TSTP Solution File: ARI617_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : ARI617_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 : n027.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 3.58s 1.94s
% Output   : CNFRefutation 3.70s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   50 (  33 unt;   5 typ;   0 def)
%            Number of atoms       :   63 (  23 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :   48 (  30   ~;  13   |;   4   &)
%                                         (   0 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   89 (  36 atm;  25 fun;  16 num;  12 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (;  12   !;   0   ?;  12   :)

% Comments : 
%------------------------------------------------------------------------------
%$ #nlpp > g > 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(g,type,
    g: $int > $int ).

tff(f_46,negated_conjecture,
    ~ ( ( ! [Xa: $int] :
            ( $lesseq(Xa,f(Xa))
            & $lesseq($uminus(Xa),f(Xa))
            & ( $lesseq(f(Xa),Xa)
              | $lesseq(f(Xa),$uminus(Xa)) ) )
        & ! [Xa: $int] :
            ( $lesseq(0,g(Xa))
            & ( ( g(Xa) = Xa )
              | ( g(Xa) = $uminus(Xa) ) ) ) )
     => ! [Xa: $int] : ( f(Xa) = g(Xa) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',absolute_value_defs) ).

tff(c_25,plain,
    g('#skF_1') != f('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_115,plain,
    g('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_116,plain,
    g('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_20,plain,
    ! [X_2a: $int] :
      ( ( g(X_2a) = $uminus(X_2a) )
      | ( g(X_2a) = X_2a ) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_125,plain,
    ( ( $uminus('#skF_1') = '#skE_1' )
    | ( g('#skF_1') = '#skF_1' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_116,c_20]) ).

tff(c_142,plain,
    ( ( $uminus('#skF_1') = '#skE_1' )
    | ( '#skF_1' = '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_115,c_125]) ).

tff(c_144,plain,
    ( ( '#skF_1' = $uminus('#skE_1') )
    | ( '#skF_1' = '#skE_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_142]) ).

tff(c_165,plain,
    '#skF_1' = '#skE_1',
    inference(splitLeft,[status(thm)],[c_144]) ).

tff(c_89,plain,
    f('#skF_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_86,plain,
    f('#skF_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_15,plain,
    ! [X_1a: $int] :
      ( $lesseq(f(X_1a),$uminus(X_1a))
      | $lesseq(f(X_1a),X_1a) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_157,plain,
    ! [X_17a: $int] :
      ( ~ $less(0,$sum(X_17a,f(X_17a)))
      | ~ $less(X_17a,f(X_17a)) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_15]) ).

tff(c_160,plain,
    ( ~ $less(0,$sum('#skF_1','#skE_2'))
    | ~ $less('#skF_1',f('#skF_1')) ),
    inference(superposition,[status(thm),theory(equality)],[c_86,c_157]) ).

tff(c_163,plain,
    ( ~ $less(0,$sum('#skF_1','#skE_2'))
    | ~ $less('#skF_1','#skE_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_89,c_160]) ).

tff(c_312,plain,
    ( ~ $less(0,$sum('#skE_1','#skE_2'))
    | ~ $less('#skE_1','#skE_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_165,c_165,c_163]) ).

tff(c_314,plain,
    ~ $less('#skE_1','#skE_2'),
    inference(splitLeft,[status(thm)],[c_312]) ).

tff(c_90,plain,
    f('#skF_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_9,plain,
    ! [X_1a: $int] : $lesseq(X_1a,f(X_1a)),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_19,plain,
    ! [X_1a: $int] : ~ $less(f(X_1a),X_1a),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).

tff(c_110,plain,
    ~ $less('#skE_2','#skF_1'),
    inference(superposition,[status(thm),theory(equality)],[c_90,c_19]) ).

tff(c_189,plain,
    ~ $less('#skE_2','#skE_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_165,c_110]) ).

tff(c_76,plain,
    f('#skF_1') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_75,plain,
    g('#skF_1') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_25]) ).

tff(c_27,plain,
    g('#skF_1') != f('#skF_1'),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_87,plain,
    '#skE_2' != '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_76,c_75,c_27]) ).

tff(c_317,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_314,c_189,c_87]) ).

tff(c_320,plain,
    ~ $less(0,$sum('#skE_1','#skE_2')),
    inference(splitRight,[status(thm)],[c_312]) ).

tff(c_4,plain,
    ! [X_2a: $int] : $lesseq(0,g(X_2a)),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_21,plain,
    ! [X_2a: $int] : ~ $less(g(X_2a),0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_4]) ).

tff(c_146,plain,
    ~ $less('#skE_1',0),
    inference(superposition,[status(thm),theory(equality)],[c_116,c_21]) ).

