TSTP Solution File: DAT086_1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : DAT086_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/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 : n026.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 10:37:07 EDT 2023

% Result   : Theorem 254.96s 206.28s
% Output   : CNFRefutation 254.96s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   64 (  32 unt;  16 typ;   0 def)
%            Number of atoms       :   92 (  41 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   53 (   9   ~;  38   |;   4   &)
%                                         (   1 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number arithmetic     :  154 (  42 atm;  12 fun;  47 num;  53 var)
%            Number of types       :    3 (   1 usr;   1 ari)
%            Number of type conns  :   25 (  14   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  13 usr;   6 con; 0-2 aty)
%            Number of variables   :  103 (; 101   !;   2   ?; 103   :)

% 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_70,axiom,
    length(nil) = 0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l) ).

tff(f_87,axiom,
    ! [L: list] : ( append(nil,L) = L ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_6) ).

tff(f_89,axiom,
    ! [Ia: $int,K: list,L: list] : ( append(cons(Ia,K),L) = cons(Ia,append(K,L)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_7) ).

tff(f_72,axiom,
    ! [Ha: $int,T: list] : ( length(cons(Ha,T)) = $sum(1,length(T)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l_1) ).

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

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

tff(f_101,negated_conjecture,
    ~ ~ ! [L: list,Na: $int] :
          ( ( $greatereq(Na,3)
            & $greatereq(length(L),4) )
         => inRange(Na,L) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_9) ).

tff(f_68,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/sandbox/benchmark/theBenchmark.p',inRange) ).

tff(c_65,plain,
    length(nil) = 0,
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_311400,plain,
    ! [L_4142: list] : ( append(nil,L_4142) = L_4142 ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_311669,plain,
    ! [I_4221: $int,K_4222: list,L_4223: list] : ( cons(I_4221,append(K_4222,L_4223)) = append(cons(I_4221,K_4222),L_4223) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_311712,plain,
    ! [I_4221: $int,L_4142: list] : ( cons(I_4221,L_4142) = append(cons(I_4221,nil),L_4142) ),
    inference(superposition,[status(thm),theory(equality)],[c_311400,c_311669]) ).

tff(c_311399,plain,
    ! [I_4139: $int,K_4140: list,L_4141: list] : ( cons(I_4139,append(K_4140,L_4141)) = append(cons(I_4139,K_4140),L_4141) ),
    inference(cnfTransformation,[status(thm)],[f_89]) ).

tff(c_311805,plain,
    ! [I_4239: $int,L_4240: list] : ( cons(I_4239,L_4240) = append(cons(I_4239,nil),L_4240) ),
    inference(superposition,[status(thm),theory(equality)],[c_311400,c_311669]) ).

tff(c_314294,plain,
    ! [I_4390: $int,K_4391: list,L_4392: list] : ( append(cons(I_4390,nil),append(K_4391,L_4392)) = append(cons(I_4390,K_4391),L_4392) ),
    inference(superposition,[status(thm),theory(equality)],[c_311399,c_311805]) ).

tff(c_314568,plain,
    ! [I_4221: $int,L_4142: list,L_4392: list] : ( append(append(cons(I_4221,nil),L_4142),L_4392) = append(cons(I_4221,nil),append(L_4142,L_4392)) ),
    inference(superposition,[status(thm),theory(equality)],[c_311712,c_314294]) ).

tff(c_311404,plain,
    ! [H_4149: $int,T_4150: list] : ( length(cons(H_4149,T_4150)) = $sum(1,length(T_4150)) ),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_311833,plain,
    ! [I_4139: $int,I_4239: $int,L_4240: list] : ( cons(I_4139,cons(I_4239,L_4240)) = append(cons(I_4139,cons(I_4239,nil)),L_4240) ),
    inference(superposition,[status(thm),theory(equality)],[c_311805,c_311399]) ).

tff(c_320914,plain,
    ! [I_4601: $int,I_4602: $int,L_4603: list] : ( cons(I_4601,cons(I_4602,L_4603)) = append(append(cons(I_4601,nil),cons(I_4602,nil)),L_4603) ),
    inference(demodulation,[status(thm),theory(equality)],[c_311712,c_311833]) ).

tff(c_321232,plain,
    ! [I_4601: $int,I_4602: $int,L_4603: list] : ( length(append(append(cons(I_4601,nil),cons(I_4602,nil)),L_4603)) = $sum(1,length(cons(I_4602,L_4603))) ),
    inference(superposition,[status(thm),theory(equality)],[c_320914,c_311404]) ).

tff(c_321463,plain,
    ! [I_4601: $int,I_4602: $int,L_4603: list] : ( length(append(append(cons(I_4601,nil),cons(I_4602,nil)),L_4603)) = $sum(1,$sum(1,length(L_4603))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_311404,c_321232]) ).

