TSTP Solution File: SEU284+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU284+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/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 : n008.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 10:58:16 EDT 2023

% Result   : Theorem 6.44s 2.53s
% Output   : CNFRefutation 6.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   26
% Syntax   : Number of formulae    :   79 (  23 unt;  24 typ;   0 def)
%            Number of atoms       :  132 (  71 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  142 (  65   ~;  63   |;  10   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    3 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  16   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   36 (;  34   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > relation_empty_yielding > relation > function > empty > apply > #nlpp > singleton > relation_dom > empty_set > #skF_9 > #skF_7 > #skF_5 > #skF_2 > #skF_4 > #skF_11 > #skF_8 > #skF_10 > #skF_14 > #skF_13 > #skF_3 > #skF_1 > #skF_6 > #skF_12

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_78,axiom,
    ! [A] :
      ( ( ! [B,C,D] :
            ( ( in(B,A)
              & ( C = singleton(B) )
              & ( D = singleton(B) ) )
           => ( C = D ) )
        & ! [B] :
            ~ ( in(B,A)
              & ! [C] : ( C != singleton(B) ) ) )
     => ? [B] :
          ( relation(B)
          & function(B)
          & ( relation_dom(B) = A )
          & ! [C] :
              ( in(C,A)
             => ( apply(B,C) = singleton(C) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s2_funct_1__e16_22__wellord2__1) ).

tff(f_39,negated_conjecture,
    ~ ! [A] :
      ? [B] :
        ( relation(B)
        & function(B)
        & ( relation_dom(B) = A )
        & ! [C] :
            ( in(C,A)
           => ( apply(B,C) = singleton(C) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_funct_1__e16_22__wellord2) ).

tff(c_50,plain,
    ! [A_8] :
      ( ( '#skF_5'(A_8) != '#skF_6'(A_8) )
      | function('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_38,plain,
    ! [A_8] :
      ( ( singleton('#skF_4'(A_8)) = '#skF_5'(A_8) )
      | ( relation_dom('#skF_8'(A_8)) = A_8 ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_459,plain,
    ! [A_88] :
      ( ( singleton('#skF_4'(A_88)) = '#skF_6'(A_88) )
      | ( relation_dom('#skF_8'(A_88)) = A_88 ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_471,plain,
    ! [A_8] :
      ( ( '#skF_5'(A_8) = '#skF_6'(A_8) )
      | ( relation_dom('#skF_8'(A_8)) = A_8 )
      | ( relation_dom('#skF_8'(A_8)) = A_8 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_38,c_459]) ).

tff(c_1302,plain,
    ! [A_8] :
      ( ( '#skF_5'(A_8) = '#skF_6'(A_8) )
      | ( relation_dom('#skF_8'(A_8)) = A_8 ) ),
    inference(factorization,[status(thm),theory(equality)],[c_471]) ).

tff(c_66,plain,
    ! [A_8] :
      ( ( '#skF_5'(A_8) != '#skF_6'(A_8) )
      | relation('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_4,plain,
    ! [B_4] :
      ( in('#skF_2'(B_4),'#skF_1')
      | ( relation_dom(B_4) != '#skF_1' )
      | ~ function(B_4)
      | ~ relation(B_4) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_484,plain,
    ! [A_93,C_94] :
      ( in('#skF_4'(A_93),A_93)
      | ( apply('#skF_8'(A_93),C_94) = singleton(C_94) )
      | ~ in(C_94,A_93) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2,plain,
    ! [B_4] :
      ( ( apply(B_4,'#skF_2'(B_4)) != singleton('#skF_2'(B_4)) )
      | ( relation_dom(B_4) != '#skF_1' )
      | ~ function(B_4)
      | ~ relation(B_4) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_682,plain,
    ! [A_104] :
      ( ( relation_dom('#skF_8'(A_104)) != '#skF_1' )
      | ~ function('#skF_8'(A_104))
      | ~ relation('#skF_8'(A_104))
      | in('#skF_4'(A_104),A_104)
      | ~ in('#skF_2'('#skF_8'(A_104)),A_104) ),
    inference(superposition,[status(thm),theory(equality)],[c_484,c_2]) ).

tff(c_697,plain,
    ( in('#skF_4'('#skF_1'),'#skF_1')
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1'))
    | ~ relation('#skF_8'('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4,c_682]) ).

tff(c_982,plain,
    ~ relation('#skF_8'('#skF_1')),
    inference(splitLeft,[status(thm)],[c_697]) ).

tff(c_1000,plain,
    '#skF_5'('#skF_1') != '#skF_6'('#skF_1'),
    inference(resolution,[status(thm)],[c_66,c_982]) ).

tff(c_68,plain,
    ! [A_8] :
      ( ( singleton('#skF_4'(A_8)) = '#skF_6'(A_8) )
      | relation('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_999,plain,
    singleton('#skF_4'('#skF_1')) = '#skF_6'('#skF_1'),
    inference(resolution,[status(thm)],[c_68,c_982]) ).

