TSTP Solution File: DAT105_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT105_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 : n029.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 10:37:10 EDT 2023

% Result   : Theorem 3.07s 1.72s
% Output   : CNFRefutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   24 (   6 unt;   8 typ;   0 def)
%            Number of atoms       :   46 (  11 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   54 (  24   ~;  24   |;   4   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :   64 (  21 atm;   7 fun;  14 num;  22 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (;  34   !;   2   ?;  36   :)

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

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

%Background operators:

%Foreground operators:
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_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_41,axiom,
    ! [Ka: $int,L: list] : ( cons(Ka,L) != nil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).

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

tff(f_64,negated_conjecture,
    ~ ~ ! [L: list,Na: $int] :
          ( ( ( L != nil )
            & inRange(Na,L) )
         => $greatereq($difference(Na,head(L)),2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).

tff(c_27,plain,
    ! [N_8a: $int] : inRange(N_8a,nil),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_33,plain,
    ! [K_6a: $int,L_7: list] : ( cons(K_6a,L_7) != nil ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_36,plain,
    ! [K_1a: $int,L_2: list] : ( head(cons(K_1a,L_2)) = K_1a ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_19,plain,
    ! [N_8a: $int,T_15: list,K_14a: $int] :
      ( ~ inRange(N_8a,T_15)
      | inRange(N_8a,cons(K_14a,T_15))
      | ~ $lesseq(0,K_14a)
      | ~ $less(K_14a,N_8a) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_140,plain,
    ! [N_38a: $int,T_39: list,K_40a: $int] :
      ( ~ inRange(N_38a,T_39)
      | inRange(N_38a,cons(K_40a,T_39))
      | $less(K_40a,0)
      | ~ $less(K_40a,N_38a) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_19]) ).

tff(c_24,plain,
    ! [N_17a: $int,L_16: list] :
      ( $greatereq($difference(N_17a,head(L_16)),2)
      | ~ inRange(N_17a,L_16)
      | ( nil = L_16 ) ),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_26,plain,
    ! [N_17a: $int,L_16: list] :
      ( ~ $less(N_17a,$sum(2,head(L_16)))
      | ~ inRange(N_17a,L_16)
      | ( nil = L_16 ) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_24]) ).

tff(c_149,plain,
    ! [N_38a: $int,K_40a: $int,T_39: list] :
      ( ~ $less(N_38a,$sum(2,head(cons(K_40a,T_39))))
      | ( cons(K_40a,T_39) = nil )
      | ~ inRange(N_38a,T_39)
      | $less(K_40a,0)
      | ~ $less(K_40a,N_38a) ),
    inference(resolution,[status(thm)],[c_140,c_26]) ).

tff(c_165,plain,
    ! [N_38a: $int,K_40a: $int,T_39: list] :
      ( ~ $less(N_38a,$sum(2,K_40a))
      | ( cons(K_40a,T_39) = nil )
      | ~ inRange(N_38a,T_39)
      | $less(K_40a,0)
      | ~ $less(K_40a,N_38a) ),
    inference(demodulation,[status(thm),theory(equality)],[c_36,c_149]) ).

tff(c_176,plain,
    ! [N_41a: $int,K_42a: $int,T_43: list] :
      ( ~ $less(N_41a,$sum(2,K_42a))
      | ~ inRange(N_41a,T_43)
      | $less(K_42a,0)
      | ~ $less(K_42a,N_41a) ),
    inference(negUnitSimplification,[status(thm)],[c_33,c_165]) ).

tff(c_189,plain,
    ! [N_8a: $int,K_42a: $int] :
      ( ~ $less(N_8a,$sum(2,K_42a))
      | $less(K_42a,0)
      | ~ $less(K_42a,N_8a) ),
    inference(resolution,[status(thm)],[c_27,c_176]) ).

tff(c_191,plain,
    $false,
    inference(quantifierElimination,[status(thm),theory('LIA')],[c_189]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT105_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.13  % 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
% 0.13/0.34  % Computer : n029.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 13:30:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.07/1.72  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.07/1.72  
% 3.07/1.72  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.74  
% 3.15/1.74  Inference rules
% 3.15/1.74  ----------------------
% 3.15/1.74  #Ref     : 0
% 3.15/1.74  #Sup     : 26
% 3.15/1.74  #Fact    : 0
% 3.15/1.74  #Define  : 0
% 3.15/1.74  #Split   : 0
% 3.15/1.74  #Chain   : 0
% 3.15/1.74  #Close   : 0
% 3.15/1.74  
% 3.15/1.74  Ordering : LPO
% 3.15/1.74  
% 3.15/1.74  Simplification rules
% 3.15/1.74  ----------------------
% 3.15/1.74  #Subsume      : 3
% 3.15/1.74  #Demod        : 3
% 3.15/1.74  #Tautology    : 13
% 3.15/1.74  #SimpNegUnit  : 7
% 3.15/1.74  #BackRed      : 0
% 3.15/1.74  
% 3.15/1.74  #Partial instantiations: 0
% 3.15/1.74  #Strategies tried      : 1
% 3.15/1.74  
% 3.15/1.74  Timing (in seconds)
% 3.15/1.74  ----------------------
% 3.15/1.75  Preprocessing        : 0.49
% 3.15/1.75  Parsing              : 0.27
% 3.15/1.75  CNF conversion       : 0.03
% 3.15/1.75  Main loop            : 0.23
% 3.15/1.75  Inferencing          : 0.08
% 3.15/1.75  Reduction            : 0.05
% 3.15/1.75  Demodulation         : 0.04
% 3.15/1.75  BG Simplification    : 0.03
% 3.15/1.75  Subsumption          : 0.04
% 3.15/1.75  Abstraction          : 0.01
% 3.15/1.75  MUC search           : 0.00
% 3.15/1.75  Cooper               : 0.02
% 3.15/1.75  Total                : 0.76
% 3.15/1.75  Index Insertion      : 0.00
% 3.15/1.75  Index Deletion       : 0.00
% 3.15/1.75  Index Matching       : 0.00
% 3.15/1.75  BG Taut test         : 0.00
%------------------------------------------------------------------------------