TSTP Solution File: DAT026_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT026_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 : n026.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 10:36:59 EDT 2023

% Result   : Theorem 3.50s 1.90s
% Output   : CNFRefutation 3.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   33 (  13 unt;   9 typ;   0 def)
%            Number of atoms       :   44 (   9 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   33 (  13   ~;  12   |;   3   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   53 (  11 atm;   8 fun;  18 num;  16 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (   7 usr;   7 con; 0-2 aty)
%            Number of variables   :   22 (;  22   !;   0   ?;  22   :)

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

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

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

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

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

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

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_95,negated_conjecture,
    ~ ! [U: collection,V: collection,Wa: $int] :
        ( ( ! [Xa: $int] :
              ( in(Xa,V)
             => $greater(Xa,0) )
          & in(Wa,V)
          & ( U = add($sum(Wa,2),remove(Wa,V)) ) )
       => ! [Ya: $int] :
            ( in(Ya,U)
           => $greater(Ya,0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_71,axiom,
    ! [Za: $int,X1: collection,X2a: $int] :
      ( ( in(Za,X1)
        | ( Za = X2a ) )
    <=> in(Za,add(X2a,X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax4) ).

tff(f_78,axiom,
    ! [X3a: $int,X4: collection,X5a: $int] :
      ( ( in(X3a,X4)
        & ( X3a != X5a ) )
    <=> in(X3a,remove(X5a,X4)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT002_0.ax',ax5) ).

tff(c_17,plain,
    ~ $greater('#skF_4',0),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_40,plain,
    ~ $less(0,'#skF_4'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).

tff(c_39,plain,
    in('#skF_4','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_35,plain,
    add($sum(2,'#skF_3'),remove('#skF_3','#skF_2')) = '#skF_1',
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_111,plain,
    ! [Z_45a: $int,X1_46: collection,X2_47a: $int] :
      ( in(Z_45a,X1_46)
      | ~ in(Z_45a,add(X2_47a,X1_46))
      | ( Z_45a = X2_47a ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_140,plain,
    ! [Z_51a: $int] :
      ( in(Z_51a,remove('#skF_3','#skF_2'))
      | ~ in(Z_51a,'#skF_1')
      | ( Z_51a = $sum(2,'#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_35,c_111]) ).

tff(c_41,plain,
    ! [X3_9a: $int,X4_10: collection,X5_11a: $int] :
      ( in(X3_9a,X4_10)
      | ~ in(X3_9a,remove(X5_11a,X4_10)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_183,plain,
    ! [Z_56a: $int] :
      ( in(Z_56a,'#skF_2')
      | ~ in(Z_56a,'#skF_1')
      | ( Z_56a = $sum(2,'#skF_3') ) ),
    inference(resolution,[status(thm)],[c_140,c_41]) ).

tff(c_200,plain,
    ( in('#skF_4','#skF_2')
    | ( '#skF_4' = $sum(2,'#skF_3') ) ),
    inference(resolution,[status(thm)],[c_39,c_183]) ).

tff(c_203,plain,
    '#skF_4' = $sum(2,'#skF_3'),
    inference(splitLeft,[status(thm)],[c_200]) ).

tff(c_212,plain,
    ~ $less(0,$sum(2,'#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_203,c_40]) ).

tff(c_217,plain,
    ~ $less($uminus(2),'#skF_3'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_212]) ).

tff(c_31,plain,
    in('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_25,plain,
    ! [X_14a: $int] :
      ( ~ in(X_14a,'#skF_2')
      | $greater(X_14a,0) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_62,plain,
    ! [X_30a: $int] :
      ( ~ in(X_30a,'#skF_2')
      | $less(0,X_30a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).

tff(c_67,plain,
    $less(0,'#skF_3'),
    inference(resolution,[status(thm)],[c_31,c_62]) ).

tff(c_218,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_217,c_67]) ).

tff(c_227,plain,
    in('#skF_4','#skF_2'),
    inference(splitRight,[status(thm)],[c_200]) ).

tff(c_27,plain,
    ! [X_14a: $int] :
      ( ~ in(X_14a,'#skF_2')
      | $less(0,X_14a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_25]) ).

tff(c_232,plain,
    $less(0,'#skF_4'),
    inference(resolution,[status(thm)],[c_227,c_27]) ).

tff(c_233,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_40,c_232]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT026_1 : TPTP v8.1.2. Released v5.0.0.
% 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 : n026.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 13:29:46 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.50/1.90  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.50/1.91  
% 3.50/1.91  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.50/1.94  
% 3.50/1.94  Inference rules
% 3.50/1.94  ----------------------
% 3.50/1.94  #Ref     : 0
% 3.50/1.94  #Sup     : 21
% 3.50/1.94  #Fact    : 0
% 3.50/1.94  #Define  : 0
% 3.50/1.94  #Split   : 1
% 3.50/1.94  #Chain   : 0
% 3.50/1.94  #Close   : 1
% 3.50/1.94  
% 3.50/1.94  Ordering : LPO
% 3.50/1.94  
% 3.50/1.94  Simplification rules
% 3.50/1.94  ----------------------
% 3.50/1.94  #Subsume      : 1
% 3.50/1.94  #Demod        : 6
% 3.50/1.94  #Tautology    : 14
% 3.50/1.94  #SimpNegUnit  : 1
% 3.50/1.94  #BackRed      : 2
% 3.50/1.94  
% 3.50/1.94  #Partial instantiations: 0
% 3.50/1.94  #Strategies tried      : 1
% 3.50/1.94  
% 3.50/1.94  Timing (in seconds)
% 3.50/1.94  ----------------------
% 3.50/1.94  Preprocessing        : 0.57
% 3.50/1.94  Parsing              : 0.30
% 3.50/1.94  CNF conversion       : 0.03
% 3.50/1.94  Main loop            : 0.31
% 3.50/1.94  Inferencing          : 0.10
% 3.50/1.94  Reduction            : 0.08
% 3.50/1.94  Demodulation         : 0.05
% 3.50/1.94  BG Simplification    : 0.03
% 3.50/1.94  Subsumption          : 0.07
% 3.50/1.94  Abstraction          : 0.01
% 3.50/1.94  MUC search           : 0.00
% 3.50/1.94  Cooper               : 0.02
% 3.50/1.94  Total                : 0.93
% 3.50/1.94  Index Insertion      : 0.00
% 3.50/1.94  Index Deletion       : 0.00
% 3.50/1.94  Index Matching       : 0.00
% 3.50/1.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------