TSTP Solution File: SEU019+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU019+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 : n013.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 10:57:30 EDT 2023

% Result   : Theorem 17.04s 7.09s
% Output   : CNFRefutation 17.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   30
% Syntax   : Number of formulae    :   57 (   8 unt;  26 typ;   0 def)
%            Number of atoms       :   87 (  22 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   91 (  35   ~;  44   |;   6   &)
%                                         (   2 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   23 (  18   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   8 con; 0-2 aty)
%            Number of variables   :   34 (;  34   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

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

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

tff('#skF_2',type,
    '#skF_2': $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(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_12',type,
    '#skF_12': ( $i * $i ) > $i ).

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_13',type,
    '#skF_13': $i ).

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

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

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

tff(f_72,axiom,
    ! [A] :
      ( relation(identity_relation(A))
      & function(identity_relation(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).

tff(f_54,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ( one_to_one(A)
      <=> ! [B,C] :
            ( ( in(B,relation_dom(A))
              & in(C,relation_dom(A))
              & ( apply(A,B) = apply(A,C) ) )
           => ( B = C ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

tff(f_163,negated_conjecture,
    ~ ! [A] : one_to_one(identity_relation(A)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t52_funct_1) ).

tff(f_150,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/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).

tff(c_34,plain,
    ! [A_16] : function(identity_relation(A_16)),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_32,plain,
    ! [A_16] : relation(identity_relation(A_16)),
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_569,plain,
    ! [A_105] :
      ( ( '#skF_2'(A_105) != '#skF_1'(A_105) )
      | one_to_one(A_105)
      | ~ function(A_105)
      | ~ relation(A_105) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_578,plain,
    ! [A_16] :
      ( ( '#skF_2'(identity_relation(A_16)) != '#skF_1'(identity_relation(A_16)) )
      | one_to_one(identity_relation(A_16))
      | ~ function(identity_relation(A_16)) ),
    inference(resolution,[status(thm)],[c_32,c_569]) ).

tff(c_1175,plain,
    ! [A_147] :
      ( ( '#skF_2'(identity_relation(A_147)) != '#skF_1'(identity_relation(A_147)) )
      | one_to_one(identity_relation(A_147)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_578]) ).

tff(c_94,plain,
    ~ one_to_one(identity_relation('#skF_13')),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_1188,plain,
    '#skF_2'(identity_relation('#skF_13')) != '#skF_1'(identity_relation('#skF_13')),
    inference(resolution,[status(thm)],[c_1175,c_94]) ).

tff(c_86,plain,
    ! [A_29] :
      ( ( relation_dom(identity_relation(A_29)) = A_29 )
      | ~ function(identity_relation(A_29))
      | ~ relation(identity_relation(A_29)) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_104,plain,
    ! [A_29] :
      ( ( relation_dom(identity_relation(A_29)) = A_29 )
      | ~ relation(identity_relation(A_29)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_86]) ).

tff(c_108,plain,
    ! [A_29] : ( relation_dom(identity_relation(A_29)) = A_29 ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_104]) ).

tff(c_629,plain,
    ! [A_112] :
      ( in('#skF_1'(A_112),relation_dom(A_112))
      | one_to_one(A_112)
      | ~ function(A_112)
      | ~ relation(A_112) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_651,plain,
    ! [A_29] :
      ( in('#skF_1'(identity_relation(A_29)),A_29)
      | one_to_one(identity_relation(A_29))
      | ~ function(identity_relation(A_29))
      | ~ relation(identity_relation(A_29)) ),
    inference(superposition,[status(thm),theory(equality)],[c_108,c_629]) ).

tff(c_662,plain,
    ! [A_29] :
      ( in('#skF_1'(identity_relation(A_29)),A_29)
      | one_to_one(identity_relation(A_29)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_651]) ).

tff(c_670,plain,
    ! [A_115] :
      ( in('#skF_2'(A_115),relation_dom(A_115))
      | one_to_one(A_115)
      | ~ function(A_115)
      | ~ relation(A_115) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_692,plain,
    ! [A_29] :
      ( in('#skF_2'(identity_relation(A_29)),A_29)
      | one_to_one(identity_relation(A_29))
      | ~ function(identity_relation(A_29))
      | ~ relation(identity_relation(A_29)) ),
    inference(superposition,[status(thm),theory(equality)],[c_108,c_670]) ).

tff(c_703,plain,
    ! [A_29] :
      ( in('#skF_2'(identity_relation(A_29)),A_29)
      | one_to_one(identity_relation(A_29)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_692]) ).

tff(c_84,plain,
    ! [A_29,C_33] :
      ( ( apply(identity_relation(A_29),C_33) = C_33 )
      | ~ in(C_33,A_29)
      | ~ function(identity_relation(A_29))
      | ~ relation(identity_relation(A_29)) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_106,plain,
    ! [A_29,C_33] :
      ( ( apply(identity_relation(A_29),C_33) = C_33 )
      | ~ in(C_33,A_29)
      | ~ relation(identity_relation(A_29)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_34,c_84]) ).