tff(c_70,plain,
    ! [A_8] :
      ( ( singleton('#skF_4'(A_8)) = '#skF_5'(A_8) )
      | relation('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_998,plain,
    singleton('#skF_4'('#skF_1')) = '#skF_5'('#skF_1'),
    inference(resolution,[status(thm)],[c_70,c_982]) ).

tff(c_1115,plain,
    '#skF_5'('#skF_1') = '#skF_6'('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_999,c_998]) ).

tff(c_1117,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1000,c_1115]) ).

tff(c_1118,plain,
    ( ~ function('#skF_8'('#skF_1'))
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | in('#skF_4'('#skF_1'),'#skF_1') ),
    inference(splitRight,[status(thm)],[c_697]) ).

tff(c_1984,plain,
    relation_dom('#skF_8'('#skF_1')) != '#skF_1',
    inference(splitLeft,[status(thm)],[c_1118]) ).

tff(c_2003,plain,
    '#skF_5'('#skF_1') = '#skF_6'('#skF_1'),
    inference(superposition,[status(thm),theory(equality)],[c_1302,c_1984]) ).

tff(c_34,plain,
    ! [A_8] :
      ( ( '#skF_5'(A_8) != '#skF_6'(A_8) )
      | ( relation_dom('#skF_8'(A_8)) = A_8 ) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2005,plain,
    '#skF_5'('#skF_1') != '#skF_6'('#skF_1'),
    inference(superposition,[status(thm),theory(equality)],[c_34,c_1984]) ).

tff(c_2011,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2003,c_2005]) ).

tff(c_2012,plain,
    ( ~ function('#skF_8'('#skF_1'))
    | in('#skF_4'('#skF_1'),'#skF_1') ),
    inference(splitRight,[status(thm)],[c_1118]) ).

tff(c_2089,plain,
    ~ function('#skF_8'('#skF_1')),
    inference(splitLeft,[status(thm)],[c_2012]) ).

tff(c_2110,plain,
    '#skF_5'('#skF_1') != '#skF_6'('#skF_1'),
    inference(resolution,[status(thm)],[c_50,c_2089]) ).

tff(c_52,plain,
    ! [A_8] :
      ( ( singleton('#skF_4'(A_8)) = '#skF_6'(A_8) )
      | function('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2108,plain,
    singleton('#skF_4'('#skF_1')) = '#skF_6'('#skF_1'),
    inference(resolution,[status(thm)],[c_52,c_2089]) ).

tff(c_54,plain,
    ! [A_8] :
      ( ( singleton('#skF_4'(A_8)) = '#skF_5'(A_8) )
      | function('#skF_8'(A_8)) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_2109,plain,
    singleton('#skF_4'('#skF_1')) = '#skF_5'('#skF_1'),
    inference(resolution,[status(thm)],[c_54,c_2089]) ).

tff(c_2137,plain,
    '#skF_5'('#skF_1') = '#skF_6'('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_2108,c_2109]) ).

tff(c_2138,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2110,c_2137]) ).

tff(c_2140,plain,
    function('#skF_8'('#skF_1')),
    inference(splitRight,[status(thm)],[c_2012]) ).

tff(c_2013,plain,
    relation_dom('#skF_8'('#skF_1')) = '#skF_1',
    inference(splitRight,[status(thm)],[c_1118]) ).

tff(c_1119,plain,
    relation('#skF_8'('#skF_1')),
    inference(splitRight,[status(thm)],[c_697]) ).

tff(c_553,plain,
    ! [A_100,C_101] :
      ( ( '#skF_5'(A_100) != '#skF_6'(A_100) )
      | ( apply('#skF_8'(A_100),C_101) = singleton(C_101) )
      | ~ in(C_101,A_100) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1120,plain,
    ! [A_114] :
      ( ( relation_dom('#skF_8'(A_114)) != '#skF_1' )
      | ~ function('#skF_8'(A_114))
      | ~ relation('#skF_8'(A_114))
      | ( '#skF_5'(A_114) != '#skF_6'(A_114) )
      | ~ in('#skF_2'('#skF_8'(A_114)),A_114) ),
    inference(superposition,[status(thm),theory(equality)],[c_553,c_2]) ).

tff(c_1137,plain,
    ( ( '#skF_5'('#skF_1') != '#skF_6'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1'))
    | ~ relation('#skF_8'('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4,c_1120]) ).

tff(c_1143,plain,
    ( ( '#skF_5'('#skF_1') != '#skF_6'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1119,c_1137]) ).

tff(c_2254,plain,
    '#skF_5'('#skF_1') != '#skF_6'('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_2140,c_2013,c_1143]) ).

