TSTP Solution File: DAT070_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT070_1 : TPTP v8.1.2. Released v5.5.0.
% 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 : n028.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 10:37:05 EDT 2023

% Result   : Theorem 3.59s 1.89s
% Output   : CNFRefutation 3.59s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   43 (  21 unt;  14 typ;   0 def)
%            Number of atoms       :   37 (  30 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   16 (   8   ~;   6   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :   59 (   5 atm;  23 fun;  19 num;  12 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   15 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :   18 (;  18   !;   0   ?;  18   :)

% Comments : 
%------------------------------------------------------------------------------
%$ lsls > sel > app > #nlpp > toop > length > get > empty > #skF_3

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

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

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

tff('#skF_2',type,
    '#skF_2': $int ).

tff('#skE_3',type,
    '#skE_3': $int ).

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

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

tff(lsls,type,
    lsls: ( heap * heap ) > $o ).

tff(empty,type,
    empty: heap ).

tff('#skF_3',type,
    '#skF_3': heap ).

tff(get,type,
    get: heap > heap ).

tff(sel,type,
    sel: ( heap * $int ) > $int ).

tff(app,type,
    app: ( heap * $int ) > heap ).

tff(length,type,
    length: heap > $int ).

tff(f_113,negated_conjecture,
    ~ ! [Na: $int,Ma: $int,H: heap] :
        ( ( sel(app(H,Na),Ma) = sel(H,Ma) )
        | ~ $less(Ma,$sum(1,length(H))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',th_5) ).

tff(f_62,axiom,
    ! [H: heap,Ma: $int,Na: $int] :
      ( ( Ma = $sum(1,length(H)) )
     => ( sel(app(H,Na),Ma) = Na ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT006_0.ax',ax_2) ).

tff(f_67,axiom,
    ! [Na: $int,H: heap,Ma: $int] :
      ( ( Ma != $sum(1,length(H)) )
     => ( sel(app(H,Na),Ma) = sel(H,Ma) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/DAT006_0.ax',ax_3) ).

tff(c_49,plain,
    $less('#skF_2',$sum(1,length('#skF_3'))),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_121,plain,
    length('#skF_3') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_49]) ).

tff(c_217,plain,
    ! [H_77: heap,N_78a: $int] : ( sel(app(H_77,N_78a),$sum(1,length(H_77))) = N_78a ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_294,plain,
    ! [N_92a: $int] : ( sel(app('#skF_3',N_92a),$sum(1,'#skE_1')) = N_92a ),
    inference(superposition,[status(thm),theory(equality)],[c_121,c_217]) ).

tff(c_45,plain,
    sel(app('#skF_3','#skF_1'),'#skF_2') != sel('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_197,plain,
    sel(app('#skF_3','#skF_1'),'#skF_2') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_45]) ).

tff(c_311,plain,
    ( ( '#skF_1' = '#skE_2' )
    | ( '#skF_2' != $sum(1,'#skE_1') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_294,c_197]) ).

tff(c_318,plain,
    '#skF_2' != $sum(1,'#skE_1'),
    inference(splitLeft,[status(thm)],[c_311]) ).

tff(c_190,plain,
    sel('#skF_3','#skF_2') = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_45]) ).

tff(c_189,plain,
    sel(app('#skF_3','#skF_1'),'#skF_2') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_45]) ).

tff(c_64,plain,
    sel(app('#skF_3','#skF_1'),'#skF_2') != sel('#skF_3','#skF_2'),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_201,plain,
    '#skE_3' != '#skE_2',
    inference(demodulation,[status(thm),theory(equality)],[c_190,c_189,c_64]) ).

tff(c_203,plain,
    sel('#skF_3','#skF_2') = '#skE_3',
    inference(define,[status(thm),theory(equality)],[c_45]) ).

