TSTP Solution File: NUM414+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM414+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 : n014.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 5.17s 2.12s
% Output   : CNFRefutation 5.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   38
% Syntax   : Number of formulae    :   56 (   9 unt;  34 typ;   0 def)
%            Number of atoms       :   56 (   9 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   64 (  30   ~;  23   |;   5   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  17   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   17 (  15 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  17 con; 0-1 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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(powerset,type,
    powerset: $i > $i ).

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

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

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

tff(f_254,negated_conjecture,
    ~ ! [A] :
        ( ordinal(A)
       => ! [B] :
            ( ordinal(B)
           => ~ ( ~ proper_subset(A,B)
                & ( A != B )
                & ~ proper_subset(B,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t50_ordinal1) ).

tff(f_210,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
      <=> subset(A,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).

tff(f_91,axiom,
    ! [A,B] :
      ( proper_subset(A,B)
    <=> ( subset(A,B)
        & ( A != B ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_xboole_0) ).

tff(f_84,axiom,
    ! [A,B] :
      ( ( ordinal(A)
        & ordinal(B) )
     => ( ordinal_subset(A,B)
        | ordinal_subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).

tff(c_166,plain,
    '#skF_17' != '#skF_16',
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_172,plain,
    ordinal('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_170,plain,
    ordinal('#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_563,plain,
    ! [A_104,B_105] :
      ( subset(A_104,B_105)
      | ~ ordinal_subset(A_104,B_105)
      | ~ ordinal(B_105)
      | ~ ordinal(A_104) ),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_30,plain,
    ! [A_13,B_14] :
      ( proper_subset(A_13,B_14)
      | ( B_14 = A_13 )
      | ~ subset(A_13,B_14) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_605,plain,
    ! [A_117,B_118] :
      ( proper_subset(A_117,B_118)
      | ( B_118 = A_117 )
      | ~ ordinal_subset(A_117,B_118)
      | ~ ordinal(B_118)
      | ~ ordinal(A_117) ),
    inference(resolution,[status(thm)],[c_563,c_30]) ).

tff(c_168,plain,
    ~ proper_subset('#skF_16','#skF_17'),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_621,plain,
    ( ( '#skF_17' = '#skF_16' )
    | ~ ordinal_subset('#skF_16','#skF_17')
    | ~ ordinal('#skF_17')
    | ~ ordinal('#skF_16') ),
    inference(resolution,[status(thm)],[c_605,c_168]) ).

tff(c_632,plain,
    ( ( '#skF_17' = '#skF_16' )
    | ~ ordinal_subset('#skF_16','#skF_17') ),
    inference(demodulation,[status(thm),theory(equality)],[c_172,c_170,c_621]) ).

tff(c_633,plain,
    ~ ordinal_subset('#skF_16','#skF_17'),
    inference(negUnitSimplification,[status(thm)],[c_166,c_632]) ).

tff(c_28,plain,
    ! [B_12,A_11] :
      ( ordinal_subset(B_12,A_11)
      | ordinal_subset(A_11,B_12)
      | ~ ordinal(B_12)
      | ~ ordinal(A_11) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_164,plain,
    ~ proper_subset('#skF_17','#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_254]) ).

tff(c_624,plain,
    ( ( '#skF_17' = '#skF_16' )
    | ~ ordinal_subset('#skF_17','#skF_16')
    | ~ ordinal('#skF_16')
    | ~ ordinal('#skF_17') ),
    inference(resolution,[status(thm)],[c_605,c_164]) ).

tff(c_636,plain,
    ( ( '#skF_17' = '#skF_16' )
    | ~ ordinal_subset('#skF_17','#skF_16') ),
    inference(demodulation,[status(thm),theory(equality)],[c_170,c_172,c_624]) ).

tff(c_637,plain,
    ~ ordinal_subset('#skF_17','#skF_16'),
    inference(negUnitSimplification,[status(thm)],[c_166,c_636]) ).

tff(c_642,plain,
    ( ordinal_subset('#skF_16','#skF_17')
    | ~ ordinal('#skF_17')
    | ~ ordinal('#skF_16') ),
    inference(resolution,[status(thm)],[c_28,c_637]) ).

tff(c_648,plain,
    ordinal_subset('#skF_16','#skF_17'),
    inference(demodulation,[status(thm),theory(equality)],[c_172,c_170,c_642]) ).

tff(c_650,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_633,c_648]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : NUM414+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
% 0.13/0.35  % Computer : n014.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 14:33:48 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.17/2.12  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.17/2.12  
% 5.17/2.12  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.17/2.15  
% 5.17/2.15  Inference rules
% 5.17/2.15  ----------------------
% 5.17/2.15  #Ref     : 0
% 5.17/2.15  #Sup     : 86
% 5.17/2.15  #Fact    : 2
% 5.17/2.15  #Define  : 0
% 5.17/2.15  #Split   : 5
% 5.17/2.15  #Chain   : 0
% 5.17/2.15  #Close   : 0
% 5.17/2.15  
% 5.17/2.15  Ordering : KBO
% 5.17/2.15  
% 5.17/2.15  Simplification rules
% 5.17/2.15  ----------------------
% 5.17/2.15  #Subsume      : 12
% 5.17/2.15  #Demod        : 75
% 5.17/2.15  #Tautology    : 58
% 5.17/2.15  #SimpNegUnit  : 11
% 5.17/2.15  #BackRed      : 34
% 5.17/2.15  
% 5.17/2.15  #Partial instantiations: 0
% 5.17/2.15  #Strategies tried      : 1
% 5.17/2.15  
% 5.17/2.15  Timing (in seconds)
% 5.17/2.15  ----------------------
% 5.17/2.15  Preprocessing        : 0.57
% 5.17/2.15  Parsing              : 0.29
% 5.17/2.15  CNF conversion       : 0.05
% 5.17/2.15  Main loop            : 0.49
% 5.17/2.15  Inferencing          : 0.17
% 5.17/2.15  Reduction            : 0.15
% 5.17/2.15  Demodulation         : 0.10
% 5.17/2.15  BG Simplification    : 0.03
% 5.17/2.15  Subsumption          : 0.09
% 5.17/2.15  Abstraction          : 0.02
% 5.17/2.16  MUC search           : 0.00
% 5.17/2.16  Cooper               : 0.00
% 5.17/2.16  Total                : 1.10
% 5.17/2.16  Index Insertion      : 0.00
% 5.17/2.16  Index Deletion       : 0.00
% 5.17/2.16  Index Matching       : 0.00
% 5.17/2.16  BG Taut test         : 0.00
%------------------------------------------------------------------------------