tff(c_322,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_320,c_189,c_146,c_87]) ).

tff(c_325,plain,
    '#skF_1' = $uminus('#skE_1'),
    inference(splitRight,[status(thm)],[c_144]) ).

tff(c_486,plain,
    ( ~ $less(0,$sum($uminus('#skE_1'),'#skE_2'))
    | ~ $less($uminus('#skE_1'),'#skE_2') ),
    inference(demodulation,[status(thm),theory(equality)],[c_325,c_325,c_163]) ).

tff(c_488,plain,
    ( ~ $less('#skE_1','#skE_2')
    | ~ $less(0,$sum('#skE_2','#skE_1')) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_486]) ).

tff(c_490,plain,
    ~ $less(0,$sum('#skE_2','#skE_1')),
    inference(splitLeft,[status(thm)],[c_488]) ).

tff(c_12,plain,
    ! [X_1a: $int] : $lesseq($uminus(X_1a),f(X_1a)),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_18,plain,
    ! [X_1a: $int] : ~ $less($sum(X_1a,f(X_1a)),0),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_12]) ).

tff(c_106,plain,
    ~ $less($sum('#skF_1','#skE_2'),0),
    inference(superposition,[status(thm),theory(equality)],[c_90,c_18]) ).

tff(c_108,plain,
    ~ $less($sum('#skE_2','#skF_1'),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_106]) ).

tff(c_330,plain,
    ~ $less($sum('#skE_2',$uminus('#skE_1')),0),
    inference(demodulation,[status(thm),theory(equality)],[c_325,c_108]) ).

tff(c_350,plain,
    ~ $less('#skE_2','#skE_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_330]) ).

tff(c_491,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_490,c_350,c_146,c_87]) ).

tff(c_494,plain,
    ~ $less('#skE_1','#skE_2'),
    inference(splitRight,[status(thm)],[c_488]) ).

tff(c_496,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_494,c_350,c_87]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : ARI617_1 : TPTP v8.1.2. Released v5.1.0.
% 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
% 0.15/0.34  % Computer : n027.cluster.edu
% 0.15/0.34  % Model    : x86_64 x86_64
% 0.15/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34  % Memory   : 8042.1875MB
% 0.15/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34  % CPULimit : 300
% 0.15/0.34  % WCLimit  : 300
% 0.15/0.34  % DateTime : Fri Aug  4 00:33:54 EDT 2023
% 0.15/0.34  % CPUTime  : 
% 3.58/1.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.70/1.95  
% 3.70/1.95  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.70/1.98  
% 3.70/1.98  Inference rules
% 3.70/1.98  ----------------------
% 3.70/1.98  #Ref     : 0
% 3.70/1.98  #Sup     : 62
% 3.70/1.98  #Fact    : 1
% 3.70/1.98  #Define  : 2
% 3.70/1.98  #Split   : 5
% 3.70/1.98  #Chain   : 0
% 3.70/1.98  #Close   : 4
% 3.70/1.98  
% 3.70/1.98  Ordering : LPO
% 3.70/1.98  
% 3.70/1.98  Simplification rules
% 3.70/1.98  ----------------------
% 3.70/1.98  #Subsume      : 12
% 3.70/1.98  #Demod        : 32
% 3.70/1.98  #Tautology    : 37
% 3.70/1.98  #SimpNegUnit  : 6
% 3.70/1.98  #BackRed      : 11
% 3.70/1.98  
% 3.70/1.98  #Partial instantiations: 0
% 3.70/1.98  #Strategies tried      : 1
% 3.70/1.98  
% 3.70/1.98  Timing (in seconds)
% 3.70/1.98  ----------------------
% 3.70/1.99  Preprocessing        : 0.51
% 3.70/1.99  Parsing              : 0.27
% 3.70/1.99  CNF conversion       : 0.02
% 3.70/1.99  Main loop            : 0.42
% 3.70/1.99  Inferencing          : 0.09
% 3.70/1.99  Reduction            : 0.08
% 3.70/1.99  Demodulation         : 0.05
% 3.70/1.99  BG Simplification    : 0.05
% 3.70/1.99  Subsumption          : 0.07
% 3.70/1.99  Abstraction          : 0.01
% 3.70/1.99  MUC search           : 0.04
% 3.70/1.99  Cooper               : 0.10
% 3.70/1.99  Total                : 0.99
% 3.70/1.99  Index Insertion      : 0.00
% 3.70/1.99  Index Deletion       : 0.00
% 3.70/1.99  Index Matching       : 0.00
% 3.70/1.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------