pair(U,V),cross_product(X,Y)) ),
    file(unknown,unknown) ).

tff(f_661,axiom,
    ! [U,V,X,Y] :
      ( ~ member(ordered_pair(U,V),cross_product(X,Y))
      | member(U,universal_class) ),
    file(unknown,unknown) ).

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

tff(f_120,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file(unknown,unknown) ).

tff(f_129,axiom,
    ! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
    file(unknown,unknown) ).

tff(f_117,axiom,
    ! [Y,X] :
      ( ~ member(Y,universal_class)
      | member(Y,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X,Y] :
      ( ~ member(not_subclass_element(X,Y),Y)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

tff(c_218,plain,
    ~ subclass(singleton(x),unordered_pair(x,y)),
    inference(cnfTransformation,[status(thm)],[f_746]) ).

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_62]) ).

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

tff(c_767,plain,
    ! [Y_304,U_305,X_306] :
      ( ( Y_304 = U_305 )
      | ( X_306 = U_305 )
      | ~ member(U_305,unordered_pair(X_306,Y_304)) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_837,plain,
    ! [X_311,U_312] :
      ( ( X_311 = U_312 )
      | ( X_311 = U_312 )
      | ~ member(U_312,singleton(X_311)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_767]) ).

tff(c_4088,plain,
    ! [X_519,Y_520] :
      ( ( not_subclass_element(singleton(X_519),Y_520) = X_519 )
      | subclass(singleton(X_519),Y_520) ),
    inference(resolution,[status(thm)],[c_4,c_837]) ).

tff(c_4139,plain,
    not_subclass_element(singleton(x),unordered_pair(x,y)) = x,
    inference(resolution,[status(thm)],[c_4088,c_218]) ).

tff(c_3328,plain,
    ! [U_478,V_479,X_480,Y_481] :
      ( member(ordered_pair(U_478,V_479),cross_product(X_480,Y_481))
      | ~ member(V_479,Y_481)
      | ~ member(U_478,X_480) ),
    inference(cnfTransformation,[status(thm)],[f_151]) ).

tff(c_188,plain,
    ! [U_185,V_186,X_187,Y_188] :
      ( member(U_185,universal_class)
      | ~ member(ordered_pair(U_185,V_186),cross_product(X_187,Y_188)) ),
    inference(cnfTransformation,[status(thm)],[f_661]) ).

tff(c_3358,plain,
    ! [U_478,V_479,Y_481,X_480] :
      ( member(U_478,universal_class)
      | ~ member(V_479,Y_481)
      | ~ member(U_478,X_480) ),
    inference(resolution,[status(thm)],[c_3328,c_188]) ).

tff(c_3501,plain,
    ! [V_479,Y_481] : ~ member(V_479,Y_481),
    inference(splitLeft,[status(thm)],[c_3358]) ).

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_22,plain,
    ! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
    inference(cnfTransformation,[status(thm)],[f_120]) ).

tff(c_1505,plain,
    ! [X_359,Y_360] : ( unordered_pair(singleton(X_359),unordered_pair(X_359,singleton(Y_360))) = ordered_pair(X_359,Y_360) ),
    inference(cnfTransformation,[status(thm)],[f_129]) ).

tff(c_20,plain,
    ! [Y_20,X_21] :
      ( member(Y_20,unordered_pair(X_21,Y_20))
      | ~ member(Y_20,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_1519,plain,
    ! [X_359,Y_360] :
      ( member(unordered_pair(X_359,singleton(Y_360)),ordered_pair(X_359,Y_360))
      | ~ member(unordered_pair(X_359,singleton(Y_360)),universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1505,c_20]) ).

tff(c_1595,plain,
    ! [X_366,Y_367] : member(unordered_pair(X_366,singleton(Y_367)),ordered_pair(X_366,Y_367)),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_1519]) ).

tff(c_1605,plain,
    ! [Y_367,Y_212] : member(unordered_pair(singleton(Y_367),Y_212),ordered_pair(Y_212,Y_367)),
    inference(superposition,[status(thm),theory(equality)],[c_216,c_1595]) ).

