TSTP Solution File: SWV019-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n016.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 11:02:40 EDT 2023

% Result   : Unsatisfiable 3.32s 1.82s
% Output   : CNFRefutation 3.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   55 (  24 unt;  10 typ;   0 def)
%            Number of atoms       :   88 (   6 equ)
%            Maximal formula atoms :    7 (   1 avg)
%            Number of connectives :   79 (  36   ~;  43   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :   25 (;  25   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ less_than > in_array_bounds > array_value_at > #nlpp > successor > upper_bound > maximal_value > lower_bound > index_of_maximal > array > an_index

%Foreground sorts:

%Background operators:

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

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

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

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

tff(array_value_at,type,
    array_value_at: ( $i * $i ) > $i ).

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

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

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

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

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

tff(f_53,axiom,
    ~ less_than(an_index,lower_bound),
    file(unknown,unknown) ).

tff(f_55,axiom,
    ~ less_than(upper_bound,an_index),
    file(unknown,unknown) ).

tff(f_51,axiom,
    less_than(index_of_maximal,an_index),
    file(unknown,unknown) ).

tff(f_46,axiom,
    ! [X] : less_than(X,successor(X)),
    file(unknown,unknown) ).

tff(f_44,axiom,
    ! [X,Y,Z] :
      ( ~ less_than(X,Y)
      | ~ less_than(Y,Z)
      | less_than(X,Z) ),
    file(unknown,unknown) ).

tff(f_31,axiom,
    ! [X1] :
      ( less_than(X1,lower_bound)
      | less_than(upper_bound,X1)
      | in_array_bounds(array,X1) ),
    file(unknown,unknown) ).

tff(f_57,axiom,
    ~ less_than(index_of_maximal,lower_bound),
    file(unknown,unknown) ).

tff(f_50,axiom,
    ( ~ in_array_bounds(array,index_of_maximal)
    | ( maximal_value = array_value_at(array,index_of_maximal) ) ),
    file(unknown,unknown) ).

tff(f_74,axiom,
    ( ~ in_array_bounds(array,an_index)
    | less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | ~ less_than(index_of_maximal,successor(an_index))
    | ~ in_array_bounds(array,index_of_maximal)
    | ( maximal_value != array_value_at(array,index_of_maximal) ) ),
    file(unknown,unknown) ).

tff(f_36,axiom,
    ! [X,Y] :
      ( ~ less_than(successor(X),successor(Y))
      | less_than(X,Y) ),
    file(unknown,unknown) ).

tff(c_14,plain,
    ~ less_than(an_index,lower_bound),
    inference(cnfTransformation,[status(thm)],[f_53]) ).

tff(c_16,plain,
    ~ less_than(upper_bound,an_index),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_12,plain,
    less_than(index_of_maximal,an_index),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_8,plain,
    ! [X_7] : less_than(X_7,successor(X_7)),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_84,plain,
    ! [X_19,Z_20,Y_21] :
      ( less_than(X_19,Z_20)
      | ~ less_than(Y_21,Z_20)
      | ~ less_than(X_19,Y_21) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_95,plain,
    ! [X_19,X_7] :
      ( less_than(X_19,successor(X_7))
      | ~ less_than(X_19,X_7) ),
    inference(resolution,[status(thm)],[c_8,c_84]) ).

tff(c_75,plain,
    ! [X1_18] :
      ( in_array_bounds(array,X1_18)
      | less_than(upper_bound,X1_18)
      | less_than(X1_18,lower_bound) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_78,plain,
    ( in_array_bounds(array,an_index)
    | less_than(an_index,lower_bound) ),
    inference(resolution,[status(thm)],[c_75,c_16]) ).

tff(c_83,plain,
    in_array_bounds(array,an_index),
    inference(negUnitSimplification,[status(thm)],[c_14,c_78]) ).

tff(c_18,plain,
    ~ less_than(index_of_maximal,lower_bound),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_10,plain,
    ( ( array_value_at(array,index_of_maximal) = maximal_value )
    | ~ in_array_bounds(array,index_of_maximal) ),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_23,plain,
    ~ in_array_bounds(array,index_of_maximal),
    inference(splitLeft,[status(thm)],[c_10]) ).

tff(c_2,plain,
    ! [X1_1] :
      ( in_array_bounds(array,X1_1)
      | less_than(upper_bound,X1_1)
      | less_than(X1_1,lower_bound) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_40,plain,
    ! [X_12,Z_13,Y_14] :
      ( less_than(X_12,Z_13)
      | ~ less_than(Y_14,Z_13)
      | ~ less_than(X_12,Y_14) ),
    inference(cnfTransformation,[status(thm)],[f_44]) ).

tff(c_53,plain,
    ! [X_15] :
      ( less_than(X_15,an_index)
      | ~ less_than(X_15,index_of_maximal) ),
    inference(resolution,[status(thm)],[c_12,c_40]) ).

tff(c_57,plain,
    ( less_than(upper_bound,an_index)
    | in_array_bounds(array,index_of_maximal)
    | less_than(index_of_maximal,lower_bound) ),
    inference(resolution,[status(thm)],[c_2,c_53]) ).

tff(c_61,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_23,c_16,c_57]) ).

tff(c_63,plain,
    in_array_bounds(array,index_of_maximal),
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_62,plain,
    array_value_at(array,index_of_maximal) = maximal_value,
    inference(splitRight,[status(thm)],[c_10]) ).

