TSTP Solution File: DAT030_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT030_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 : n031.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 3.38s 1.85s
% Output   : CNFRefutation 3.41s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   47 (  24 unt;  12 typ;   0 def)
%            Number of atoms       :   52 (  15 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   31 (  14   ~;  10   |;   3   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :   52 (   9 atm;  23 fun;   9 num;  11 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   13 (;  11   !;   2   ?;  13   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > remove > add > #nlpp > empty > #skF_1 > #skF_3 > #skF_2 > #skF_4

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

%Background operators:
tff('#skE_2',type,
    '#skE_2': $int ).

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

tff('#skF_5',type,
    '#skF_5': $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('#skF_4',type,
    '#skF_4': $int > $int ).

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

tff(f_100,negated_conjecture,
    ~ ! [U: collection,V: collection] :
        ( ( ! [Wa: $int] :
              ( in(Wa,V)
             => $greater(Wa,0) )
          & ! [Xa: $int] :
              ( in(Xa,U)
             => ? [Ya: $int,Za: $int] :
                  ( in(Ya,V)
                  & in(Za,V)
                  & ( Xa = $sum(Ya,Za) ) ) ) )
       => ! [X1a: $int] :
            ( in(X1a,U)
           => $greater(X1a,1) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(c_37,plain,
    in('#skF_5','#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_24,plain,
    ! [X_20a: $int] :
      ( ( $sum('#skF_3'(X_20a),'#skF_4'(X_20a)) = X_20a )
      | ~ in(X_20a,'#skF_1') ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_59,plain,
    ! [X_37a: $int] :
      ( ( '#skF_3'(X_37a) = $sum(X_37a,$uminus('#skF_4'(X_37a))) )
      | ~ in(X_37a,'#skF_1') ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).

tff(c_65,plain,
    '#skF_3'('#skF_5') = $sum('#skF_5',$uminus('#skF_4'('#skF_5'))),
    inference(resolution,[status(thm)],[c_37,c_59]) ).

tff(c_95,plain,
    '#skF_4'('#skF_5') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_65]) ).

tff(c_94,plain,
    '#skF_3'('#skF_5') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_65]) ).

tff(c_93,plain,
    '#skF_3'('#skF_5') = $sum('#skF_5',$uminus('#skF_4'('#skF_5'))),
    inference(resolution,[status(thm)],[c_37,c_59]) ).

tff(c_97,plain,
    $sum('#skF_5',$uminus('#skE_2')) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_95,c_94,c_93]) ).

tff(c_107,plain,
    '#skF_5' = $sum('#skE_2','#skE_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_97]) ).

tff(c_110,plain,
    in($sum('#skE_2','#skE_1'),'#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_37]) ).

tff(c_116,plain,
    in($sum('#skE_1','#skE_2'),'#skF_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_110]) ).

tff(c_182,plain,
    in($sum('#skE_2','#skE_1'),'#skF_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_116]) ).

tff(c_102,plain,
    '#skF_3'('#skF_5') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_65]) ).

tff(c_124,plain,
    '#skF_3'($sum('#skE_2','#skE_1')) = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_102]) ).

tff(c_129,plain,
    '#skF_3'($sum('#skE_1','#skE_2')) = '#skE_1',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_124]) ).

tff(c_30,plain,
    ! [X_20a: $int] :
      ( in('#skF_3'(X_20a),'#skF_2')
      | ~ in(X_20a,'#skF_1') ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_143,plain,
    ( in('#skE_1','#skF_2')
    | ~ in($sum('#skE_1','#skE_2'),'#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_129,c_30]) ).

tff(c_146,plain,
    ( in('#skE_1','#skF_2')
    | ~ in($sum('#skE_2','#skE_1'),'#skF_1') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_143]) ).

tff(c_214,plain,
    in('#skE_1','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_146]) ).

tff(c_21,plain,
    ! [W_19a: $int] :
      ( ~ in(W_19a,'#skF_2')
      | $greater(W_19a,0) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_33,plain,
    ! [W_19a: $int] :
      ( ~ in(W_19a,'#skF_2')
      | $less(0,W_19a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_21]) ).

