TSTP Solution File: SET586+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET586+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/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 : n001.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 10:56:37 EDT 2023

% Result   : Theorem 6.32s 2.69s
% Output   : CNFRefutation 6.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   36 (   9 unt;   9 typ;   0 def)
%            Number of atoms       :   58 (   2 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   55 (  24   ~;  26   |;   1   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   57 (;  57   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(intersection,type,
    intersection: ( $i * $i ) > $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('#skF_4',type,
    '#skF_4': $i ).

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

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

tff(f_45,axiom,
    ! [B,C] : ( intersection(B,C) = intersection(C,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).

tff(f_42,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).

tff(f_34,axiom,
    ! [B,C,D] :
      ( member(D,intersection(B,C))
    <=> ( member(D,B)
        & member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).

tff(f_62,negated_conjecture,
    ~ ! [B,C,D] :
        ( subset(B,C)
       => subset(intersection(B,D),intersection(C,D)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_intersection_of_subset) ).

tff(c_14,plain,
    ! [C_10,B_9] : ( intersection(C_10,B_9) = intersection(B_9,C_10) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_12,plain,
    ! [B_4,C_5] :
      ( member('#skF_1'(B_4,C_5),B_4)
      | subset(B_4,C_5) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_88,plain,
    ! [D_27,B_28,C_29] :
      ( member(D_27,B_28)
      | ~ member(D_27,intersection(B_28,C_29)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_211,plain,
    ! [B_47,C_48,C_49] :
      ( member('#skF_1'(intersection(B_47,C_48),C_49),B_47)
      | subset(intersection(B_47,C_48),C_49) ),
    inference(resolution,[status(thm)],[c_12,c_88]) ).

tff(c_10,plain,
    ! [B_4,C_5] :
      ( ~ member('#skF_1'(B_4,C_5),C_5)
      | subset(B_4,C_5) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_236,plain,
    ! [B_50,C_51] : subset(intersection(B_50,C_51),B_50),
    inference(resolution,[status(thm)],[c_211,c_10]) ).

tff(c_239,plain,
    ! [C_10,B_9] : subset(intersection(C_10,B_9),B_9),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_236]) ).

tff(c_235,plain,
    ! [B_47,C_48] : subset(intersection(B_47,C_48),B_47),
    inference(resolution,[status(thm)],[c_211,c_10]) ).

tff(c_100,plain,
    ! [D_30,C_31,B_32] :
      ( member(D_30,C_31)
      | ~ member(D_30,B_32)
      | ~ subset(B_32,C_31) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_103,plain,
    ! [B_4,C_5,C_31] :
      ( member('#skF_1'(B_4,C_5),C_31)
      | ~ subset(B_4,C_31)
      | subset(B_4,C_5) ),
    inference(resolution,[status(thm)],[c_12,c_100]) ).

tff(c_32,plain,
    subset('#skF_4','#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_127,plain,
    ! [B_36,C_37,C_38] :
      ( member('#skF_1'(B_36,C_37),C_38)
      | ~ subset(B_36,C_38)
      | subset(B_36,C_37) ),
    inference(resolution,[status(thm)],[c_12,c_100]) ).

tff(c_8,plain,
    ! [D_8,C_5,B_4] :
      ( member(D_8,C_5)
      | ~ member(D_8,B_4)
      | ~ subset(B_4,C_5) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_380,plain,
    ! [B_75,C_76,C_77,C_78] :
      ( member('#skF_1'(B_75,C_76),C_77)
      | ~ subset(C_78,C_77)
      | ~ subset(B_75,C_78)
      | subset(B_75,C_76) ),
    inference(resolution,[status(thm)],[c_127,c_8]) ).

tff(c_392,plain,
    ! [B_75,C_76] :
      ( member('#skF_1'(B_75,C_76),'#skF_5')
      | ~ subset(B_75,'#skF_4')
      | subset(B_75,C_76) ),
    inference(resolution,[status(thm)],[c_32,c_380]) ).

