TSTP Solution File: SEU118+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU118+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 10:57:38 EDT 2023

% Result   : Theorem 4.88s 2.30s
% Output   : CNFRefutation 4.88s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   54 (   7 unt;  33 typ;   0 def)
%            Number of atoms       :   47 (   1 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   43 (  17   ~;  13   |;   5   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  26   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   17 (  17 usr;   7 con; 0-2 aty)
%            Number of variables   :   25 (;  25   !;   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_8 > #skF_7 > #skF_10 > #skF_14 > #skF_5 > #skF_13 > #skF_4 > #skF_3 > #skF_11 > #skF_2 > #skF_12 > #skF_1 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_3',type,
    '#skF_3': $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(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('#skF_6',type,
    '#skF_6': $i > $i ).

tff(f_199,negated_conjecture,
    ~ ! [A,B] :
        ( element(B,powerset(A))
       => ( finite(A)
         => element(B,finite_subsets(A)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_finsub_1) ).

tff(f_203,axiom,
    ! [A,B] :
      ( element(A,powerset(B))
    <=> subset(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).

tff(f_182,axiom,
    ! [A,B] :
      ( ( subset(A,B)
        & finite(B) )
     => finite(A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13_finset_1) ).

tff(f_96,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_69,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_186,axiom,
    ! [A,B] :
      ( in(A,B)
     => element(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

tff(c_128,plain,
    element('#skF_14',powerset('#skF_13')),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_304,plain,
    ! [A_109,B_110] :
      ( subset(A_109,B_110)
      | ~ element(A_109,powerset(B_110)) ),
    inference(cnfTransformation,[status(thm)],[f_203]) ).

tff(c_333,plain,
    subset('#skF_14','#skF_13'),
    inference(resolution,[status(thm)],[c_128,c_304]) ).

tff(c_126,plain,
    finite('#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_118,plain,
    ! [A_34,B_35] :
      ( finite(A_34)
      | ~ finite(B_35)
      | ~ subset(A_34,B_35) ),
    inference(cnfTransformation,[status(thm)],[f_182]) ).

tff(c_336,plain,
    ( finite('#skF_14')
    | ~ finite('#skF_13') ),
    inference(resolution,[status(thm)],[c_333,c_118]) ).

tff(c_339,plain,
    finite('#skF_14'),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_336]) ).

tff(c_56,plain,
    ! [A_21] : preboolean(finite_subsets(A_21)),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_28,plain,
    ! [C_15,A_11] :
      ( in(C_15,finite_subsets(A_11))
      | ~ finite(C_15)
      | ~ subset(C_15,A_11)
      | ~ preboolean(finite_subsets(A_11)) ),
    inference(cnfTransformation,[status(thm)],[f_69]) ).

tff(c_505,plain,
    ! [C_135,A_136] :
      ( in(C_135,finite_subsets(A_136))
      | ~ finite(C_135)
      | ~ subset(C_135,A_136) ),
    inference(demodulation,[status(thm),theory(equality)],[c_56,c_28]) ).

tff(c_120,plain,
    ! [A_36,B_37] :
      ( element(A_36,B_37)
      | ~ in(A_36,B_37) ),
    inference(cnfTransformation,[status(thm)],[f_186]) ).

tff(c_979,plain,
    ! [C_177,A_178] :
      ( element(C_177,finite_subsets(A_178))
      | ~ finite(C_177)
      | ~ subset(C_177,A_178) ),
    inference(resolution,[status(thm)],[c_505,c_120]) ).

tff(c_124,plain,
    ~ element('#skF_14',finite_subsets('#skF_13')),
    inference(cnfTransformation,[status(thm)],[f_199]) ).

tff(c_988,plain,
    ( ~ finite('#skF_14')
    | ~ subset('#skF_14','#skF_13') ),
    inference(resolution,[status(thm)],[c_979,c_124]) ).

tff(c_994,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_333,c_339,c_988]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU118+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
% 0.13/0.35  % Computer : n011.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 11:29:51 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 4.88/2.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.88/2.30  
% 4.88/2.30  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.88/2.33  
% 4.88/2.33  Inference rules
% 4.88/2.33  ----------------------
% 4.88/2.33  #Ref     : 0
% 4.88/2.33  #Sup     : 167
% 4.88/2.33  #Fact    : 0
% 4.88/2.33  #Define  : 0
% 4.88/2.33  #Split   : 5
% 4.88/2.33  #Chain   : 0
% 4.88/2.33  #Close   : 0
% 5.52/2.33  
% 5.52/2.33  Ordering : KBO
% 5.52/2.33  
% 5.52/2.33  Simplification rules
% 5.52/2.33  ----------------------
% 5.52/2.33  #Subsume      : 22
% 5.52/2.33  #Demod        : 73
% 5.52/2.33  #Tautology    : 56
% 5.52/2.33  #SimpNegUnit  : 2
% 5.52/2.33  #BackRed      : 28
% 5.52/2.33  
% 5.52/2.33  #Partial instantiations: 0
% 5.52/2.33  #Strategies tried      : 1
% 5.52/2.33  
% 5.52/2.33  Timing (in seconds)
% 5.52/2.33  ----------------------
% 5.52/2.33  Preprocessing        : 0.64
% 5.52/2.33  Parsing              : 0.35
% 5.52/2.33  CNF conversion       : 0.05
% 5.52/2.33  Main loop            : 0.61
% 5.52/2.33  Inferencing          : 0.22
% 5.52/2.33  Reduction            : 0.18
% 5.52/2.33  Demodulation         : 0.13
% 5.52/2.33  BG Simplification    : 0.04
% 5.52/2.33  Subsumption          : 0.13
% 5.52/2.33  Abstraction          : 0.02
% 5.52/2.33  MUC search           : 0.00
% 5.52/2.33  Cooper               : 0.00
% 5.52/2.33  Total                : 1.29
% 5.52/2.33  Index Insertion      : 0.00
% 5.52/2.33  Index Deletion       : 0.00
% 5.52/2.33  Index Matching       : 0.00
% 5.52/2.33  BG Taut test         : 0.00
%------------------------------------------------------------------------------