TSTP Solution File: NUM404+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : NUM404+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 : n025.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 10:51:35 EDT 2023

% Result   : Theorem 11.86s 3.93s
% Output   : CNFRefutation 11.86s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   41
% Syntax   : Number of formulae    :   82 (  13 unt;  33 typ;   0 def)
%            Number of atoms       :  108 (   9 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  102 (  43   ~;  40   |;   7   &)
%                                         (   5 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  18   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   14 (  12 usr;   1 prp; 0-2 aty)
%            Number of functors    :   21 (  21 usr;  15 con; 0-2 aty)
%            Number of variables   :   44 (;  44   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_non_empty > relation_empty_yielding > relation > ordinal > one_to_one > function > epsilon_transitive > epsilon_connected > empty > #nlpp > powerset > empty_set > #skF_5 > #skF_2 > #skF_18 > #skF_17 > #skF_11 > #skF_15 > #skF_1 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #skF_12 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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_19',type,
    '#skF_19': $i ).

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

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

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

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

tff('#skF_13',type,
    '#skF_13': $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_3',type,
    '#skF_3': $i > $i ).

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

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

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

tff(f_95,axiom,
    ! [A] :
      ( epsilon_connected(A)
    <=> ! [B,C] :
          ~ ( in(B,A)
            & in(C,A)
            & ~ in(B,C)
            & ( B != C )
            & ~ in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_ordinal1) ).

tff(f_78,axiom,
    ! [A] :
      ( epsilon_transitive(A)
    <=> ! [B] :
          ( in(B,A)
         => subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_ordinal1) ).

tff(f_250,negated_conjecture,
    ~ ! [A] :
        ~ ! [B] :
            ( in(B,A)
          <=> ordinal(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t37_ordinal1) ).

tff(f_108,axiom,
    ! [A] :
      ( ordinal(A)
    <=> ( epsilon_transitive(A)
        & epsilon_connected(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_ordinal1) ).

tff(f_31,axiom,
    ! [A,B] :
      ( in(A,B)
     => ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).

tff(f_102,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_222,axiom,
    ! [A,B] :
      ( ordinal(B)
     => ( in(A,B)
       => ordinal(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_ordinal1) ).

tff(f_237,axiom,
    ! [A] :
      ( ordinal(A)
     => ! [B] :
          ( ordinal(B)
         => ~ ( ~ in(A,B)
              & ( A != B )
              & ~ in(B,A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_ordinal1) ).

tff(c_1613,plain,
    ! [A_195] :
      ( ( '#skF_2'(A_195) != '#skF_3'(A_195) )
      | epsilon_connected(A_195) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_365,plain,
    ! [A_74] :
      ( in('#skF_1'(A_74),A_74)
      | epsilon_transitive(A_74) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_168,plain,
    ! [B_40] :
      ( ordinal(B_40)
      | ~ in(B_40,'#skF_19') ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_374,plain,
    ( ordinal('#skF_1'('#skF_19'))
    | epsilon_transitive('#skF_19') ),
    inference(resolution,[status(thm)],[c_365,c_168]) ).

tff(c_376,plain,
    epsilon_transitive('#skF_19'),
    inference(splitLeft,[status(thm)],[c_374]) ).

tff(c_334,plain,
    ! [A_71] :
      ( in('#skF_2'(A_71),A_71)
      | epsilon_connected(A_71) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_343,plain,
    ( ordinal('#skF_2'('#skF_19'))
    | epsilon_connected('#skF_19') ),
    inference(resolution,[status(thm)],[c_334,c_168]) ).

tff(c_344,plain,
    epsilon_connected('#skF_19'),
    inference(splitLeft,[status(thm)],[c_343]) ).

tff(c_50,plain,
    ! [A_25] :
      ( ordinal(A_25)
      | ~ epsilon_connected(A_25)
      | ~ epsilon_transitive(A_25) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_170,plain,
    ! [B_40] :
      ( in(B_40,'#skF_19')
      | ~ ordinal(B_40) ),
    inference(cnfTransformation,[status(thm)],[f_250]) ).

