TSTP Solution File: SEU115+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU115+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 : n006.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 4.11s 1.91s
% Output   : CNFRefutation 4.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   36
% Syntax   : Number of formulae    :   51 (  16 unt;  30 typ;   0 def)
%            Number of atoms       :   34 (  14 equ)
%            Maximal formula atoms :   10 (   1 avg)
%            Number of connectives :   19 (   6   ~;   2   |;   9   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   28 (  25   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-2 aty)
%            Number of functors    :   14 (  14 usr;   5 con; 0-1 aty)
%            Number of variables   :   11 (;   9   !;   2   ?;   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 > singleton > powerset > finite_subsets > empty_set > #skF_7 > #skF_5 > #skF_4 > #skF_1 > #skF_8 > #skF_10 > #skF_2 > #skF_3 > #skF_9 > #skF_6

%Foreground sorts:

%Background operators:

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

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

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

tff('#skF_1',type,
    '#skF_1': $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_10',type,
    '#skF_10': $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_210,axiom,
    ? [A] : empty(A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).

tff(f_217,axiom,
    ! [A] :
      ( empty(A)
     => ( A = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

tff(f_224,axiom,
    powerset(empty_set) = singleton(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_zfmisc_1) ).

tff(f_219,negated_conjecture,
    finite_subsets(empty_set) != singleton(empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finsub_1) ).

tff(f_165,axiom,
    ! [A] :
    ? [B] :
      ( element(B,powerset(A))
      & empty(B)
      & relation(B)
      & function(B)
      & one_to_one(B)
      & epsilon_transitive(B)
      & epsilon_connected(B)
      & ordinal(B)
      & natural(B)
      & finite(B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_finset_1) ).

tff(f_223,axiom,
    ! [A] :
      ( finite(A)
     => ( finite_subsets(A) = powerset(A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t27_finsub_1) ).

tff(c_118,plain,
    empty('#skF_9'),
    inference(cnfTransformation,[status(thm)],[f_210]) ).

tff(c_152,plain,
    ! [A_70] :
      ( ( empty_set = A_70 )
      | ~ empty(A_70) ),
    inference(cnfTransformation,[status(thm)],[f_217]) ).

tff(c_167,plain,
    empty_set = '#skF_9',
    inference(resolution,[status(thm)],[c_118,c_152]) ).

tff(c_128,plain,
    singleton(empty_set) = powerset(empty_set),
    inference(cnfTransformation,[status(thm)],[f_224]) ).

tff(c_124,plain,
    singleton(empty_set) != finite_subsets(empty_set),
    inference(cnfTransformation,[status(thm)],[f_219]) ).

tff(c_129,plain,
    powerset(empty_set) != finite_subsets(empty_set),
    inference(demodulation,[status(thm),theory(equality)],[c_128,c_124]) ).

tff(c_171,plain,
    powerset('#skF_9') != finite_subsets('#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_167,c_129]) ).

tff(c_88,plain,
    ! [A_35] : empty('#skF_4'(A_35)),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_165,plain,
    ! [A_35] : ( '#skF_4'(A_35) = empty_set ),
    inference(resolution,[status(thm)],[c_88,c_152]) ).

tff(c_178,plain,
    ! [A_35] : ( '#skF_4'(A_35) = '#skF_9' ),
    inference(demodulation,[status(thm),theory(equality)],[c_167,c_165]) ).

tff(c_72,plain,
    ! [A_35] : finite('#skF_4'(A_35)),
    inference(cnfTransformation,[status(thm)],[f_165]) ).

tff(c_179,plain,
    finite('#skF_9'),
    inference(demodulation,[status(thm),theory(equality)],[c_178,c_72]) ).

tff(c_281,plain,
    ! [A_92] :
      ( ( powerset(A_92) = finite_subsets(A_92) )
      | ~ finite(A_92) ),
    inference(cnfTransformation,[status(thm)],[f_223]) ).

tff(c_299,plain,
    powerset('#skF_9') = finite_subsets('#skF_9'),
    inference(resolution,[status(thm)],[c_179,c_281]) ).

tff(c_314,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_171,c_299]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU115+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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
% 0.14/0.35  % Computer : n006.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 11:38:29 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 4.11/1.91  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.11/1.91  
% 4.11/1.91  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.11/1.94  
% 4.11/1.94  Inference rules
% 4.11/1.94  ----------------------
% 4.11/1.94  #Ref     : 0
% 4.11/1.94  #Sup     : 32
% 4.11/1.94  #Fact    : 0
% 4.11/1.94  #Define  : 0
% 4.11/1.94  #Split   : 0
% 4.11/1.94  #Chain   : 0
% 4.11/1.94  #Close   : 0
% 4.11/1.94  
% 4.11/1.94  Ordering : KBO
% 4.11/1.94  
% 4.11/1.94  Simplification rules
% 4.11/1.94  ----------------------
% 4.11/1.94  #Subsume      : 3
% 4.11/1.94  #Demod        : 32
% 4.11/1.94  #Tautology    : 23
% 4.11/1.94  #SimpNegUnit  : 1
% 4.11/1.94  #BackRed      : 13
% 4.11/1.94  
% 4.11/1.94  #Partial instantiations: 0
% 4.11/1.94  #Strategies tried      : 1
% 4.11/1.94  
% 4.11/1.94  Timing (in seconds)
% 4.11/1.94  ----------------------
% 4.11/1.94  Preprocessing        : 0.56
% 4.11/1.94  Parsing              : 0.29
% 4.11/1.94  CNF conversion       : 0.04
% 4.11/1.94  Main loop            : 0.34
% 4.11/1.94  Inferencing          : 0.12
% 4.11/1.94  Reduction            : 0.11
% 4.11/1.94  Demodulation         : 0.08
% 4.11/1.94  BG Simplification    : 0.02
% 4.24/1.94  Subsumption          : 0.06
% 4.24/1.94  Abstraction          : 0.01
% 4.24/1.94  MUC search           : 0.00
% 4.24/1.94  Cooper               : 0.00
% 4.24/1.94  Total                : 0.94
% 4.24/1.94  Index Insertion      : 0.00
% 4.24/1.94  Index Deletion       : 0.00
% 4.24/1.94  Index Matching       : 0.00
% 4.24/1.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------