TSTP Solution File: SET084-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET084-6 : 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 : n031.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 10:55:54 EDT 2023

% Result   : Unsatisfiable 5.46s 2.35s
% Output   : CNFRefutation 5.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   67 (  11 unt;  49 typ;   0 def)
%            Number of atoms       :   28 (  13 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   19 (   9   ~;  10   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    2 (   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   :   15 (;  15   !;   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_647,axiom,
    x != y,
    file(unknown,unknown) ).

tff(f_645,axiom,
    member(y,universal_class),
    file(unknown,unknown) ).

tff(f_644,axiom,
    singleton(x) = singleton(y),
    file(unknown,unknown) ).

tff(f_123,axiom,
    ! [X] : ( unordered_pair(X,X) = singleton(X) ),
    file(unknown,unknown) ).

tff(f_109,axiom,
    ! [X,Y] :
      ( ~ member(X,universal_class)
      | member(X,unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_102,axiom,
    ! [U,X,Y] :
      ( ~ member(U,unordered_pair(X,Y))
      | ( U = X )
      | ( U = Y ) ),
    file(unknown,unknown) ).

tff(c_188,plain,
    y != x,
    inference(cnfTransformation,[status(thm)],[f_647]) ).

tff(c_186,plain,
    member(y,universal_class),
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_184,plain,
    singleton(y) = singleton(x),
    inference(cnfTransformation,[status(thm)],[f_644]) ).

tff(c_24,plain,
    ! [X_24] : ( unordered_pair(X_24,X_24) = singleton(X_24) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_389,plain,
    ! [X_231,Y_232] :
      ( member(X_231,unordered_pair(X_231,Y_232))
      | ~ member(X_231,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_393,plain,
    ! [X_233] :
      ( member(X_233,singleton(X_233))
      | ~ member(X_233,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_389]) ).

tff(c_396,plain,
    ( member(y,singleton(x))
    | ~ member(y,universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_184,c_393]) ).

tff(c_398,plain,
    member(y,singleton(x)),
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_396]) ).

tff(c_805,plain,
    ! [Y_273,U_274,X_275] :
      ( ( Y_273 = U_274 )
      | ( X_275 = U_274 )
      | ~ member(U_274,unordered_pair(X_275,Y_273)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_1047,plain,
    ! [X_294,U_295] :
      ( ( X_294 = U_295 )
      | ( X_294 = U_295 )
      | ~ member(U_295,singleton(X_294)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_805]) ).

tff(c_1062,plain,
    y = x,
    inference(resolution,[status(thm)],[c_398,c_1047]) ).

tff(c_1083,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_188,c_188,c_1062]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET084-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.12  % 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
% 0.11/0.33  % Computer : n031.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Thu Aug  3 17:04:14 EDT 2023
% 0.11/0.34  % CPUTime  : 
% 5.46/2.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.46/2.35  
% 5.46/2.35  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.84/2.38  
% 5.84/2.38  Inference rules
% 5.84/2.38  ----------------------
% 5.84/2.38  #Ref     : 0
% 5.84/2.38  #Sup     : 207
% 5.84/2.38  #Fact    : 0
% 5.84/2.38  #Define  : 0
% 5.84/2.38  #Split   : 8
% 5.84/2.38  #Chain   : 0
% 5.84/2.38  #Close   : 0
% 5.84/2.38  
% 5.84/2.38  Ordering : KBO
% 5.84/2.38  
% 5.84/2.38  Simplification rules
% 5.84/2.38  ----------------------
% 5.84/2.38  #Subsume      : 23
% 5.84/2.38  #Demod        : 25
% 5.84/2.38  #Tautology    : 57
% 5.84/2.38  #SimpNegUnit  : 2
% 5.84/2.38  #BackRed      : 1
% 5.84/2.38  
% 5.84/2.38  #Partial instantiations: 0
% 5.84/2.38  #Strategies tried      : 1
% 5.84/2.38  
% 5.84/2.38  Timing (in seconds)
% 5.84/2.38  ----------------------
% 5.94/2.38  Preprocessing        : 0.72
% 5.94/2.38  Parsing              : 0.38
% 5.94/2.38  CNF conversion       : 0.05
% 5.94/2.38  Main loop            : 0.54
% 5.94/2.38  Inferencing          : 0.18
% 5.94/2.38  Reduction            : 0.17
% 5.94/2.38  Demodulation         : 0.12
% 5.94/2.38  BG Simplification    : 0.04
% 5.94/2.38  Subsumption          : 0.12
% 5.94/2.38  Abstraction          : 0.02
% 5.94/2.38  MUC search           : 0.00
% 5.94/2.38  Cooper               : 0.00
% 5.94/2.38  Total                : 1.31
% 5.94/2.38  Index Insertion      : 0.00
% 5.94/2.38  Index Deletion       : 0.00
% 5.94/2.38  Index Matching       : 0.00
% 5.94/2.38  BG Taut test         : 0.00
%------------------------------------------------------------------------------