TSTP Solution File: SET603+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET603+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 : n001.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 10:56:40 EDT 2023

% Result   : Theorem 22.75s 11.53s
% Output   : CNFRefutation 22.75s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   37 (   8 unt;  16 typ;   0 def)
%            Number of atoms       :   40 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  12   ~;  13   |;   2   &)
%                                         (   3 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    3 (   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   :   38 (;  38   !;   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_88,axiom,
    ! [B,A,E] :
      ( member(B,difference(E,A))
    <=> ( member(B,E)
        & ~ member(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',difference) ).

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

tff(f_62,axiom,
    ! [A,B] :
      ( equal_set(A,B)
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SET006+0.ax',equal_set) ).

tff(f_117,negated_conjecture,
    ~ ! [E] : equal_set(difference(E,empty_set),E),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thI30) ).

tff(c_100,plain,
    ! [A_68,B_69] :
      ( member('#skF_1'(A_68,B_69),A_68)
      | subset(A_68,B_69) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_36,plain,
    ! [B_17,E_19,A_18] :
      ( member(B_17,E_19)
      | ~ member(B_17,difference(E_19,A_18)) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_7096,plain,
    ! [E_399,A_400,B_401] :
      ( member('#skF_1'(difference(E_399,A_400),B_401),E_399)
      | subset(difference(E_399,A_400),B_401) ),
    inference(resolution,[status(thm)],[c_100,c_36]) ).

tff(c_4,plain,
    ! [A_1,B_2] :
      ( ~ member('#skF_1'(A_1,B_2),B_2)
      | subset(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_7222,plain,
    ! [E_399,A_400] : subset(difference(E_399,A_400),E_399),
    inference(resolution,[status(thm)],[c_7096,c_4]) ).

tff(c_6,plain,
    ! [A_1,B_2] :
      ( member('#skF_1'(A_1,B_2),A_1)
      | subset(A_1,B_2) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_685,plain,
    ! [B_131,E_132,A_133] :
      ( member(B_131,difference(E_132,A_133))
      | member(B_131,A_133)
      | ~ member(B_131,E_132) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_19667,plain,
    ! [A_839,E_840,A_841] :
      ( subset(A_839,difference(E_840,A_841))
      | member('#skF_1'(A_839,difference(E_840,A_841)),A_841)
      | ~ member('#skF_1'(A_839,difference(E_840,A_841)),E_840) ),
    inference(resolution,[status(thm)],[c_685,c_4]) ).

tff(c_44119,plain,
    ! [A_1315,A_1316] :
      ( member('#skF_1'(A_1315,difference(A_1315,A_1316)),A_1316)
      | subset(A_1315,difference(A_1315,A_1316)) ),
    inference(resolution,[status(thm)],[c_6,c_19667]) ).

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

tff(c_44420,plain,
    ! [A_1317] : subset(A_1317,difference(A_1317,empty_set)),
    inference(resolution,[status(thm)],[c_44119,c_30]) ).

tff(c_8,plain,
    ! [A_6,B_7] :
      ( equal_set(A_6,B_7)
      | ~ subset(B_7,A_6)
      | ~ subset(A_6,B_7) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_44476,plain,
    ! [A_1317] :
      ( equal_set(difference(A_1317,empty_set),A_1317)
      | ~ subset(difference(A_1317,empty_set),A_1317) ),
    inference(resolution,[status(thm)],[c_44420,c_8]) ).

tff(c_44503,plain,
    ! [A_1317] : equal_set(difference(A_1317,empty_set),A_1317),
    inference(demodulation,[status(thm),theory(equality)],[c_7222,c_44476]) ).

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

tff(c_44508,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_44503,c_60]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET603+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n001.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 17:16:10 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 22.75/11.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.75/11.54  
% 22.75/11.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 22.75/11.56  
% 22.75/11.56  Inference rules
% 22.75/11.56  ----------------------
% 22.75/11.56  #Ref     : 0
% 22.75/11.56  #Sup     : 10181
% 22.75/11.56  #Fact    : 6
% 22.75/11.56  #Define  : 0
% 22.75/11.56  #Split   : 1
% 22.75/11.56  #Chain   : 0
% 22.75/11.56  #Close   : 0
% 22.75/11.56  
% 22.75/11.56  Ordering : KBO
% 22.75/11.56  
% 22.75/11.56  Simplification rules
% 22.75/11.56  ----------------------
% 22.75/11.56  #Subsume      : 723
% 22.75/11.56  #Demod        : 1776
% 22.75/11.56  #Tautology    : 1793
% 22.75/11.56  #SimpNegUnit  : 56
% 22.75/11.56  #BackRed      : 4
% 22.75/11.56  
% 22.75/11.56  #Partial instantiations: 0
% 22.75/11.56  #Strategies tried      : 1
% 22.75/11.56  
% 22.75/11.56  Timing (in seconds)
% 22.75/11.56  ----------------------
% 22.75/11.57  Preprocessing        : 0.50
% 22.75/11.57  Parsing              : 0.26
% 22.75/11.57  CNF conversion       : 0.04
% 22.75/11.57  Main loop            : 9.92
% 22.75/11.57  Inferencing          : 1.65
% 22.75/11.57  Reduction            : 4.75
% 22.75/11.57  Demodulation         : 3.70
% 22.75/11.57  BG Simplification    : 0.08
% 22.75/11.57  Subsumption          : 2.79
% 22.75/11.57  Abstraction          : 0.11
% 22.75/11.57  MUC search           : 0.00
% 22.75/11.57  Cooper               : 0.00
% 22.75/11.57  Total                : 10.46
% 22.75/11.57  Index Insertion      : 0.00
% 22.75/11.57  Index Deletion       : 0.00
% 22.75/11.57  Index Matching       : 0.00
% 22.75/11.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------