tff(c_931,plain,
    ! [A_108,C_109] :
      ( ( singleton('#skF_4'(A_108)) = '#skF_5'(A_108) )
      | ( apply('#skF_8'(A_108),C_109) = singleton(C_109) )
      | ~ in(C_109,A_108) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1258,plain,
    ! [A_129] :
      ( ( relation_dom('#skF_8'(A_129)) != '#skF_1' )
      | ~ function('#skF_8'(A_129))
      | ~ relation('#skF_8'(A_129))
      | ( singleton('#skF_4'(A_129)) = '#skF_5'(A_129) )
      | ~ in('#skF_2'('#skF_8'(A_129)),A_129) ),
    inference(superposition,[status(thm),theory(equality)],[c_931,c_2]) ).

tff(c_1275,plain,
    ( ( singleton('#skF_4'('#skF_1')) = '#skF_5'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1'))
    | ~ relation('#skF_8'('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4,c_1258]) ).

tff(c_1281,plain,
    ( ( singleton('#skF_4'('#skF_1')) = '#skF_5'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1119,c_1275]) ).

tff(c_2546,plain,
    singleton('#skF_4'('#skF_1')) = '#skF_5'('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_2140,c_2013,c_1281]) ).

tff(c_1178,plain,
    ! [A_121,C_122] :
      ( ( singleton('#skF_4'(A_121)) = '#skF_6'(A_121) )
      | ( apply('#skF_8'(A_121),C_122) = singleton(C_122) )
      | ~ in(C_122,A_121) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_1449,plain,
    ! [A_136] :
      ( ( relation_dom('#skF_8'(A_136)) != '#skF_1' )
      | ~ function('#skF_8'(A_136))
      | ~ relation('#skF_8'(A_136))
      | ( singleton('#skF_4'(A_136)) = '#skF_6'(A_136) )
      | ~ in('#skF_2'('#skF_8'(A_136)),A_136) ),
    inference(superposition,[status(thm),theory(equality)],[c_1178,c_2]) ).

tff(c_1466,plain,
    ( ( singleton('#skF_4'('#skF_1')) = '#skF_6'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1'))
    | ~ relation('#skF_8'('#skF_1')) ),
    inference(resolution,[status(thm)],[c_4,c_1449]) ).

tff(c_1472,plain,
    ( ( singleton('#skF_4'('#skF_1')) = '#skF_6'('#skF_1') )
    | ( relation_dom('#skF_8'('#skF_1')) != '#skF_1' )
    | ~ function('#skF_8'('#skF_1')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1119,c_1466]) ).

tff(c_3397,plain,
    '#skF_5'('#skF_1') = '#skF_6'('#skF_1'),
    inference(demodulation,[status(thm),theory(equality)],[c_2140,c_2013,c_2546,c_1472]) ).

tff(c_3398,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2254,c_3397]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU284+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/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
% 0.12/0.34  % Computer : n008.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 12:03:33 EDT 2023
% 0.12/0.35  % CPUTime  : 
% 6.44/2.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.44/2.54  
% 6.44/2.54  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.61/2.57  
% 6.61/2.57  Inference rules
% 6.61/2.57  ----------------------
% 6.61/2.57  #Ref     : 0
% 6.61/2.57  #Sup     : 905
% 6.61/2.57  #Fact    : 2
% 6.61/2.57  #Define  : 0
% 6.61/2.57  #Split   : 7
% 6.61/2.57  #Chain   : 0
% 6.61/2.57  #Close   : 0
% 6.61/2.57  
% 6.61/2.57  Ordering : KBO
% 6.61/2.57  
% 6.61/2.57  Simplification rules
% 6.61/2.57  ----------------------
% 6.61/2.57  #Subsume      : 322
% 6.61/2.57  #Demod        : 237
% 6.61/2.57  #Tautology    : 177
% 6.61/2.57  #SimpNegUnit  : 14
% 6.61/2.57  #BackRed      : 8
% 6.61/2.57  
% 6.61/2.57  #Partial instantiations: 0
% 6.61/2.57  #Strategies tried      : 1
% 6.61/2.57  
% 6.61/2.57  Timing (in seconds)
% 6.61/2.57  ----------------------
% 6.61/2.58  Preprocessing        : 0.58
% 6.61/2.58  Parsing              : 0.28
% 6.61/2.58  CNF conversion       : 0.04
% 6.61/2.58  Main loop            : 0.88
% 6.61/2.58  Inferencing          : 0.30
% 6.61/2.58  Reduction            : 0.23
% 6.61/2.58  Demodulation         : 0.15
% 6.61/2.58  BG Simplification    : 0.05
% 6.61/2.58  Subsumption          : 0.23
% 6.61/2.58  Abstraction          : 0.04
% 6.61/2.58  MUC search           : 0.00
% 6.61/2.58  Cooper               : 0.00
% 6.61/2.58  Total                : 1.51
% 6.61/2.58  Index Insertion      : 0.00
% 6.61/2.58  Index Deletion       : 0.00
% 6.61/2.58  Index Matching       : 0.00
% 6.61/2.58  BG Taut test         : 0.00
%------------------------------------------------------------------------------