TSTP Solution File: NUM913_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM913_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 : n018.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 10:53:03 EDT 2023

% Result   : Theorem 3.42s 2.17s
% Output   : CNFRefutation 3.74s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   48 (  30 unt;   4 typ;   0 def)
%            Number of atoms       :   65 (  19 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   56 (  35   ~;  20   |;   0   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number arithmetic     :   38 (  36 atm;   0 fun;   0 num;   2 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    2 (;   2   !;   0   ?;   2   :)

% Comments : 
%------------------------------------------------------------------------------
%$ #nlpp

%Foreground sorts:

%Background operators:
tff('#skF_2',type,
    '#skF_2': $real ).

tff('#skF_4',type,
    '#skF_4': $real ).

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

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

%Foreground operators:

tff(f_34,negated_conjecture,
    ~ ! [Xa: $real,Ya: $real] :
        ( $lesseq(Xa,Ya)
      <=> ( $less(Xa,Ya)
          | ( Xa = Ya ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_combined_problem_1) ).

tff(c_4,plain,
    ( ~ $less('#skF_3','#skF_4')
    | ~ $lesseq('#skF_1','#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_62,plain,
    ~ $lesseq('#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_4]) ).

tff(c_9,plain,
    ( $lesseq('#skF_3','#skF_4')
    | $less('#skF_1','#skF_2')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_10,plain,
    ( ~ $less('#skF_4','#skF_3')
    | ~ $lesseq('#skF_2','#skF_1')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_9]) ).

tff(c_24,plain,
    ~ $lesseq('#skF_2','#skF_1'),
    inference(splitLeft,[status(thm)],[c_10]) ).

tff(c_1,plain,
    ( ( '#skF_4' != '#skF_3' )
    | ~ $lesseq('#skF_1','#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_11,plain,
    ~ $lesseq('#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_1]) ).

tff(c_25,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_24,c_11]) ).

tff(c_26,plain,
    ( ~ $less('#skF_4','#skF_3')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_29,plain,
    ~ $less('#skF_4','#skF_3'),
    inference(splitLeft,[status(thm)],[c_26]) ).

tff(c_5,plain,
    ( ~ $less('#skF_3','#skF_4')
    | $less('#skF_1','#skF_2')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_6,plain,
    ( ~ $less('#skF_3','#skF_4')
    | ~ $lesseq('#skF_2','#skF_1')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_5]) ).

tff(c_18,plain,
    ~ $lesseq('#skF_2','#skF_1'),
    inference(splitLeft,[status(thm)],[c_6]) ).

tff(c_19,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_18,c_11]) ).

tff(c_20,plain,
    ( ~ $less('#skF_3','#skF_4')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(splitRight,[status(thm)],[c_6]) ).

tff(c_23,plain,
    ~ $less('#skF_3','#skF_4'),
    inference(splitLeft,[status(thm)],[c_20]) ).

tff(c_2,plain,
    ( ( '#skF_4' != '#skF_3' )
    | $less('#skF_1','#skF_2')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_3,plain,
    ( ( '#skF_4' != '#skF_3' )
    | ~ $lesseq('#skF_2','#skF_1')
    | ( '#skF_2' = '#skF_1' ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_2]) ).

tff(c_12,plain,
    ~ $lesseq('#skF_2','#skF_1'),
    inference(splitLeft,[status(thm)],[c_3]) ).

tff(c_13,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_12,c_11]) ).

tff(c_14,plain,
    ( ( '#skF_4' != '#skF_3' )
    | ( '#skF_2' = '#skF_1' ) ),
    inference(splitRight,[status(thm)],[c_3]) ).

tff(c_17,plain,
    '#skF_4' != '#skF_3',
    inference(splitLeft,[status(thm)],[c_14]) ).

tff(c_30,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_29,c_23,c_17]) ).

tff(c_31,plain,
    '#skF_2' = '#skF_1',
    inference(splitRight,[status(thm)],[c_26]) ).

tff(c_36,plain,
    ~ $lesseq('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_31,c_11]) ).

tff(c_38,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_36]) ).

tff(c_39,plain,
    '#skF_2' = '#skF_1',
    inference(splitRight,[status(thm)],[c_20]) ).