tff(c_3554,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_3501,c_1605]) ).

tff(c_3565,plain,
    ! [U_487,X_488] :
      ( member(U_487,universal_class)
      | ~ member(U_487,X_488) ),
    inference(splitRight,[status(thm)],[c_3358]) ).

tff(c_3666,plain,
    ! [X_4,Y_5] :
      ( member(not_subclass_element(X_4,Y_5),universal_class)
      | subclass(X_4,Y_5) ),
    inference(resolution,[status(thm)],[c_4,c_3565]) ).

tff(c_4144,plain,
    ( member(x,universal_class)
    | subclass(singleton(x),unordered_pair(x,y)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4139,c_3666]) ).

tff(c_4159,plain,
    member(x,universal_class),
    inference(negUnitSimplification,[status(thm)],[c_218,c_4144]) ).

tff(c_18,plain,
    ! [X_18,Y_19] :
      ( member(X_18,unordered_pair(X_18,Y_19))
      | ~ member(X_18,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

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_67]) ).

tff(c_4153,plain,
    ( subclass(singleton(x),unordered_pair(x,y))
    | ~ member(x,unordered_pair(x,y)) ),
    inference(superposition,[status(thm),theory(equality)],[c_4139,c_6]) ).

tff(c_4160,plain,
    ~ member(x,unordered_pair(x,y)),
    inference(negUnitSimplification,[status(thm)],[c_218,c_4153]) ).

tff(c_4197,plain,
    ~ member(x,universal_class),
    inference(resolution,[status(thm)],[c_18,c_4160]) ).

tff(c_4201,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_4159,c_4197]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET067-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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
% 0.12/0.35  % Computer : n028.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Thu Aug  3 16:25:24 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 8.94/3.25  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.23/3.26  
% 9.23/3.26  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.30/3.31  
% 9.30/3.31  Inference rules
% 9.30/3.31  ----------------------
% 9.30/3.31  #Ref     : 0
% 9.30/3.31  #Sup     : 962
% 9.30/3.31  #Fact    : 2
% 9.30/3.31  #Define  : 0
% 9.30/3.31  #Split   : 25
% 9.30/3.31  #Chain   : 0
% 9.30/3.31  #Close   : 0
% 9.30/3.31  
% 9.30/3.31  Ordering : KBO
% 9.30/3.31  
% 9.30/3.31  Simplification rules
% 9.30/3.31  ----------------------
% 9.30/3.31  #Subsume      : 213
% 9.30/3.31  #Demod        : 147
% 9.30/3.31  #Tautology    : 191
% 9.30/3.31  #SimpNegUnit  : 74
% 9.30/3.31  #BackRed      : 29
% 9.30/3.31  
% 9.30/3.31  #Partial instantiations: 0
% 9.30/3.31  #Strategies tried      : 1
% 9.30/3.31  
% 9.30/3.31  Timing (in seconds)
% 9.30/3.31  ----------------------
% 9.30/3.31  Preprocessing        : 0.77
% 9.30/3.31  Parsing              : 0.39
% 9.30/3.31  CNF conversion       : 0.05
% 9.30/3.31  Main loop            : 1.28
% 9.30/3.31  Inferencing          : 0.42
% 9.30/3.31  Reduction            : 0.43
% 9.30/3.31  Demodulation         : 0.30
% 9.30/3.31  BG Simplification    : 0.06
% 9.30/3.31  Subsumption          : 0.27
% 9.30/3.31  Abstraction          : 0.04
% 9.30/3.31  MUC search           : 0.00
% 9.30/3.31  Cooper               : 0.00
% 9.50/3.31  Total                : 2.13
% 9.50/3.31  Index Insertion      : 0.00
% 9.50/3.31  Index Deletion       : 0.00
% 9.50/3.31  Index Matching       : 0.00
% 9.50/3.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------