TSTP Solution File: SET366+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 10:56:23 EDT 2023

% Result   : Theorem 3.30s 1.77s
% Output   : CNFRefutation 3.46s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   27 (   7 unt;  16 typ;   0 def)
%            Number of atoms       :   16 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   6   ~;   2   |;   0   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   24 (  14   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   13 (;  13   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(equal_set,type,
    equal_set: ( $i * $i ) > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_56,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',subset) ).

tff(f_81,axiom,
    ! [X] : ~ member(X,empty_set),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',empty_set) ).

tff(f_66,axiom,
    ! [X,A] :
      ( member(X,power_set(A))
    <=> subset(X,A) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',power_set) ).

tff(f_117,negated_conjecture,
    ~ ! [A] : member(empty_set,power_set(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI47) ).

tff(c_111,plain,
    ! [A_65,B_66] :
      ( member('#skF_1'(A_65,B_66),A_65)
      | subset(A_65,B_66) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_30,plain,
    ! [X_16] : ~ member(X_16,empty_set),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_141,plain,
    ! [B_66] : subset(empty_set,B_66),
    inference(resolution,[status(thm)],[c_111,c_30]) ).

tff(c_74,plain,
    ! [X_49,A_50] :
      ( member(X_49,power_set(A_50))
      | ~ subset(X_49,A_50) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_60,plain,
    ~ member(empty_set,power_set('#skF_4')),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_82,plain,
    ~ subset(empty_set,'#skF_4'),
    inference(resolution,[status(thm)],[c_74,c_60]) ).

tff(c_151,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_141,c_82]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET366+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % 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
% 0.17/0.34  % Computer : n022.cluster.edu
% 0.17/0.34  % Model    : x86_64 x86_64
% 0.17/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34  % Memory   : 8042.1875MB
% 0.17/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34  % CPULimit : 300
% 0.17/0.34  % WCLimit  : 300
% 0.17/0.34  % DateTime : Thu Aug  3 16:50:48 EDT 2023
% 0.17/0.35  % CPUTime  : 
% 3.30/1.77  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.30/1.77  
% 3.30/1.77  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.46/1.80  
% 3.46/1.80  Inference rules
% 3.46/1.80  ----------------------
% 3.46/1.80  #Ref     : 0
% 3.46/1.80  #Sup     : 15
% 3.46/1.80  #Fact    : 0
% 3.46/1.80  #Define  : 0
% 3.46/1.80  #Split   : 0
% 3.46/1.80  #Chain   : 0
% 3.46/1.80  #Close   : 0
% 3.46/1.80  
% 3.46/1.80  Ordering : KBO
% 3.46/1.80  
% 3.46/1.80  Simplification rules
% 3.46/1.80  ----------------------
% 3.46/1.80  #Subsume      : 0
% 3.46/1.80  #Demod        : 1
% 3.46/1.80  #Tautology    : 2
% 3.46/1.80  #SimpNegUnit  : 0
% 3.46/1.80  #BackRed      : 1
% 3.46/1.80  
% 3.46/1.80  #Partial instantiations: 0
% 3.46/1.80  #Strategies tried      : 1
% 3.46/1.80  
% 3.46/1.80  Timing (in seconds)
% 3.46/1.80  ----------------------
% 3.46/1.80  Preprocessing        : 0.50
% 3.46/1.80  Parsing              : 0.26
% 3.46/1.80  CNF conversion       : 0.04
% 3.46/1.80  Main loop            : 0.25
% 3.46/1.80  Inferencing          : 0.09
% 3.46/1.80  Reduction            : 0.07
% 3.46/1.80  Demodulation         : 0.05
% 3.46/1.80  BG Simplification    : 0.02
% 3.46/1.80  Subsumption          : 0.06
% 3.46/1.80  Abstraction          : 0.01
% 3.46/1.80  MUC search           : 0.00
% 3.46/1.80  Cooper               : 0.00
% 3.46/1.80  Total                : 0.79
% 3.46/1.80  Index Insertion      : 0.00
% 3.46/1.80  Index Deletion       : 0.00
% 3.46/1.80  Index Matching       : 0.00
% 3.46/1.80  BG Taut test         : 0.00
%------------------------------------------------------------------------------