TSTP Solution File: SET063+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET063+3 : 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/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 : n006.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 10:55:46 EDT 2023

% Result   : Theorem 2.79s 1.64s
% Output   : CNFRefutation 2.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   17 (   6 unt;   7 typ;   0 def)
%            Number of atoms       :   16 (   6 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   11 (   5   ~;   3   |;   1   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :    7 (;   7   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > empty > #nlpp > empty_set > #skF_2 > #skF_3 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

tff(empty,type,
    empty: $i > $o ).

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

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

tff(f_64,negated_conjecture,
    ~ ! [B] :
        ( subset(B,empty_set)
       => ( B = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_subset_of_empty_set_is_empty_set) ).

tff(f_29,axiom,
    ! [B] : subset(empty_set,B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_subset) ).

tff(f_48,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

tff(c_24,plain,
    empty_set != '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_2,plain,
    ! [B_1] : subset(empty_set,B_1),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_26,plain,
    subset('#skF_3',empty_set),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_54,plain,
    ! [C_23,B_24] :
      ( ( C_23 = B_24 )
      | ~ subset(C_23,B_24)
      | ~ subset(B_24,C_23) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_58,plain,
    ( ( empty_set = '#skF_3' )
    | ~ subset(empty_set,'#skF_3') ),
    inference(resolution,[status(thm)],[c_26,c_54]) ).

tff(c_67,plain,
    empty_set = '#skF_3',
    inference(demodulation,[status(thm),theory(equality)],[c_2,c_58]) ).

tff(c_69,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_24,c_67]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET063+3 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % 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 : n006.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 16:42:43 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 2.79/1.64  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.79/1.64  
% 2.79/1.64  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.79/1.67  
% 2.79/1.67  Inference rules
% 2.79/1.67  ----------------------
% 2.79/1.67  #Ref     : 0
% 2.79/1.67  #Sup     : 7
% 2.79/1.67  #Fact    : 0
% 2.79/1.67  #Define  : 0
% 2.79/1.67  #Split   : 0
% 2.79/1.67  #Chain   : 0
% 2.79/1.67  #Close   : 0
% 2.79/1.67  
% 2.79/1.67  Ordering : KBO
% 2.79/1.67  
% 2.79/1.67  Simplification rules
% 2.79/1.67  ----------------------
% 2.79/1.67  #Subsume      : 0
% 2.79/1.67  #Demod        : 5
% 2.79/1.67  #Tautology    : 5
% 2.79/1.67  #SimpNegUnit  : 1
% 2.79/1.67  #BackRed      : 0
% 2.79/1.67  
% 2.79/1.67  #Partial instantiations: 0
% 2.79/1.67  #Strategies tried      : 1
% 2.79/1.67  
% 2.79/1.67  Timing (in seconds)
% 2.79/1.67  ----------------------
% 2.79/1.67  Preprocessing        : 0.46
% 2.79/1.67  Parsing              : 0.24
% 2.79/1.67  CNF conversion       : 0.03
% 2.79/1.67  Main loop            : 0.15
% 2.79/1.67  Inferencing          : 0.06
% 2.79/1.67  Reduction            : 0.04
% 2.79/1.67  Demodulation         : 0.03
% 2.79/1.67  BG Simplification    : 0.01
% 2.79/1.67  Subsumption          : 0.03
% 2.79/1.67  Abstraction          : 0.01
% 2.79/1.67  MUC search           : 0.00
% 2.79/1.67  Cooper               : 0.00
% 2.79/1.67  Total                : 0.65
% 2.79/1.67  Index Insertion      : 0.00
% 2.79/1.67  Index Deletion       : 0.00
% 2.79/1.67  Index Matching       : 0.00
% 2.79/1.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------