TSTP Solution File: SET103-6 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET103-6 : 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 : n020.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 10:55:59 EDT 2023

% Result   : Unsatisfiable 14.50s 4.83s
% Output   : CNFRefutation 14.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   83 (  18 unt;  49 typ;   0 def)
%            Number of atoms       :   60 (  24 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   47 (  21   ~;  26   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    4 (   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   :   42 (;  42   !;   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_482,axiom,
    function(choice),
    file(unknown,unknown) ).

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

tff(f_119,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file(unknown,unknown) ).

tff(f_489,axiom,
    ! [Y] :
      ( ~ member(Y,universal_class)
      | ( Y = null_class )
      | member(apply(choice,Y),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(f_464,axiom,
    ! [Xf,X] :
      ( ~ function(Xf)
      | ~ member(X,universal_class)
      | member(image(Xf,X),universal_class) ),
    file(unknown,unknown) ).

tff(f_478,axiom,
    ! [Xf,Y] : ( sum_class(image(Xf,singleton(Y))) = apply(Xf,Y) ),
    file(unknown,unknown) ).

tff(f_390,axiom,
    ! [X] :
      ( ~ member(X,universal_class)
      | member(sum_class(X),universal_class) ),
    file(unknown,unknown) ).

tff(f_647,axiom,
    ~ member(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_645,axiom,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    file(unknown,unknown) ).

tff(c_138,plain,
    function(choice),
    inference(cnfTransformation,[status(thm)],[f_482]) ).

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

tff(c_216,plain,
    ! [X_183,Y_184] : member(unordered_pair(X_183,Y_184),universal_class),
    inference(cnfTransformation,[status(thm)],[f_119]) ).

tff(c_218,plain,
    ! [X_24] : member(singleton(X_24),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_216]) ).

tff(c_1035,plain,
    ! [Y_310] :
      ( member(apply(choice,Y_310),Y_310)
      | ( null_class = Y_310 )
      | ~ member(Y_310,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_489]) ).

tff(c_625,plain,
    ! [Y_271,U_272,X_273] :
      ( ( Y_271 = U_272 )
      | ( X_273 = U_272 )
      | ~ member(U_272,unordered_pair(X_273,Y_271)) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_646,plain,
    ! [X_24,U_272] :
      ( ( X_24 = U_272 )
      | ( X_24 = U_272 )
      | ~ member(U_272,singleton(X_24)) ),
    inference(superposition,[status(thm),theory(equality)],[c_24,c_625]) ).

tff(c_1039,plain,
    ! [X_24] :
      ( ( apply(choice,singleton(X_24)) = X_24 )
      | ( singleton(X_24) = null_class )
      | ~ member(singleton(X_24),universal_class) ),
    inference(resolution,[status(thm)],[c_1035,c_646]) ).

tff(c_1063,plain,
    ! [X_24] :
      ( ( apply(choice,singleton(X_24)) = X_24 )
      | ( singleton(X_24) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_1039]) ).

tff(c_130,plain,
    ! [Xf_129,X_130] :
      ( member(image(Xf_129,X_130),universal_class)
      | ~ member(X_130,universal_class)
      | ~ function(Xf_129) ),
    inference(cnfTransformation,[status(thm)],[f_464]) ).

tff(c_491,plain,
    ! [Xf_243,Y_244] : ( sum_class(image(Xf_243,singleton(Y_244))) = apply(Xf_243,Y_244) ),
    inference(cnfTransformation,[status(thm)],[f_478]) ).

tff(c_108,plain,
    ! [X_111] :
      ( member(sum_class(X_111),universal_class)
      | ~ member(X_111,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_390]) ).

tff(c_11954,plain,
    ! [Xf_835,Y_836] :
      ( member(apply(Xf_835,Y_836),universal_class)
      | ~ member(image(Xf_835,singleton(Y_836)),universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_491,c_108]) ).

