TSTP Solution File: SET072+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET072+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 : n024.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 10:55:49 EDT 2023

% Result   : Theorem 5.44s 2.28s
% Output   : CNFRefutation 5.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   44
% Syntax   : Number of formulae    :   64 (  13 unt;  41 typ;   0 def)
%            Number of atoms       :   40 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   26 (   9   ~;  12   |;   3   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 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  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   36 (  36 usr;  10 con; 0-3 aty)
%            Number of variables   :   17 (;  17   !;   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_10 > #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('#skF_10',type,
    '#skF_10': $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_384,negated_conjecture,
    ~ ! [X,Y,Z] :
        ( ( member(X,universal_class)
          & member(Y,universal_class)
          & ( unordered_pair(X,Z) = unordered_pair(Y,Z) ) )
       => ( X = Y ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_cancellation) ).

tff(f_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

tff(f_87,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( ( U = X )
          | ( U = Y ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).

tff(c_180,plain,
    '#skF_9' != '#skF_8',
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_186,plain,
    member('#skF_8',universal_class),
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_26,plain,
    ! [X_14] : ( unordered_pair(X_14,X_14) = singleton(X_14) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_184,plain,
    member('#skF_9',universal_class),
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_182,plain,
    unordered_pair('#skF_9','#skF_10') = unordered_pair('#skF_8','#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_384]) ).

tff(c_343,plain,
    ! [X_135,Y_136] :
      ( member(X_135,unordered_pair(X_135,Y_136))
      | ~ member(X_135,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_349,plain,
    ( member('#skF_9',unordered_pair('#skF_8','#skF_10'))
    | ~ member('#skF_9',universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_182,c_343]) ).

tff(c_351,plain,
    member('#skF_9',unordered_pair('#skF_8','#skF_10')),
    inference(demodulation,[status(thm),theory(equality)],[c_184,c_349]) ).

tff(c_1090,plain,
    ! [Y_226,U_227,X_228] :
      ( ( Y_226 = U_227 )
      | ( X_228 = U_227 )
      | ~ member(U_227,unordered_pair(X_228,Y_226)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1108,plain,
    ( ( '#skF_10' = '#skF_9' )
    | ( '#skF_9' = '#skF_8' ) ),
    inference(resolution,[status(thm)],[c_351,c_1090]) ).

tff(c_1133,plain,
    '#skF_10' = '#skF_9',
    inference(negUnitSimplification,[status(thm)],[c_180,c_1108]) ).

tff(c_1139,plain,
    unordered_pair('#skF_9','#skF_9') = unordered_pair('#skF_8','#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_1133,c_1133,c_182]) ).

tff(c_1140,plain,
    unordered_pair('#skF_8','#skF_9') = singleton('#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_26,c_1139]) ).

tff(c_22,plain,
    ! [X_10,Y_11] :
      ( member(X_10,unordered_pair(X_10,Y_11))
      | ~ member(X_10,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_1176,plain,
    ( member('#skF_8',singleton('#skF_9'))
    | ~ member('#skF_8',universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_1140,c_22]) ).

tff(c_1184,plain,
    member('#skF_8',singleton('#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_186,c_1176]) ).

tff(c_1125,plain,
    ! [U_227] :
      ( ( U_227 = '#skF_10' )
      | ( U_227 = '#skF_9' )
      | ~ member(U_227,unordered_pair('#skF_8','#skF_10')) ),
    inference(superposition,[status(thm),theory(equality)],[c_182,c_1090]) ).

tff(c_1486,plain,
    ! [U_244] :
      ( ( U_244 = '#skF_9' )
      | ( U_244 = '#skF_9' )
      | ~ member(U_244,singleton('#skF_9')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1140,c_1133,c_1133,c_1125]) ).

tff(c_1489,plain,
    '#skF_9' = '#skF_8',
    inference(resolution,[status(thm)],[c_1184,c_1486]) ).

tff(c_1520,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_180,c_180,c_1489]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SET072+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.14  % 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 : n024.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 16:17:45 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 5.44/2.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.44/2.28  
% 5.44/2.28  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.44/2.31  
% 5.44/2.31  Inference rules
% 5.44/2.31  ----------------------
% 5.44/2.31  #Ref     : 0
% 5.44/2.31  #Sup     : 298
% 5.44/2.31  #Fact    : 0
% 5.44/2.31  #Define  : 0
% 5.44/2.31  #Split   : 7
% 5.44/2.31  #Chain   : 0
% 5.44/2.31  #Close   : 0
% 5.44/2.31  
% 5.44/2.31  Ordering : KBO
% 5.44/2.31  
% 5.44/2.31  Simplification rules
% 5.44/2.31  ----------------------
% 5.44/2.31  #Subsume      : 49
% 5.44/2.31  #Demod        : 41
% 5.44/2.31  #Tautology    : 59
% 5.44/2.31  #SimpNegUnit  : 3
% 5.44/2.31  #BackRed      : 3
% 5.44/2.31  
% 5.44/2.31  #Partial instantiations: 0
% 5.44/2.31  #Strategies tried      : 1
% 5.44/2.31  
% 5.44/2.31  Timing (in seconds)
% 5.44/2.31  ----------------------
% 5.44/2.31  Preprocessing        : 0.63
% 5.44/2.31  Parsing              : 0.32
% 5.44/2.31  CNF conversion       : 0.05
% 5.44/2.31  Main loop            : 0.57
% 5.44/2.31  Inferencing          : 0.20
% 5.44/2.31  Reduction            : 0.18
% 5.44/2.31  Demodulation         : 0.12
% 5.44/2.31  BG Simplification    : 0.04
% 5.44/2.31  Subsumption          : 0.12
% 5.44/2.31  Abstraction          : 0.02
% 5.44/2.31  MUC search           : 0.00
% 5.44/2.31  Cooper               : 0.00
% 5.44/2.31  Total                : 1.24
% 5.44/2.31  Index Insertion      : 0.00
% 5.44/2.31  Index Deletion       : 0.00
% 5.44/2.31  Index Matching       : 0.00
% 5.44/2.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------