TSTP Solution File: SET025+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET025+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/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 : n014.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 10:55:36 EDT 2023

% Result   : Theorem 6.02s 2.39s
% Output   : CNFRefutation 6.02s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   43
% Syntax   : Number of formulae    :   48 (   8 unt;  40 typ;   0 def)
%            Number of atoms       :    8 (   2 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   3 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   47 (  31   >;  16   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :   12 (;  12   !;   0   ?;   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_9 > #skF_8 > #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('#skF_9',type,
    '#skF_9': $i ).

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

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

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

tff('#skF_8',type,
    '#skF_8': $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_103,axiom,
    ! [X,Y] : ( ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).

tff(f_97,axiom,
    ! [X,Y] : member(unordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair) ).

tff(f_378,negated_conjecture,
    ~ ! [X,Y] : member(ordered_pair(X,Y),universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ordered_pair_is_set) ).

tff(c_2048,plain,
    ! [X_295,Y_296] : ( unordered_pair(singleton(X_295),unordered_pair(X_295,singleton(Y_296))) = ordered_pair(X_295,Y_296) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_24,plain,
    ! [X_12,Y_13] : member(unordered_pair(X_12,Y_13),universal_class),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_2078,plain,
    ! [X_295,Y_296] : member(ordered_pair(X_295,Y_296),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_2048,c_24]) ).

tff(c_180,plain,
    ~ member(ordered_pair('#skF_8','#skF_9'),universal_class),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_2097,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2078,c_180]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET025+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13  % 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 : n014.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 16:59:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.02/2.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.02/2.39  
% 6.02/2.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.02/2.42  
% 6.02/2.42  Inference rules
% 6.02/2.42  ----------------------
% 6.02/2.42  #Ref     : 0
% 6.02/2.42  #Sup     : 427
% 6.02/2.42  #Fact    : 0
% 6.02/2.42  #Define  : 0
% 6.02/2.42  #Split   : 10
% 6.02/2.42  #Chain   : 0
% 6.02/2.42  #Close   : 0
% 6.02/2.42  
% 6.02/2.42  Ordering : KBO
% 6.02/2.42  
% 6.02/2.42  Simplification rules
% 6.02/2.42  ----------------------
% 6.02/2.42  #Subsume      : 87
% 6.02/2.42  #Demod        : 54
% 6.02/2.42  #Tautology    : 64
% 6.02/2.42  #SimpNegUnit  : 2
% 6.02/2.42  #BackRed      : 3
% 6.02/2.42  
% 6.02/2.42  #Partial instantiations: 0
% 6.02/2.42  #Strategies tried      : 1
% 6.02/2.42  
% 6.02/2.42  Timing (in seconds)
% 6.02/2.42  ----------------------
% 6.02/2.42  Preprocessing        : 0.66
% 6.02/2.42  Parsing              : 0.33
% 6.02/2.42  CNF conversion       : 0.05
% 6.02/2.42  Main loop            : 0.71
% 6.02/2.42  Inferencing          : 0.27
% 6.02/2.42  Reduction            : 0.20
% 6.02/2.42  Demodulation         : 0.14
% 6.02/2.42  BG Simplification    : 0.04
% 6.02/2.42  Subsumption          : 0.15
% 6.02/2.42  Abstraction          : 0.03
% 6.02/2.42  MUC search           : 0.00
% 6.02/2.42  Cooper               : 0.00
% 6.02/2.42  Total                : 1.41
% 6.02/2.42  Index Insertion      : 0.00
% 6.02/2.42  Index Deletion       : 0.00
% 6.02/2.42  Index Matching       : 0.00
% 6.02/2.42  BG Taut test         : 0.00
%------------------------------------------------------------------------------