TSTP Solution File: DAT103_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT103_1 : TPTP v8.1.2. Released v6.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n003.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 10:37:09 EDT 2023

% Result   : Theorem 3.23s 1.97s
% Output   : CNFRefutation 3.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   39 (  20 unt;  12 typ;   0 def)
%            Number of atoms       :   41 (  21 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   20 (   6   ~;   8   |;   5   &)
%                                         (   1 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   31 (  13 atm;   5 fun;   6 num;   7 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  10 usr;   7 con; 0-2 aty)
%            Number of variables   :   14 (;  10   !;   4   ?;  14   :)

% Comments : 
%------------------------------------------------------------------------------
%$ inRange > cons > #nlpp > tail > head > nil > #skF_3 > #skF_1 > #skF_2

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

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

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

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

%Foreground operators:
tff('#skF_3',type,
    '#skF_3': list ).

tff(inRange,type,
    inRange: ( $int * list ) > $o ).

tff(tail,type,
    tail: list > list ).

tff(nil,type,
    nil: list ).

tff(head,type,
    head: list > $int ).

tff(cons,type,
    cons: ( $int * list ) > list ).

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

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

tff(f_64,negated_conjecture,
    ~ ~ ? [L: list,Na: $int] :
          ( ( L != nil )
          & inRange(Na,L)
          & $less($difference(Na,head(L)),1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).

tff(f_55,axiom,
    ! [Na: $int,L: list] :
      ( inRange(Na,L)
    <=> ( ( L = nil )
        | ? [Ka: $int,T: list] :
            ( ( L = cons(Ka,T) )
            & $lesseq(0,Ka)
            & $less(Ka,Na)
            & inRange(Na,T) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inRange) ).

tff(f_31,axiom,
    ! [Ka: $int,L: list] : ( head(cons(Ka,L)) = Ka ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).

tff(c_24,plain,
    $less($difference('#skF_4',head('#skF_3')),1),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_37,plain,
    $less('#skF_4',$sum(1,head('#skF_3'))),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).

tff(c_78,plain,
    head('#skF_3') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_37]) ).

tff(c_29,plain,
    nil != '#skF_3',
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_33,plain,
    inRange('#skF_4','#skF_3'),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_145,plain,
    ! [N_34a: $int,L_35: list] :
      ( $less('#skF_1'(N_34a,L_35),N_34a)
      | ( nil = L_35 )
      | ~ inRange(N_34a,L_35) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_151,plain,
    ( $less('#skF_1'('#skF_4','#skF_3'),'#skF_4')
    | ( nil = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_33,c_145]) ).

tff(c_161,plain,
    $less('#skF_1'('#skF_4','#skF_3'),'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_29,c_151]) ).

tff(c_176,plain,
    '#skF_1'('#skF_4','#skF_3') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_161]) ).

tff(c_209,plain,
    ! [N_43a: $int,L_44: list] :
      ( ( cons('#skF_1'(N_43a,L_44),'#skF_2'(N_43a,L_44)) = L_44 )
      | ( nil = L_44 )
      | ~ inRange(N_43a,L_44) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_215,plain,
    ( ( cons('#skF_1'('#skF_4','#skF_3'),'#skF_2'('#skF_4','#skF_3')) = '#skF_3' )
    | ( nil = '#skF_3' ) ),
    inference(resolution,[status(thm)],[c_33,c_209]) ).

tff(c_223,plain,
    ( ( cons('#skE_2','#skF_2'('#skF_4','#skF_3')) = '#skF_3' )
    | ( nil = '#skF_3' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_176,c_215]) ).

tff(c_233,plain,
    cons('#skE_2','#skF_2'('#skF_4','#skF_3')) = '#skF_3',
    inference(negUnitSimplification,[status(thm)],[c_29,c_223]) ).

tff(c_47,plain,
    ! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_252,plain,
    head('#skF_3') = '#skE_2',
    inference(superposition,[status(thm),theory(equality)],[c_233,c_47]) ).

tff(c_261,plain,
    '#skE_2' = '#skE_1',
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_252]) ).

tff(c_167,plain,
    '#skF_1'('#skF_4','#skF_3') = '#skE_2',
    inference(define,[status(thm),theory(equality)],[c_161]) ).

tff(c_166,plain,
    $less('#skF_1'('#skF_4','#skF_3'),'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_29,c_151]) ).

tff(c_174,plain,
    $less('#skE_2','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_166]) ).

tff(c_283,plain,
    $less('#skE_1','#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_261,c_174]) ).

tff(c_75,plain,
    head('#skF_3') = '#skE_1',
    inference(define,[status(thm),theory(equality)],[c_37]) ).

tff(c_49,plain,
    $less('#skF_4',$sum(1,head('#skF_3'))),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).

tff(c_79,plain,
    $less('#skF_4',$sum(1,'#skE_1')),
    inference(demodulation,[status(thm),theory(equality)],[c_75,c_49]) ).

tff(c_284,plain,
    $false,
    inference(close,[status(thm),theory('LIA')],[c_283,c_79]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : DAT103_1 : TPTP v8.1.2. Released v6.1.0.
% 0.12/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 13:14:38 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.23/1.97  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.44/1.97  
% 3.44/1.97  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.44/2.00  
% 3.44/2.00  Inference rules
% 3.44/2.00  ----------------------
% 3.44/2.00  #Ref     : 0
% 3.44/2.00  #Sup     : 32
% 3.44/2.00  #Fact    : 0
% 3.44/2.00  #Define  : 2
% 3.44/2.00  #Split   : 0
% 3.44/2.00  #Chain   : 0
% 3.44/2.00  #Close   : 1
% 3.44/2.00  
% 3.44/2.00  Ordering : LPO
% 3.44/2.00  
% 3.44/2.00  Simplification rules
% 3.44/2.00  ----------------------
% 3.44/2.00  #Subsume      : 2
% 3.44/2.00  #Demod        : 12
% 3.44/2.00  #Tautology    : 21
% 3.44/2.00  #SimpNegUnit  : 6
% 3.44/2.00  #BackRed      : 4
% 3.44/2.00  
% 3.44/2.00  #Partial instantiations: 0
% 3.44/2.00  #Strategies tried      : 1
% 3.44/2.00  
% 3.44/2.00  Timing (in seconds)
% 3.44/2.00  ----------------------
% 3.44/2.00  Preprocessing        : 0.55
% 3.44/2.00  Parsing              : 0.29
% 3.44/2.00  CNF conversion       : 0.03
% 3.44/2.00  Main loop            : 0.29
% 3.44/2.00  Inferencing          : 0.09
% 3.44/2.00  Reduction            : 0.07
% 3.44/2.00  Demodulation         : 0.05
% 3.44/2.00  BG Simplification    : 0.03
% 3.44/2.00  Subsumption          : 0.04
% 3.44/2.00  Abstraction          : 0.01
% 3.44/2.00  MUC search           : 0.00
% 3.44/2.00  Cooper               : 0.03
% 3.44/2.00  Total                : 0.88
% 3.44/2.00  Index Insertion      : 0.00
% 3.44/2.00  Index Deletion       : 0.00
% 3.44/2.00  Index Matching       : 0.00
% 3.44/2.00  BG Taut test         : 0.00
%------------------------------------------------------------------------------