TSTP Solution File: ARI618_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ARI618_1 : TPTP v8.1.2. Released v5.1.0.
% 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 : n013.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 10:34:07 EDT 2023

% Result   : Theorem 3.11s 1.83s
% Output   : CNFRefutation 3.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   32 (  23 unt;   4 typ;   0 def)
%            Number of atoms       :   36 (  12 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   28 (  20   ~;   5   |;   2   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   48 (  22 atm;  11 fun;   7 num;   8 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    1 (   1   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   4 usr;   4 con; 0-2 aty)
%            Number of variables   :    8 (;   8   !;   0   ?;   8   :)

% Comments : 
%------------------------------------------------------------------------------
%$ #nlpp > f

%Foreground sorts:

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

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

tff('#skF_1',type,
    '#skF_1': $int ).

%Foreground operators:
tff(f,type,
    f: $int > $int ).

tff(f_39,negated_conjecture,
    ~ ( ! [Xa: $int] :
          ( $lesseq(Xa,f(Xa))
          & $lesseq($uminus(Xa),f(Xa))
          & ( $lesseq(f(Xa),Xa)
            | $lesseq(f(Xa),$uminus(Xa)) ) )
     => ! [Xa: $int] : ( f(f(Xa)) = f(Xa) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_value_idempotent) ).

tff(c_18,plain,
    f(f('#skF_1')) != f('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_23,plain,
    f('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_18]) ).

tff(c_20,plain,
    f(f('#skF_1')) != f('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_33,plain,
    f('#skE_1') != '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_23,c_23,c_20]) ).

tff(c_71,plain,
    f('#skE_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_33]) ).

tff(c_68,plain,
    f('#skE_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_33]) ).

tff(c_10,plain,
    ! [X_1a: $int] :
      ( $lesseq(f(X_1a),$uminus(X_1a))
      | $lesseq(f(X_1a),X_1a) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_110,plain,
    ! [X_16a: $int] :
      ( ~ $less(0,$sum(X_16a,f(X_16a)))
      | ~ $less(X_16a,f(X_16a)) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_10]) ).

tff(c_113,plain,
    ( ~ $less(0,$sum('#skE_1','#skE_2'))
    | ~ $less('#skE_1',f('#skE_1')) ),
    inference(superposition,[status(thm),theory(equality)],[c_68,c_110]) ).

tff(c_119,plain,
    ( ~ $less(0,$sum('#skE_1','#skE_2'))
    | ~ $less('#skE_1','#skE_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_71,c_113]) ).

tff(c_131,plain,
    ~ $less('#skE_1','#skE_2'),
    inference(splitLeft,[status(thm)],[c_119]) ).

tff(c_72,plain,
    f('#skE_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_33]) ).

tff(c_4,plain,
    ! [X_1a: $int] : $lesseq(X_1a,f(X_1a)),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_14,plain,
    ! [X_1a: $int] : ~ $less(f(X_1a),X_1a),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).

tff(c_102,plain,
    ~ $less('#skE_2','#skE_1'),
    inference(superposition,[status(thm),theory(equality)],[c_72,c_14]) ).

tff(c_62,plain,
    f('#skE_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_33]) ).

tff(c_61,plain,
    f('#skE_1') != '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_23,c_23,c_20]) ).

tff(c_69,plain,
    '#skE_2' != '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_61]) ).

tff(c_132,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_131,c_102,c_69]) ).

tff(c_135,plain,
    ~ $less(0,$sum('#skE_1','#skE_2')),
    inference(splitRight,[status(thm)],[c_119]) ).

tff(c_36,plain,
    f('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_18]) ).

tff(c_7,plain,
    ! [X_1a: $int] : $lesseq($uminus(X_1a),f(X_1a)),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_13,plain,
    ! [X_1a: $int] : ~ $less($sum(X_1a,f(X_1a)),0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).

tff(c_52,plain,
    ~ $less($sum('#skF_1','#skE_1'),0),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_13]) ).

tff(c_54,plain,
    ~ $less($sum('#skE_1','#skF_1'),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_52]) ).

tff(c_56,plain,
    ~ $less('#skE_1','#skF_1'),
    inference(superposition,[status(thm),theory(equality)],[c_36,c_14]) ).

tff(c_137,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_135,c_54,c_102,c_69,c_56]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : ARI618_1 : TPTP v8.1.2. Released v5.1.0.
% 0.00/0.15  % 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
% 0.15/0.36  % Computer : n013.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Fri Aug  4 00:03:17 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 3.11/1.83  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.11/1.84  
% 3.11/1.84  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.11/1.87  
% 3.11/1.87  Inference rules
% 3.11/1.87  ----------------------
% 3.11/1.87  #Ref     : 0
% 3.11/1.87  #Sup     : 12
% 3.11/1.87  #Fact    : 0
% 3.11/1.87  #Define  : 2
% 3.11/1.87  #Split   : 2
% 3.11/1.87  #Chain   : 0
% 3.11/1.87  #Close   : 3
% 3.11/1.87  
% 3.11/1.87  Ordering : LPO
% 3.11/1.87  
% 3.11/1.87  Simplification rules
% 3.11/1.87  ----------------------
% 3.11/1.87  #Subsume      : 1
% 3.11/1.87  #Demod        : 5
% 3.11/1.87  #Tautology    : 4
% 3.11/1.87  #SimpNegUnit  : 2
% 3.11/1.87  #BackRed      : 0
% 3.11/1.87  
% 3.11/1.87  #Partial instantiations: 0
% 3.11/1.87  #Strategies tried      : 1
% 3.11/1.87  
% 3.11/1.87  Timing (in seconds)
% 3.11/1.87  ----------------------
% 3.11/1.87  Preprocessing        : 0.48
% 3.11/1.87  Parsing              : 0.26
% 3.11/1.87  CNF conversion       : 0.03
% 3.11/1.87  Main loop            : 0.30
% 3.11/1.87  Inferencing          : 0.04
% 3.11/1.87  Reduction            : 0.04
% 3.11/1.87  Demodulation         : 0.02
% 3.11/1.87  BG Simplification    : 0.03
% 3.11/1.87  Subsumption          : 0.06
% 3.38/1.87  Abstraction          : 0.01
% 3.38/1.87  MUC search           : 0.04
% 3.38/1.87  Cooper               : 0.11
% 3.38/1.87  Total                : 0.83
% 3.38/1.87  Index Insertion      : 0.00
% 3.38/1.87  Index Deletion       : 0.00
% 3.38/1.87  Index Matching       : 0.00
% 3.38/1.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------