TSTP Solution File: SEU110+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU110+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 : n011.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 10:57:37 EDT 2023

% Result   : Theorem 15.19s 5.35s
% Output   : CNFRefutation 15.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   60 (   6 unt;  34 typ;   0 def)
%            Number of atoms       :   61 (   1 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   59 (  24   ~;  23   |;   5   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  27   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;   7 con; 0-2 aty)
%            Number of variables   :   40 (;  40   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > relation > preboolean > ordinal > one_to_one > natural > function > finite > epsilon_transitive > epsilon_connected > empty > diff_closed > cup_closed > cap_closed > #nlpp > powerset > finite_subsets > empty_set > #skF_9 > #skF_7 > #skF_4 > #skF_11 > #skF_15 > #skF_3 > #skF_14 > #skF_5 > #skF_10 > #skF_6 > #skF_8 > #skF_13 > #skF_2 > #skF_12 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(epsilon_connected,type,
    epsilon_connected: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_198,negated_conjecture,
    ~ ! [A,B] :
        ( subset(A,B)
       => subset(finite_subsets(A),finite_subsets(B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_finsub_1) ).

tff(f_65,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_103,axiom,
    ! [A] :
      ( ~ empty(finite_subsets(A))
      & cup_closed(finite_subsets(A))
      & diff_closed(finite_subsets(A))
      & preboolean(finite_subsets(A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_finsub_1) ).

tff(f_76,axiom,
    ! [A,B] :
      ( preboolean(B)
     => ( ( B = finite_subsets(A) )
      <=> ! [C] :
            ( in(C,B)
          <=> ( subset(C,A)
              & finite(C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_finsub_1) ).

tff(f_193,axiom,
    ! [A,B,C] :
      ( ( subset(A,B)
        & subset(B,C) )
     => subset(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_xboole_1) ).

tff(c_128,plain,
    ~ subset(finite_subsets('#skF_14'),finite_subsets('#skF_15')),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_334,plain,
    ! [A_120,B_121] :
      ( in('#skF_1'(A_120,B_121),A_120)
      | subset(A_120,B_121) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_62,plain,
    ! [A_26] : preboolean(finite_subsets(A_26)),
    inference(cnfTransformation,[status(thm)],[f_103]) ).

tff(c_36,plain,
    ! [C_20,A_16] :
      ( finite(C_20)
      | ~ in(C_20,finite_subsets(A_16))
      | ~ preboolean(finite_subsets(A_16)) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_151,plain,
    ! [C_20,A_16] :
      ( finite(C_20)
      | ~ in(C_20,finite_subsets(A_16)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_36]) ).

tff(c_352,plain,
    ! [A_16,B_121] :
      ( finite('#skF_1'(finite_subsets(A_16),B_121))
      | subset(finite_subsets(A_16),B_121) ),
    inference(resolution,[status(thm)],[c_334,c_151]) ).

tff(c_38,plain,
    ! [C_20,A_16] :
      ( subset(C_20,A_16)
      | ~ in(C_20,finite_subsets(A_16))
      | ~ preboolean(finite_subsets(A_16)) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_149,plain,
    ! [C_20,A_16] :
      ( subset(C_20,A_16)
      | ~ in(C_20,finite_subsets(A_16)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_38]) ).

tff(c_351,plain,
    ! [A_16,B_121] :
      ( subset('#skF_1'(finite_subsets(A_16),B_121),A_16)
      | subset(finite_subsets(A_16),B_121) ),
    inference(resolution,[status(thm)],[c_334,c_149]) ).

tff(c_130,plain,
    subset('#skF_14','#skF_15'),
    inference(cnfTransformation,[status(thm)],[f_198]) ).

tff(c_569,plain,
    ! [A_152,C_153,B_154] :
      ( subset(A_152,C_153)
      | ~ subset(B_154,C_153)
      | ~ subset(A_152,B_154) ),
    inference(cnfTransformation,[status(thm)],[f_193]) ).

tff(c_599,plain,
    ! [A_152] :
      ( subset(A_152,'#skF_15')
      | ~ subset(A_152,'#skF_14') ),
    inference(resolution,[status(thm)],[c_130,c_569]) ).

