TSTP Solution File: SEU242+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% 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 10:58:09 EDT 2023

% Result   : Theorem 12.26s 4.09s
% Output   : CNFRefutation 12.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   83 (  21 unt;  27 typ;   0 def)
%            Number of atoms       :  148 (  22 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  162 (  70   ~;  78   |;   8   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   26 (  18   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;   9 con; 0-2 aty)
%            Number of variables   :   37 (;  37   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ is_connected_in > in > element > relation > one_to_one > function > empty > connected > unordered_pair > set_union2 > ordered_pair > #nlpp > singleton > relation_rng > relation_field > relation_dom > empty_set > #skF_11 > #skF_7 > #skF_10 > #skF_5 > #skF_6 > #skF_9 > #skF_8 > #skF_4 > #skF_3 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

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

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

tff(f_125,negated_conjecture,
    ~ ! [A] :
        ( relation(A)
       => ( connected(A)
        <=> ! [B,C] :
              ~ ( in(B,relation_field(A))
                & in(C,relation_field(A))
                & ( B != C )
                & ~ in(ordered_pair(B,C),A)
                & ~ in(ordered_pair(C,B),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).

tff(f_83,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( is_connected_in(A,B)
        <=> ! [C,D] :
              ~ ( in(C,B)
                & in(D,B)
                & ( C != D )
                & ~ in(ordered_pair(C,D),A)
                & ~ in(ordered_pair(D,C),A) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).

tff(f_57,axiom,
    ! [A] :
      ( relation(A)
     => ( connected(A)
      <=> is_connected_in(A,relation_field(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).

tff(c_72,plain,
    ( ( '#skF_5' != '#skF_6' )
    | ~ connected('#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_123,plain,
    ~ connected('#skF_4'),
    inference(splitLeft,[status(thm)],[c_72]) ).

tff(c_66,plain,
    relation('#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_34,plain,
    ! [A_13,B_23] :
      ( in('#skF_1'(A_13,B_23),B_23)
      | is_connected_in(A_13,B_23)
      | ~ relation(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_32,plain,
    ! [A_13,B_23] :
      ( in('#skF_2'(A_13,B_23),B_23)
      | is_connected_in(A_13,B_23)
      | ~ relation(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_90,plain,
    ! [C_45,B_44] :
      ( connected('#skF_4')
      | in(ordered_pair(C_45,B_44),'#skF_4')
      | in(ordered_pair(B_44,C_45),'#skF_4')
      | ( C_45 = B_44 )
      | ~ in(C_45,relation_field('#skF_4'))
      | ~ in(B_44,relation_field('#skF_4')) ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_415,plain,
    ! [C_45,B_44] :
      ( in(ordered_pair(C_45,B_44),'#skF_4')
      | in(ordered_pair(B_44,C_45),'#skF_4')
      | ( C_45 = B_44 )
      | ~ in(C_45,relation_field('#skF_4'))
      | ~ in(B_44,relation_field('#skF_4')) ),
    inference(negUnitSimplification,[status(thm)],[c_123,c_90]) ).

tff(c_1050,plain,
    ! [A_138,B_139] :
      ( ~ in(ordered_pair('#skF_2'(A_138,B_139),'#skF_1'(A_138,B_139)),A_138)
      | is_connected_in(A_138,B_139)
      | ~ relation(A_138) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_1058,plain,
    ! [B_139] :
      ( is_connected_in('#skF_4',B_139)
      | ~ relation('#skF_4')
      | in(ordered_pair('#skF_1'('#skF_4',B_139),'#skF_2'('#skF_4',B_139)),'#skF_4')
      | ( '#skF_2'('#skF_4',B_139) = '#skF_1'('#skF_4',B_139) )
      | ~ in('#skF_1'('#skF_4',B_139),relation_field('#skF_4'))
      | ~ in('#skF_2'('#skF_4',B_139),relation_field('#skF_4')) ),
    inference(resolution,[status(thm)],[c_415,c_1050]) ).

tff(c_3767,plain,
    ! [B_196] :
      ( is_connected_in('#skF_4',B_196)
      | in(ordered_pair('#skF_1'('#skF_4',B_196),'#skF_2'('#skF_4',B_196)),'#skF_4')
      | ( '#skF_2'('#skF_4',B_196) = '#skF_1'('#skF_4',B_196) )
      | ~ in('#skF_1'('#skF_4',B_196),relation_field('#skF_4'))
      | ~ in('#skF_2'('#skF_4',B_196),relation_field('#skF_4')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_1058]) ).

tff(c_28,plain,
    ! [A_13,B_23] :
      ( ~ in(ordered_pair('#skF_1'(A_13,B_23),'#skF_2'(A_13,B_23)),A_13)
      | is_connected_in(A_13,B_23)
      | ~ relation(A_13) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_3774,plain,
    ! [B_196] :
      ( ~ relation('#skF_4')
      | is_connected_in('#skF_4',B_196)
      | ( '#skF_2'('#skF_4',B_196) = '#skF_1'('#skF_4',B_196) )
      | ~ in('#skF_1'('#skF_4',B_196),relation_field('#skF_4'))
      | ~ in('#skF_2'('#skF_4',B_196),relation_field('#skF_4')) ),
    inference(resolution,[status(thm)],[c_3767,c_28]) ).