tff(c_219,plain,
    $less(0,'#skE_1'),
    inference(resolution,[status(thm)],[c_214,c_33]) ).

tff(c_105,plain,
    '#skF_4'('#skF_5') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_65]) ).

tff(c_153,plain,
    '#skF_4'($sum('#skE_2','#skE_1')) = '#skE_2',
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_105]) ).

tff(c_159,plain,
    '#skF_4'($sum('#skE_1','#skE_2')) = '#skE_2',
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_153]) ).

tff(c_31,plain,
    ! [X_20a: $int] :
      ( in('#skF_4'(X_20a),'#skF_2')
      | ~ in(X_20a,'#skF_1') ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_173,plain,
    ( in('#skE_2','#skF_2')
    | ~ in($sum('#skE_1','#skE_2'),'#skF_1') ),
    inference(superposition,[status(thm),theory(equality)],[c_159,c_31]) ).

tff(c_176,plain,
    ( in('#skE_2','#skF_2')
    | ~ in($sum('#skE_2','#skE_1'),'#skF_1') ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_173]) ).

tff(c_199,plain,
    in('#skE_2','#skF_2'),
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_176]) ).

tff(c_204,plain,
    $less(0,'#skE_2'),
    inference(resolution,[status(thm)],[c_199,c_33]) ).

tff(c_17,plain,
    ~ $greater('#skF_5',1),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_38,plain,
    ~ $less(1,'#skF_5'),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_17]) ).

tff(c_120,plain,
    ~ $less(1,$sum('#skE_2','#skE_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_107,c_38]) ).

tff(c_221,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_219,c_204,c_120]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : DAT030_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
% 0.16/0.36  % Computer : n031.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Thu Aug  3 13:38:29 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 3.38/1.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.41/1.85  
% 3.41/1.85  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.41/1.88  
% 3.41/1.88  Inference rules
% 3.41/1.88  ----------------------
% 3.41/1.88  #Ref     : 0
% 3.41/1.88  #Sup     : 14
% 3.41/1.88  #Fact    : 0
% 3.41/1.88  #Define  : 2
% 3.41/1.88  #Split   : 0
% 3.41/1.88  #Chain   : 0
% 3.41/1.88  #Close   : 1
% 3.41/1.88  
% 3.41/1.88  Ordering : LPO
% 3.41/1.88  
% 3.41/1.88  Simplification rules
% 3.41/1.88  ----------------------
% 3.41/1.88  #Subsume      : 1
% 3.41/1.88  #Demod        : 9
% 3.41/1.88  #Tautology    : 9
% 3.41/1.88  #SimpNegUnit  : 0
% 3.41/1.88  #BackRed      : 2
% 3.41/1.88  
% 3.41/1.88  #Partial instantiations: 0
% 3.41/1.88  #Strategies tried      : 1
% 3.41/1.88  
% 3.41/1.88  Timing (in seconds)
% 3.41/1.88  ----------------------
% 3.41/1.88  Preprocessing        : 0.55
% 3.41/1.88  Parsing              : 0.28
% 3.41/1.88  CNF conversion       : 0.03
% 3.41/1.88  Main loop            : 0.27
% 3.41/1.88  Inferencing          : 0.08
% 3.41/1.88  Reduction            : 0.07
% 3.41/1.88  Demodulation         : 0.05
% 3.41/1.88  BG Simplification    : 0.05
% 3.41/1.88  Subsumption          : 0.04
% 3.41/1.88  Abstraction          : 0.01
% 3.41/1.88  MUC search           : 0.00
% 3.41/1.88  Cooper               : 0.03
% 3.41/1.88  Total                : 0.86
% 3.41/1.88  Index Insertion      : 0.00
% 3.41/1.88  Index Deletion       : 0.00
% 3.41/1.88  Index Matching       : 0.00
% 3.41/1.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------