TSTP Solution File: SEU089+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU089+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/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 : n021.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 10:57:35 EDT 2023

% Result   : Theorem 6.71s 2.53s
% Output   : CNFRefutation 6.71s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   55
% Syntax   : Number of formulae    :   66 (   8 unt;  52 typ;   0 def)
%            Number of atoms       :   25 (   2 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   22 (  11   ~;   6   |;   3   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   32 (  26   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :   20 (  18 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;  26 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > transfinite_sequence > relation_non_empty > relation_empty_yielding > relation > ordinal_yielding > ordinal > one_to_one > natural > function_yielding > function > finite > epsilon_transitive > epsilon_connected > empty > being_limit_ordinal > cartesian_product3 > cartesian_product2 > #nlpp > powerset > positive_rationals > empty_set > #skF_9 > #skF_18 > #skF_11 > #skF_15 > #skF_1 > #skF_25 > #skF_19 > #skF_7 > #skF_10 > #skF_16 > #skF_26 > #skF_14 > #skF_5 > #skF_6 > #skF_13 > #skF_2 > #skF_3 > #skF_21 > #skF_8 > #skF_4 > #skF_17 > #skF_22 > #skF_29 > #skF_28 > #skF_24 > #skF_27 > #skF_23 > #skF_12 > #skF_20

%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(positive_rationals,type,
    positive_rationals: $i ).

tff('#skF_18',type,
    '#skF_18': $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('#skF_1',type,
    '#skF_1': $i > $i ).

tff('#skF_25',type,
    '#skF_25': $i ).

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

tff(cartesian_product3,type,
    cartesian_product3: ( $i * $i * $i ) > $i ).

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

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

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

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

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

tff('#skF_19',type,
    '#skF_19': $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(ordinal,type,
    ordinal: $i > $o ).

tff('#skF_26',type,
    '#skF_26': $i ).

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

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

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

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

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

tff('#skF_21',type,
    '#skF_21': $i ).

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

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

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

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

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

tff('#skF_17',type,
    '#skF_17': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i ).

tff('#skF_29',type,
    '#skF_29': $i ).

tff('#skF_28',type,
    '#skF_28': $i ).

tff('#skF_24',type,
    '#skF_24': $i ).

tff('#skF_27',type,
    '#skF_27': $i ).

tff('#skF_23',type,
    '#skF_23': $i ).

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

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

tff(f_391,negated_conjecture,
    ~ ! [A,B,C] :
        ( ( finite(A)
          & finite(B)
          & finite(C) )
       => finite(cartesian_product3(A,B,C)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_finset_1) ).

tff(f_378,axiom,
    ! [A,B] :
      ( ( finite(A)
        & finite(B) )
     => finite(cartesian_product2(A,B)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t19_finset_1) ).

tff(f_123,axiom,
    ! [A,B,C] : ( cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_zfmisc_1) ).

tff(c_278,plain,
    finite('#skF_27'),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_276,plain,
    finite('#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_268,plain,
    ! [A_44,B_45] :
      ( finite(cartesian_product2(A_44,B_45))
      | ~ finite(B_45)
      | ~ finite(A_44) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_274,plain,
    finite('#skF_29'),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_1049,plain,
    ! [A_153,B_154,C_155] : ( cartesian_product2(cartesian_product2(A_153,B_154),C_155) = cartesian_product3(A_153,B_154,C_155) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_1345,plain,
    ! [A_221,B_222,C_223] :
      ( finite(cartesian_product3(A_221,B_222,C_223))
      | ~ finite(C_223)
      | ~ finite(cartesian_product2(A_221,B_222)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1049,c_268]) ).

tff(c_272,plain,
    ~ finite(cartesian_product3('#skF_27','#skF_28','#skF_29')),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_1348,plain,
    ( ~ finite('#skF_29')
    | ~ finite(cartesian_product2('#skF_27','#skF_28')) ),
    inference(resolution,[status(thm)],[c_1345,c_272]) ).

tff(c_1351,plain,
    ~ finite(cartesian_product2('#skF_27','#skF_28')),
    inference(demodulation,[status(thm),theory(equality)],[c_274,c_1348]) ).

tff(c_1354,plain,
    ( ~ finite('#skF_28')
    | ~ finite('#skF_27') ),
    inference(resolution,[status(thm)],[c_268,c_1351]) ).

tff(c_1361,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_276,c_1354]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU089+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/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
% 0.13/0.34  % Computer : n021.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 11:35:21 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 6.71/2.53  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.71/2.53  
% 6.71/2.53  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.71/2.56  
% 6.71/2.56  Inference rules
% 6.71/2.56  ----------------------
% 6.71/2.56  #Ref     : 0
% 6.71/2.56  #Sup     : 208
% 6.71/2.56  #Fact    : 0
% 6.71/2.56  #Define  : 0
% 6.71/2.56  #Split   : 11
% 6.71/2.56  #Chain   : 0
% 6.71/2.56  #Close   : 0
% 6.71/2.56  
% 6.71/2.56  Ordering : KBO
% 6.71/2.56  
% 6.71/2.56  Simplification rules
% 6.71/2.56  ----------------------
% 6.71/2.56  #Subsume      : 39
% 6.71/2.56  #Demod        : 145
% 6.71/2.56  #Tautology    : 117
% 6.71/2.56  #SimpNegUnit  : 7
% 6.71/2.56  #BackRed      : 39
% 6.71/2.56  
% 6.71/2.56  #Partial instantiations: 0
% 6.71/2.56  #Strategies tried      : 1
% 6.71/2.56  
% 6.71/2.56  Timing (in seconds)
% 6.71/2.56  ----------------------
% 6.71/2.56  Preprocessing        : 0.62
% 6.71/2.56  Parsing              : 0.33
% 6.71/2.56  CNF conversion       : 0.06
% 6.71/2.56  Main loop            : 0.82
% 6.71/2.56  Inferencing          : 0.29
% 6.71/2.56  Reduction            : 0.27
% 6.71/2.56  Demodulation         : 0.18
% 6.71/2.56  BG Simplification    : 0.04
% 6.71/2.56  Subsumption          : 0.15
% 6.71/2.56  Abstraction          : 0.02
% 6.71/2.56  MUC search           : 0.00
% 6.71/2.56  Cooper               : 0.00
% 6.71/2.57  Total                : 1.49
% 6.71/2.57  Index Insertion      : 0.00
% 6.71/2.57  Index Deletion       : 0.00
% 6.71/2.57  Index Matching       : 0.00
% 6.71/2.57  BG Taut test         : 0.00
%------------------------------------------------------------------------------