tff(c_321465,plain,
    ! [I_4601: $int,I_4602: $int,L_4603: list] : ( length(append(append(cons(I_4601,nil),cons(I_4602,nil)),L_4603)) = $sum(2,length(L_4603)) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_321463]) ).

tff(c_325605,plain,
    ! [I_4661: $int,I_4662: $int,L_4663: list] : ( length(append(cons(I_4661,nil),append(cons(I_4662,nil),L_4663))) = $sum(2,length(L_4663)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_314568,c_321465]) ).

tff(c_325712,plain,
    ! [I_4661: $int,I_4221: $int,L_4142: list] : ( length(append(cons(I_4661,nil),cons(I_4221,L_4142))) = $sum(2,length(L_4142)) ),
    inference(superposition,[status(thm),theory(equality)],[c_311712,c_325605]) ).

tff(c_311417,plain,
    ! [K_4176: $int,L_4177: list] : ( cons(K_4176,L_4177) != nil ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_311710,plain,
    ! [I_4221: $int,K_4222: list,L_4223: list] : ( append(cons(I_4221,K_4222),L_4223) != nil ),
    inference(superposition,[status(thm),theory(equality)],[c_311669,c_311417]) ).

tff(c_311420,plain,
    ! [K_4181: $int,L_4182: list] : ( head(cons(K_4181,L_4182)) = K_4181 ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_311708,plain,
    ! [I_4221: $int,K_4222: list,L_4223: list] : ( head(append(cons(I_4221,K_4222),L_4223)) = I_4221 ),
    inference(superposition,[status(thm),theory(equality)],[c_311669,c_311420]) ).

tff(c_55,plain,
    ! [N_48a: $int,L_47: list] :
      ( inRange(N_48a,L_47)
      | ~ $greatereq(length(L_47),4)
      | ~ $greatereq(N_48a,3) ),
    inference(cnfTransformation,[status(thm)],[f_101]) ).

tff(c_311396,plain,
    ! [N_4133: $int,L_4134: list] :
      ( inRange(N_4133,L_4134)
      | $less(length(L_4134),4)
      | $less(N_4133,3) ),
    inference(backgroundSimplification,[status(thm),theory('LRFIA')],[c_55]) ).

tff(c_312113,plain,
    ! [N_4272: $int,L_4273: list] :
      ( ( cons('#skF_5'(N_4272,L_4273),'#skF_6'(N_4272,L_4273)) = L_4273 )
      | ( nil = L_4273 )
      | ~ inRange(N_4272,L_4273) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_312149,plain,
    ! [N_4277: $int,L_4278: list] :
      ( ( cons('#skF_5'(N_4277,L_4278),'#skF_6'(N_4277,L_4278)) = L_4278 )
      | ( nil = L_4278 )
      | $less(length(L_4278),4)
      | $less(N_4277,3) ),
    inference(resolution,[status(thm)],[c_311396,c_312113]) ).

tff(c_312937,plain,
    ! [L_4327: list,N_4328: $int] :
      ( ( head(L_4327) = '#skF_5'(N_4328,L_4327) )
      | ( nil = L_4327 )
      | $less(length(L_4327),4)
      | $less(N_4328,3) ),
    inference(superposition,[status(thm),theory(equality)],[c_312149,c_311420]) ).

tff(c_311713,plain,
    ! [N_4224: $int,L_4225: list] :
      ( $less('#skF_5'(N_4224,L_4225),N_4224)
      | ( nil = L_4225 )
      | ~ inRange(N_4224,L_4225) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_311726,plain,
    ! [N_4133: $int,L_4134: list] :
      ( $less('#skF_5'(N_4133,L_4134),N_4133)
      | ( nil = L_4134 )
      | $less(length(L_4134),4)
      | $less(N_4133,3) ),
    inference(resolution,[status(thm)],[c_311396,c_311713]) ).

tff(c_313039,plain,
    ! [L_4327: list,N_4328: $int] :
      ( $less(head(L_4327),N_4328)
      | ( nil = L_4327 )
      | $less(length(L_4327),4)
      | $less(N_4328,3)
      | ( nil = L_4327 )
      | $less(length(L_4327),4)
      | $less(N_4328,3) ),
    inference(superposition,[status(thm),theory(equality)],[c_312937,c_311726]) ).

tff(c_345307,plain,
    ! [L_4949: list,N_4950: $int] :
      ( $less(head(L_4949),N_4950)
      | ( nil = L_4949 )
      | $less(length(L_4949),4)
      | $less(N_4950,3) ),
    inference(factorization,[status(thm),theory(equality)],[c_313039]) ).

tff(c_345325,plain,
    ! [I_4661: $int,I_4221: $int,L_4142: list,N_4950: $int] :
      ( $less(head(append(cons(I_4661,nil),cons(I_4221,L_4142))),N_4950)
      | ( append(cons(I_4661,nil),cons(I_4221,L_4142)) = nil )
      | $less($sum(2,length(L_4142)),4)
      | $less(N_4950,3) ),
    inference(superposition,[status(thm),theory(equality)],[c_325712,c_345307]) ).

