TSTP Solution File: SET090-7 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET090-7 : 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 : n018.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 10:55:55 EDT 2023

% Result   : Unsatisfiable 12.20s 3.92s
% Output   : CNFRefutation 12.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   54
% Syntax   : Number of formulae    :   69 (   9 unt;  49 typ;   0 def)
%            Number of atoms       :   34 (  26 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   27 (  13   ~;  14   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   66 (  40   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   40 (  40 usr;   9 con; 0-3 aty)
%            Number of variables   :   11 (;  11   !;   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_of > inverse > flip > first > domain_of > diagonalise > complement > cantor > universal_class > u > 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(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(u,type,
    u: $i ).

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(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_900,axiom,
    member_of(singleton(u)) != u,
    file(unknown,unknown) ).

tff(f_897,axiom,
    ! [X] :
      ( ( singleton(member_of(X)) = X )
      | ( member_of(X) = X ) ),
    file(unknown,unknown) ).

tff(f_898,axiom,
    member(u,universal_class),
    file(unknown,unknown) ).

tff(f_864,axiom,
    ! [X,Y] :
      ( ( singleton(X) != singleton(Y) )
      | ~ member(Y,universal_class)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_889,axiom,
    ! [Y] :
      ( ~ member(Y,universal_class)
      | ( singleton(member_of(singleton(Y))) = singleton(Y) ) ),
    file(unknown,unknown) ).

tff(c_270,plain,
    member_of(singleton(u)) != u,
    inference(cnfTransformation,[status(thm)],[f_900]) ).

tff(c_266,plain,
    ! [X_258] :
      ( ( member_of(X_258) = X_258 )
      | ( singleton(member_of(X_258)) = X_258 ) ),
    inference(cnfTransformation,[status(thm)],[f_897]) ).

tff(c_268,plain,
    member(u,universal_class),
    inference(cnfTransformation,[status(thm)],[f_898]) ).

tff(c_1762,plain,
    ! [Y_409,X_410] :
      ( ( Y_409 = X_410 )
      | ~ member(Y_409,universal_class)
      | ( singleton(Y_409) != singleton(X_410) ) ),
    inference(cnfTransformation,[status(thm)],[f_864]) ).

tff(c_1844,plain,
    ! [X_413] :
      ( ( u = X_413 )
      | ( singleton(u) != singleton(X_413) ) ),
    inference(resolution,[status(thm)],[c_268,c_1762]) ).

tff(c_1847,plain,
    ! [X_258] :
      ( ( member_of(X_258) = u )
      | ( singleton(u) != X_258 )
      | ( member_of(X_258) = X_258 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_266,c_1844]) ).

tff(c_11032,plain,
    ( ( member_of(singleton(u)) = u )
    | ( member_of(singleton(u)) = singleton(u) ) ),
    inference(reflexivity,[status(thm),theory(equality)],[c_1847]) ).

tff(c_11033,plain,
    member_of(singleton(u)) = singleton(u),
    inference(negUnitSimplification,[status(thm)],[c_270,c_11032]) ).

tff(c_11035,plain,
    singleton(u) != u,
    inference(demodulation,[status(thm),theory(equality)],[c_11033,c_270]) ).

tff(c_262,plain,
    ! [Y_256] :
      ( ( singleton(member_of(singleton(Y_256))) = singleton(Y_256) )
      | ~ member(Y_256,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_889]) ).

tff(c_11054,plain,
    ( ( singleton(singleton(u)) = singleton(u) )
    | ~ member(u,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_11033,c_262]) ).

tff(c_11080,plain,
    singleton(singleton(u)) = singleton(u),
    inference(demodulation,[status(thm),theory(equality)],[c_268,c_11054]) ).

tff(c_1823,plain,
    ! [X_410] :
      ( ( u = X_410 )
      | ( singleton(u) != singleton(X_410) ) ),
    inference(resolution,[status(thm)],[c_268,c_1762]) ).

tff(c_11215,plain,
    singleton(u) = u,
    inference(superposition,[status(thm),theory(equality)],[c_11080,c_1823]) ).

tff(c_11317,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_11035,c_11215]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET090-7 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.15  % 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
% 0.15/0.38  % Computer : n018.cluster.edu
% 0.15/0.38  % Model    : x86_64 x86_64
% 0.15/0.38  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38  % Memory   : 8042.1875MB
% 0.15/0.38  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38  % CPULimit : 300
% 0.15/0.38  % WCLimit  : 300
% 0.15/0.38  % DateTime : Thu Aug  3 16:38:50 EDT 2023
% 0.15/0.38  % CPUTime  : 
% 12.20/3.92  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.20/3.92  
% 12.20/3.92  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.20/3.95  
% 12.20/3.95  Inference rules
% 12.20/3.95  ----------------------
% 12.20/3.95  #Ref     : 6
% 12.20/3.95  #Sup     : 2767
% 12.20/3.95  #Fact    : 6
% 12.20/3.95  #Define  : 0
% 12.20/3.95  #Split   : 37
% 12.20/3.95  #Chain   : 0
% 12.20/3.95  #Close   : 0
% 12.20/3.95  
% 12.20/3.95  Ordering : KBO
% 12.20/3.95  
% 12.20/3.95  Simplification rules
% 12.20/3.95  ----------------------
% 12.20/3.95  #Subsume      : 813
% 12.20/3.95  #Demod        : 818
% 12.20/3.95  #Tautology    : 700
% 12.20/3.95  #SimpNegUnit  : 194
% 12.20/3.95  #BackRed      : 61
% 12.20/3.95  
% 12.20/3.95  #Partial instantiations: 0
% 12.20/3.95  #Strategies tried      : 1
% 12.20/3.95  
% 12.20/3.95  Timing (in seconds)
% 12.20/3.95  ----------------------
% 12.20/3.95  Preprocessing        : 0.75
% 12.20/3.95  Parsing              : 0.36
% 12.20/3.95  CNF conversion       : 0.06
% 12.20/3.95  Main loop            : 2.11
% 12.20/3.95  Inferencing          : 0.60
% 12.20/3.95  Reduction            : 0.80
% 12.20/3.96  Demodulation         : 0.55
% 12.20/3.96  BG Simplification    : 0.07
% 12.20/3.96  Subsumption          : 0.47
% 12.20/3.96  Abstraction          : 0.06
% 12.20/3.96  MUC search           : 0.00
% 12.20/3.96  Cooper               : 0.00
% 12.20/3.96  Total                : 2.91
% 12.20/3.96  Index Insertion      : 0.00
% 12.20/3.96  Index Deletion       : 0.00
% 12.20/3.96  Index Matching       : 0.00
% 12.20/3.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------