TSTP Solution File: SEU212+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU212+3 : 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 : n032.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 10:58:01 EDT 2023

% Result   : Theorem 5.67s 2.36s
% Output   : CNFRefutation 5.98s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   62 (  19 unt;  30 typ;   0 def)
%            Number of atoms       :   67 (  13 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :   62 (  27   ~;  21   |;   4   &)
%                                         (   5 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  20   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;  10 con; 0-3 aty)
%            Number of variables   :   18 (;  17   !;   1   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation_empty_yielding > relation > function > empty > unordered_pair > ordered_pair > apply > #nlpp > singleton > relation_dom > powerset > empty_set > #skF_5 > #skF_15 > #skF_8 > #skF_4 > #skF_7 > #skF_3 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_11 > #skF_2 > #skF_1 > #skF_12

%Foreground sorts:

%Background operators:

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

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

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

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

tff('#skF_15',type,
    '#skF_15': $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('#skF_8',type,
    '#skF_8': $i > $i ).

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

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

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

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

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

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

tff('#skF_16',type,
    '#skF_16': $i ).

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

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

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

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

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

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

tff(f_203,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( relation(C)
          & function(C) )
       => ( in(ordered_pair(A,B),C)
        <=> ( in(A,relation_dom(C))
            & ( B = apply(C,A) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).

tff(f_59,axiom,
    ! [A] :
      ( ( relation(A)
        & function(A) )
     => ! [B,C] :
          ( ( in(B,relation_dom(A))
           => ( ( C = apply(A,B) )
            <=> in(ordered_pair(B,C),A) ) )
          & ( ~ in(B,relation_dom(A))
           => ( ( C = apply(A,B) )
            <=> ( C = empty_set ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).

tff(f_70,axiom,
    ! [A] :
      ( relation(A)
     => ! [B] :
          ( ( B = relation_dom(A) )
        <=> ! [C] :
              ( in(C,B)
            <=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).

tff(c_118,plain,
    ( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
    | ( apply('#skF_16','#skF_14') = '#skF_15' ) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_130,plain,
    apply('#skF_16','#skF_14') = '#skF_15',
    inference(splitLeft,[status(thm)],[c_118]) ).

tff(c_122,plain,
    ( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
    | in('#skF_14',relation_dom('#skF_16')) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_126,plain,
    in('#skF_14',relation_dom('#skF_16')),
    inference(splitLeft,[status(thm)],[c_122]) ).

tff(c_112,plain,
    ( ( apply('#skF_16','#skF_14') != '#skF_15' )
    | ~ in('#skF_14',relation_dom('#skF_16'))
    | ~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16') ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_175,plain,
    ~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(splitLeft,[status(thm)],[c_112]) ).

tff(c_110,plain,
    relation('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_108,plain,
    function('#skF_16'),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_766,plain,
    ! [B_171,A_172] :
      ( in(ordered_pair(B_171,apply(A_172,B_171)),A_172)
      | ~ in(B_171,relation_dom(A_172))
      | ~ function(A_172)
      | ~ relation(A_172) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_810,plain,
    ( in(ordered_pair('#skF_14','#skF_15'),'#skF_16')
    | ~ in('#skF_14',relation_dom('#skF_16'))
    | ~ function('#skF_16')
    | ~ relation('#skF_16') ),
    inference(superposition,[status(thm),theory(equality)],[c_130,c_766]) ).

tff(c_831,plain,
    in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_126,c_810]) ).

tff(c_833,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_175,c_831]) ).

tff(c_834,plain,
    ( ~ in('#skF_14',relation_dom('#skF_16'))
    | ( apply('#skF_16','#skF_14') != '#skF_15' ) ),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_957,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_130,c_126,c_834]) ).

tff(c_959,plain,
    apply('#skF_16','#skF_14') != '#skF_15',
    inference(splitRight,[status(thm)],[c_118]) ).

tff(c_958,plain,
    in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(splitRight,[status(thm)],[c_118]) ).

tff(c_1004,plain,
    ~ in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(splitLeft,[status(thm)],[c_112]) ).

tff(c_1048,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_958,c_1004]) ).

