TSTP Solution File: SET062-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET062-6 : 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 : n021.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 10:55:46 EDT 2023

% Result   : Unsatisfiable 9.83s 3.44s
% Output   : CNFRefutation 9.83s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   83 (   8 unt;  48 typ;   0 def)
%            Number of atoms       :   67 (  11 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   61 (  29   ~;  32   |;   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   :   55 (;  55   !;   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 > 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(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_61,axiom,
    ! [X,Y] :
      ( member(not_subclass_element(X,Y),X)
      | subclass(X,Y) ),
    file(unknown,unknown) ).

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

tff(f_191,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,Y) ),
    file(unknown,unknown) ).

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

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

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

tff(f_185,axiom,
    ! [Z,X,Y] :
      ( ~ member(Z,intersection(X,Y))
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_645,axiom,
    ~ subclass(null_class,x),
    file(unknown,unknown) ).

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_132,plain,
    ! [X_131] :
      ( member(regular(X_131),X_131)
      | ( null_class = X_131 ) ),
    inference(cnfTransformation,[status(thm)],[f_470]) ).

tff(c_519,plain,
    ! [Z_249,Y_250,X_251] :
      ( member(Z_249,Y_250)
      | ~ member(Z_249,intersection(X_251,Y_250)) ),
    inference(cnfTransformation,[status(thm)],[f_191]) ).

tff(c_3847,plain,
    ! [X_531,Y_532] :
      ( member(regular(intersection(X_531,Y_532)),Y_532)
      | ( intersection(X_531,Y_532) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_519]) ).

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

tff(c_706,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_741,plain,
    ! [X_131,Y_281] :
      ( member(regular(X_131),Y_281)
      | ~ subclass(X_131,Y_281)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_132,c_706]) ).

tff(c_1212,plain,
    ! [X_326,Y_327] :
      ( member(regular(X_326),Y_327)
      | ~ subclass(X_326,Y_327)
      | ( null_class = X_326 ) ),
    inference(resolution,[status(thm)],[c_132,c_706]) ).

tff(c_234,plain,
    ! [Z_200,X_201] :
      ( ~ member(Z_200,X_201)
      | ~ member(Z_200,complement(X_201)) ),
    inference(cnfTransformation,[status(thm)],[f_207]) ).

tff(c_243,plain,
    ! [X_201] :
      ( ~ member(regular(complement(X_201)),X_201)
      | ( complement(X_201) = null_class ) ),
    inference(resolution,[status(thm)],[c_132,c_234]) ).

tff(c_1267,plain,
    ! [Y_328] :
      ( ~ subclass(complement(Y_328),Y_328)
      | ( complement(Y_328) = null_class ) ),
    inference(resolution,[status(thm)],[c_1212,c_243]) ).

tff(c_1289,plain,
    complement(universal_class) = null_class,
    inference(resolution,[status(thm)],[c_8,c_1267]) ).

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_1387,plain,
    ! [Z_334] :
      ( ~ member(Z_334,universal_class)
      | ~ member(Z_334,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1289,c_48]) ).

tff(c_1391,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ~ subclass(X_131,universal_class)
      | ( null_class = X_131 ) ),
    inference(resolution,[status(thm)],[c_741,c_1387]) ).

tff(c_1439,plain,
    ! [X_131] :
      ( ~ member(regular(X_131),null_class)
      | ( null_class = X_131 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_1391]) ).

tff(c_3960,plain,
    ! [X_533] : ( intersection(X_533,null_class) = null_class ),
    inference(resolution,[status(thm)],[c_3847,c_1439]) ).

tff(c_42,plain,
    ! [Z_46,X_47,Y_48] :
      ( member(Z_46,X_47)
      | ~ member(Z_46,intersection(X_47,Y_48)) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_4973,plain,
    ! [Z_571,X_572] :
      ( member(Z_571,X_572)
      | ~ member(Z_571,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_3960,c_42]) ).

tff(c_6224,plain,
    ! [Y_608,X_609] :
      ( member(not_subclass_element(null_class,Y_608),X_609)
      | subclass(null_class,Y_608) ),
    inference(resolution,[status(thm)],[c_4,c_4973]) ).

tff(c_475,plain,
    ! [X_242,Y_243] :
      ( subclass(X_242,Y_243)
      | member(not_subclass_element(X_242,Y_243),X_242) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_3143,plain,
    ! [X_513,Y_514] :
      ( ~ member(not_subclass_element(complement(X_513),Y_514),X_513)
      | subclass(complement(X_513),Y_514) ),
    inference(resolution,[status(thm)],[c_475,c_48]) ).

tff(c_3186,plain,
    ! [Y_514] :
      ( ~ member(not_subclass_element(null_class,Y_514),universal_class)
      | subclass(complement(universal_class),Y_514) ),
    inference(superposition,[status(thm),theory(equality)],[c_1289,c_3143]) ).

tff(c_3216,plain,
    ! [Y_514] :
      ( ~ member(not_subclass_element(null_class,Y_514),universal_class)
      | subclass(null_class,Y_514) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1289,c_3186]) ).

tff(c_6323,plain,
    ! [Y_608] : subclass(null_class,Y_608),
    inference(resolution,[status(thm)],[c_6224,c_3216]) ).

tff(c_184,plain,
    ~ subclass(null_class,x),
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_6347,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_6323,c_184]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : SET062-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.12/0.14  % 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 : n021.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 16:18:21 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 9.83/3.44  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.83/3.45  
% 9.83/3.45  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.83/3.48  
% 9.83/3.48  Inference rules
% 9.83/3.48  ----------------------
% 9.83/3.48  #Ref     : 0
% 9.83/3.48  #Sup     : 1468
% 9.83/3.48  #Fact    : 0
% 9.83/3.48  #Define  : 0
% 9.83/3.48  #Split   : 43
% 9.83/3.48  #Chain   : 0
% 9.83/3.48  #Close   : 0
% 9.83/3.48  
% 9.83/3.48  Ordering : KBO
% 9.83/3.48  
% 9.83/3.48  Simplification rules
% 9.83/3.48  ----------------------
% 9.83/3.48  #Subsume      : 287
% 9.83/3.48  #Demod        : 366
% 9.83/3.48  #Tautology    : 207
% 9.83/3.48  #SimpNegUnit  : 14
% 9.83/3.48  #BackRed      : 98
% 9.83/3.48  
% 9.83/3.48  #Partial instantiations: 0
% 9.83/3.48  #Strategies tried      : 1
% 9.83/3.48  
% 9.83/3.48  Timing (in seconds)
% 9.83/3.48  ----------------------
% 9.83/3.49  Preprocessing        : 0.71
% 9.83/3.49  Parsing              : 0.38
% 9.83/3.49  CNF conversion       : 0.05
% 9.83/3.49  Main loop            : 1.62
% 9.83/3.49  Inferencing          : 0.56
% 9.83/3.49  Reduction            : 0.53
% 9.83/3.49  Demodulation         : 0.36
% 9.83/3.49  BG Simplification    : 0.06
% 9.83/3.49  Subsumption          : 0.34
% 9.83/3.49  Abstraction          : 0.05
% 9.83/3.49  MUC search           : 0.00
% 9.83/3.49  Cooper               : 0.00
% 9.83/3.49  Total                : 2.39
% 9.83/3.49  Index Insertion      : 0.00
% 9.83/3.49  Index Deletion       : 0.00
% 9.83/3.49  Index Matching       : 0.00
% 9.83/3.49  BG Taut test         : 0.00
%------------------------------------------------------------------------------