TSTP Solution File: SET102-7 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET102-7 : 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 : n025.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 10:55:58 EDT 2023

% Result   : Unsatisfiable 8.06s 2.86s
% Output   : CNFRefutation 8.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   62 (   8 unt;  51 typ;   0 def)
%            Number of atoms       :   14 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   5   ~;   3   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   67 (  41   >;  26   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   42 (  42 usr;  10 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   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_of1 > member_of > 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(member_of1,type,
    member_of1: $i > $i ).

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_119,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [X,Y] : ( unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) = ordered_pair(X,Y) ),
    file(unknown,unknown) ).

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

tff(f_976,axiom,
    ~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
    file(unknown,unknown) ).

tff(c_22,plain,
    ! [X_22,Y_23] : member(unordered_pair(X_22,Y_23),universal_class),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_3446,plain,
    ! [X_526,Y_527] : ( unordered_pair(singleton(X_526),unordered_pair(X_526,singleton(Y_527))) = ordered_pair(X_526,Y_527) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

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_116]) ).

tff(c_3472,plain,
    ! [X_526,Y_527] :
      ( member(unordered_pair(X_526,singleton(Y_527)),ordered_pair(X_526,Y_527))
      | ~ member(unordered_pair(X_526,singleton(Y_527)),universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_3446,c_20]) ).

tff(c_3562,plain,
    ! [X_526,Y_527] : member(unordered_pair(X_526,singleton(Y_527)),ordered_pair(X_526,Y_527)),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_3472]) ).

tff(c_292,plain,
    ~ member(unordered_pair(x,singleton(y)),ordered_pair(x,y)),
    inference(cnfTransformation,[status(thm)],[f_976]) ).

tff(c_3623,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3562,c_292]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET102-7 : 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
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 16:46:04 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 8.06/2.86  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.06/2.87  
% 8.06/2.87  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.06/2.92  
% 8.06/2.92  Inference rules
% 8.06/2.92  ----------------------
% 8.06/2.92  #Ref     : 3
% 8.06/2.92  #Sup     : 854
% 8.06/2.92  #Fact    : 0
% 8.06/2.92  #Define  : 0
% 8.06/2.92  #Split   : 9
% 8.06/2.92  #Chain   : 0
% 8.06/2.92  #Close   : 0
% 8.06/2.92  
% 8.06/2.92  Ordering : KBO
% 8.06/2.92  
% 8.06/2.92  Simplification rules
% 8.06/2.92  ----------------------
% 8.06/2.92  #Subsume      : 157
% 8.06/2.92  #Demod        : 129
% 8.06/2.92  #Tautology    : 205
% 8.06/2.92  #SimpNegUnit  : 1
% 8.06/2.92  #BackRed      : 7
% 8.06/2.92  
% 8.06/2.92  #Partial instantiations: 0
% 8.06/2.92  #Strategies tried      : 1
% 8.06/2.92  
% 8.06/2.92  Timing (in seconds)
% 8.06/2.92  ----------------------
% 8.06/2.92  Preprocessing        : 0.76
% 8.06/2.92  Parsing              : 0.36
% 8.06/2.92  CNF conversion       : 0.06
% 8.06/2.92  Main loop            : 1.05
% 8.06/2.92  Inferencing          : 0.33
% 8.06/2.92  Reduction            : 0.38
% 8.06/2.92  Demodulation         : 0.27
% 8.06/2.92  BG Simplification    : 0.06
% 8.06/2.93  Subsumption          : 0.22
% 8.06/2.93  Abstraction          : 0.04
% 8.06/2.93  MUC search           : 0.00
% 8.06/2.93  Cooper               : 0.00
% 8.06/2.93  Total                : 1.89
% 8.06/2.93  Index Insertion      : 0.00
% 8.06/2.93  Index Deletion       : 0.00
% 8.06/2.93  Index Matching       : 0.00
% 8.06/2.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------