TSTP Solution File: SET065+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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 : n002.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 10:55:47 EDT 2023

% Result   : Theorem 4.62s 2.25s
% Output   : CNFRefutation 4.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   52 (   7 unt;  38 typ;   0 def)
%            Number of atoms       :   27 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (   9   ~;   6   |;   3   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  31   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   33 (  33 usr;   7 con; 0-3 aty)
%            Number of variables   :   16 (;  15   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subclass > member > disjoint > inductive > function > restrict > unordered_pair > union > ordered_pair > intersection > image > cross_product > compose > apply > #nlpp > sum_class > successor > singleton > second > rotate > range_of > power_class > inverse > flip > first > domain_of > complement > universal_class > successor_relation > null_class > identity_relation > element_relation > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_1 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(null_class,type,
    null_class: $i ).

tff(rotate,type,
    rotate: $i > $i ).

tff('#skF_4',type,
    '#skF_4': $i > $i ).

tff(subclass,type,
    subclass: ( $i * $i ) > $o ).

tff(singleton,type,
    singleton: $i > $i ).

tff(sum_class,type,
    sum_class: $i > $i ).

tff(apply,type,
    apply: ( $i * $i ) > $i ).

tff(unordered_pair,type,
    unordered_pair: ( $i * $i ) > $i ).

tff(inverse,type,
    inverse: $i > $i ).

tff(ordered_pair,type,
    ordered_pair: ( $i * $i ) > $i ).

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('#skF_7',type,
    '#skF_7': $i ).

tff('#skF_3',type,
    '#skF_3': ( $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(restrict,type,
    restrict: ( $i * $i * $i ) > $i ).

tff(complement,type,
    complement: $i > $i ).

tff(member,type,
    member: ( $i * $i ) > $o ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff(disjoint,type,
    disjoint: ( $i * $i ) > $o ).

tff(first,type,
    first: $i > $i ).

tff(image,type,
    image: ( $i * $i ) > $i ).

tff(range_of,type,
    range_of: $i > $i ).

tff(inductive,type,
    inductive: $i > $o ).

tff(compose,type,
    compose: ( $i * $i ) > $i ).

tff(domain_of,type,
    domain_of: $i > $i ).

tff(successor,type,
    successor: $i > $i ).

tff(successor_relation,type,
    successor_relation: $i ).

tff('#skF_1',type,
    '#skF_1': ( $i * $i ) > $i ).

tff(identity_relation,type,
    identity_relation: $i ).

tff('#skF_5',type,
    '#skF_5': ( $i * $i ) > $i ).

tff('#skF_6',type,
    '#skF_6': $i > $i ).

tff(universal_class,type,
    universal_class: $i ).

tff(f_377,negated_conjecture,
    ~ member(null_class,universal_class),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',null_class_is_a_set) ).

tff(f_70,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',class_elements_are_sets) ).

tff(f_252,axiom,
    ! [X] :
      ( inductive(X)
    <=> ( member(null_class,X)
        & subclass(image(successor_relation,X),X) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',inductive_defn) ).

tff(f_67,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',subclass_defn) ).

tff(f_262,axiom,
    ? [X] :
      ( member(X,universal_class)
      & inductive(X)
      & ! [Y] :
          ( inductive(Y)
         => subclass(X,Y) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',infinity) ).

tff(c_180,plain,
    ~ member(null_class,universal_class),
    inference(cnfTransformation,[status(thm)],[f_377]) ).

tff(c_8,plain,
    ! [X_6] : subclass(X_6,universal_class),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_116,plain,
    ! [X_59] :
      ( member(null_class,X_59)
      | ~ inductive(X_59) ),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_943,plain,
    ! [U_212,Y_213,X_214] :
      ( member(U_212,Y_213)
      | ~ member(U_212,X_214)
      | ~ subclass(X_214,Y_213) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_1337,plain,
    ! [Y_238,X_239] :
      ( member(null_class,Y_238)
      | ~ subclass(X_239,Y_238)
      | ~ inductive(X_239) ),
    inference(resolution,[status(thm)],[c_116,c_943]) ).

tff(c_1373,plain,
    ! [X_6] :
      ( member(null_class,universal_class)
      | ~ inductive(X_6) ),
    inference(resolution,[status(thm)],[c_8,c_1337]) ).

tff(c_1392,plain,
    ! [X_6] : ~ inductive(X_6),
    inference(negUnitSimplification,[status(thm)],[c_180,c_1373]) ).

tff(c_120,plain,
    inductive('#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_262]) ).

tff(c_1395,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1392,c_120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET065+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 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
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 17:06:01 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 4.62/2.25  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.62/2.25  
% 4.62/2.25  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.62/2.28  
% 4.62/2.28  Inference rules
% 4.62/2.28  ----------------------
% 4.62/2.28  #Ref     : 0
% 4.62/2.28  #Sup     : 263
% 4.62/2.28  #Fact    : 0
% 4.62/2.28  #Define  : 0
% 4.62/2.28  #Split   : 2
% 4.62/2.28  #Chain   : 0
% 4.62/2.28  #Close   : 0
% 4.62/2.28  
% 4.62/2.28  Ordering : KBO
% 4.62/2.28  
% 4.62/2.28  Simplification rules
% 4.62/2.28  ----------------------
% 4.62/2.28  #Subsume      : 58
% 4.62/2.28  #Demod        : 24
% 4.62/2.28  #Tautology    : 47
% 4.62/2.28  #SimpNegUnit  : 10
% 4.62/2.28  #BackRed      : 1
% 4.62/2.28  
% 4.62/2.28  #Partial instantiations: 0
% 4.62/2.28  #Strategies tried      : 1
% 4.62/2.28  
% 4.62/2.28  Timing (in seconds)
% 4.62/2.28  ----------------------
% 4.62/2.28  Preprocessing        : 0.65
% 4.62/2.28  Parsing              : 0.33
% 4.62/2.28  CNF conversion       : 0.05
% 4.62/2.28  Main loop            : 0.56
% 4.62/2.28  Inferencing          : 0.19
% 4.62/2.28  Reduction            : 0.16
% 4.62/2.28  Demodulation         : 0.11
% 4.62/2.28  BG Simplification    : 0.04
% 4.62/2.28  Subsumption          : 0.12
% 4.62/2.28  Abstraction          : 0.02
% 4.62/2.28  MUC search           : 0.00
% 4.62/2.28  Cooper               : 0.00
% 4.62/2.28  Total                : 1.25
% 4.62/2.28  Index Insertion      : 0.00
% 4.62/2.28  Index Deletion       : 0.00
% 4.62/2.28  Index Matching       : 0.00
% 4.62/2.28  BG Taut test         : 0.00
%------------------------------------------------------------------------------