tff(c_44,plain,
    ~ $lesseq('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_39,c_11]) ).

tff(c_46,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_44]) ).

tff(c_47,plain,
    '#skF_2' = '#skF_1',
    inference(splitRight,[status(thm)],[c_14]) ).

tff(c_51,plain,
    ~ $lesseq('#skF_1','#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_47,c_11]) ).

tff(c_53,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_51]) ).

tff(c_55,plain,
    $lesseq('#skF_1','#skF_2'),
    inference(splitRight,[status(thm)],[c_1]) ).

tff(c_56,plain,
    ~ $less('#skF_2','#skF_1'),
    inference(backgroundSimplification,[status(thm),theory('LFA')],[c_55]) ).

tff(c_63,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_62,c_56]) ).

tff(c_64,plain,
    ~ $less('#skF_3','#skF_4'),
    inference(splitRight,[status(thm)],[c_4]) ).

tff(c_7,plain,
    ( $lesseq('#skF_3','#skF_4')
    | ~ $lesseq('#skF_1','#skF_2') ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_8,plain,
    ( ~ $less('#skF_4','#skF_3')
    | ~ $lesseq('#skF_1','#skF_2') ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_7]) ).

tff(c_57,plain,
    ~ $lesseq('#skF_1','#skF_2'),
    inference(splitLeft,[status(thm)],[c_8]) ).

tff(c_58,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_57,c_56]) ).

tff(c_59,plain,
    ~ $less('#skF_4','#skF_3'),
    inference(splitRight,[status(thm)],[c_8]) ).

tff(c_54,plain,
    '#skF_4' != '#skF_3',
    inference(splitRight,[status(thm)],[c_1]) ).

tff(c_67,plain,
    $false,
    inference(close,[status(thm),theory('LFA')],[c_64,c_59,c_54]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : NUM913_1 : TPTP v8.1.2. Released v5.0.0.
% 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
% 0.15/0.37  % Computer : n018.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 300
% 0.15/0.37  % DateTime : Thu Aug  3 15:12:35 EDT 2023
% 0.15/0.37  % CPUTime  : 
% 3.42/2.17  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.42/2.18  
% 3.42/2.18  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.74/2.22  
% 3.74/2.22  Inference rules
% 3.74/2.22  ----------------------
% 3.74/2.22  #Ref     : 0
% 3.74/2.22  #Sup     : 0
% 3.74/2.22  #Fact    : 0
% 3.74/2.22  #Define  : 0
% 3.74/2.22  #Split   : 9
% 3.74/2.22  #Chain   : 0
% 3.74/2.22  #Close   : 7
% 3.74/2.22  
% 3.74/2.22  Ordering : LPO
% 3.74/2.22  
% 3.74/2.22  Simplification rules
% 3.74/2.22  ----------------------
% 3.74/2.22  #Subsume      : 5
% 3.74/2.22  #Demod        : 6
% 3.74/2.22  #Tautology    : 3
% 3.74/2.22  #SimpNegUnit  : 0
% 3.74/2.22  #BackRed      : 3
% 3.74/2.22  
% 3.74/2.22  #Partial instantiations: 0
% 3.74/2.22  #Strategies tried      : 1
% 3.74/2.22  
% 3.74/2.22  Timing (in seconds)
% 3.74/2.22  ----------------------
% 3.74/2.22  Preprocessing        : 0.50
% 3.74/2.22  Parsing              : 0.25
% 3.74/2.22  CNF conversion       : 0.02
% 3.74/2.22  Main loop            : 0.53
% 3.74/2.22  Inferencing          : 0.00
% 3.74/2.22  Reduction            : 0.05
% 3.74/2.22  Demodulation         : 0.04
% 3.74/2.22  BG Simplification    : 0.03
% 3.74/2.22  Subsumption          : 0.04
% 3.74/2.22  Abstraction          : 0.00
% 3.74/2.22  MUC search           : 0.20
% 3.74/2.22  Cooper               : 0.00
% 3.74/2.22  Total                : 1.10
% 3.74/2.22  Index Insertion      : 0.00
% 3.74/2.22  Index Deletion       : 0.00
% 3.74/2.22  Index Matching       : 0.00
% 3.74/2.22  BG Taut test         : 0.00
%------------------------------------------------------------------------------