TSTP Solution File: SET200+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET200+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 : n009.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 10:56:11 EDT 2023

% Result   : Theorem 119.51s 94.26s
% Output   : CNFRefutation 119.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   63 (  15 unt;  10 typ;   0 def)
%            Number of atoms       :  119 (  21 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  105 (  39   ~;  59   |;   1   &)
%                                         (   4 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   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    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :  119 (; 119   !;   0   ?;   0   :)

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

%Foreground sorts:

%Background operators:

%Foreground operators:
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('#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_64,negated_conjecture,
    ~ ! [B,C,D,E] :
        ( ( subset(B,C)
          & subset(D,E) )
       => subset(union(B,D),union(C,E)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_th34) ).

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

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,union(B,C))
    <=> ( member(D,B)
        | member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).

tff(f_56,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ! [D] :
          ( member(D,B)
        <=> member(D,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).

tff(c_30,plain,
    ~ subset(union('#skF_4','#skF_6'),union('#skF_5','#skF_7')),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

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

tff(c_32,plain,
    subset('#skF_6','#skF_7'),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

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_111,plain,
    ! [D_33,C_34,B_35] :
      ( member(D_33,C_34)
      | member(D_33,B_35)
      | ~ member(D_33,union(B_35,C_34)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_1765,plain,
    ! [B_171,C_172,C_173] :
      ( member('#skF_1'(union(B_171,C_172),C_173),C_172)
      | member('#skF_1'(union(B_171,C_172),C_173),B_171)
      | subset(union(B_171,C_172),C_173) ),
    inference(resolution,[status(thm)],[c_12,c_111]) ).

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_1960,plain,
    ! [B_181,C_182] :
      ( member('#skF_1'(union(B_181,C_182),C_182),B_181)
      | subset(union(B_181,C_182),C_182) ),
    inference(resolution,[status(thm)],[c_1765,c_10]) ).

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_73670,plain,
    ! [B_1749,C_1750,C_1751] :
      ( member('#skF_1'(union(B_1749,C_1750),C_1750),C_1751)
      | ~ subset(B_1749,C_1751)
      | subset(union(B_1749,C_1750),C_1750) ),
    inference(resolution,[status(thm)],[c_1960,c_8]) ).

tff(c_73828,plain,
    ! [B_1752,C_1753] :
      ( ~ subset(B_1752,C_1753)
      | subset(union(B_1752,C_1753),C_1753) ),
    inference(resolution,[status(thm)],[c_73670,c_10]) ).

tff(c_74111,plain,
    ! [B_9,C_10] :
      ( ~ subset(B_9,C_10)
      | subset(union(C_10,B_9),C_10) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_73828]) ).

tff(c_6,plain,
    ! [D_3,B_1,C_2] :
      ( ~ member(D_3,B_1)
      | member(D_3,union(B_1,C_2)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_77,plain,
    ! [B_25,C_26] :
      ( ~ member('#skF_1'(B_25,C_26),C_26)
      | subset(B_25,C_26) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_262,plain,
    ! [B_58,B_59,C_60] :
      ( subset(B_58,union(B_59,C_60))
      | ~ member('#skF_1'(B_58,union(B_59,C_60)),B_59) ),
    inference(resolution,[status(thm)],[c_6,c_77]) ).

tff(c_288,plain,
    ! [B_4,C_60] : subset(B_4,union(B_4,C_60)),
    inference(resolution,[status(thm)],[c_12,c_262]) ).

tff(c_202,plain,
    ! [B_52,C_53] :
      ( member('#skF_2'(B_52,C_53),C_53)
      | member('#skF_3'(B_52,C_53),B_52)
      | ( C_53 = B_52 ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_622,plain,
    ! [B_93,C_94,C_95] :
      ( member('#skF_3'(B_93,C_94),C_95)
      | ~ subset(B_93,C_95)
      | member('#skF_2'(B_93,C_94),C_94)
      | ( C_94 = B_93 ) ),
    inference(resolution,[status(thm)],[c_202,c_8]) ).