tff(c_378,plain,
    ! [B_77,A_78] :
      ( ~ in(B_77,A_78)
      | ~ in(A_78,B_77) ),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_391,plain,
    ! [B_79] :
      ( ~ in('#skF_19',B_79)
      | ~ ordinal(B_79) ),
    inference(resolution,[status(thm)],[c_170,c_378]) ).

tff(c_396,plain,
    ~ ordinal('#skF_19'),
    inference(resolution,[status(thm)],[c_170,c_391]) ).

tff(c_399,plain,
    ( ~ epsilon_connected('#skF_19')
    | ~ epsilon_transitive('#skF_19') ),
    inference(resolution,[status(thm)],[c_50,c_396]) ).

tff(c_406,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_376,c_344,c_399]) ).

tff(c_408,plain,
    ~ epsilon_transitive('#skF_19'),
    inference(splitRight,[status(thm)],[c_374]) ).

tff(c_407,plain,
    ordinal('#skF_1'('#skF_19')),
    inference(splitRight,[status(thm)],[c_374]) ).

tff(c_695,plain,
    ! [A_114,B_115] :
      ( in('#skF_4'(A_114,B_115),A_114)
      | subset(A_114,B_115) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_162,plain,
    ! [A_32,B_33] :
      ( ordinal(A_32)
      | ~ in(A_32,B_33)
      | ~ ordinal(B_33) ),
    inference(cnfTransformation,[status(thm)],[f_222]) ).

tff(c_1520,plain,
    ! [A_190,B_191] :
      ( ordinal('#skF_4'(A_190,B_191))
      | ~ ordinal(A_190)
      | subset(A_190,B_191) ),
    inference(resolution,[status(thm)],[c_695,c_162]) ).

tff(c_521,plain,
    ! [A_102,B_103] :
      ( ~ in('#skF_4'(A_102,B_103),B_103)
      | subset(A_102,B_103) ),
    inference(cnfTransformation,[status(thm)],[f_102]) ).

tff(c_526,plain,
    ! [A_102] :
      ( subset(A_102,'#skF_19')
      | ~ ordinal('#skF_4'(A_102,'#skF_19')) ),
    inference(resolution,[status(thm)],[c_170,c_521]) ).

tff(c_1534,plain,
    ! [A_192] :
      ( ~ ordinal(A_192)
      | subset(A_192,'#skF_19') ),
    inference(resolution,[status(thm)],[c_1520,c_526]) ).

tff(c_28,plain,
    ! [A_9] :
      ( ~ subset('#skF_1'(A_9),A_9)
      | epsilon_transitive(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1556,plain,
    ( epsilon_transitive('#skF_19')
    | ~ ordinal('#skF_1'('#skF_19')) ),
    inference(resolution,[status(thm)],[c_1534,c_28]) ).

tff(c_1565,plain,
    epsilon_transitive('#skF_19'),
    inference(demodulation,[status(thm),theory(equality)],[c_407,c_1556]) ).

tff(c_1567,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_408,c_1565]) ).

tff(c_1569,plain,
    ~ epsilon_connected('#skF_19'),
    inference(splitRight,[status(thm)],[c_343]) ).

tff(c_1617,plain,
    '#skF_2'('#skF_19') != '#skF_3'('#skF_19'),
    inference(resolution,[status(thm)],[c_1613,c_1569]) ).

tff(c_1574,plain,
    ! [A_193] :
      ( in('#skF_3'(A_193),A_193)
      | epsilon_connected(A_193) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_1581,plain,
    ( ordinal('#skF_3'('#skF_19'))
    | epsilon_connected('#skF_19') ),
    inference(resolution,[status(thm)],[c_1574,c_168]) ).

tff(c_1585,plain,
    ordinal('#skF_3'('#skF_19')),
    inference(negUnitSimplification,[status(thm)],[c_1569,c_1581]) ).

tff(c_1568,plain,
    ordinal('#skF_2'('#skF_19')),
    inference(splitRight,[status(thm)],[c_343]) ).

tff(c_2251,plain,
    ! [B_275,A_276] :
      ( in(B_275,A_276)
      | ( B_275 = A_276 )
      | in(A_276,B_275)
      | ~ ordinal(B_275)
      | ~ ordinal(A_276) ),
    inference(cnfTransformation,[status(thm)],[f_237]) ).

