TSTP Solution File: SET800+4 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET800+4 : 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/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 : n017.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 10:57:02 EDT 2023

% Result   : Theorem 8.73s 3.09s
% Output   : CNFRefutation 9.04s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   52
% Syntax   : Number of formulae    :   67 (   9 unt;  48 typ;   0 def)
%            Number of atoms       :   42 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   33 (  10   ~;   8   |;   6   &)
%                                         (   3 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   99 (  41   >;  58   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  14 usr;   1 prp; 0-4 aty)
%            Number of functors    :   34 (  34 usr;   7 con; 0-4 aty)
%            Number of variables   :   36 (;  36   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ least_upper_bound > greatest_lower_bound > upper_bound > min > max > lower_bound > least > greatest > apply > total_order > subset > order > member > equal_set > unordered_pair > union > intersection > difference > #nlpp > sum > singleton > product > power_set > empty_set > #skF_13 > #skF_11 > #skF_6 > #skF_17 > #skF_20 > #skF_25 > #skF_12 > #skF_18 > #skF_19 > #skF_3 > #skF_10 > #skF_8 > #skF_21 > #skF_15 > #skF_14 > #skF_22 > #skF_2 > #skF_24 > #skF_23 > #skF_7 > #skF_1 > #skF_9 > #skF_5 > #skF_4 > #skF_16

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_13',type,
    '#skF_13': ( $i * $i * $i ) > $i ).

tff('#skF_11',type,
    '#skF_11': ( $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

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

tff('#skF_20',type,
    '#skF_20': $i ).

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

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

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

tff('#skF_25',type,
    '#skF_25': $i ).

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

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

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

tff('#skF_12',type,
    '#skF_12': ( $i * $i * $i ) > $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i * $i ) > $i ).

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

tff('#skF_19',type,
    '#skF_19': ( $i * $i * $i * $i ) > $i ).

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

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

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

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

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

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

tff('#skF_10',type,
    '#skF_10': ( $i * $i ) > $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': $i ).

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

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_22',type,
    '#skF_22': $i ).

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

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

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

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

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

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

tff('#skF_16',type,
    '#skF_16': ( $i * $i * $i ) > $i ).

tff(f_282,negated_conjecture,
    ~ ! [R,E] :
        ( order(R,E)
       => ! [X1,X2] :
            ( ( subset(X1,E)
              & subset(X2,E)
              & subset(X1,X2) )
           => ! [M1,M2] :
                ( ( greatest_lower_bound(M1,X1,R,E)
                  & greatest_lower_bound(M2,X2,R,E) )
               => apply(R,M2,M1) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV12) ).

tff(f_263,axiom,
    ! [A,X,R,E] :
      ( greatest_lower_bound(A,X,R,E)
    <=> ( member(A,X)
        & lower_bound(A,R,X)
        & ! [M] :
            ( ( member(M,E)
              & lower_bound(M,R,X) )
           => apply(R,M,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest_lower_bound) ).

tff(f_57,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [X] :
          ( member(X,A)
         => member(X,B) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+0.ax',subset) ).

tff(f_197,axiom,
    ! [R,E,M] :
      ( lower_bound(M,R,E)
    <=> ! [X] :
          ( member(X,E)
         => apply(R,M,X) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',lower_bound) ).

tff(c_270,plain,
    ~ apply('#skF_20','#skF_25','#skF_24'),
    inference(cnfTransformation,[status(thm)],[f_282]) ).

tff(c_272,plain,
    greatest_lower_bound('#skF_25','#skF_23','#skF_20','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_282]) ).

tff(c_1305,plain,
    ! [A_239,R_240,X_241,E_242] :
      ( lower_bound(A_239,R_240,X_241)
      | ~ greatest_lower_bound(A_239,X_241,R_240,E_242) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_1313,plain,
    lower_bound('#skF_25','#skF_20','#skF_23'),
    inference(resolution,[status(thm)],[c_272,c_1305]) ).

tff(c_276,plain,
    subset('#skF_22','#skF_23'),
    inference(cnfTransformation,[status(thm)],[f_282]) ).

