TSTP Solution File: SET074-6 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET074-6 : 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/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 : n011.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 10:55:50 EDT 2023

% Result   : Unsatisfiable 4.75s 2.18s
% Output   : CNFRefutation 4.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   70 (   8 unt;  49 typ;   0 def)
%            Number of atoms       :   35 (  10 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   28 (  14   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   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   :   21 (;  21   !;   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_644,axiom,
    member(y,universal_class),
    file(unknown,unknown) ).

tff(f_645,axiom,
    unordered_pair(x,y) = null_class,
    file(unknown,unknown) ).

tff(f_116,axiom,
    ! [Y,X] :
      ( ~ member(Y,universal_class)
      | member(Y,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_474,axiom,
    ! [X] :
      ( ( X = null_class )
      | ( intersection(X,regular(X)) = null_class ) ),
    file(unknown,unknown) ).

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

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

tff(c_184,plain,
    member(y,universal_class),
    inference(cnfTransformation,[status(thm)],[f_644]) ).

tff(c_186,plain,
    unordered_pair(x,y) = null_class,
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_332,plain,
    ! [Y_216,X_217] :
      ( member(Y_216,unordered_pair(X_217,Y_216))
      | ~ member(Y_216,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_116]) ).

tff(c_338,plain,
    ( member(y,null_class)
    | ~ member(y,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_186,c_332]) ).

tff(c_340,plain,
    member(y,null_class),
    inference(demodulation,[status(thm),theory(equality)],[c_184,c_338]) ).

tff(c_134,plain,
    ! [X_132] :
      ( ( intersection(X_132,regular(X_132)) = null_class )
      | ( null_class = X_132 ) ),
    inference(cnfTransformation,[status(thm)],[f_474]) ).

tff(c_518,plain,
    ! [Z_248,X_249,Y_250] :
      ( member(Z_248,X_249)
      | ~ member(Z_248,intersection(X_249,Y_250)) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_591,plain,
    ! [Z_259,X_260] :
      ( member(Z_259,X_260)
      | ~ member(Z_259,null_class)
      | ( null_class = X_260 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_134,c_518]) ).

tff(c_641,plain,
    ! [X_264] :
      ( member(y,X_264)
      | ( null_class = X_264 ) ),
    inference(resolution,[status(thm)],[c_340,c_591]) ).

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_661,plain,
    ! [X_265] :
      ( ~ member(y,X_265)
      | ( complement(X_265) = null_class ) ),
    inference(resolution,[status(thm)],[c_641,c_48]) ).

tff(c_700,plain,
    complement(null_class) = null_class,
    inference(resolution,[status(thm)],[c_340,c_661]) ).

tff(c_1180,plain,
    ! [Z_280] :
      ( ~ member(Z_280,null_class)
      | ~ member(Z_280,null_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_700,c_48]) ).

tff(c_1188,plain,
    ~ member(y,null_class),
    inference(resolution,[status(thm)],[c_340,c_1180]) ).

tff(c_1203,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_340,c_1188]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET074-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % 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
% 0.19/0.36  % Computer : n011.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit : 300
% 0.19/0.36  % WCLimit  : 300
% 0.19/0.36  % DateTime : Thu Aug  3 16:05:51 EDT 2023
% 0.19/0.36  % CPUTime  : 
% 4.75/2.18  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.75/2.18  
% 4.75/2.18  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.75/2.21  
% 4.75/2.21  Inference rules
% 4.75/2.21  ----------------------
% 4.75/2.21  #Ref     : 0
% 4.75/2.21  #Sup     : 252
% 4.75/2.21  #Fact    : 0
% 4.75/2.21  #Define  : 0
% 4.75/2.21  #Split   : 5
% 4.75/2.21  #Chain   : 0
% 4.75/2.21  #Close   : 0
% 4.75/2.21  
% 4.75/2.21  Ordering : KBO
% 4.75/2.21  
% 4.75/2.21  Simplification rules
% 4.75/2.21  ----------------------
% 4.75/2.21  #Subsume      : 14
% 4.75/2.21  #Demod        : 56
% 4.75/2.21  #Tautology    : 89
% 4.75/2.21  #SimpNegUnit  : 1
% 4.75/2.21  #BackRed      : 20
% 4.75/2.21  
% 4.75/2.21  #Partial instantiations: 0
% 4.75/2.21  #Strategies tried      : 1
% 4.75/2.21  
% 4.75/2.21  Timing (in seconds)
% 4.75/2.21  ----------------------
% 4.75/2.21  Preprocessing        : 0.66
% 4.75/2.21  Parsing              : 0.34
% 4.75/2.21  CNF conversion       : 0.04
% 4.75/2.21  Main loop            : 0.50
% 4.75/2.21  Inferencing          : 0.16
% 4.75/2.21  Reduction            : 0.16
% 4.75/2.21  Demodulation         : 0.12
% 4.75/2.21  BG Simplification    : 0.04
% 4.75/2.21  Subsumption          : 0.11
% 4.75/2.21  Abstraction          : 0.02
% 4.75/2.21  MUC search           : 0.00
% 4.75/2.21  Cooper               : 0.00
% 4.75/2.21  Total                : 1.20
% 4.75/2.21  Index Insertion      : 0.00
% 4.75/2.21  Index Deletion       : 0.00
% 4.75/2.21  Index Matching       : 0.00
% 4.75/2.21  BG Taut test         : 0.00
%------------------------------------------------------------------------------