tff(c_38,plain,
    ! [A_13] :
      ( ~ in('#skF_2'(A_13),'#skF_3'(A_13))
      | epsilon_connected(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_5931,plain,
    ! [A_463] :
      ( epsilon_connected(A_463)
      | in('#skF_3'(A_463),'#skF_2'(A_463))
      | ( '#skF_2'(A_463) = '#skF_3'(A_463) )
      | ~ ordinal('#skF_3'(A_463))
      | ~ ordinal('#skF_2'(A_463)) ),
    inference(resolution,[status(thm)],[c_2251,c_38]) ).

tff(c_34,plain,
    ! [A_13] :
      ( ~ in('#skF_3'(A_13),'#skF_2'(A_13))
      | epsilon_connected(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_13140,plain,
    ! [A_587] :
      ( epsilon_connected(A_587)
      | ( '#skF_2'(A_587) = '#skF_3'(A_587) )
      | ~ ordinal('#skF_3'(A_587))
      | ~ ordinal('#skF_2'(A_587)) ),
    inference(resolution,[status(thm)],[c_5931,c_34]) ).

tff(c_13149,plain,
    ( epsilon_connected('#skF_19')
    | ( '#skF_2'('#skF_19') = '#skF_3'('#skF_19') )
    | ~ ordinal('#skF_3'('#skF_19')) ),
    inference(resolution,[status(thm)],[c_1568,c_13140]) ).

tff(c_13157,plain,
    ( epsilon_connected('#skF_19')
    | ( '#skF_2'('#skF_19') = '#skF_3'('#skF_19') ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1585,c_13149]) ).

tff(c_13159,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1617,c_1569,c_13157]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14  % Problem  : NUM404+1 : TPTP v8.1.2. Released v3.2.0.
% 0.13/0.15  % 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
% 0.15/0.36  % Computer : n025.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 15:01:49 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 11.86/3.93  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.86/3.93  
% 11.86/3.93  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.86/3.97  
% 11.86/3.97  Inference rules
% 11.86/3.97  ----------------------
% 11.86/3.97  #Ref     : 0
% 11.86/3.97  #Sup     : 2779
% 12.15/3.97  #Fact    : 8
% 12.15/3.97  #Define  : 0
% 12.15/3.97  #Split   : 29
% 12.15/3.97  #Chain   : 0
% 12.15/3.97  #Close   : 0
% 12.15/3.97  
% 12.15/3.97  Ordering : KBO
% 12.15/3.97  
% 12.15/3.97  Simplification rules
% 12.15/3.97  ----------------------
% 12.15/3.97  #Subsume      : 1304
% 12.15/3.97  #Demod        : 741
% 12.15/3.97  #Tautology    : 465
% 12.15/3.97  #SimpNegUnit  : 213
% 12.15/3.97  #BackRed      : 204
% 12.15/3.97  
% 12.15/3.97  #Partial instantiations: 0
% 12.15/3.97  #Strategies tried      : 1
% 12.15/3.97  
% 12.15/3.97  Timing (in seconds)
% 12.15/3.97  ----------------------
% 12.15/3.97  Preprocessing        : 0.59
% 12.15/3.97  Parsing              : 0.30
% 12.15/3.97  CNF conversion       : 0.05
% 12.15/3.97  Main loop            : 2.29
% 12.15/3.97  Inferencing          : 0.73
% 12.15/3.97  Reduction            : 0.74
% 12.15/3.97  Demodulation         : 0.52
% 12.15/3.97  BG Simplification    : 0.06
% 12.15/3.97  Subsumption          : 0.58
% 12.15/3.97  Abstraction          : 0.06
% 12.15/3.97  MUC search           : 0.00
% 12.15/3.97  Cooper               : 0.00
% 12.15/3.97  Total                : 2.93
% 12.15/3.97  Index Insertion      : 0.00
% 12.15/3.97  Index Deletion       : 0.00
% 12.15/3.97  Index Matching       : 0.00
% 12.15/3.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------