tff(c_24,plain,
    ! [B_12,C_13] :
      ( member('#skF_2'(B_12,C_13),C_13)
      | ~ member('#skF_3'(B_12,C_13),C_13)
      | ( C_13 = B_12 ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_650,plain,
    ! [B_93,C_95] :
      ( ~ subset(B_93,C_95)
      | member('#skF_2'(B_93,C_95),C_95)
      | ( C_95 = B_93 ) ),
    inference(resolution,[status(thm)],[c_622,c_24]) ).

tff(c_149,plain,
    ! [B_44,C_45] :
      ( ~ member('#skF_2'(B_44,C_45),B_44)
      | member('#skF_3'(B_44,C_45),B_44)
      | ( C_45 = B_44 ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_775,plain,
    ! [B_104,C_105,C_106] :
      ( member('#skF_3'(B_104,C_105),C_106)
      | ~ subset(B_104,C_106)
      | ~ member('#skF_2'(B_104,C_105),B_104)
      | ( C_105 = B_104 ) ),
    inference(resolution,[status(thm)],[c_149,c_8]) ).

tff(c_22600,plain,
    ! [B_916,C_917,C_918,C_919] :
      ( member('#skF_3'(union(B_916,C_917),C_918),C_919)
      | ~ subset(union(B_916,C_917),C_919)
      | ( union(B_916,C_917) = C_918 )
      | ~ member('#skF_2'(union(B_916,C_917),C_918),B_916) ),
    inference(resolution,[status(thm)],[c_6,c_775]) ).

tff(c_259173,plain,
    ! [C_3394,C_3395,C_3396] :
      ( member('#skF_3'(union(C_3394,C_3395),C_3394),C_3396)
      | ~ subset(union(C_3394,C_3395),C_3396)
      | ~ subset(union(C_3394,C_3395),C_3394)
      | ( union(C_3394,C_3395) = C_3394 ) ),
    inference(resolution,[status(thm)],[c_650,c_22600]) ).

tff(c_658,plain,
    ! [B_96,C_97] :
      ( ~ subset(B_96,C_97)
      | member('#skF_2'(B_96,C_97),C_97)
      | ( C_97 = B_96 ) ),
    inference(resolution,[status(thm)],[c_622,c_24]) ).

tff(c_863,plain,
    ! [B_112,C_113,C_114] :
      ( member('#skF_2'(B_112,C_113),C_114)
      | ~ subset(C_113,C_114)
      | ~ subset(B_112,C_113)
      | ( C_113 = B_112 ) ),
    inference(resolution,[status(thm)],[c_658,c_8]) ).

tff(c_22,plain,
    ! [B_12,C_13] :
      ( ~ member('#skF_2'(B_12,C_13),B_12)
      | ~ member('#skF_3'(B_12,C_13),C_13)
      | ( C_13 = B_12 ) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_884,plain,
    ! [C_114,C_113] :
      ( ~ member('#skF_3'(C_114,C_113),C_113)
      | ~ subset(C_113,C_114)
      | ~ subset(C_114,C_113)
      | ( C_114 = C_113 ) ),
    inference(resolution,[status(thm)],[c_863,c_22]) ).

tff(c_259310,plain,
    ! [C_3396,C_3395] :
      ( ~ subset(C_3396,union(C_3396,C_3395))
      | ~ subset(union(C_3396,C_3395),C_3396)
      | ( union(C_3396,C_3395) = C_3396 ) ),
    inference(resolution,[status(thm)],[c_259173,c_884]) ).

tff(c_259485,plain,
    ! [C_3397,C_3398] :
      ( ~ subset(union(C_3397,C_3398),C_3397)
      | ( union(C_3397,C_3398) = C_3397 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_288,c_259310]) ).

tff(c_259959,plain,
    ! [C_3399,B_3400] :
      ( ( union(C_3399,B_3400) = C_3399 )
      | ~ subset(B_3400,C_3399) ),
    inference(resolution,[status(thm)],[c_74111,c_259485]) ).

tff(c_261506,plain,
    union('#skF_7','#skF_6') = '#skF_7',
    inference(resolution,[status(thm)],[c_32,c_259959]) ).

tff(c_264006,plain,
    union('#skF_6','#skF_7') = '#skF_7',
    inference(superposition,[status(thm),theory(equality)],[c_14,c_261506]) ).

