TSTP Solution File: DAT088_1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT088_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 : n002.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 10:37:08 EDT 2023

% Result   : Theorem 3.15s 1.77s
% Output   : CNFRefutation 3.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   35 (  12 unt;  16 typ;   0 def)
%            Number of atoms       :   29 (  16 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :   17 (   7   ~;   5   |;   2   &)
%                                         (   2 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number arithmetic     :   36 (   6 atm;   0 fun;   9 num;  21 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   25 (  14   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  13 usr;   2 con; 0-2 aty)
%            Number of variables   :   38 (;  34   !;   4   ?;  38   :)

% Comments : 
%------------------------------------------------------------------------------
%$ inRange > in > count > cons > append > #nlpp > tail > length > head > nil > #skF_4 > #skF_1 > #skF_2 > #skF_6 > #skF_3 > #skF_5

%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(length,type,
    length: list > $int ).

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

tff(append,type,
    append: ( list * list ) > list ).

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

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

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

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

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

tff('#skF_6',type,
    '#skF_6': ( $int * list ) > list ).

tff('#skF_3',type,
    '#skF_3': ( $int * list ) > $int ).

tff('#skF_5',type,
    '#skF_5': ( $int * list ) > $int ).

tff(f_75,axiom,
    ! [Ka: $int] : ( count(Ka,nil) = 0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a) ).

tff(f_41,axiom,
    ! [Ka: $int,L: list] : ( cons(Ka,L) != nil ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).

tff(f_33,axiom,
    ! [Ka: $int,L: list] : ( tail(cons(Ka,L)) = L ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2) ).

tff(f_100,negated_conjecture,
    ~ ~ ! [Na: $int,L: list] :
          ( ( L != nil )
         => ( count(Na,L) = count(Na,tail(L)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c) ).

tff(f_54,axiom,
    ! [Xa: $int,L: list] :
      ( in(Xa,L)
    <=> ( ? [Ha: $int,T: list] :
            ( ( L = cons(Ha,T) )
            & ( Xa = Ha ) )
        | ? [Ha: $int,T: list] :
            ( ( L = cons(Ha,T) )
            & in(Xa,T) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_conv) ).

tff(f_93,axiom,
    ! [Na: $int,L: list] :
      ( in(Na,L)
    <=> $greater(count(Na,L),0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_8) ).

tff(c_63,plain,
    ! [K_32a: $int] : ( count(K_32a,nil) = 0 ),
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_78,plain,
    ! [K_6a: $int,L_7: list] : ( cons(K_6a,L_7) != nil ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_80,plain,
    ! [K_3a: $int,L_4: list] : ( tail(cons(K_3a,L_4)) = L_4 ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_130,plain,
    ! [N_63a: $int,L_64: list] :
      ( ( count(N_63a,tail(L_64)) = count(N_63a,L_64) )
      | ( nil = L_64 ) ),
    inference(cnfTransformation,[status(thm)],[f_100]) ).

tff(c_139,plain,
    ! [N_63a: $int,K_3a: $int,L_4: list] :
      ( ( count(N_63a,cons(K_3a,L_4)) = count(N_63a,L_4) )
      | ( cons(K_3a,L_4) = nil ) ),
    inference(superposition,[status(thm),theory(equality)],[c_80,c_130]) ).

tff(c_145,plain,
    ! [N_63a: $int,K_3a: $int,L_4: list] : ( count(N_63a,cons(K_3a,L_4)) = count(N_63a,L_4) ),
    inference(negUnitSimplification,[status(thm)],[c_78,c_139]) ).

tff(c_72,plain,
    ! [H_18a: $int,T_19: list] : in(H_18a,cons(H_18a,T_19)),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_50,plain,
    ! [N_45a: $int,L_46: list] :
      ( $greater(count(N_45a,L_46),0)
      | ~ in(N_45a,L_46) ),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_178,plain,
    ! [N_70a: $int,L_71: list] :
      ( $less(0,count(N_70a,L_71))
      | ~ in(N_70a,L_71) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_50]) ).

tff(c_193,plain,
    ! [H_18a: $int,T_19: list] : $less(0,count(H_18a,cons(H_18a,T_19))),
    inference(resolution,[status(thm)],[c_72,c_178]) ).

tff(c_222,plain,
    ! [H_79a: $int,T_80: list] : $less(0,count(H_79a,T_80)),
    inference(demodulation,[status(thm),theory(equality)],[c_145,c_193]) ).

tff(c_228,plain,
    $less(0,0),
    inference(superposition,[status(thm),theory(equality)],[c_63,c_222]) ).

tff(c_233,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_228]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : DAT088_1 : TPTP v8.1.2. Released v6.1.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n002.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 13:28:46 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 3.15/1.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.36/1.78  
% 3.36/1.78  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.36/1.80  
% 3.36/1.80  Inference rules
% 3.36/1.80  ----------------------
% 3.36/1.80  #Ref     : 0
% 3.36/1.80  #Sup     : 28
% 3.36/1.80  #Fact    : 0
% 3.36/1.80  #Define  : 0
% 3.36/1.80  #Split   : 0
% 3.36/1.80  #Chain   : 0
% 3.36/1.80  #Close   : 0
% 3.36/1.80  
% 3.36/1.80  Ordering : LPO
% 3.36/1.80  
% 3.36/1.80  Simplification rules
% 3.36/1.80  ----------------------
% 3.36/1.80  #Subsume      : 0
% 3.36/1.80  #Demod        : 7
% 3.36/1.80  #Tautology    : 25
% 3.36/1.80  #SimpNegUnit  : 3
% 3.36/1.80  #BackRed      : 2
% 3.36/1.80  
% 3.36/1.80  #Partial instantiations: 0
% 3.36/1.80  #Strategies tried      : 1
% 3.36/1.80  
% 3.36/1.80  Timing (in seconds)
% 3.36/1.80  ----------------------
% 3.36/1.80  Preprocessing        : 0.56
% 3.36/1.80  Parsing              : 0.29
% 3.36/1.80  CNF conversion       : 0.04
% 3.36/1.80  Main loop            : 0.20
% 3.36/1.80  Inferencing          : 0.07
% 3.36/1.80  Reduction            : 0.06
% 3.36/1.80  Demodulation         : 0.04
% 3.36/1.80  BG Simplification    : 0.04
% 3.36/1.81  Subsumption          : 0.04
% 3.36/1.81  Abstraction          : 0.01
% 3.36/1.81  MUC search           : 0.00
% 3.36/1.81  Cooper               : 0.00
% 3.36/1.81  Total                : 0.80
% 3.36/1.81  Index Insertion      : 0.00
% 3.36/1.81  Index Deletion       : 0.00
% 3.36/1.81  Index Matching       : 0.00
% 3.36/1.81  BG Taut test         : 0.00
%------------------------------------------------------------------------------