tff(c_104,plain,
    ! [D_33,B_34,C_35] :
      ( member(D_33,intersection(B_34,C_35))
      | ~ member(D_33,C_35)
      | ~ member(D_33,B_34) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_1761,plain,
    ! [B_205,B_206,C_207] :
      ( subset(B_205,intersection(B_206,C_207))
      | ~ member('#skF_1'(B_205,intersection(B_206,C_207)),C_207)
      | ~ member('#skF_1'(B_205,intersection(B_206,C_207)),B_206) ),
    inference(resolution,[status(thm)],[c_104,c_10]) ).

tff(c_2309,plain,
    ! [B_223,B_224] :
      ( ~ member('#skF_1'(B_223,intersection(B_224,'#skF_5')),B_224)
      | ~ subset(B_223,'#skF_4')
      | subset(B_223,intersection(B_224,'#skF_5')) ),
    inference(resolution,[status(thm)],[c_392,c_1761]) ).

tff(c_2605,plain,
    ! [B_234,C_235] :
      ( ~ subset(B_234,'#skF_4')
      | ~ subset(B_234,C_235)
      | subset(B_234,intersection(C_235,'#skF_5')) ),
    inference(resolution,[status(thm)],[c_103,c_2309]) ).

tff(c_30,plain,
    ~ subset(intersection('#skF_4','#skF_6'),intersection('#skF_5','#skF_6')),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_33,plain,
    ~ subset(intersection('#skF_4','#skF_6'),intersection('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_30]) ).

tff(c_2640,plain,
    ( ~ subset(intersection('#skF_4','#skF_6'),'#skF_4')
    | ~ subset(intersection('#skF_4','#skF_6'),'#skF_6') ),
    inference(resolution,[status(thm)],[c_2605,c_33]) ).

tff(c_2669,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_239,c_235,c_2640]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET586+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/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
% 0.13/0.35  % Computer : n001.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 17:31:55 EDT 2023
% 0.20/0.35  % CPUTime  : 
% 6.32/2.69  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.68/2.70  
% 6.68/2.70  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.68/2.73  
% 6.68/2.73  Inference rules
% 6.68/2.73  ----------------------
% 6.68/2.73  #Ref     : 0
% 6.68/2.73  #Sup     : 678
% 6.68/2.73  #Fact    : 0
% 6.68/2.73  #Define  : 0
% 6.68/2.73  #Split   : 1
% 6.68/2.73  #Chain   : 0
% 6.68/2.73  #Close   : 0
% 6.68/2.73  
% 6.68/2.73  Ordering : KBO
% 6.68/2.73  
% 6.68/2.73  Simplification rules
% 6.68/2.73  ----------------------
% 6.68/2.73  #Subsume      : 179
% 6.68/2.73  #Demod        : 42
% 6.68/2.73  #Tautology    : 58
% 6.68/2.73  #SimpNegUnit  : 0
% 6.68/2.73  #BackRed      : 0
% 6.68/2.73  
% 6.68/2.73  #Partial instantiations: 0
% 6.68/2.73  #Strategies tried      : 1
% 6.68/2.73  
% 6.68/2.73  Timing (in seconds)
% 6.68/2.73  ----------------------
% 6.68/2.73  Preprocessing        : 0.47
% 6.68/2.73  Parsing              : 0.25
% 6.68/2.73  CNF conversion       : 0.03
% 6.68/2.73  Main loop            : 1.12
% 6.68/2.73  Inferencing          : 0.38
% 6.68/2.73  Reduction            : 0.30
% 6.68/2.73  Demodulation         : 0.23
% 6.68/2.73  BG Simplification    : 0.04
% 6.68/2.73  Subsumption          : 0.33
% 6.68/2.73  Abstraction          : 0.04
% 6.68/2.73  MUC search           : 0.00
% 6.68/2.73  Cooper               : 0.00
% 6.68/2.73  Total                : 1.64
% 6.68/2.73  Index Insertion      : 0.00
% 6.68/2.73  Index Deletion       : 0.00
% 6.68/2.73  Index Matching       : 0.00
% 6.68/2.73  BG Taut test         : 0.00
%------------------------------------------------------------------------------