tff(c_6,plain,
    ! [H_6: heap,N_5a: $int,M_7a: $int] :
      ( ( sel(app(H_6,N_5a),M_7a) = sel(H_6,M_7a) )
      | ( $sum(1,length(H_6)) = M_7a ) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_371,plain,
    ! [H_106: heap,N_107a: $int,M_108a: $int] :
      ( ( sel(app(H_106,N_107a),M_108a) = sel(H_106,M_108a) )
      | ( length(H_106) = $sum($uminus(1),M_108a) ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_6]) ).

tff(c_386,plain,
    ( ( sel('#skF_3','#skF_2') = '#skE_2' )
    | ( length('#skF_3') = $sum($uminus(1),'#skF_2') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_371,c_197]) ).

tff(c_418,plain,
    ( ( '#skE_3' = '#skE_2' )
    | ( $sum($uminus(1),'#skF_2') = '#skE_1' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_121,c_203,c_386]) ).

tff(c_419,plain,
    $sum($uminus(1),'#skF_2') = '#skE_1',
    inference(negUnitSimplification,[status(thm)],[c_201,c_418]) ).

tff(c_421,plain,
    '#skF_2' = $sum(1,'#skE_1'),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_419]) ).

tff(c_444,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_318,c_421]) ).

tff(c_448,plain,
    '#skF_2' = $sum(1,'#skE_1'),
    inference(splitRight,[status(thm)],[c_311]) ).

tff(c_118,plain,
    length('#skF_3') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_49]) ).

tff(c_65,plain,
    $less('#skF_2',$sum(1,length('#skF_3'))),
    inference(cnfTransformation,[status(thm)],[f_113]) ).

tff(c_122,plain,
    $less('#skF_2',$sum(1,'#skE_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_118,c_65]) ).

tff(c_462,plain,
    $less($sum(1,'#skE_1'),$sum(1,'#skE_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_448,c_122]) ).

tff(c_468,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_462]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT070_1 : TPTP v8.1.2. Released v5.5.0.
% 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
% 0.15/0.35  % Computer : n028.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 13:29:23 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 3.59/1.89  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.59/1.90  
% 3.59/1.90  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.59/1.92  
% 3.59/1.92  Inference rules
% 3.59/1.92  ----------------------
% 3.59/1.92  #Ref     : 2
% 3.59/1.92  #Sup     : 58
% 3.59/1.92  #Fact    : 0
% 3.59/1.92  #Define  : 3
% 3.59/1.92  #Split   : 2
% 3.59/1.92  #Chain   : 0
% 3.59/1.92  #Close   : 0
% 3.59/1.92  
% 3.59/1.92  Ordering : LPO
% 3.59/1.92  
% 3.59/1.92  Simplification rules
% 3.59/1.92  ----------------------
% 3.59/1.92  #Subsume      : 2
% 3.59/1.92  #Demod        : 22
% 3.59/1.92  #Tautology    : 43
% 3.59/1.92  #SimpNegUnit  : 6
% 3.59/1.92  #BackRed      : 3
% 3.59/1.92  
% 3.59/1.92  #Partial instantiations: 0
% 3.59/1.92  #Strategies tried      : 1
% 3.59/1.92  
% 3.59/1.92  Timing (in seconds)
% 3.59/1.92  ----------------------
% 3.59/1.92  Preprocessing        : 0.54
% 3.59/1.92  Parsing              : 0.29
% 3.59/1.92  CNF conversion       : 0.03
% 3.59/1.92  Main loop            : 0.33
% 3.59/1.92  Inferencing          : 0.10
% 3.59/1.92  Reduction            : 0.09
% 3.59/1.92  Demodulation         : 0.07
% 3.59/1.92  BG Simplification    : 0.04
% 3.59/1.92  Subsumption          : 0.06
% 3.59/1.92  Abstraction          : 0.01
% 3.59/1.92  MUC search           : 0.00
% 3.59/1.92  Cooper               : 0.02
% 3.59/1.93  Total                : 0.91
% 3.59/1.93  Index Insertion      : 0.00
% 3.59/1.93  Index Deletion       : 0.00
% 3.59/1.93  Index Matching       : 0.00
% 3.59/1.93  BG Taut test         : 0.00
%------------------------------------------------------------------------------