TSTP Solution File: SET103+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET103+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 : n029.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   : Theorem 8.42s 3.00s
% Output   : CNFRefutation 8.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   46
% Syntax   : Number of formulae    :   66 (  13 unt;  40 typ;   0 def)
%            Number of atoms       :   49 (  25 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   33 (  10   ~;  19   |;   2   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   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    :   35 (  35 usr;   9 con; 0-3 aty)
%            Number of variables   :   36 (;  35   !;   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_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_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',singleton_set_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_372,axiom,
    ? [XF] :
      ( function(XF)
      & ! [Y] :
          ( member(Y,universal_class)
         => ( ( Y = null_class )
            | member(apply(XF,Y),Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',choice) ).

tff(f_87,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( ( U = X )
          | ( U = Y ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET005+0.ax',unordered_pair_defn) ).

tff(f_380,negated_conjecture,
    ~ ! [X,Y] :
        ( ( unordered_pair(singleton(X),unordered_pair(X,null_class)) = ordered_pair(X,Y) )
        | member(Y,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',property_1_of_ordered_pair) ).

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(c_188,plain,
    ! [X_100] : ( unordered_pair(X_100,X_100) = singleton(X_100) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

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_193,plain,
    ! [X_100] : member(singleton(X_100),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_188,c_24]) ).

tff(c_176,plain,
    ! [Y_94] :
      ( member(apply('#skF_7',Y_94),Y_94)
      | ( null_class = Y_94 )
      | ~ member(Y_94,universal_class) ),
    inference(cnfTransformation,[status(thm)],[f_372]) ).

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

tff(c_1864,plain,
    ! [Y_259,U_260,X_261] :
      ( ( Y_259 = U_260 )
      | ( X_261 = U_260 )
      | ~ member(U_260,unordered_pair(X_261,Y_259)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_3625,plain,
    ! [X_380,U_381] :
      ( ( X_380 = U_381 )
      | ( X_380 = U_381 )
      | ~ member(U_381,singleton(X_380)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_1864]) ).

tff(c_3629,plain,
    ! [X_380] :
      ( ( apply('#skF_7',singleton(X_380)) = X_380 )
      | ( singleton(X_380) = null_class )
      | ~ member(singleton(X_380),universal_class) ),
    inference(resolution,[status(thm)],[c_176,c_3625]) ).

tff(c_4607,plain,
    ! [X_458] :
      ( ( apply('#skF_7',singleton(X_458)) = X_458 )
      | ( singleton(X_458) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_193,c_3629]) ).

tff(c_4613,plain,
    ! [X_458] :
      ( member(X_458,singleton(X_458))
      | ( singleton(X_458) = null_class )
      | ~ member(singleton(X_458),universal_class)
      | ( singleton(X_458) = null_class ) ),
    inference(superposition,[status(thm),theory(equality)],[c_4607,c_176]) ).

tff(c_4885,plain,
    ! [X_462] :
      ( member(X_462,singleton(X_462))
      | ( singleton(X_462) = null_class ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_193,c_4613]) ).

tff(c_587,plain,
    ! [U_184,X_185,Y_186] :
      ( member(U_184,universal_class)
      | ~ member(U_184,unordered_pair(X_185,Y_186)) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_615,plain,
    ! [U_184,X_14] :
      ( member(U_184,universal_class)
      | ~ member(U_184,singleton(X_14)) ),
    inference(superposition,[status(thm),theory(equality)],[c_26,c_587]) ).

tff(c_4951,plain,
    ! [X_463] :
      ( member(X_463,universal_class)
      | ( singleton(X_463) = null_class ) ),
    inference(resolution,[status(thm)],[c_4885,c_615]) ).

tff(c_180,plain,
    ~ member('#skF_9',universal_class),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_5015,plain,
    singleton('#skF_9') = null_class,
    inference(resolution,[status(thm)],[c_4951,c_180]) ).

tff(c_28,plain,
    ! [X_15,Y_16] : ( unordered_pair(singleton(X_15),unordered_pair(X_15,singleton(Y_16))) = ordered_pair(X_15,Y_16) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_5055,plain,
    ! [X_15] : ( unordered_pair(singleton(X_15),unordered_pair(X_15,null_class)) = ordered_pair(X_15,'#skF_9') ),
    inference(superposition,[status(thm),theory(equality)],[c_5015,c_28]) ).

tff(c_182,plain,
    unordered_pair(singleton('#skF_8'),unordered_pair('#skF_8',null_class)) != ordered_pair('#skF_8','#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_5614,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_5055,c_182]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET103+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
% 0.14/0.35  % Computer : n029.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 16:56:07 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 8.42/3.00  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.42/3.01  
% 8.42/3.01  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.76/3.04  
% 8.76/3.04  Inference rules
% 8.76/3.04  ----------------------
% 8.76/3.04  #Ref     : 0
% 8.76/3.04  #Sup     : 1173
% 8.76/3.04  #Fact    : 0
% 8.76/3.04  #Define  : 0
% 8.76/3.04  #Split   : 24
% 8.76/3.04  #Chain   : 0
% 8.76/3.04  #Close   : 0
% 8.76/3.04  
% 8.76/3.04  Ordering : KBO
% 8.76/3.04  
% 8.76/3.04  Simplification rules
% 8.76/3.04  ----------------------
% 8.76/3.04  #Subsume      : 250
% 8.76/3.04  #Demod        : 332
% 8.76/3.04  #Tautology    : 169
% 8.76/3.04  #SimpNegUnit  : 24
% 8.76/3.04  #BackRed      : 119
% 8.76/3.04  
% 8.76/3.04  #Partial instantiations: 0
% 8.76/3.04  #Strategies tried      : 1
% 8.76/3.04  
% 8.76/3.04  Timing (in seconds)
% 8.76/3.04  ----------------------
% 8.76/3.04  Preprocessing        : 0.66
% 8.76/3.04  Parsing              : 0.33
% 8.76/3.04  CNF conversion       : 0.05
% 8.76/3.04  Main loop            : 1.34
% 8.76/3.04  Inferencing          : 0.44
% 8.76/3.04  Reduction            : 0.43
% 8.76/3.04  Demodulation         : 0.27
% 8.76/3.04  BG Simplification    : 0.05
% 8.76/3.04  Subsumption          : 0.30
% 8.76/3.04  Abstraction          : 0.05
% 8.76/3.04  MUC search           : 0.00
% 8.76/3.04  Cooper               : 0.00
% 8.76/3.04  Total                : 2.04
% 8.76/3.04  Index Insertion      : 0.00
% 8.76/3.04  Index Deletion       : 0.00
% 8.76/3.04  Index Matching       : 0.00
% 8.76/3.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------