TSTP Solution File: SEU230+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU230+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 : n004.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 10:58:06 EDT 2023

% Result   : Theorem 4.83s 2.24s
% Output   : CNFRefutation 5.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   39 (   7 unt;  28 typ;   0 def)
%            Number of atoms       :   18 (   5 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   12 (   5   ~;   3   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   25 (  16   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;  12 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > element > relation_non_empty > relation_empty_yielding > relation > one_to_one > function > empty > set_union2 > #nlpp > succ > singleton > empty_set > #skF_5 > #skF_11 > #skF_15 > #skF_4 > #skF_7 > #skF_10 > #skF_16 > #skF_14 > #skF_6 > #skF_13 > #skF_9 > #skF_8 > #skF_3 > #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('#skF_11',type,
    '#skF_11': $i ).

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

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

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

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

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

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

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

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

tff(f_62,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).

tff(f_55,axiom,
    ! [A] : ( succ(A) = set_union2(A,singleton(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_ordinal1) ).

tff(f_71,axiom,
    ! [A,B,C] :
      ( ( C = set_union2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).

tff(f_155,negated_conjecture,
    ~ ! [A] : in(A,succ(A)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_ordinal1) ).

tff(c_20,plain,
    ! [C_13] : in(C_13,singleton(C_13)),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_16,plain,
    ! [A_8] : ( set_union2(A_8,singleton(A_8)) = succ(A_8) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_405,plain,
    ! [D_71,B_72,A_73] :
      ( ~ in(D_71,B_72)
      | in(D_71,set_union2(A_73,B_72)) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_1540,plain,
    ! [D_157,A_158] :
      ( ~ in(D_157,singleton(A_158))
      | in(D_157,succ(A_158)) ),
    inference(superposition,[status(thm),theory(equality)],[c_16,c_405]) ).

tff(c_116,plain,
    ~ in('#skF_16',succ('#skF_16')),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_1615,plain,
    ~ in('#skF_16',singleton('#skF_16')),
    inference(resolution,[status(thm)],[c_1540,c_116]) ).

tff(c_1642,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_1615]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU230+3 : 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
% 0.12/0.34  % Computer : n004.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 11:34:56 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 4.83/2.24  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.83/2.25  
% 4.83/2.25  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.58/2.27  
% 5.58/2.27  Inference rules
% 5.58/2.27  ----------------------
% 5.58/2.27  #Ref     : 0
% 5.58/2.27  #Sup     : 351
% 5.58/2.27  #Fact    : 2
% 5.58/2.27  #Define  : 0
% 5.58/2.27  #Split   : 6
% 5.58/2.27  #Chain   : 0
% 5.58/2.27  #Close   : 0
% 5.58/2.27  
% 5.58/2.27  Ordering : KBO
% 5.58/2.27  
% 5.58/2.27  Simplification rules
% 5.58/2.27  ----------------------
% 5.58/2.27  #Subsume      : 89
% 5.58/2.27  #Demod        : 59
% 5.58/2.27  #Tautology    : 95
% 5.58/2.27  #SimpNegUnit  : 10
% 5.58/2.27  #BackRed      : 11
% 5.58/2.27  
% 5.58/2.27  #Partial instantiations: 0
% 5.58/2.27  #Strategies tried      : 1
% 5.58/2.27  
% 5.58/2.27  Timing (in seconds)
% 5.58/2.27  ----------------------
% 5.58/2.27  Preprocessing        : 0.58
% 5.58/2.28  Parsing              : 0.30
% 5.58/2.28  CNF conversion       : 0.05
% 5.58/2.28  Main loop            : 0.66
% 5.58/2.28  Inferencing          : 0.22
% 5.58/2.28  Reduction            : 0.20
% 5.58/2.28  Demodulation         : 0.14
% 5.58/2.28  BG Simplification    : 0.03
% 5.58/2.28  Subsumption          : 0.14
% 5.58/2.28  Abstraction          : 0.03
% 5.58/2.28  MUC search           : 0.00
% 5.58/2.28  Cooper               : 0.00
% 5.58/2.28  Total                : 1.28
% 5.58/2.28  Index Insertion      : 0.00
% 5.58/2.28  Index Deletion       : 0.00
% 5.58/2.28  Index Matching       : 0.00
% 5.58/2.28  BG Taut test         : 0.00
%------------------------------------------------------------------------------