TSTP Solution File: SEU096+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU096+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 : n010.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 6.78s 2.51s
% Output   : CNFRefutation 6.78s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   56
% Syntax   : Number of formulae    :   68 (   8 unt;  53 typ;   0 def)
%            Number of atoms       :   36 (   4 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :   34 (  13   ~;  11   |;   4   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  28   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;  25 con; 0-2 aty)
%            Number of variables   :   10 (;  10   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > element > with_non_empty_elements > 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 > relation_inverse_image > relation_image > #nlpp > relation_rng > 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(with_non_empty_elements,type,
    with_non_empty_elements: $i > $o ).

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(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(relation_inverse_image,type,
    relation_inverse_image: ( $i * $i ) > $i ).

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(relation_image,type,
    relation_image: ( $i * $i ) > $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(powerset,type,
    powerset: $i > $i ).

tff(relation_rng,type,
    relation_rng: $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_400,negated_conjecture,
    ~ ! [A,B] :
        ( ( relation(B)
          & function(B) )
       => ( ( subset(A,relation_rng(B))
            & finite(relation_inverse_image(B,A)) )
         => finite(A) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_finset_1) ).

tff(f_377,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( subset(A,relation_rng(B))
       => ( relation_image(B,relation_inverse_image(B,A)) = A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t147_funct_1) ).

tff(f_385,axiom,
    ! [A,B] :
      ( ( relation(B)
        & function(B) )
     => ( finite(A)
       => finite(relation_image(B,A)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_finset_1) ).

tff(c_274,plain,
    ~ finite('#skF_27'),
    inference(cnfTransformation,[status(thm)],[f_400]) ).

tff(c_282,plain,
    relation('#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_400]) ).

tff(c_280,plain,
    function('#skF_28'),
    inference(cnfTransformation,[status(thm)],[f_400]) ).

tff(c_276,plain,
    finite(relation_inverse_image('#skF_28','#skF_27')),
    inference(cnfTransformation,[status(thm)],[f_400]) ).

tff(c_278,plain,
    subset('#skF_27',relation_rng('#skF_28')),
    inference(cnfTransformation,[status(thm)],[f_400]) ).

tff(c_1167,plain,
    ! [B_152,A_153] :
      ( ( relation_image(B_152,relation_inverse_image(B_152,A_153)) = A_153 )
      | ~ subset(A_153,relation_rng(B_152))
      | ~ function(B_152)
      | ~ relation(B_152) ),
    inference(cnfTransformation,[status(thm)],[f_377]) ).

tff(c_1188,plain,
    ( ( relation_image('#skF_28',relation_inverse_image('#skF_28','#skF_27')) = '#skF_27' )
    | ~ function('#skF_28')
    | ~ relation('#skF_28') ),
    inference(resolution,[status(thm)],[c_278,c_1167]) ).

tff(c_1198,plain,
    relation_image('#skF_28',relation_inverse_image('#skF_28','#skF_27')) = '#skF_27',
    inference(demodulation,[status(thm),theory(equality)],[c_282,c_280,c_1188]) ).

tff(c_270,plain,
    ! [B_39,A_38] :
      ( finite(relation_image(B_39,A_38))
      | ~ finite(A_38)
      | ~ function(B_39)
      | ~ relation(B_39) ),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_1202,plain,
    ( finite('#skF_27')
    | ~ finite(relation_inverse_image('#skF_28','#skF_27'))
    | ~ function('#skF_28')
    | ~ relation('#skF_28') ),
    inference(superposition,[status(thm),theory(equality)],[c_1198,c_270]) ).

tff(c_1206,plain,
    finite('#skF_27'),
    inference(demodulation,[status(thm),theory(equality)],[c_282,c_280,c_276,c_1202]) ).

tff(c_1208,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_274,c_1206]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU096+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/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
% 0.15/0.35  % Computer : n010.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 11:41:43 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 6.78/2.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.78/2.52  
% 6.78/2.52  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.78/2.54  
% 6.78/2.54  Inference rules
% 6.78/2.54  ----------------------
% 6.78/2.54  #Ref     : 0
% 6.78/2.54  #Sup     : 179
% 6.78/2.54  #Fact    : 0
% 6.78/2.54  #Define  : 0
% 6.78/2.54  #Split   : 13
% 6.78/2.54  #Chain   : 0
% 6.78/2.54  #Close   : 0
% 6.78/2.54  
% 6.78/2.54  Ordering : KBO
% 6.78/2.54  
% 6.78/2.54  Simplification rules
% 6.78/2.54  ----------------------
% 6.78/2.54  #Subsume      : 36
% 6.78/2.54  #Demod        : 162
% 6.78/2.54  #Tautology    : 111
% 6.78/2.54  #SimpNegUnit  : 2
% 6.78/2.54  #BackRed      : 42
% 6.78/2.54  
% 6.78/2.54  #Partial instantiations: 0
% 6.78/2.54  #Strategies tried      : 1
% 6.78/2.54  
% 6.78/2.54  Timing (in seconds)
% 6.78/2.54  ----------------------
% 6.78/2.54  Preprocessing        : 0.65
% 6.78/2.54  Parsing              : 0.34
% 6.78/2.54  CNF conversion       : 0.06
% 6.78/2.54  Main loop            : 0.76
% 6.78/2.54  Inferencing          : 0.25
% 6.78/2.54  Reduction            : 0.27
% 6.78/2.54  Demodulation         : 0.19
% 6.78/2.54  BG Simplification    : 0.04
% 6.78/2.54  Subsumption          : 0.13
% 6.78/2.54  Abstraction          : 0.02
% 6.78/2.54  MUC search           : 0.00
% 6.78/2.54  Cooper               : 0.00
% 6.78/2.54  Total                : 1.46
% 6.78/2.54  Index Insertion      : 0.00
% 6.78/2.54  Index Deletion       : 0.00
% 6.78/2.54  Index Matching       : 0.00
% 6.78/2.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------