TSTP Solution File: SET101+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET101+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 10:55:58 EDT 2023

% Result   : Theorem 6.35s 2.74s
% Output   : CNFRefutation 7.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   45
% Syntax   : Number of formulae    :   54 (  11 unt;  40 typ;   0 def)
%            Number of atoms       :   19 (   6 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :    9 (   4   ~;   3   |;   1   &)
%                                         (   1 <=>;   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  :   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   :   22 (;  22   !;   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_100,axiom,
    ! [X] : ( singleton(X) = unordered_pair(X,X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).

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

tff(f_103,axiom,
    ! [X,Y] : ( ordered_pair(X,Y) = unordered_pair(singleton(X),unordered_pair(X,singleton(Y))) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_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(f_378,negated_conjecture,
    ~ ! [X,Y] : member(singleton(X),ordered_pair(X,Y)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_member_of_ordered_pair) ).

tff(c_187,plain,
    ! [X_101] : ( unordered_pair(X_101,X_101) = singleton(X_101) ),
    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_192,plain,
    ! [X_101] : member(singleton(X_101),universal_class),
    inference(superposition,[status(thm),theory(equality)],[c_187,c_24]) ).

tff(c_3582,plain,
    ! [X_348,Y_349] : ( unordered_pair(singleton(X_348),unordered_pair(X_348,singleton(Y_349))) = ordered_pair(X_348,Y_349) ),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

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_3595,plain,
    ! [X_348,Y_349] :
      ( member(singleton(X_348),ordered_pair(X_348,Y_349))
      | ~ member(singleton(X_348),universal_class) ),
    inference(superposition,[status(thm),theory(equality)],[c_3582,c_22]) ).

tff(c_3614,plain,
    ! [X_348,Y_349] : member(singleton(X_348),ordered_pair(X_348,Y_349)),
    inference(demodulation,[status(thm),theory(equality)],[c_192,c_3595]) ).

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

tff(c_3721,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_3614,c_180]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.15  % Problem  : SET101+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.16  % 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
% 0.16/0.39  % Computer : n024.cluster.edu
% 0.16/0.39  % Model    : x86_64 x86_64
% 0.16/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.39  % Memory   : 8042.1875MB
% 0.16/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.39  % CPULimit : 300
% 0.16/0.39  % WCLimit  : 300
% 0.16/0.39  % DateTime : Thu Aug  3 17:00:00 EDT 2023
% 0.16/0.39  % CPUTime  : 
% 6.35/2.74  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.35/2.74  
% 6.35/2.74  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.03/2.77  
% 7.03/2.77  Inference rules
% 7.03/2.77  ----------------------
% 7.03/2.77  #Ref     : 0
% 7.03/2.77  #Sup     : 782
% 7.03/2.77  #Fact    : 0
% 7.03/2.77  #Define  : 0
% 7.03/2.77  #Split   : 17
% 7.03/2.77  #Chain   : 0
% 7.03/2.77  #Close   : 0
% 7.03/2.77  
% 7.03/2.77  Ordering : KBO
% 7.03/2.77  
% 7.03/2.77  Simplification rules
% 7.03/2.77  ----------------------
% 7.03/2.77  #Subsume      : 121
% 7.03/2.77  #Demod        : 130
% 7.03/2.77  #Tautology    : 127
% 7.03/2.77  #SimpNegUnit  : 8
% 7.03/2.77  #BackRed      : 4
% 7.03/2.77  
% 7.03/2.77  #Partial instantiations: 0
% 7.03/2.77  #Strategies tried      : 1
% 7.03/2.77  
% 7.03/2.77  Timing (in seconds)
% 7.03/2.77  ----------------------
% 7.03/2.77  Preprocessing        : 0.65
% 7.03/2.77  Parsing              : 0.34
% 7.03/2.77  CNF conversion       : 0.05
% 7.03/2.77  Main loop            : 0.92
% 7.03/2.77  Inferencing          : 0.32
% 7.03/2.77  Reduction            : 0.27
% 7.03/2.77  Demodulation         : 0.18
% 7.03/2.77  BG Simplification    : 0.05
% 7.03/2.77  Subsumption          : 0.21
% 7.03/2.77  Abstraction          : 0.04
% 7.03/2.77  MUC search           : 0.00
% 7.03/2.77  Cooper               : 0.00
% 7.03/2.77  Total                : 1.62
% 7.03/2.77  Index Insertion      : 0.00
% 7.03/2.77  Index Deletion       : 0.00
% 7.03/2.77  Index Matching       : 0.00
% 7.03/2.77  BG Taut test         : 0.00
%------------------------------------------------------------------------------