tff(c_20,plain,
    ( ( array_value_at(array,index_of_maximal) != maximal_value )
    | ~ in_array_bounds(array,index_of_maximal)
    | ~ less_than(index_of_maximal,successor(an_index))
    | less_than(index_of_maximal,lower_bound)
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(successor(an_index),lower_bound)
    | ~ in_array_bounds(array,an_index) ),
    inference(cnfTransformation,[status(thm)],[f_74]) ).

tff(c_21,plain,
    ( ( array_value_at(array,index_of_maximal) != maximal_value )
    | ~ in_array_bounds(array,index_of_maximal)
    | ~ less_than(index_of_maximal,successor(an_index))
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(successor(an_index),lower_bound)
    | ~ in_array_bounds(array,an_index) ),
    inference(negUnitSimplification,[status(thm)],[c_18,c_20]) ).

tff(c_209,plain,
    ( ~ less_than(index_of_maximal,successor(an_index))
    | less_than(successor(upper_bound),successor(an_index))
    | less_than(successor(an_index),lower_bound) ),
    inference(demodulation,[status(thm),theory(equality)],[c_83,c_63,c_62,c_21]) ).

tff(c_210,plain,
    ~ less_than(index_of_maximal,successor(an_index)),
    inference(splitLeft,[status(thm)],[c_209]) ).

tff(c_213,plain,
    ~ less_than(index_of_maximal,an_index),
    inference(resolution,[status(thm)],[c_95,c_210]) ).

tff(c_217,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12,c_213]) ).

tff(c_218,plain,
    ( less_than(successor(an_index),lower_bound)
    | less_than(successor(upper_bound),successor(an_index)) ),
    inference(splitRight,[status(thm)],[c_209]) ).

tff(c_284,plain,
    less_than(successor(upper_bound),successor(an_index)),
    inference(splitLeft,[status(thm)],[c_218]) ).

tff(c_4,plain,
    ! [X_2,Y_3] :
      ( less_than(X_2,Y_3)
      | ~ less_than(successor(X_2),successor(Y_3)) ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_295,plain,
    less_than(upper_bound,an_index),
    inference(resolution,[status(thm)],[c_284,c_4]) ).

tff(c_302,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_16,c_295]) ).

tff(c_303,plain,
    less_than(successor(an_index),lower_bound),
    inference(splitRight,[status(thm)],[c_218]) ).

tff(c_105,plain,
    ! [X_23,X_24] :
      ( less_than(X_23,successor(X_24))
      | ~ less_than(X_23,X_24) ),
    inference(resolution,[status(thm)],[c_8,c_84]) ).

tff(c_113,plain,
    ! [X_2,X_24] :
      ( less_than(X_2,X_24)
      | ~ less_than(successor(X_2),X_24) ),
    inference(resolution,[status(thm)],[c_105,c_4]) ).

tff(c_310,plain,
    less_than(an_index,lower_bound),
    inference(resolution,[status(thm)],[c_303,c_113]) ).

tff(c_317,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14,c_310]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWV019-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n016.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 23:06:38 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 3.32/1.82  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.32/1.83  
% 3.32/1.83  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.32/1.86  
% 3.32/1.86  Inference rules
% 3.32/1.86  ----------------------
% 3.32/1.86  #Ref     : 0
% 3.32/1.86  #Sup     : 57
% 3.32/1.86  #Fact    : 0
% 3.32/1.86  #Define  : 0
% 3.32/1.86  #Split   : 3
% 3.32/1.86  #Chain   : 0
% 3.32/1.86  #Close   : 0
% 3.32/1.86  
% 3.32/1.86  Ordering : KBO
% 3.32/1.86  
% 3.32/1.86  Simplification rules
% 3.32/1.86  ----------------------
% 3.32/1.86  #Subsume      : 1
% 3.32/1.86  #Demod        : 14
% 3.32/1.86  #Tautology    : 12
% 3.32/1.86  #SimpNegUnit  : 7
% 3.32/1.86  #BackRed      : 0
% 3.32/1.86  
% 3.32/1.86  #Partial instantiations: 0
% 3.32/1.86  #Strategies tried      : 1
% 3.32/1.86  
% 3.32/1.86  Timing (in seconds)
% 3.32/1.86  ----------------------
% 3.32/1.86  Preprocessing        : 0.44
% 3.32/1.86  Parsing              : 0.25
% 3.32/1.86  CNF conversion       : 0.02
% 3.32/1.87  Main loop            : 0.36
% 3.32/1.87  Inferencing          : 0.15
% 3.32/1.87  Reduction            : 0.08
% 3.32/1.87  Demodulation         : 0.06
% 3.32/1.87  BG Simplification    : 0.02
% 3.32/1.87  Subsumption          : 0.08
% 3.32/1.87  Abstraction          : 0.01
% 3.32/1.87  MUC search           : 0.00
% 3.32/1.87  Cooper               : 0.00
% 3.32/1.87  Total                : 0.85
% 3.32/1.87  Index Insertion      : 0.00
% 3.32/1.87  Index Deletion       : 0.00
% 3.32/1.87  Index Matching       : 0.00
% 3.32/1.87  BG Taut test         : 0.00
%------------------------------------------------------------------------------