TSTP Solution File: NUM016-1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n006.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 10:50:51 EDT 2023

% Result   : Unsatisfiable 3.06s 1.73s
% Output   : CNFRefutation 3.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   32 (  11 unt;   6 typ;   0 def)
%            Number of atoms       :   45 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   43 (  24   ~;  19   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   1 con; 0-1 aty)
%            Number of variables   :   20 (;  20   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less > divides > prime > #nlpp > prime_divisor > factorial_plus_one > a

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(prime_divisor,type,
    prime_divisor: $i > $i ).

tff(factorial_plus_one,type,
    factorial_plus_one: $i > $i ).

tff(a,type,
    a: $i ).

tff(less,type,
    less: ( $i * $i ) > $o ).

tff(prime,type,
    prime: $i > $o ).

tff(divides,type,
    divides: ( $i * $i ) > $o ).

tff(f_54,axiom,
    ! [X] : less(X,factorial_plus_one(X)),
    file(unknown,unknown) ).

tff(f_80,axiom,
    ! [X] :
      ( ~ prime(X)
      | ~ less(a,X)
      | less(factorial_plus_one(a),X) ),
    file(unknown,unknown) ).

tff(f_30,axiom,
    ! [X] : ~ less(X,X),
    file(unknown,unknown) ).

tff(f_63,axiom,
    ! [X] :
      ( prime(X)
      | divides(prime_divisor(X),X) ),
    file(unknown,unknown) ).

tff(f_59,axiom,
    ! [X,Y] :
      ( ~ divides(X,factorial_plus_one(Y))
      | less(Y,X) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [X] :
      ( prime(X)
      | prime(prime_divisor(X)) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [X,Y] :
      ( ~ divides(X,Y)
      | ~ less(Y,X) ),
    file(unknown,unknown) ).

tff(c_12,plain,
    ! [X_10] : less(X_10,factorial_plus_one(X_10)),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_71,plain,
    ! [X_34] :
      ( less(factorial_plus_one(a),X_34)
      | ~ less(a,X_34)
      | ~ prime(X_34) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_2,plain,
    ! [X_1] : ~ less(X_1,X_1),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_88,plain,
    ( ~ less(a,factorial_plus_one(a))
    | ~ prime(factorial_plus_one(a)) ),
    inference(resolution,[status(thm)],[c_71,c_2]) ).

tff(c_97,plain,
    ~ prime(factorial_plus_one(a)),
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_88]) ).

tff(c_16,plain,
    ! [X_13] :
      ( divides(prime_divisor(X_13),X_13)
      | prime(X_13) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_51,plain,
    ! [Y_31,X_32] :
      ( less(Y_31,X_32)
      | ~ divides(X_32,factorial_plus_one(Y_31)) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_60,plain,
    ! [Y_31] :
      ( less(Y_31,prime_divisor(factorial_plus_one(Y_31)))
      | prime(factorial_plus_one(Y_31)) ),
    inference(resolution,[status(thm)],[c_16,c_51]) ).

tff(c_18,plain,
    ! [X_14] :
      ( prime(prime_divisor(X_14))
      | prime(X_14) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_10,plain,
    ! [Y_9,X_8] :
      ( ~ less(Y_9,X_8)
      | ~ divides(X_8,Y_9) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_107,plain,
    ! [X_40] :
      ( ~ divides(X_40,factorial_plus_one(a))
      | ~ less(a,X_40)
      | ~ prime(X_40) ),
    inference(resolution,[status(thm)],[c_71,c_10]) ).

tff(c_111,plain,
    ( ~ less(a,prime_divisor(factorial_plus_one(a)))
    | ~ prime(prime_divisor(factorial_plus_one(a)))
    | prime(factorial_plus_one(a)) ),
    inference(resolution,[status(thm)],[c_16,c_107]) ).

tff(c_118,plain,
    ( ~ less(a,prime_divisor(factorial_plus_one(a)))
    | ~ prime(prime_divisor(factorial_plus_one(a))) ),
    inference(negUnitSimplification,[status(thm)],[c_97,c_111]) ).

tff(c_155,plain,
    ~ prime(prime_divisor(factorial_plus_one(a))),
    inference(splitLeft,[status(thm)],[c_118]) ).

tff(c_158,plain,
    prime(factorial_plus_one(a)),
    inference(resolution,[status(thm)],[c_18,c_155]) ).

tff(c_162,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_97,c_158]) ).

tff(c_163,plain,
    ~ less(a,prime_divisor(factorial_plus_one(a))),
    inference(splitRight,[status(thm)],[c_118]) ).

tff(c_167,plain,
    prime(factorial_plus_one(a)),
    inference(resolution,[status(thm)],[c_60,c_163]) ).

tff(c_171,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_97,c_167]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : NUM016-1 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.13/0.35  % Computer : n006.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 14:34:28 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.06/1.73  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.06/1.74  
% 3.06/1.74  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.06/1.76  
% 3.06/1.76  Inference rules
% 3.06/1.76  ----------------------
% 3.06/1.76  #Ref     : 0
% 3.06/1.76  #Sup     : 24
% 3.06/1.76  #Fact    : 0
% 3.06/1.76  #Define  : 0
% 3.06/1.77  #Split   : 1
% 3.06/1.77  #Chain   : 0
% 3.06/1.77  #Close   : 0
% 3.06/1.77  
% 3.06/1.77  Ordering : KBO
% 3.06/1.77  
% 3.06/1.77  Simplification rules
% 3.06/1.77  ----------------------
% 3.06/1.77  #Subsume      : 6
% 3.06/1.77  #Demod        : 6
% 3.06/1.77  #Tautology    : 2
% 3.06/1.77  #SimpNegUnit  : 4
% 3.06/1.77  #BackRed      : 0
% 3.06/1.77  
% 3.06/1.77  #Partial instantiations: 0
% 3.06/1.77  #Strategies tried      : 1
% 3.06/1.77  
% 3.06/1.77  Timing (in seconds)
% 3.06/1.77  ----------------------
% 3.06/1.77  Preprocessing        : 0.42
% 3.06/1.77  Parsing              : 0.23
% 3.06/1.77  CNF conversion       : 0.02
% 3.06/1.77  Main loop            : 0.29
% 3.06/1.77  Inferencing          : 0.13
% 3.06/1.77  Reduction            : 0.06
% 3.06/1.77  Demodulation         : 0.04
% 3.06/1.77  BG Simplification    : 0.01
% 3.06/1.77  Subsumption          : 0.07
% 3.06/1.77  Abstraction          : 0.01
% 3.06/1.77  MUC search           : 0.00
% 3.06/1.77  Cooper               : 0.00
% 3.06/1.77  Total                : 0.76
% 3.06/1.77  Index Insertion      : 0.00
% 3.06/1.77  Index Deletion       : 0.00
% 3.06/1.77  Index Matching       : 0.00
% 3.06/1.77  BG Taut test         : 0.00
%------------------------------------------------------------------------------