TSTP Solution File: SEU009+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU009+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/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 : n020.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 10:57:29 EDT 2023

% Result   : Theorem 12.78s 3.99s
% Output   : CNFRefutation 12.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   70 (  24 unt;  26 typ;   0 def)
%            Number of atoms       :  111 (   6 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  125 (  58   ~;  51   |;   8   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  16   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   19 (  19 usr;  10 con; 0-2 aty)
%            Number of variables   :   36 (;  36   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_199,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( relation(C)
          & function(C) )
       => ( in(B,relation_dom(relation_composition(C,identity_relation(A))))
        <=> ( in(B,relation_dom(C))
            & in(apply(C,B),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t40_funct_1) ).

tff(f_83,axiom,
    ! [A] :
      ( relation(identity_relation(A))
      & function(identity_relation(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).

tff(f_184,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( ( B = identity_relation(A) )
      <=> ( ( relation_dom(B) = A )
          & ! [C] :
              ( in(C,A)
             => ( apply(B,C) = C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).

tff(f_165,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ! [C] :
          ( ( relation(C)
            & function(C) )
         => ( in(A,relation_dom(relation_composition(C,B)))
          <=> ( in(A,relation_dom(C))
              & in(apply(C,A),relation_dom(B)) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).

tff(c_112,plain,
    ( in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11'))))
    | in(apply('#skF_13','#skF_12'),'#skF_11') ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_143,plain,
    in(apply('#skF_13','#skF_12'),'#skF_11'),
    inference(splitLeft,[status(thm)],[c_112]) ).

tff(c_116,plain,
    ( in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11'))))
    | in('#skF_12',relation_dom('#skF_13')) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_139,plain,
    in('#skF_12',relation_dom('#skF_13')),
    inference(splitLeft,[status(thm)],[c_116]) ).

tff(c_104,plain,
    relation('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_102,plain,
    function('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_32,plain,
    ! [A_15] : relation(identity_relation(A_15)),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_34,plain,
    ! [A_15] : function(identity_relation(A_15)),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_96,plain,
    ! [A_34] :
      ( ( relation_dom(identity_relation(A_34)) = A_34 )
      | ~ function(identity_relation(A_34))
      | ~ relation(identity_relation(A_34)) ),
    inference(cnfTransformation,[status(thm)],[f_184]) ).

tff(c_128,plain,
    ! [A_34] :
      ( ( relation_dom(identity_relation(A_34)) = A_34 )
      | ~ relation(identity_relation(A_34)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_96]) ).

tff(c_132,plain,
    ! [A_34] : ( relation_dom(identity_relation(A_34)) = A_34 ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_128]) ).

tff(c_3516,plain,
    ! [A_201,C_202,B_203] :
      ( in(A_201,relation_dom(relation_composition(C_202,B_203)))
      | ~ in(apply(C_202,A_201),relation_dom(B_203))
      | ~ in(A_201,relation_dom(C_202))
      | ~ function(C_202)
      | ~ relation(C_202)
      | ~ function(B_203)
      | ~ relation(B_203) ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_3534,plain,
    ! [A_201,C_202,A_34] :
      ( in(A_201,relation_dom(relation_composition(C_202,identity_relation(A_34))))
      | ~ in(apply(C_202,A_201),A_34)
      | ~ in(A_201,relation_dom(C_202))
      | ~ function(C_202)
      | ~ relation(C_202)
      | ~ function(identity_relation(A_34))
      | ~ relation(identity_relation(A_34)) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_3516]) ).

tff(c_14117,plain,
    ! [A_346,C_347,A_348] :
      ( in(A_346,relation_dom(relation_composition(C_347,identity_relation(A_348))))
      | ~ in(apply(C_347,A_346),A_348)
      | ~ in(A_346,relation_dom(C_347))
      | ~ function(C_347)
      | ~ relation(C_347) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_3534]) ).

tff(c_106,plain,
    ( ~ in(apply('#skF_13','#skF_12'),'#skF_11')
    | ~ in('#skF_12',relation_dom('#skF_13'))
    | ~ in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))) ),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_189,plain,
    ~ in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitLeft,[status(thm)],[c_106]) ).

tff(c_14162,plain,
    ( ~ in(apply('#skF_13','#skF_12'),'#skF_11')
    | ~ in('#skF_12',relation_dom('#skF_13'))
    | ~ function('#skF_13')
    | ~ relation('#skF_13') ),
    inference(resolution,[status(thm)],[c_14117,c_189]) ).

tff(c_14244,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_102,c_139,c_143,c_14162]) ).

tff(c_14245,plain,
    ( ~ in('#skF_12',relation_dom('#skF_13'))
    | ~ in(apply('#skF_13','#skF_12'),'#skF_11') ),
    inference(splitRight,[status(thm)],[c_106]) ).

tff(c_14401,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_143,c_139,c_14245]) ).

tff(c_14403,plain,
    ~ in(apply('#skF_13','#skF_12'),'#skF_11'),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_14449,plain,
    ~ in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitLeft,[status(thm)],[c_106]) ).

tff(c_14402,plain,
    in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_14587,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14449,c_14402]) ).

tff(c_14589,plain,
    in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitRight,[status(thm)],[c_106]) ).

