TSTP Solution File: NUM405+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM405+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n004.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 10:51:36 EDT 2023

% Result   : Theorem 8.00s 2.81s
% Output   : CNFRefutation 8.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   64 (   8 unt;  30 typ;   0 def)
%            Number of atoms       :   68 (   0 equ)
%            Maximal formula atoms :    3 (   2 avg)
%            Number of connectives :   65 (  31   ~;  26   |;   3   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   17 (  15   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  11 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  15 con; 0-1 aty)
%            Number of variables   :   31 (;  30   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > empty_set > #skF_16 > #skF_18 > #skF_11 > #skF_1 > #skF_7 > #skF_10 > #skF_15 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_9 > #skF_8 > #skF_4 > #skF_17 > #skF_12

%Foreground sorts:

%Background operators:

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

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

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff('#skF_18',type,
    '#skF_18': $i ).

tff('#skF_11',type,
    '#skF_11': $i ).

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

tff('#skF_1',type,
    '#skF_1': $i > $i ).

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

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

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

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

tff('#skF_7',type,
    '#skF_7': $i ).

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

tff('#skF_10',type,
    '#skF_10': $i ).

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

tff('#skF_15',type,
    '#skF_15': $i > $i ).

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

tff('#skF_14',type,
    '#skF_14': $i ).

tff('#skF_5',type,
    '#skF_5': $i ).

tff('#skF_6',type,
    '#skF_6': $i ).

tff('#skF_13',type,
    '#skF_13': $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_3',type,
    '#skF_3': $i ).

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

tff('#skF_9',type,
    '#skF_9': $i ).

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

tff('#skF_8',type,
    '#skF_8': $i ).

tff('#skF_4',type,
    '#skF_4': $i ).

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff('#skF_12',type,
    '#skF_12': $i ).

tff(f_197,axiom,
    ! [A] :
      ~ ! [B] :
          ( in(B,A)
        <=> ordinal(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).

tff(f_181,axiom,
    ! [A] :
    ? [B] :
    ! [C] :
      ( in(C,B)
    <=> ( in(C,A)
        & ordinal(C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e2_43__ordinal1) ).

tff(f_41,axiom,
    ! [A] :
      ( ordinal(A)
     => ( epsilon_transitive(A)
        & epsilon_connected(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_ordinal1) ).

tff(f_63,axiom,
    ! [A] :
      ( ( epsilon_transitive(A)
        & epsilon_connected(A) )
     => ordinal(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc2_ordinal1) ).

tff(f_204,negated_conjecture,
    ~ ! [A] :
        ~ ! [B] :
            ( ordinal(B)
           => in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t38_ordinal1) ).

tff(c_410,plain,
    ! [A_60] :
      ( ordinal('#skF_16'(A_60))
      | in('#skF_17'(A_60),A_60) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_130,plain,
    ! [C_16,A_11] :
      ( ordinal(C_16)
      | ~ in(C_16,'#skF_15'(A_11)) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_592,plain,
    ! [A_78] :
      ( ordinal('#skF_17'('#skF_15'(A_78)))
      | ordinal('#skF_16'('#skF_15'(A_78))) ),
    inference(resolution,[status(thm)],[c_410,c_130]) ).

tff(c_8,plain,
    ! [A_4] :
      ( epsilon_transitive(A_4)
      | ~ ordinal(A_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_635,plain,
    ! [A_82] :
      ( epsilon_transitive('#skF_16'('#skF_15'(A_82)))
      | ordinal('#skF_17'('#skF_15'(A_82))) ),
    inference(resolution,[status(thm)],[c_592,c_8]) ).

tff(c_317,plain,
    ! [A_51] :
      ( ordinal('#skF_16'(A_51))
      | ~ ordinal('#skF_17'(A_51)) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_325,plain,
    ! [A_51] :
      ( epsilon_transitive('#skF_16'(A_51))
      | ~ ordinal('#skF_17'(A_51)) ),
    inference(resolution,[status(thm)],[c_317,c_8]) ).

tff(c_649,plain,
    ! [A_82] : epsilon_transitive('#skF_16'('#skF_15'(A_82))),
    inference(resolution,[status(thm)],[c_635,c_325]) ).

tff(c_6,plain,
    ! [A_4] :
      ( epsilon_connected(A_4)
      | ~ ordinal(A_4) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_618,plain,
    ! [A_81] :
      ( epsilon_connected('#skF_16'('#skF_15'(A_81)))
      | ordinal('#skF_17'('#skF_15'(A_81))) ),
    inference(resolution,[status(thm)],[c_592,c_6]) ).

tff(c_324,plain,
    ! [A_51] :
      ( epsilon_connected('#skF_16'(A_51))
      | ~ ordinal('#skF_17'(A_51)) ),
    inference(resolution,[status(thm)],[c_317,c_6]) ).

tff(c_631,plain,
    ! [A_81] : epsilon_connected('#skF_16'('#skF_15'(A_81))),
    inference(resolution,[status(thm)],[c_618,c_324]) ).

tff(c_18,plain,
    ! [A_7] :
      ( ordinal(A_7)
      | ~ epsilon_connected(A_7)
      | ~ epsilon_transitive(A_7) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_146,plain,
    ! [B_24] :
      ( in(B_24,'#skF_18')
      | ~ ordinal(B_24) ),
    inference(cnfTransformation,[status(thm)],[f_204]) ).

