TSTP Solution File: SEU148+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 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 : n013.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 10:57:46 EDT 2023

% Result   : Theorem 2.70s 1.78s
% Output   : CNFRefutation 3.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   26 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :   24 (  15 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   15 (   6   ~;   5   |;   0   &)
%                                         (   3 <=>;   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  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   14 (;  14   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > #nlpp > singleton > empty_set > #skF_5 > #skF_6 > #skF_3 > #skF_4 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(singleton,type,
    singleton: $i > $i ).

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

tff('#skF_5',type,
    '#skF_5': $i ).

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

tff('#skF_6',type,
    '#skF_6': $i ).

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

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

tff(f_60,negated_conjecture,
    ~ ! [A,B] :
        ( subset(singleton(A),singleton(B))
       => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).

tff(f_42,axiom,
    ! [A] : ( singleton(A) != empty_set ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_zfmisc_1) ).

tff(f_48,axiom,
    ! [A,B] :
      ( subset(A,singleton(B))
    <=> ( ( A = empty_set )
        | ( A = singleton(B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l4_zfmisc_1) ).

tff(f_38,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(c_32,plain,
    '#skF_5' != '#skF_6',
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_18,plain,
    ! [A_8] : ( singleton(A_8) != empty_set ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_34,plain,
    subset(singleton('#skF_5'),singleton('#skF_6')),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_51,plain,
    ! [B_22,A_23] :
      ( ( singleton(B_22) = A_23 )
      | ( empty_set = A_23 )
      | ~ subset(A_23,singleton(B_22)) ),
    inference(cnfTransformation,[status(thm)],[f_48]) ).

tff(c_54,plain,
    ( ( singleton('#skF_5') = singleton('#skF_6') )
    | ( singleton('#skF_5') = empty_set ) ),
    inference(resolution,[status(thm)],[c_34,c_51]) ).

tff(c_64,plain,
    singleton('#skF_5') = singleton('#skF_6'),
    inference(negUnitSimplification,[status(thm)],[c_18,c_54]) ).

tff(c_6,plain,
    ! [C_7] : in(C_7,singleton(C_7)),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_89,plain,
    in('#skF_5',singleton('#skF_6')),
    inference(superposition,[status(thm),theory(equality)],[c_64,c_6]) ).

tff(c_4,plain,
    ! [C_7,A_3] :
      ( ( C_7 = A_3 )
      | ~ in(C_7,singleton(A_3)) ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_102,plain,
    '#skF_5' = '#skF_6',
    inference(resolution,[status(thm)],[c_89,c_4]) ).

tff(c_107,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_102]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU148+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 11:41:32 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 2.70/1.78  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.70/1.79  
% 2.70/1.79  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.04/1.81  
% 3.04/1.81  Inference rules
% 3.04/1.81  ----------------------
% 3.04/1.81  #Ref     : 0
% 3.04/1.81  #Sup     : 15
% 3.04/1.81  #Fact    : 0
% 3.04/1.81  #Define  : 0
% 3.04/1.81  #Split   : 0
% 3.04/1.81  #Chain   : 0
% 3.04/1.81  #Close   : 0
% 3.04/1.81  
% 3.04/1.81  Ordering : KBO
% 3.04/1.81  
% 3.04/1.81  Simplification rules
% 3.04/1.81  ----------------------
% 3.04/1.81  #Subsume      : 3
% 3.04/1.81  #Demod        : 5
% 3.04/1.81  #Tautology    : 8
% 3.04/1.81  #SimpNegUnit  : 4
% 3.04/1.81  #BackRed      : 1
% 3.04/1.81  
% 3.04/1.81  #Partial instantiations: 0
% 3.04/1.81  #Strategies tried      : 1
% 3.04/1.81  
% 3.04/1.81  Timing (in seconds)
% 3.04/1.81  ----------------------
% 3.04/1.82  Preprocessing        : 0.47
% 3.04/1.82  Parsing              : 0.24
% 3.04/1.82  CNF conversion       : 0.03
% 3.04/1.82  Main loop            : 0.18
% 3.04/1.82  Inferencing          : 0.06
% 3.04/1.82  Reduction            : 0.06
% 3.04/1.82  Demodulation         : 0.04
% 3.04/1.82  BG Simplification    : 0.02
% 3.04/1.82  Subsumption          : 0.05
% 3.04/1.82  Abstraction          : 0.01
% 3.04/1.82  MUC search           : 0.00
% 3.04/1.82  Cooper               : 0.00
% 3.04/1.82  Total                : 0.70
% 3.04/1.82  Index Insertion      : 0.00
% 3.04/1.82  Index Deletion       : 0.00
% 3.04/1.82  Index Matching       : 0.00
% 3.04/1.82  BG Taut test         : 0.00
%------------------------------------------------------------------------------