TSTP Solution File: DAT029_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT029_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n003.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 10:37:00 EDT 2023

% Result   : Theorem 3.15s 1.76s
% Output   : CNFRefutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   29 (  12 unt;  10 typ;   0 def)
%            Number of atoms       :   31 (   2 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   21 (   9   ~;   6   |;   2   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :   57 (  13 atm;  14 fun;  21 num;   9 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (   8 usr;   8 con; 0-2 aty)
%            Number of variables   :   11 (;  10   !;   1   ?;  11   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > empty > #skF_1 > #skF_3 > #skF_2

%Foreground sorts:
tff(collection,type,
    collection: $tType ).

%Background operators:
tff('#skE_1',type,
    '#skE_1': $int ).

tff('#skF_4',type,
    '#skF_4': $int ).

%Foreground operators:
tff(empty,type,
    empty: collection ).

tff('#skF_1',type,
    '#skF_1': collection ).

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

tff('#skF_2',type,
    '#skF_2': collection ).

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

tff(remove,type,
    remove: ( $int * collection ) > collection ).

tff(add,type,
    add: ( $int * collection ) > collection ).

tff(f_98,negated_conjecture,
    ~ ! [U: collection,V: collection] :
        ( ( ! [Wa: $int] :
              ( in(Wa,V)
             => $greater(Wa,0) )
          & ! [Xa: $int] :
              ( in(Xa,U)
             => ? [Ya: $int] :
                  ( in(Ya,V)
                  & $greater($difference($product(2,Xa),$product(5,Ya)),0) ) ) )
       => ! [Za: $int] :
            ( in(Za,U)
           => $greater(Za,2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(c_37,plain,
    in('#skF_4','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_24,plain,
    ! [X_18a: $int] :
      ( $greater($difference($product(2,X_18a),$product(5,'#skF_3'(X_18a))),0)
      | ~ in(X_18a,'#skF_1') ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_61,plain,
    ! [X_38a: $int] :
      ( $less($product(5,'#skF_3'(X_38a)),$product(2,X_38a))
      | ~ in(X_38a,'#skF_1') ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).

tff(c_67,plain,
    $less($product(5,'#skF_3'('#skF_4')),$product(2,'#skF_4')),
    inference(resolution,[status(thm)],[c_37,c_61]) ).

tff(c_95,plain,
    '#skF_3'('#skF_4') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_67]) ).

tff(c_94,plain,
    $less($product(5,'#skF_3'('#skF_4')),$product(2,'#skF_4')),
    inference(resolution,[status(thm)],[c_37,c_61]) ).

tff(c_102,plain,
    $less($product(5,'#skE_1'),$product(2,'#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_95,c_94]) ).

tff(c_51,plain,
    in('#skF_4','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_105,plain,
    '#skF_3'('#skF_4') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_67]) ).

tff(c_28,plain,
    ! [X_18a: $int] :
      ( in('#skF_3'(X_18a),'#skF_2')
      | ~ in(X_18a,'#skF_1') ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_112,plain,
    ( in('#skE_1','#skF_2')
    | ~ in('#skF_4','#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_105,c_28]) ).

tff(c_131,plain,
    in('#skE_1','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_51,c_112]) ).

tff(c_21,plain,
    ! [W_17a: $int] :
      ( ~ in(W_17a,'#skF_2')
      | $greater(W_17a,0) ),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_33,plain,
    ! [W_17a: $int] :
      ( ~ in(W_17a,'#skF_2')
      | $less(0,W_17a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).

tff(c_136,plain,
    $less(0,'#skE_1'),
    inference(resolution,[status(thm)],[c_131,c_33]) ).

tff(c_17,plain,
    ~ $greater('#skF_4',2),
    inference(cnfTransformation,[status(thm)],[f_98]) ).

tff(c_38,plain,
    ~ $less(2,'#skF_4'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).

tff(c_137,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_102,c_136,c_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : DAT029_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.15  % 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
% 0.13/0.36  % Computer : n003.cluster.edu
% 0.13/0.36  % Model    : x86_64 x86_64
% 0.13/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36  % Memory   : 8042.1875MB
% 0.13/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36  % CPULimit : 300
% 0.13/0.36  % WCLimit  : 300
% 0.13/0.36  % DateTime : Thu Aug  3 13:17:38 EDT 2023
% 0.13/0.36  % CPUTime  : 
% 3.15/1.76  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.15/1.76  
% 3.15/1.76  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.15/1.79  
% 3.15/1.79  Inference rules
% 3.15/1.79  ----------------------
% 3.15/1.79  #Ref     : 0
% 3.15/1.79  #Sup     : 9
% 3.15/1.79  #Fact    : 0
% 3.15/1.79  #Define  : 1
% 3.15/1.79  #Split   : 0
% 3.15/1.79  #Chain   : 0
% 3.15/1.79  #Close   : 1
% 3.15/1.79  
% 3.15/1.79  Ordering : LPO
% 3.15/1.79  
% 3.15/1.79  Simplification rules
% 3.15/1.79  ----------------------
% 3.15/1.79  #Subsume      : 1
% 3.15/1.79  #Demod        : 3
% 3.15/1.79  #Tautology    : 7
% 3.15/1.79  #SimpNegUnit  : 0
% 3.15/1.79  #BackRed      : 0
% 3.15/1.79  
% 3.15/1.79  #Partial instantiations: 0
% 3.15/1.79  #Strategies tried      : 1
% 3.15/1.79  
% 3.15/1.79  Timing (in seconds)
% 3.15/1.79  ----------------------
% 3.15/1.79  Preprocessing        : 0.50
% 3.15/1.79  Parsing              : 0.27
% 3.15/1.79  CNF conversion       : 0.03
% 3.15/1.79  Main loop            : 0.22
% 3.15/1.79  Inferencing          : 0.07
% 3.15/1.79  Reduction            : 0.05
% 3.15/1.79  Demodulation         : 0.03
% 3.15/1.79  BG Simplification    : 0.03
% 3.15/1.79  Subsumption          : 0.04
% 3.15/1.79  Abstraction          : 0.01
% 3.15/1.79  MUC search           : 0.00
% 3.15/1.79  Cooper               : 0.03
% 3.15/1.79  Total                : 0.77
% 3.15/1.79  Index Insertion      : 0.00
% 3.15/1.79  Index Deletion       : 0.00
% 3.15/1.79  Index Matching       : 0.00
% 3.15/1.79  BG Taut test         : 0.00
%------------------------------------------------------------------------------