tff(c_1050,plain,
    in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_2489,plain,
    ! [A_348,B_349,C_350] :
      ( ( apply(A_348,B_349) = C_350 )
      | ~ in(ordered_pair(B_349,C_350),A_348)
      | ~ in(B_349,relation_dom(A_348))
      | ~ function(A_348)
      | ~ relation(A_348) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_2506,plain,
    ( ( apply('#skF_16','#skF_14') = '#skF_15' )
    | ~ in('#skF_14',relation_dom('#skF_16'))
    | ~ function('#skF_16')
    | ~ relation('#skF_16') ),
    inference(resolution,[status(thm)],[c_1050,c_2489]) ).

tff(c_2514,plain,
    apply('#skF_16','#skF_14') = '#skF_15',
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_108,c_126,c_2506]) ).

tff(c_2516,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_959,c_2514]) ).

tff(c_2518,plain,
    ~ in('#skF_14',relation_dom('#skF_16')),
    inference(splitRight,[status(thm)],[c_122]) ).

tff(c_2517,plain,
    in(ordered_pair('#skF_14','#skF_15'),'#skF_16'),
    inference(splitRight,[status(thm)],[c_122]) ).

tff(c_2868,plain,
    ! [C_407,A_408,D_409] :
      ( in(C_407,relation_dom(A_408))
      | ~ in(ordered_pair(C_407,D_409),A_408)
      | ~ relation(A_408) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_2875,plain,
    ( in('#skF_14',relation_dom('#skF_16'))
    | ~ relation('#skF_16') ),
    inference(resolution,[status(thm)],[c_2517,c_2868]) ).

tff(c_2879,plain,
    in('#skF_14',relation_dom('#skF_16')),
    inference(demodulation,[status(thm),theory(equality)],[c_110,c_2875]) ).

tff(c_2881,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2518,c_2879]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SEU212+3 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12  % 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
% 0.12/0.32  % Computer : n032.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Thu Aug  3 11:51:21 EDT 2023
% 0.12/0.32  % CPUTime  : 
% 5.67/2.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.67/2.36  
% 5.67/2.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.98/2.39  
% 5.98/2.39  Inference rules
% 5.98/2.39  ----------------------
% 5.98/2.39  #Ref     : 0
% 5.98/2.39  #Sup     : 657
% 5.98/2.39  #Fact    : 0
% 5.98/2.39  #Define  : 0
% 5.98/2.39  #Split   : 16
% 5.98/2.39  #Chain   : 0
% 5.98/2.39  #Close   : 0
% 5.98/2.39  
% 5.98/2.39  Ordering : KBO
% 5.98/2.39  
% 5.98/2.39  Simplification rules
% 5.98/2.39  ----------------------
% 5.98/2.39  #Subsume      : 143
% 5.98/2.39  #Demod        : 223
% 5.98/2.39  #Tautology    : 236
% 5.98/2.39  #SimpNegUnit  : 36
% 5.98/2.39  #BackRed      : 28
% 5.98/2.39  
% 5.98/2.39  #Partial instantiations: 0
% 5.98/2.39  #Strategies tried      : 1
% 5.98/2.39  
% 5.98/2.39  Timing (in seconds)
% 5.98/2.39  ----------------------
% 5.98/2.39  Preprocessing        : 0.56
% 5.98/2.40  Parsing              : 0.29
% 5.98/2.40  CNF conversion       : 0.05
% 5.98/2.40  Main loop            : 0.84
% 5.98/2.40  Inferencing          : 0.28
% 5.98/2.40  Reduction            : 0.27
% 5.98/2.40  Demodulation         : 0.18
% 5.98/2.40  BG Simplification    : 0.03
% 5.98/2.40  Subsumption          : 0.17
% 5.98/2.40  Abstraction          : 0.03
% 5.98/2.40  MUC search           : 0.00
% 5.98/2.40  Cooper               : 0.00
% 5.98/2.40  Total                : 1.45
% 5.98/2.40  Index Insertion      : 0.00
% 5.98/2.40  Index Deletion       : 0.00
% 5.98/2.40  Index Matching       : 0.00
% 5.98/2.40  BG Taut test         : 0.00
%------------------------------------------------------------------------------