tff(c_8220,plain,
    ! [B_251] :
      ( is_connected_in('#skF_4',B_251)
      | ( '#skF_2'('#skF_4',B_251) = '#skF_1'('#skF_4',B_251) )
      | ~ in('#skF_1'('#skF_4',B_251),relation_field('#skF_4'))
      | ~ in('#skF_2'('#skF_4',B_251),relation_field('#skF_4')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_3774]) ).

tff(c_8224,plain,
    ( ( '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')) )
    | ~ in('#skF_1'('#skF_4',relation_field('#skF_4')),relation_field('#skF_4'))
    | is_connected_in('#skF_4',relation_field('#skF_4'))
    | ~ relation('#skF_4') ),
    inference(resolution,[status(thm)],[c_32,c_8220]) ).

tff(c_8230,plain,
    ( ( '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')) )
    | ~ in('#skF_1'('#skF_4',relation_field('#skF_4')),relation_field('#skF_4'))
    | is_connected_in('#skF_4',relation_field('#skF_4')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8224]) ).

tff(c_8232,plain,
    ~ in('#skF_1'('#skF_4',relation_field('#skF_4')),relation_field('#skF_4')),
    inference(splitLeft,[status(thm)],[c_8230]) ).

tff(c_8235,plain,
    ( is_connected_in('#skF_4',relation_field('#skF_4'))
    | ~ relation('#skF_4') ),
    inference(resolution,[status(thm)],[c_34,c_8232]) ).

tff(c_8241,plain,
    is_connected_in('#skF_4',relation_field('#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8235]) ).

tff(c_16,plain,
    ! [A_9] :
      ( connected(A_9)
      | ~ is_connected_in(A_9,relation_field(A_9))
      | ~ relation(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_8245,plain,
    ( connected('#skF_4')
    | ~ relation('#skF_4') ),
    inference(resolution,[status(thm)],[c_8241,c_16]) ).

tff(c_8248,plain,
    connected('#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8245]) ).

tff(c_8250,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_123,c_8248]) ).

tff(c_8251,plain,
    ( is_connected_in('#skF_4',relation_field('#skF_4'))
    | ( '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')) ) ),
    inference(splitRight,[status(thm)],[c_8230]) ).

tff(c_8456,plain,
    '#skF_2'('#skF_4',relation_field('#skF_4')) = '#skF_1'('#skF_4',relation_field('#skF_4')),
    inference(splitLeft,[status(thm)],[c_8251]) ).

tff(c_751,plain,
    ! [A_123,B_124] :
      ( ( '#skF_2'(A_123,B_124) != '#skF_1'(A_123,B_124) )
      | is_connected_in(A_123,B_124)
      | ~ relation(A_123) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_756,plain,
    ! [A_123] :
      ( connected(A_123)
      | ( '#skF_2'(A_123,relation_field(A_123)) != '#skF_1'(A_123,relation_field(A_123)) )
      | ~ relation(A_123) ),
    inference(resolution,[status(thm)],[c_751,c_16]) ).

tff(c_8494,plain,
    ( connected('#skF_4')
    | ~ relation('#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_8456,c_756]) ).

tff(c_8526,plain,
    connected('#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8494]) ).

tff(c_8528,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_123,c_8526]) ).

tff(c_8529,plain,
    is_connected_in('#skF_4',relation_field('#skF_4')),
    inference(splitRight,[status(thm)],[c_8251]) ).

tff(c_8533,plain,
    ( connected('#skF_4')
    | ~ relation('#skF_4') ),
    inference(resolution,[status(thm)],[c_8529,c_16]) ).

tff(c_8536,plain,
    connected('#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8533]) ).

tff(c_8538,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_123,c_8536]) ).

tff(c_8539,plain,
    '#skF_5' != '#skF_6',
    inference(splitRight,[status(thm)],[c_72]) ).

tff(c_8540,plain,
    connected('#skF_4'),
    inference(splitRight,[status(thm)],[c_72]) ).

tff(c_68,plain,
    ( ~ in(ordered_pair('#skF_6','#skF_5'),'#skF_4')
    | ~ connected('#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_8644,plain,
    ~ in(ordered_pair('#skF_6','#skF_5'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_8540,c_68]) ).

tff(c_76,plain,
    ( in('#skF_5',relation_field('#skF_4'))
    | ~ connected('#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_8548,plain,
    in('#skF_5',relation_field('#skF_4')),
    inference(demodulation,[status(thm),theory(equality)],[c_8540,c_76]) ).

tff(c_18,plain,
    ! [A_9] :
      ( is_connected_in(A_9,relation_field(A_9))
      | ~ connected(A_9)
      | ~ relation(A_9) ),
    inference(cnfTransformation,[status(thm)],[f_57]) ).

tff(c_74,plain,
    ( in('#skF_6',relation_field('#skF_4'))
    | ~ connected('#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_8541,plain,
    ~ connected('#skF_4'),
    inference(splitLeft,[status(thm)],[c_74]) ).