tff(c_345397,plain,
    ! [I_4661: $int,N_4950: $int,I_4221: $int,L_4142: list] :
      ( $less(I_4661,N_4950)
      | ( append(cons(I_4661,nil),cons(I_4221,L_4142)) = nil )
      | $less($sum(2,length(L_4142)),4)
      | $less(N_4950,3) ),
    inference(demodulation,[status(thm),theory(equality)],[c_311708,c_345325]) ).

tff(c_345398,plain,
    ! [I_4661: $int,N_4950: $int,L_4142: list] :
      ( $less(I_4661,N_4950)
      | $less($sum(2,length(L_4142)),4)
      | $less(N_4950,3) ),
    inference(negUnitSimplification,[status(thm)],[c_311710,c_345397]) ).

tff(c_345400,plain,
    ! [I_4661: $int,N_4950: $int,L_4142: list] :
      ( $less(I_4661,N_4950)
      | $less(length(L_4142),2)
      | $less(N_4950,3) ),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_345398]) ).

tff(c_345449,plain,
    ! [I_4661: $int,N_4950: $int] :
      ( $less(I_4661,N_4950)
      | $less(N_4950,3) ),
    inference(splitLeft,[status(thm)],[c_345400]) ).

tff(c_345451,plain,
    $false,
    inference(quantifierElimination,[status(thm),theory('LIA')],[c_345449]) ).

tff(c_345454,plain,
    ! [L_4951: list] : $less(length(L_4951),2),
    inference(splitRight,[status(thm)],[c_345400]) ).

tff(c_345462,plain,
    ! [L_4142: list] : $less($sum(2,length(L_4142)),2),
    inference(superposition,[status(thm),theory(equality)],[c_325712,c_345454]) ).

tff(c_345503,plain,
    ! [L_4952: list] : $less(length(L_4952),0),
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_345462]) ).

tff(c_345527,plain,
    $less(0,0),
    inference(superposition,[status(thm),theory(equality)],[c_65,c_345503]) ).

tff(c_345552,plain,
    $false,
    inference(backgroundSimplification,[status(thm),theory('LIA')],[c_345527]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : DAT086_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/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
% 0.13/0.34  % Computer : n026.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 13:30:31 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 129.24/101.60  ***********************************************************************
% 129.24/101.60  After 100.0 sec it's time to try something different, got 99.7 sec left
% 129.24/101.60  ***********************************************************************
% 245.22/201.49  ***********************************************************************
% 245.22/201.49  After 199.9 sec it's time to try something different, got 99.5 sec left
% 245.22/201.49  ***********************************************************************
% 254.96/206.28  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 254.96/206.28  
% 254.96/206.28  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 254.96/206.31  
% 254.96/206.31  Inference rules
% 254.96/206.31  ----------------------
% 254.96/206.31  #Ref     : 0
% 254.96/206.31  #Sup     : 70203
% 254.96/206.31  #Fact    : 5
% 254.96/206.31  #Define  : 0
% 254.96/206.31  #Split   : 5
% 254.96/206.31  #Chain   : 0
% 254.96/206.31  #Close   : 0
% 254.96/206.31  
% 254.96/206.31  Ordering : LPO
% 254.96/206.31  
% 254.96/206.31  Simplification rules
% 254.96/206.31  ----------------------
% 254.96/206.31  #Subsume      : 10543
% 254.96/206.31  #Demod        : 297153
% 254.96/206.31  #Tautology    : 15432
% 254.96/206.31  #SimpNegUnit  : 2349
% 254.96/206.31  #BackRed      : 33
% 254.96/206.31  
% 254.96/206.31  #Partial instantiations: 0
% 254.96/206.31  #Strategies tried      : 3
% 254.96/206.31  
% 254.96/206.31  Timing (in seconds)
% 254.96/206.31  ----------------------
% 254.96/206.31  Preprocessing        : 0.59
% 254.96/206.31  Parsing              : 0.31
% 254.96/206.31  CNF conversion       : 0.04
% 254.96/206.31  Main loop            : 204.66
% 254.96/206.32  Inferencing          : 8.88
% 254.96/206.32  Reduction            : 166.06
% 254.96/206.32  Demodulation         : 161.45
% 254.96/206.32  BG Simplification    : 3.03
% 254.96/206.32  Subsumption          : 19.95
% 254.96/206.32  Abstraction          : 2.52
% 254.96/206.32  MUC search           : 0.00
% 254.96/206.32  Cooper               : 0.02
% 254.96/206.32  Total                : 205.30
% 254.96/206.32  Index Insertion      : 0.00
% 254.96/206.32  Index Deletion       : 0.00
% 254.96/206.32  Index Matching       : 0.00
% 254.96/206.32  BG Taut test         : 0.00
%------------------------------------------------------------------------------