TSTP Solution File: SEU097+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU097+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 : n008.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 10:57:36 EDT 2023

% Result   : Theorem 7.10s 2.60s
% Output   : CNFRefutation 7.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   70 (  11 unt;  52 typ;   0 def)
%            Number of atoms       :   29 (   2 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   24 (  13   ~;   6   |;   2   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 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  :   20 (  18 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;  25 con; 0-2 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 > symmetric_difference > set_union2 > set_difference > #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_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(set_difference,type,
    set_difference: ( $i * $i ) > $i ).

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(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(symmetric_difference,type,
    symmetric_difference: ( $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(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_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(set_union2,type,
    set_union2: ( $i * $i ) > $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('#skF_20',type,
    '#skF_20': $i > $i ).

tff(f_404,negated_conjecture,
    ~ ! [A,B] :
        ( ( finite(A)
          & finite(B) )
       => finite(symmetric_difference(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t28_finset_1) ).

tff(f_391,axiom,
    ! [A,B] :
      ( finite(A)
     => finite(set_difference(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_finset_1) ).

tff(f_123,axiom,
    ! [A,B] : ( symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_xboole_0) ).

tff(f_197,axiom,
    ! [A,B] :
      ( ( finite(A)
        & finite(B) )
     => finite(set_union2(A,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_finset_1) ).

tff(c_288,plain,
    finite('#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_280,plain,
    ! [A_53,B_54] :
      ( finite(set_difference(A_53,B_54))
      | ~ finite(A_53) ),
    inference(cnfTransformation,[status(thm)],[f_391]) ).

tff(c_290,plain,
    finite('#skF_27'),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_1473,plain,
    ! [A_193,B_194] : ( set_union2(set_difference(A_193,B_194),set_difference(B_194,A_193)) = symmetric_difference(A_193,B_194) ),
    inference(cnfTransformation,[status(thm)],[f_123]) ).

tff(c_106,plain,
    ! [A_41,B_42] :
      ( finite(set_union2(A_41,B_42))
      | ~ finite(B_42)
      | ~ finite(A_41) ),
    inference(cnfTransformation,[status(thm)],[f_197]) ).

tff(c_1812,plain,
    ! [A_232,B_233] :
      ( finite(symmetric_difference(A_232,B_233))
      | ~ finite(set_difference(B_233,A_232))
      | ~ finite(set_difference(A_232,B_233)) ),
    inference(superposition,[status(thm),theory(equality)],[c_1473,c_106]) ).

tff(c_286,plain,
    ~ finite(symmetric_difference('#skF_27','#skF_28')),
    inference(cnfTransformation,[status(thm)],[f_404]) ).

tff(c_1831,plain,
    ( ~ finite(set_difference('#skF_28','#skF_27'))
    | ~ finite(set_difference('#skF_27','#skF_28')) ),
    inference(resolution,[status(thm)],[c_1812,c_286]) ).

tff(c_1836,plain,
    ~ finite(set_difference('#skF_27','#skF_28')),
    inference(splitLeft,[status(thm)],[c_1831]) ).

tff(c_1839,plain,
    ~ finite('#skF_27'),
    inference(resolution,[status(thm)],[c_280,c_1836]) ).

tff(c_1846,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_290,c_1839]) ).

tff(c_1847,plain,
    ~ finite(set_difference('#skF_28','#skF_27')),
    inference(splitRight,[status(thm)],[c_1831]) ).

tff(c_1851,plain,
    ~ finite('#skF_28'),
    inference(resolution,[status(thm)],[c_280,c_1847]) ).

tff(c_1858,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_288,c_1851]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU097+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 : n008.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 11:36:04 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 7.10/2.60  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.10/2.60  
% 7.10/2.60  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 7.39/2.63  
% 7.39/2.63  Inference rules
% 7.39/2.63  ----------------------
% 7.39/2.63  #Ref     : 0
% 7.39/2.63  #Sup     : 327
% 7.39/2.63  #Fact    : 0
% 7.39/2.63  #Define  : 0
% 7.39/2.63  #Split   : 11
% 7.39/2.63  #Chain   : 0
% 7.39/2.63  #Close   : 0
% 7.39/2.63  
% 7.39/2.63  Ordering : KBO
% 7.39/2.63  
% 7.39/2.63  Simplification rules
% 7.39/2.63  ----------------------
% 7.39/2.63  #Subsume      : 59
% 7.39/2.63  #Demod        : 222
% 7.39/2.63  #Tautology    : 223
% 7.39/2.63  #SimpNegUnit  : 7
% 7.39/2.63  #BackRed      : 41
% 7.39/2.63  
% 7.39/2.63  #Partial instantiations: 0
% 7.39/2.63  #Strategies tried      : 1
% 7.39/2.63  
% 7.39/2.63  Timing (in seconds)
% 7.39/2.63  ----------------------
% 7.39/2.63  Preprocessing        : 0.63
% 7.39/2.63  Parsing              : 0.33
% 7.39/2.63  CNF conversion       : 0.06
% 7.39/2.63  Main loop            : 0.94
% 7.39/2.63  Inferencing          : 0.33
% 7.39/2.63  Reduction            : 0.32
% 7.39/2.63  Demodulation         : 0.23
% 7.39/2.63  BG Simplification    : 0.04
% 7.39/2.64  Subsumption          : 0.18
% 7.39/2.64  Abstraction          : 0.02
% 7.39/2.64  MUC search           : 0.00
% 7.39/2.64  Cooper               : 0.00
% 7.39/2.64  Total                : 1.63
% 7.39/2.64  Index Insertion      : 0.00
% 7.39/2.64  Index Deletion       : 0.00
% 7.39/2.64  Index Matching       : 0.00
% 7.39/2.64  BG Taut test         : 0.00
%------------------------------------------------------------------------------