TSTP Solution File: DAT027_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT027_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 : n002.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 3.43s 1.93s
% Output   : CNFRefutation 3.43s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   39 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :   55 (  13 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   41 (  15   ~;  17   |;   4   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   56 (  13 atm;  11 fun;  13 num;  19 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   25 (;  25   !;   0   ?;  25   :)

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

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

%Background operators:
tff('#skF_5',type,
    '#skF_5': $int ).

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_97,negated_conjecture,
    ~ ! [U: collection,V: collection,Wa: $int,Xa: $int] :
        ( ( ! [Ya: $int] :
              ( in(Ya,V)
             => $greater(Ya,0) )
          & in(Wa,V)
          & $greatereq(Xa,0)
          & ( U = add($sum(Wa,Xa),remove(Wa,V)) ) )
       => ! [Za: $int] :
            ( in(Za,U)
           => $greater(Za,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_5',0),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_43,plain,
    ~ $less(0,'#skF_5'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).

tff(c_42,plain,
    in('#skF_5','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_38,plain,
    add($sum('#skF_4','#skF_3'),remove('#skF_3','#skF_2')) = '#skF_1',
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_102,plain,
    ! [Z_42a: $int,X1_43: collection,X2_44a: $int] :
      ( in(Z_42a,X1_43)
      | ~ in(Z_42a,add(X2_44a,X1_43))
      | ( Z_42a = X2_44a ) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_114,plain,
    ! [Z_42a: $int] :
      ( in(Z_42a,remove('#skF_3','#skF_2'))
      | ~ in(Z_42a,'#skF_1')
      | ( Z_42a = $sum('#skF_4','#skF_3') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_38,c_102]) ).

tff(c_146,plain,
    ! [Z_52a: $int] :
      ( in(Z_52a,remove('#skF_3','#skF_2'))
      | ~ in(Z_52a,'#skF_1')
      | ( Z_52a = $sum('#skF_3','#skF_4') ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_114]) ).

tff(c_44,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_161,plain,
    ! [Z_52a: $int] :
      ( in(Z_52a,'#skF_2')
      | ~ in(Z_52a,'#skF_1')
      | ( Z_52a = $sum('#skF_3','#skF_4') ) ),
    inference(resolution,[status(thm)],[c_146,c_44]) ).

tff(c_173,plain,
    ! [Z_56a: $int] :
      ( in(Z_56a,'#skF_2')
      | ~ in(Z_56a,'#skF_1')
      | ( Z_56a = $sum('#skF_4','#skF_3') ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_161]) ).

tff(c_189,plain,
    ( in('#skF_5','#skF_2')
    | ( '#skF_5' = $sum('#skF_4','#skF_3') ) ),
    inference(resolution,[status(thm)],[c_42,c_173]) ).

tff(c_192,plain,
    ( in('#skF_5','#skF_2')
    | ( '#skF_5' = $sum('#skF_3','#skF_4') ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_189]) ).

tff(c_216,plain,
    '#skF_5' = $sum('#skF_3','#skF_4'),
    inference(splitLeft,[status(thm)],[c_192]) ).

tff(c_218,plain,
    '#skF_5' = $sum('#skF_4','#skF_3'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_216]) ).

tff(c_232,plain,
    ~ $less(0,$sum('#skF_4','#skF_3')),
    inference(demodulation,[status(thm),theory(equality)],[c_218,c_43]) ).

tff(c_33,plain,
    in('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_27,plain,
    ! [Y_14a: $int] :
      ( ~ in(Y_14a,'#skF_2')
      | $greater(Y_14a,0) ),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_65,plain,
    ! [Y_30a: $int] :
      ( ~ in(Y_30a,'#skF_2')
      | $less(0,Y_30a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_27]) ).

tff(c_70,plain,
    $less(0,'#skF_3'),
    inference(resolution,[status(thm)],[c_33,c_65]) ).

tff(c_23,plain,
    $greatereq('#skF_4',0),
    inference(cnfTransformation,[status(thm)],[f_97]) ).

tff(c_34,plain,
    ~ $less('#skF_4',0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_23]) ).

tff(c_233,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_232,c_70,c_34]) ).

tff(c_243,plain,
    in('#skF_5','#skF_2'),
    inference(splitRight,[status(thm)],[c_192]) ).

tff(c_29,plain,
    ! [Y_14a: $int] :
      ( ~ in(Y_14a,'#skF_2')
      | $less(0,Y_14a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_27]) ).

tff(c_248,plain,
    $less(0,'#skF_5'),
    inference(resolution,[status(thm)],[c_243,c_29]) ).

tff(c_249,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_43,c_248]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT027_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.13/0.35  % Computer : n002.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 13:27:46 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.43/1.93  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.43/1.93  
% 3.43/1.93  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.43/1.95  
% 3.43/1.95  Inference rules
% 3.43/1.95  ----------------------
% 3.43/1.96  #Ref     : 0
% 3.43/1.96  #Sup     : 21
% 3.43/1.96  #Fact    : 0
% 3.43/1.96  #Define  : 0
% 3.43/1.96  #Split   : 2
% 3.43/1.96  #Chain   : 0
% 3.43/1.96  #Close   : 1
% 3.43/1.96  
% 3.43/1.96  Ordering : LPO
% 3.43/1.96  
% 3.43/1.96  Simplification rules
% 3.43/1.96  ----------------------
% 3.43/1.96  #Subsume      : 2
% 3.43/1.96  #Demod        : 6
% 3.43/1.96  #Tautology    : 12
% 3.43/1.96  #SimpNegUnit  : 1
% 3.43/1.96  #BackRed      : 3
% 3.43/1.96  
% 3.43/1.96  #Partial instantiations: 0
% 3.43/1.96  #Strategies tried      : 1
% 3.43/1.96  
% 3.43/1.96  Timing (in seconds)
% 3.43/1.96  ----------------------
% 3.43/1.96  Preprocessing        : 0.52
% 3.43/1.96  Parsing              : 0.27
% 3.43/1.96  CNF conversion       : 0.03
% 3.43/1.96  Main loop            : 0.29
% 3.43/1.96  Inferencing          : 0.08
% 3.43/1.96  Reduction            : 0.07
% 3.43/1.96  Demodulation         : 0.05
% 3.43/1.96  BG Simplification    : 0.03
% 3.43/1.96  Subsumption          : 0.05
% 3.43/1.96  Abstraction          : 0.01
% 3.43/1.96  MUC search           : 0.01
% 3.43/1.96  Cooper               : 0.04
% 3.43/1.96  Total                : 0.85
% 3.43/1.96  Index Insertion      : 0.00
% 3.43/1.96  Index Deletion       : 0.00
% 3.43/1.96  Index Matching       : 0.00
% 3.43/1.96  BG Taut test         : 0.00
%------------------------------------------------------------------------------