tff(c_110,plain,
    ! [A_29,C_33] :
      ( ( apply(identity_relation(A_29),C_33) = C_33 )
      | ~ in(C_33,A_29) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_106]) ).

tff(c_773,plain,
    ! [A_119] :
      ( ( apply(A_119,'#skF_2'(A_119)) = apply(A_119,'#skF_1'(A_119)) )
      | one_to_one(A_119)
      | ~ function(A_119)
      | ~ relation(A_119) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_787,plain,
    ! [A_29] :
      ( ( apply(identity_relation(A_29),'#skF_1'(identity_relation(A_29))) = '#skF_2'(identity_relation(A_29)) )
      | one_to_one(identity_relation(A_29))
      | ~ function(identity_relation(A_29))
      | ~ relation(identity_relation(A_29))
      | ~ in('#skF_2'(identity_relation(A_29)),A_29) ),
    inference(superposition,[status(thm),theory(equality)],[c_110,c_773]) ).

tff(c_5978,plain,
    ! [A_273] :
      ( ( apply(identity_relation(A_273),'#skF_1'(identity_relation(A_273))) = '#skF_2'(identity_relation(A_273)) )
      | one_to_one(identity_relation(A_273))
      | ~ in('#skF_2'(identity_relation(A_273)),A_273) ),
    inference(demodulation,[status(thm),theory(equality)],[c_32,c_34,c_787]) ).

tff(c_27073,plain,
    ! [A_487] :
      ( ( '#skF_2'(identity_relation(A_487)) = '#skF_1'(identity_relation(A_487)) )
      | one_to_one(identity_relation(A_487))
      | ~ in('#skF_2'(identity_relation(A_487)),A_487)
      | ~ in('#skF_1'(identity_relation(A_487)),A_487) ),
    inference(superposition,[status(thm),theory(equality)],[c_110,c_5978]) ).

tff(c_57255,plain,
    ! [A_581] :
      ( ( '#skF_2'(identity_relation(A_581)) = '#skF_1'(identity_relation(A_581)) )
      | ~ in('#skF_1'(identity_relation(A_581)),A_581)
      | one_to_one(identity_relation(A_581)) ),
    inference(resolution,[status(thm)],[c_703,c_27073]) ).

tff(c_57381,plain,
    ! [A_582] :
      ( ( '#skF_2'(identity_relation(A_582)) = '#skF_1'(identity_relation(A_582)) )
      | one_to_one(identity_relation(A_582)) ),
    inference(resolution,[status(thm)],[c_662,c_57255]) ).

tff(c_57384,plain,
    '#skF_2'(identity_relation('#skF_13')) = '#skF_1'(identity_relation('#skF_13')),
    inference(resolution,[status(thm)],[c_57381,c_94]) ).

tff(c_57502,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1188,c_57384]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem  : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.15  % 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 : n013.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 11:42:33 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 17.04/7.09  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.04/7.10  
% 17.04/7.10  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.15/7.14  
% 17.15/7.14  Inference rules
% 17.15/7.14  ----------------------
% 17.15/7.14  #Ref     : 2
% 17.15/7.14  #Sup     : 15997
% 17.15/7.14  #Fact    : 0
% 17.15/7.14  #Define  : 0
% 17.15/7.14  #Split   : 21
% 17.15/7.14  #Chain   : 0
% 17.15/7.14  #Close   : 0
% 17.15/7.14  
% 17.15/7.14  Ordering : KBO
% 17.15/7.14  
% 17.15/7.14  Simplification rules
% 17.15/7.14  ----------------------
% 17.15/7.14  #Subsume      : 8068
% 17.15/7.14  #Demod        : 14400
% 17.15/7.14  #Tautology    : 4823
% 17.15/7.14  #SimpNegUnit  : 197
% 17.15/7.14  #BackRed      : 71
% 17.15/7.14  
% 17.15/7.14  #Partial instantiations: 0
% 17.15/7.14  #Strategies tried      : 1
% 17.15/7.14  
% 17.15/7.14  Timing (in seconds)
% 17.15/7.14  ----------------------
% 17.15/7.14  Preprocessing        : 0.57
% 17.15/7.14  Parsing              : 0.29
% 17.15/7.14  CNF conversion       : 0.04
% 17.15/7.14  Main loop            : 5.48
% 17.15/7.14  Inferencing          : 1.05
% 17.15/7.14  Reduction            : 1.61
% 17.15/7.14  Demodulation         : 1.11
% 17.15/7.14  BG Simplification    : 0.09
% 17.15/7.14  Subsumption          : 2.42
% 17.15/7.14  Abstraction          : 0.14
% 17.15/7.14  MUC search           : 0.00
% 17.15/7.14  Cooper               : 0.00
% 17.15/7.14  Total                : 6.10
% 17.15/7.14  Index Insertion      : 0.00
% 17.15/7.14  Index Deletion       : 0.00
% 17.15/7.14  Index Matching       : 0.00
% 17.15/7.14  BG Taut test         : 0.00
%------------------------------------------------------------------------------