TSTP Solution File: SET877+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET877+1 : 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 : n019.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 10:57:16 EDT 2023

% Result   : Theorem 2.79s 1.70s
% Output   : CNFRefutation 2.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   23 (   8 unt;  10 typ;   0 def)
%            Number of atoms       :   19 (  13 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   10 (   4   ~;   2   |;   0   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   15 (;  15   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > set_intersection2 > #nlpp > singleton > #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('#skF_6',type,
    '#skF_6': $i ).

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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_56,negated_conjecture,
    ~ ! [A,B] :
        ( ( set_intersection2(singleton(A),singleton(B)) = singleton(A) )
       => ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t18_zfmisc_1) ).

tff(f_33,axiom,
    ! [A,B] : ( set_intersection2(A,B) = set_intersection2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

tff(f_46,axiom,
    ! [A,B] :
      ( ( set_intersection2(A,singleton(B)) = singleton(B) )
     => in(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l30_zfmisc_1) ).

tff(f_40,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(c_26,plain,
    '#skF_5' != '#skF_6',
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_28,plain,
    set_intersection2(singleton('#skF_5'),singleton('#skF_6')) = singleton('#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_4,plain,
    ! [B_4,A_3] : ( set_intersection2(B_4,A_3) = set_intersection2(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_86,plain,
    set_intersection2(singleton('#skF_6'),singleton('#skF_5')) = singleton('#skF_5'),
    inference(superposition,[status(thm),theory(equality)],[c_28,c_4]) ).

tff(c_106,plain,
    ! [B_23,A_24] :
      ( in(B_23,A_24)
      | ( set_intersection2(A_24,singleton(B_23)) != singleton(B_23) ) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_125,plain,
    in('#skF_5',singleton('#skF_6')),
    inference(superposition,[status(thm),theory(equality)],[c_86,c_106]) ).

tff(c_6,plain,
    ! [C_9,A_5] :
      ( ( C_9 = A_5 )
      | ~ in(C_9,singleton(A_5)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_133,plain,
    '#skF_5' = '#skF_6',
    inference(resolution,[status(thm)],[c_125,c_6]) ).

tff(c_138,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26,c_133]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET877+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.13/0.34  % Computer : n019.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 16:45:01 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 2.79/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.79/1.70  
% 2.79/1.70  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.79/1.73  
% 2.79/1.73  Inference rules
% 2.79/1.73  ----------------------
% 2.79/1.73  #Ref     : 0
% 2.79/1.73  #Sup     : 27
% 2.79/1.73  #Fact    : 0
% 2.79/1.73  #Define  : 0
% 2.79/1.73  #Split   : 0
% 2.79/1.73  #Chain   : 0
% 2.79/1.73  #Close   : 0
% 2.79/1.73  
% 2.79/1.73  Ordering : KBO
% 2.79/1.73  
% 2.79/1.73  Simplification rules
% 2.79/1.73  ----------------------
% 2.79/1.73  #Subsume      : 0
% 2.79/1.73  #Demod        : 4
% 2.79/1.73  #Tautology    : 19
% 2.79/1.73  #SimpNegUnit  : 1
% 2.79/1.73  #BackRed      : 0
% 2.79/1.73  
% 2.79/1.73  #Partial instantiations: 0
% 2.79/1.73  #Strategies tried      : 1
% 2.79/1.73  
% 2.79/1.73  Timing (in seconds)
% 2.79/1.73  ----------------------
% 2.79/1.73  Preprocessing        : 0.47
% 2.79/1.73  Parsing              : 0.24
% 2.79/1.73  CNF conversion       : 0.03
% 2.79/1.73  Main loop            : 0.19
% 2.79/1.73  Inferencing          : 0.06
% 2.79/1.73  Reduction            : 0.06
% 2.79/1.73  Demodulation         : 0.05
% 2.79/1.73  BG Simplification    : 0.01
% 2.79/1.73  Subsumption          : 0.05
% 2.79/1.73  Abstraction          : 0.01
% 2.79/1.73  MUC search           : 0.00
% 2.79/1.73  Cooper               : 0.00
% 2.79/1.73  Total                : 0.71
% 2.79/1.73  Index Insertion      : 0.00
% 2.79/1.73  Index Deletion       : 0.00
% 2.79/1.73  Index Matching       : 0.00
% 2.79/1.73  BG Taut test         : 0.00
%------------------------------------------------------------------------------