tff(c_554,plain,
    ! [C_73,A_74] :
      ( in(C_73,'#skF_15'(A_74))
      | ~ ordinal(C_73)
      | ~ in(C_73,A_74) ),
    inference(cnfTransformation,[status(thm)],[f_181]) ).

tff(c_138,plain,
    ! [A_21] :
      ( ~ in('#skF_16'(A_21),A_21)
      | ~ ordinal('#skF_17'(A_21)) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_1106,plain,
    ! [A_110] :
      ( ~ ordinal('#skF_17'('#skF_15'(A_110)))
      | ~ ordinal('#skF_16'('#skF_15'(A_110)))
      | ~ in('#skF_16'('#skF_15'(A_110)),A_110) ),
    inference(resolution,[status(thm)],[c_554,c_138]) ).

tff(c_1129,plain,
    ( ~ ordinal('#skF_17'('#skF_15'('#skF_18')))
    | ~ ordinal('#skF_16'('#skF_15'('#skF_18'))) ),
    inference(resolution,[status(thm)],[c_146,c_1106]) ).

tff(c_1138,plain,
    ~ ordinal('#skF_16'('#skF_15'('#skF_18'))),
    inference(splitLeft,[status(thm)],[c_1129]) ).

tff(c_1153,plain,
    ( ~ epsilon_connected('#skF_16'('#skF_15'('#skF_18')))
    | ~ epsilon_transitive('#skF_16'('#skF_15'('#skF_18'))) ),
    inference(resolution,[status(thm)],[c_18,c_1138]) ).

tff(c_1164,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_649,c_631,c_1153]) ).

tff(c_1165,plain,
    ~ ordinal('#skF_17'('#skF_15'('#skF_18'))),
    inference(splitRight,[status(thm)],[c_1129]) ).

tff(c_1166,plain,
    ordinal('#skF_16'('#skF_15'('#skF_18'))),
    inference(splitRight,[status(thm)],[c_1129]) ).

tff(c_142,plain,
    ! [A_21] :
      ( ~ in('#skF_16'(A_21),A_21)
      | in('#skF_17'(A_21),A_21) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_1199,plain,
    ! [A_114] :
      ( in('#skF_17'('#skF_15'(A_114)),'#skF_15'(A_114))
      | ~ ordinal('#skF_16'('#skF_15'(A_114)))
      | ~ in('#skF_16'('#skF_15'(A_114)),A_114) ),
    inference(resolution,[status(thm)],[c_554,c_142]) ).

tff(c_3897,plain,
    ! [A_172] :
      ( ordinal('#skF_17'('#skF_15'(A_172)))
      | ~ ordinal('#skF_16'('#skF_15'(A_172)))
      | ~ in('#skF_16'('#skF_15'(A_172)),A_172) ),
    inference(resolution,[status(thm)],[c_1199,c_130]) ).

tff(c_3933,plain,
    ( ordinal('#skF_17'('#skF_15'('#skF_18')))
    | ~ ordinal('#skF_16'('#skF_15'('#skF_18'))) ),
    inference(resolution,[status(thm)],[c_146,c_3897]) ).

tff(c_3940,plain,
    ordinal('#skF_17'('#skF_15'('#skF_18'))),
    inference(demodulation,[status(thm),theory(equality)],[c_1166,c_3933]) ).

tff(c_3942,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1165,c_3940]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM405+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 14:47:26 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 8.00/2.81  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.00/2.82  
% 8.00/2.82  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.13/2.85  
% 8.13/2.85  Inference rules
% 8.13/2.85  ----------------------
% 8.13/2.85  #Ref     : 0
% 8.13/2.85  #Sup     : 991
% 8.13/2.85  #Fact    : 0
% 8.13/2.85  #Define  : 0
% 8.13/2.85  #Split   : 14
% 8.13/2.85  #Chain   : 0
% 8.13/2.85  #Close   : 0
% 8.13/2.85  
% 8.13/2.85  Ordering : KBO
% 8.13/2.85  
% 8.13/2.85  Simplification rules
% 8.13/2.85  ----------------------
% 8.13/2.85  #Subsume      : 394
% 8.13/2.85  #Demod        : 447
% 8.13/2.85  #Tautology    : 212
% 8.13/2.85  #SimpNegUnit  : 15
% 8.13/2.85  #BackRed      : 20
% 8.13/2.85  
% 8.13/2.85  #Partial instantiations: 0
% 8.13/2.85  #Strategies tried      : 1
% 8.13/2.85  
% 8.13/2.85  Timing (in seconds)
% 8.13/2.85  ----------------------
% 8.13/2.85  Preprocessing        : 0.54
% 8.13/2.85  Parsing              : 0.29
% 8.13/2.85  CNF conversion       : 0.05
% 8.13/2.85  Main loop            : 1.25
% 8.13/2.85  Inferencing          : 0.40
% 8.13/2.85  Reduction            : 0.41
% 8.13/2.85  Demodulation         : 0.28
% 8.13/2.85  BG Simplification    : 0.05
% 8.13/2.85  Subsumption          : 0.32
% 8.13/2.85  Abstraction          : 0.04
% 8.13/2.85  MUC search           : 0.00
% 8.13/2.85  Cooper               : 0.00
% 8.13/2.85  Total                : 1.84
% 8.13/2.85  Index Insertion      : 0.00
% 8.13/2.85  Index Deletion       : 0.00
% 8.13/2.85  Index Matching       : 0.00
% 8.13/2.85  BG Taut test         : 0.00
%------------------------------------------------------------------------------