tff(c_16606,plain,
    ! [C_511,A_512,B_513] :
      ( in(apply(C_511,A_512),relation_dom(B_513))
      | ~ in(A_512,relation_dom(relation_composition(C_511,B_513)))
      | ~ function(C_511)
      | ~ relation(C_511)
      | ~ function(B_513)
      | ~ relation(B_513) ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_16635,plain,
    ! [C_511,A_512,A_34] :
      ( in(apply(C_511,A_512),A_34)
      | ~ in(A_512,relation_dom(relation_composition(C_511,identity_relation(A_34))))
      | ~ function(C_511)
      | ~ relation(C_511)
      | ~ function(identity_relation(A_34))
      | ~ relation(identity_relation(A_34)) ),
    inference(superposition,[status(thm),theory(equality)],[c_132,c_16606]) ).

tff(c_22054,plain,
    ! [C_625,A_626,A_627] :
      ( in(apply(C_625,A_626),A_627)
      | ~ in(A_626,relation_dom(relation_composition(C_625,identity_relation(A_627))))
      | ~ function(C_625)
      | ~ relation(C_625) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_16635]) ).

tff(c_22127,plain,
    ( in(apply('#skF_13','#skF_12'),'#skF_11')
    | ~ function('#skF_13')
    | ~ relation('#skF_13') ),
    inference(resolution,[status(thm)],[c_14589,c_22054]) ).

tff(c_22152,plain,
    in(apply('#skF_13','#skF_12'),'#skF_11'),
    inference(demodulation,[status(thm),theory(equality)],[c_104,c_102,c_22127]) ).

tff(c_22154,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_14403,c_22152]) ).

tff(c_22156,plain,
    ~ in('#skF_12',relation_dom('#skF_13')),
    inference(splitRight,[status(thm)],[c_116]) ).

tff(c_22155,plain,
    in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitRight,[status(thm)],[c_116]) ).

tff(c_22164,plain,
    ~ in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitLeft,[status(thm)],[c_106]) ).

tff(c_22307,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_22155,c_22164]) ).

tff(c_22309,plain,
    in('#skF_12',relation_dom(relation_composition('#skF_13',identity_relation('#skF_11')))),
    inference(splitRight,[status(thm)],[c_106]) ).

tff(c_24194,plain,
    ! [A_764,C_765,B_766] :
      ( in(A_764,relation_dom(C_765))
      | ~ in(A_764,relation_dom(relation_composition(C_765,B_766)))
      | ~ function(C_765)
      | ~ relation(C_765)
      | ~ function(B_766)
      | ~ relation(B_766) ),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_24259,plain,
    ( in('#skF_12',relation_dom('#skF_13'))
    | ~ function('#skF_13')
    | ~ relation('#skF_13')
    | ~ function(identity_relation('#skF_11'))
    | ~ relation(identity_relation('#skF_11')) ),
    inference(resolution,[status(thm)],[c_22309,c_24194]) ).

tff(c_24305,plain,
    in('#skF_12',relation_dom('#skF_13')),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_104,c_102,c_24259]) ).

tff(c_24307,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22156,c_24305]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU009+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/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
% 0.13/0.35  % Computer : n020.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 11:38:07 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 12.78/3.99  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.78/3.99  
% 12.78/3.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.78/4.02  
% 12.78/4.02  Inference rules
% 12.78/4.02  ----------------------
% 12.78/4.02  #Ref     : 0
% 12.78/4.02  #Sup     : 5474
% 12.78/4.02  #Fact    : 0
% 12.78/4.02  #Define  : 0
% 12.78/4.02  #Split   : 29
% 12.78/4.02  #Chain   : 0
% 12.78/4.02  #Close   : 0
% 12.78/4.02  
% 12.78/4.02  Ordering : KBO
% 12.78/4.02  
% 12.78/4.02  Simplification rules
% 12.78/4.02  ----------------------
% 12.78/4.02  #Subsume      : 1878
% 12.78/4.02  #Demod        : 6985
% 12.78/4.02  #Tautology    : 2979
% 12.78/4.02  #SimpNegUnit  : 148
% 12.78/4.02  #BackRed      : 84
% 12.78/4.02  
% 12.78/4.02  #Partial instantiations: 0
% 12.78/4.02  #Strategies tried      : 1
% 12.78/4.02  
% 12.78/4.02  Timing (in seconds)
% 12.78/4.02  ----------------------
% 12.78/4.02  Preprocessing        : 0.56
% 12.78/4.02  Parsing              : 0.29
% 12.78/4.02  CNF conversion       : 0.04
% 12.78/4.02  Main loop            : 2.42
% 12.78/4.02  Inferencing          : 0.71
% 12.78/4.02  Reduction            : 0.87
% 12.78/4.02  Demodulation         : 0.62
% 12.78/4.02  BG Simplification    : 0.06
% 12.78/4.03  Subsumption          : 0.63
% 12.78/4.03  Abstraction          : 0.07
% 12.78/4.03  MUC search           : 0.00
% 12.78/4.03  Cooper               : 0.00
% 12.78/4.03  Total                : 3.02
% 12.78/4.03  Index Insertion      : 0.00
% 12.78/4.03  Index Deletion       : 0.00
% 12.78/4.03  Index Matching       : 0.00
% 12.78/4.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------