tff(c_274,plain,
    greatest_lower_bound('#skF_24','#skF_22','#skF_20','#skF_21'),
    inference(cnfTransformation,[status(thm)],[f_282]) ).

tff(c_313,plain,
    ! [A_173,X_174,R_175,E_176] :
      ( member(A_173,X_174)
      | ~ greatest_lower_bound(A_173,X_174,R_175,E_176) ),
    inference(cnfTransformation,[status(thm)],[f_263]) ).

tff(c_320,plain,
    member('#skF_24','#skF_22'),
    inference(resolution,[status(thm)],[c_274,c_313]) ).

tff(c_381,plain,
    ! [X_183,B_184,A_185] :
      ( member(X_183,B_184)
      | ~ member(X_183,A_185)
      | ~ subset(A_185,B_184) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_433,plain,
    ! [B_187] :
      ( member('#skF_24',B_187)
      | ~ subset('#skF_22',B_187) ),
    inference(resolution,[status(thm)],[c_320,c_381]) ).

tff(c_456,plain,
    member('#skF_24','#skF_23'),
    inference(resolution,[status(thm)],[c_276,c_433]) ).

tff(c_3440,plain,
    ! [R_360,M_361,X_362,E_363] :
      ( apply(R_360,M_361,X_362)
      | ~ member(X_362,E_363)
      | ~ lower_bound(M_361,R_360,E_363) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_4887,plain,
    ! [R_431,M_432] :
      ( apply(R_431,M_432,'#skF_24')
      | ~ lower_bound(M_432,R_431,'#skF_23') ),
    inference(resolution,[status(thm)],[c_456,c_3440]) ).

tff(c_4890,plain,
    apply('#skF_20','#skF_25','#skF_24'),
    inference(resolution,[status(thm)],[c_1313,c_4887]) ).

tff(c_4894,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_270,c_4890]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET800+4 : TPTP v8.1.2. Released v3.2.0.
% 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 : n017.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 15:43:36 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 8.73/3.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.73/3.09  
% 8.73/3.09  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/3.12  
% 9.04/3.12  Inference rules
% 9.04/3.12  ----------------------
% 9.04/3.12  #Ref     : 0
% 9.04/3.12  #Sup     : 1059
% 9.04/3.12  #Fact    : 0
% 9.04/3.12  #Define  : 0
% 9.04/3.12  #Split   : 21
% 9.04/3.12  #Chain   : 0
% 9.04/3.12  #Close   : 0
% 9.04/3.12  
% 9.04/3.12  Ordering : KBO
% 9.04/3.12  
% 9.04/3.12  Simplification rules
% 9.04/3.12  ----------------------
% 9.04/3.12  #Subsume      : 78
% 9.04/3.12  #Demod        : 110
% 9.04/3.12  #Tautology    : 131
% 9.04/3.12  #SimpNegUnit  : 1
% 9.04/3.12  #BackRed      : 0
% 9.04/3.12  
% 9.04/3.12  #Partial instantiations: 0
% 9.04/3.12  #Strategies tried      : 1
% 9.04/3.12  
% 9.04/3.12  Timing (in seconds)
% 9.04/3.12  ----------------------
% 9.04/3.13  Preprocessing        : 0.66
% 9.04/3.13  Parsing              : 0.31
% 9.04/3.13  CNF conversion       : 0.06
% 9.04/3.13  Main loop            : 1.41
% 9.04/3.13  Inferencing          : 0.44
% 9.04/3.13  Reduction            : 0.46
% 9.04/3.13  Demodulation         : 0.28
% 9.04/3.13  BG Simplification    : 0.07
% 9.04/3.13  Subsumption          : 0.35
% 9.04/3.13  Abstraction          : 0.04
% 9.04/3.13  MUC search           : 0.00
% 9.04/3.13  Cooper               : 0.00
% 9.04/3.13  Total                : 2.12
% 9.04/3.13  Index Insertion      : 0.00
% 9.04/3.13  Index Deletion       : 0.00
% 9.04/3.13  Index Matching       : 0.00
% 9.04/3.13  BG Taut test         : 0.00
%------------------------------------------------------------------------------