tff(c_11968,plain,
    ! [Xf_129,Y_836] :
      ( member(apply(Xf_129,Y_836),universal_class)
      | ~ member(singleton(Y_836),universal_class)
      | ~ function(Xf_129) ),
    inference(resolution,[status(thm)],[c_130,c_11954]) ).

tff(c_11987,plain,
    ! [Xf_838,Y_839] :
      ( member(apply(Xf_838,Y_839),universal_class)
      | ~ function(Xf_838) ),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_11968]) ).

tff(c_12004,plain,
    ! [X_24] :
      ( member(X_24,universal_class)
      | ~ function(choice)
      | ( singleton(X_24) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1063,c_11987]) ).

tff(c_12009,plain,
    ! [X_840] :
      ( member(X_840,universal_class)
      | ( singleton(X_840) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_138,c_12004]) ).

tff(c_186,plain,
    ~ member(y,universal_class),
    inference(cnfTransformation,[status(thm)],[f_647]) ).

tff(c_12061,plain,
    singleton(y) = null_class,
    inference(resolution,[status(thm)],[c_12009,c_186]) ).

tff(c_26,plain,
    ! [X_25,Y_26] : ( unordered_pair(singleton(X_25),unordered_pair(X_25,singleton(Y_26))) = ordered_pair(X_25,Y_26) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_12122,plain,
    ! [X_25] : ( unordered_pair(singleton(X_25),unordered_pair(X_25,null_class)) = ordered_pair(X_25,y) ),
    inference(superposition,[status(thm),theory(equality)],[c_12061,c_26]) ).

tff(c_184,plain,
    unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,y),
    inference(cnfTransformation,[status(thm)],[f_645]) ).

tff(c_12831,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12122,c_184]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET103-6 : TPTP v8.1.2. Bugfixed v2.1.0.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/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 : n020.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 16:21:52 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 14.50/4.83  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.50/4.84  
% 14.50/4.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.50/4.87  
% 14.50/4.87  Inference rules
% 14.50/4.87  ----------------------
% 14.50/4.87  #Ref     : 0
% 14.50/4.87  #Sup     : 3189
% 14.50/4.87  #Fact    : 0
% 14.50/4.87  #Define  : 0
% 14.50/4.87  #Split   : 85
% 14.50/4.87  #Chain   : 0
% 14.50/4.87  #Close   : 0
% 14.50/4.87  
% 14.50/4.87  Ordering : KBO
% 14.50/4.87  
% 14.50/4.87  Simplification rules
% 14.50/4.87  ----------------------
% 14.50/4.87  #Subsume      : 811
% 14.50/4.87  #Demod        : 803
% 14.50/4.87  #Tautology    : 484
% 14.50/4.87  #SimpNegUnit  : 42
% 14.50/4.87  #BackRed      : 101
% 14.50/4.87  
% 14.50/4.87  #Partial instantiations: 0
% 14.50/4.87  #Strategies tried      : 1
% 14.50/4.87  
% 14.50/4.87  Timing (in seconds)
% 14.50/4.87  ----------------------
% 14.50/4.88  Preprocessing        : 0.72
% 14.50/4.88  Parsing              : 0.38
% 14.50/4.88  CNF conversion       : 0.05
% 14.50/4.88  Main loop            : 3.09
% 14.50/4.88  Inferencing          : 0.88
% 14.50/4.88  Reduction            : 1.15
% 14.50/4.88  Demodulation         : 0.77
% 14.50/4.88  BG Simplification    : 0.08
% 14.50/4.88  Subsumption          : 0.72
% 14.50/4.88  Abstraction          : 0.07
% 14.50/4.88  MUC search           : 0.00
% 14.50/4.88  Cooper               : 0.00
% 14.50/4.88  Total                : 3.86
% 14.50/4.88  Index Insertion      : 0.00
% 14.50/4.88  Index Deletion       : 0.00
% 14.50/4.88  Index Matching       : 0.00
% 14.50/4.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------