tff(c_8543,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8540,c_8541]) ).

tff(c_8544,plain,
    in('#skF_6',relation_field('#skF_4')),
    inference(splitRight,[status(thm)],[c_74]) ).

tff(c_9419,plain,
    ! [D_338,C_339,A_340,B_341] :
      ( in(ordered_pair(D_338,C_339),A_340)
      | in(ordered_pair(C_339,D_338),A_340)
      | ( D_338 = C_339 )
      | ~ in(D_338,B_341)
      | ~ in(C_339,B_341)
      | ~ is_connected_in(A_340,B_341)
      | ~ relation(A_340) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_9576,plain,
    ! [C_346,A_347] :
      ( in(ordered_pair('#skF_6',C_346),A_347)
      | in(ordered_pair(C_346,'#skF_6'),A_347)
      | ( C_346 = '#skF_6' )
      | ~ in(C_346,relation_field('#skF_4'))
      | ~ is_connected_in(A_347,relation_field('#skF_4'))
      | ~ relation(A_347) ),
    inference(resolution,[status(thm)],[c_8544,c_9419]) ).

tff(c_9585,plain,
    ! [C_346] :
      ( in(ordered_pair('#skF_6',C_346),'#skF_4')
      | in(ordered_pair(C_346,'#skF_6'),'#skF_4')
      | ( C_346 = '#skF_6' )
      | ~ in(C_346,relation_field('#skF_4'))
      | ~ connected('#skF_4')
      | ~ relation('#skF_4') ),
    inference(resolution,[status(thm)],[c_18,c_9576]) ).

tff(c_11038,plain,
    ! [C_390] :
      ( in(ordered_pair('#skF_6',C_390),'#skF_4')
      | in(ordered_pair(C_390,'#skF_6'),'#skF_4')
      | ( C_390 = '#skF_6' )
      | ~ in(C_390,relation_field('#skF_4')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_66,c_8540,c_9585]) ).

tff(c_70,plain,
    ( ~ in(ordered_pair('#skF_5','#skF_6'),'#skF_4')
    | ~ connected('#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_125]) ).

tff(c_8595,plain,
    ~ in(ordered_pair('#skF_5','#skF_6'),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_8540,c_70]) ).

tff(c_11072,plain,
    ( in(ordered_pair('#skF_6','#skF_5'),'#skF_4')
    | ( '#skF_5' = '#skF_6' )
    | ~ in('#skF_5',relation_field('#skF_4')) ),
    inference(resolution,[status(thm)],[c_11038,c_8595]) ).

tff(c_11095,plain,
    ( in(ordered_pair('#skF_6','#skF_5'),'#skF_4')
    | ( '#skF_5' = '#skF_6' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_8548,c_11072]) ).

tff(c_11097,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_8539,c_8644,c_11095]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU242+1 : TPTP v8.1.2. Released v3.3.0.
% 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
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 12:08:19 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 12.26/4.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.26/4.10  
% 12.26/4.10  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.26/4.13  
% 12.26/4.13  Inference rules
% 12.26/4.13  ----------------------
% 12.26/4.13  #Ref     : 0
% 12.26/4.13  #Sup     : 2787
% 12.26/4.13  #Fact    : 14
% 12.26/4.13  #Define  : 0
% 12.26/4.13  #Split   : 10
% 12.26/4.13  #Chain   : 0
% 12.26/4.13  #Close   : 0
% 12.26/4.13  
% 12.26/4.13  Ordering : KBO
% 12.26/4.13  
% 12.26/4.13  Simplification rules
% 12.26/4.13  ----------------------
% 12.26/4.13  #Subsume      : 288
% 12.26/4.13  #Demod        : 3502
% 12.26/4.13  #Tautology    : 715
% 12.26/4.13  #SimpNegUnit  : 56
% 12.26/4.13  #BackRed      : 14
% 12.26/4.13  
% 12.26/4.13  #Partial instantiations: 0
% 12.26/4.13  #Strategies tried      : 1
% 12.26/4.13  
% 12.26/4.13  Timing (in seconds)
% 12.26/4.13  ----------------------
% 12.26/4.14  Preprocessing        : 0.56
% 12.26/4.14  Parsing              : 0.28
% 12.26/4.14  CNF conversion       : 0.05
% 12.26/4.14  Main loop            : 2.51
% 12.26/4.14  Inferencing          : 0.64
% 12.26/4.14  Reduction            : 1.32
% 12.26/4.14  Demodulation         : 1.13
% 12.26/4.14  BG Simplification    : 0.09
% 12.26/4.14  Subsumption          : 0.34
% 12.26/4.14  Abstraction          : 0.16
% 12.26/4.14  MUC search           : 0.00
% 12.26/4.14  Cooper               : 0.00
% 12.26/4.14  Total                : 3.13
% 12.26/4.14  Index Insertion      : 0.00
% 12.26/4.14  Index Deletion       : 0.00
% 12.26/4.14  Index Matching       : 0.00
% 12.26/4.14  BG Taut test         : 0.00
%------------------------------------------------------------------------------