TSTP Solution File: SET638+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n022.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 10:56:46 EDT 2023

% Result   : Theorem 5.49s 2.30s
% Output   : CNFRefutation 5.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   34 (  18 unt;  13 typ;   0 def)
%            Number of atoms       :   25 (  14 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :    7 (   3   ~;   1   |;   1   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   16 (   9   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-2 aty)
%            Number of variables   :   27 (;  27   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > empty > union > intersection > #nlpp > empty_set > #skF_2 > #skF_7 > #skF_3 > #skF_5 > #skF_6 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_2',type,
    '#skF_2': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_106,negated_conjecture,
    ~ ! [B,C,D] :
        ( ( subset(B,union(C,D))
          & ( intersection(B,D) = empty_set ) )
       => subset(B,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th120) ).

tff(f_38,axiom,
    ! [B] : ( union(B,empty_set) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).

tff(f_41,axiom,
    ! [B,C,D] : ( intersection(B,union(C,D)) = union(intersection(B,C),intersection(B,D)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_distributes_over_union) ).

tff(f_35,axiom,
    ! [B,C] :
      ( subset(B,C)
     => ( intersection(B,C) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_intersection) ).

tff(f_80,axiom,
    ! [B,C] : ( intersection(B,C) = intersection(C,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

tff(f_30,axiom,
    ! [B,C] : subset(intersection(B,C),B),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_is_subset) ).

tff(c_58,plain,
    ~ subset('#skF_5','#skF_6'),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_6,plain,
    ! [B_5] : ( union(B_5,empty_set) = B_5 ),
    inference(cnfTransformation,[status(thm)],[f_38]) ).

tff(c_60,plain,
    intersection('#skF_5','#skF_7') = empty_set,
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_2116,plain,
    ! [B_135,C_136,D_137] : ( union(intersection(B_135,C_136),intersection(B_135,D_137)) = intersection(B_135,union(C_136,D_137)) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_2237,plain,
    ! [C_136] : ( union(intersection('#skF_5',C_136),empty_set) = intersection('#skF_5',union(C_136,'#skF_7')) ),
    inference(superposition,[status(thm),theory(equality)],[c_60,c_2116]) ).

tff(c_2821,plain,
    ! [C_145] : ( intersection('#skF_5',union(C_145,'#skF_7')) = intersection('#skF_5',C_145) ),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_2237]) ).

tff(c_62,plain,
    subset('#skF_5',union('#skF_6','#skF_7')),
    inference(cnfTransformation,[status(thm)],[f_106]) ).

tff(c_233,plain,
    ! [B_52,C_53] :
      ( ( intersection(B_52,C_53) = B_52 )
      | ~ subset(B_52,C_53) ),
    inference(cnfTransformation,[status(thm)],[f_35]) ).

tff(c_254,plain,
    intersection('#skF_5',union('#skF_6','#skF_7')) = '#skF_5',
    inference(resolution,[status(thm)],[c_62,c_233]) ).

tff(c_2882,plain,
    intersection('#skF_5','#skF_6') = '#skF_5',
    inference(superposition,[status(thm),theory(equality)],[c_2821,c_254]) ).

tff(c_85,plain,
    ! [C_44,B_45] : ( intersection(C_44,B_45) = intersection(B_45,C_44) ),
    inference(cnfTransformation,[status(thm)],[f_80]) ).

tff(c_2,plain,
    ! [B_1,C_2] : subset(intersection(B_1,C_2),B_1),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_100,plain,
    ! [C_44,B_45] : subset(intersection(C_44,B_45),B_45),
    inference(superposition,[status(thm),theory(equality)],[c_85,c_2]) ).

tff(c_2988,plain,
    subset('#skF_5','#skF_6'),
    inference(superposition,[status(thm),theory(equality)],[c_2882,c_100]) ).

tff(c_3017,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_58,c_2988]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET638+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.13/0.34  % Computer : n022.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 16:46:33 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 5.49/2.30  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.49/2.31  
% 5.49/2.31  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.49/2.33  
% 5.49/2.33  Inference rules
% 5.49/2.33  ----------------------
% 5.49/2.33  #Ref     : 0
% 5.49/2.33  #Sup     : 731
% 5.49/2.33  #Fact    : 0
% 5.49/2.33  #Define  : 0
% 5.49/2.33  #Split   : 6
% 5.49/2.33  #Chain   : 0
% 5.49/2.33  #Close   : 0
% 5.49/2.33  
% 5.49/2.33  Ordering : KBO
% 5.49/2.33  
% 5.49/2.33  Simplification rules
% 5.49/2.33  ----------------------
% 5.49/2.33  #Subsume      : 74
% 5.49/2.33  #Demod        : 552
% 5.49/2.33  #Tautology    : 402
% 5.49/2.33  #SimpNegUnit  : 10
% 5.49/2.33  #BackRed      : 13
% 5.49/2.33  
% 5.49/2.33  #Partial instantiations: 0
% 5.49/2.33  #Strategies tried      : 1
% 5.49/2.33  
% 5.49/2.33  Timing (in seconds)
% 5.49/2.33  ----------------------
% 5.49/2.33  Preprocessing        : 0.51
% 5.49/2.33  Parsing              : 0.26
% 5.49/2.34  CNF conversion       : 0.04
% 5.49/2.34  Main loop            : 0.77
% 5.49/2.34  Inferencing          : 0.26
% 5.49/2.34  Reduction            : 0.30
% 5.49/2.34  Demodulation         : 0.23
% 5.49/2.34  BG Simplification    : 0.03
% 5.49/2.34  Subsumption          : 0.14
% 5.49/2.34  Abstraction          : 0.03
% 5.49/2.34  MUC search           : 0.00
% 5.49/2.34  Cooper               : 0.00
% 5.49/2.34  Total                : 1.33
% 5.49/2.34  Index Insertion      : 0.00
% 5.49/2.34  Index Deletion       : 0.00
% 5.49/2.34  Index Matching       : 0.00
% 5.49/2.34  BG Taut test         : 0.00
%------------------------------------------------------------------------------