tff(c_34,plain,
    ! [C_20,A_16] :
      ( in(C_20,finite_subsets(A_16))
      | ~ finite(C_20)
      | ~ subset(C_20,A_16)
      | ~ preboolean(finite_subsets(A_16)) ),
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_993,plain,
    ! [C_179,A_180] :
      ( in(C_179,finite_subsets(A_180))
      | ~ finite(C_179)
      | ~ subset(C_179,A_180) ),
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_34]) ).

tff(c_18,plain,
    ! [A_11,B_12] :
      ( ~ in('#skF_1'(A_11,B_12),B_12)
      | subset(A_11,B_12) ),
    inference(cnfTransformation,[status(thm)],[f_65]) ).

tff(c_25149,plain,
    ! [A_755,A_756] :
      ( subset(A_755,finite_subsets(A_756))
      | ~ finite('#skF_1'(A_755,finite_subsets(A_756)))
      | ~ subset('#skF_1'(A_755,finite_subsets(A_756)),A_756) ),
    inference(resolution,[status(thm)],[c_993,c_18]) ).

tff(c_25217,plain,
    ! [A_761] :
      ( subset(A_761,finite_subsets('#skF_15'))
      | ~ finite('#skF_1'(A_761,finite_subsets('#skF_15')))
      | ~ subset('#skF_1'(A_761,finite_subsets('#skF_15')),'#skF_14') ),
    inference(resolution,[status(thm)],[c_599,c_25149]) ).

tff(c_25221,plain,
    ( ~ finite('#skF_1'(finite_subsets('#skF_14'),finite_subsets('#skF_15')))
    | subset(finite_subsets('#skF_14'),finite_subsets('#skF_15')) ),
    inference(resolution,[status(thm)],[c_351,c_25217]) ).

tff(c_25227,plain,
    ~ finite('#skF_1'(finite_subsets('#skF_14'),finite_subsets('#skF_15'))),
    inference(negUnitSimplification,[status(thm)],[c_128,c_128,c_25221]) ).

tff(c_25231,plain,
    subset(finite_subsets('#skF_14'),finite_subsets('#skF_15')),
    inference(resolution,[status(thm)],[c_352,c_25227]) ).

tff(c_25238,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_128,c_25231]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU110+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.14  % 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
% 0.14/0.36  % Computer : n011.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 11:54:51 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 15.19/5.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.19/5.36  
% 15.19/5.36  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.19/5.38  
% 15.19/5.38  Inference rules
% 15.19/5.38  ----------------------
% 15.19/5.38  #Ref     : 0
% 15.19/5.38  #Sup     : 5747
% 15.19/5.38  #Fact    : 0
% 15.19/5.38  #Define  : 0
% 15.19/5.38  #Split   : 31
% 15.19/5.38  #Chain   : 0
% 15.19/5.38  #Close   : 0
% 15.19/5.38  
% 15.19/5.38  Ordering : KBO
% 15.19/5.38  
% 15.19/5.38  Simplification rules
% 15.19/5.38  ----------------------
% 15.19/5.38  #Subsume      : 1664
% 15.19/5.38  #Demod        : 2151
% 15.19/5.38  #Tautology    : 1329
% 15.19/5.38  #SimpNegUnit  : 443
% 15.19/5.38  #BackRed      : 185
% 15.19/5.38  
% 15.19/5.39  #Partial instantiations: 0
% 15.19/5.39  #Strategies tried      : 1
% 15.19/5.39  
% 15.19/5.39  Timing (in seconds)
% 15.19/5.39  ----------------------
% 15.19/5.39  Preprocessing        : 0.57
% 15.19/5.39  Parsing              : 0.30
% 15.19/5.39  CNF conversion       : 0.05
% 15.19/5.39  Main loop            : 3.76
% 15.19/5.39  Inferencing          : 0.95
% 15.19/5.39  Reduction            : 1.32
% 15.19/5.39  Demodulation         : 0.95
% 15.19/5.39  BG Simplification    : 0.07
% 15.19/5.39  Subsumption          : 1.10
% 15.19/5.39  Abstraction          : 0.08
% 15.19/5.39  MUC search           : 0.00
% 15.19/5.39  Cooper               : 0.00
% 15.19/5.39  Total                : 4.37
% 15.19/5.39  Index Insertion      : 0.00
% 15.19/5.39  Index Deletion       : 0.00
% 15.19/5.39  Index Matching       : 0.00
% 15.19/5.39  BG Taut test         : 0.00
%------------------------------------------------------------------------------