tff(c_34,plain,
    subset('#skF_4','#skF_5'),
    inference(cnfTransformation,[status(thm)],[f_64]) ).

tff(c_261507,plain,
    union('#skF_5','#skF_4') = '#skF_5',
    inference(resolution,[status(thm)],[c_34,c_259959]) ).

tff(c_130,plain,
    ! [B_35,C_34,C_5] :
      ( member('#skF_1'(union(B_35,C_34),C_5),C_34)
      | member('#skF_1'(union(B_35,C_34),C_5),B_35)
      | subset(union(B_35,C_34),C_5) ),
    inference(resolution,[status(thm)],[c_12,c_111]) ).

tff(c_5509,plain,
    ! [B_334,B_335,C_336,C_337] :
      ( subset(B_334,union(union(B_335,C_336),C_337))
      | ~ member('#skF_1'(B_334,union(union(B_335,C_336),C_337)),B_335) ),
    inference(resolution,[status(thm)],[c_6,c_262]) ).

tff(c_212501,plain,
    ! [B_2961,C_2962,C_2963,C_2964] :
      ( member('#skF_1'(union(B_2961,C_2962),union(union(B_2961,C_2963),C_2964)),C_2962)
      | subset(union(B_2961,C_2962),union(union(B_2961,C_2963),C_2964)) ),
    inference(resolution,[status(thm)],[c_130,c_5509]) ).

tff(c_4,plain,
    ! [D_3,C_2,B_1] :
      ( ~ member(D_3,C_2)
      | member(D_3,union(B_1,C_2)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_89,plain,
    ! [D_27,C_28,B_29] :
      ( ~ member(D_27,C_28)
      | member(D_27,union(B_29,C_28)) ),
    inference(cnfTransformation,[status(thm)],[f_34]) ).

tff(c_289,plain,
    ! [B_61,B_62,C_63] :
      ( subset(B_61,union(B_62,C_63))
      | ~ member('#skF_1'(B_61,union(B_62,C_63)),C_63) ),
    inference(resolution,[status(thm)],[c_89,c_10]) ).

tff(c_313,plain,
    ! [B_61,B_62,B_1,C_2] :
      ( subset(B_61,union(B_62,union(B_1,C_2)))
      | ~ member('#skF_1'(B_61,union(B_62,union(B_1,C_2))),C_2) ),
    inference(resolution,[status(thm)],[c_4,c_289]) ).

tff(c_212890,plain,
    ! [B_2965,C_2966,C_2967,B_2968] : subset(union(B_2965,C_2966),union(union(B_2965,C_2967),union(B_2968,C_2966))),
    inference(resolution,[status(thm)],[c_212501,c_313]) ).

tff(c_213221,plain,
    ! [B_2965,C_2966,B_2968,C_2967] : subset(union(B_2965,C_2966),union(union(B_2968,C_2966),union(B_2965,C_2967))),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_212890]) ).

tff(c_330525,plain,
    ! [B_3497,C_3498] : subset(union(B_3497,'#skF_4'),union('#skF_5',union(B_3497,C_3498))),
    inference(superposition,[status(thm),theory(equality)],[c_261507,c_213221]) ).

tff(c_330707,plain,
    subset(union('#skF_6','#skF_4'),union('#skF_5','#skF_7')),
    inference(superposition,[status(thm),theory(equality)],[c_264006,c_330525]) ).

tff(c_330885,plain,
    subset(union('#skF_4','#skF_6'),union('#skF_5','#skF_7')),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_330707]) ).

tff(c_330887,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_30,c_330885]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET200+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.13/0.35  % Computer : n009.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 16:43:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 119.51/94.26  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 119.51/94.27  
% 119.51/94.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 119.65/94.30  
% 119.65/94.30  Inference rules
% 119.65/94.30  ----------------------
% 119.65/94.30  #Ref     : 0
% 119.65/94.30  #Sup     : 86496
% 119.65/94.30  #Fact    : 94
% 119.65/94.30  #Define  : 0
% 119.65/94.30  #Split   : 22
% 119.65/94.30  #Chain   : 0
% 119.65/94.30  #Close   : 0
% 119.65/94.30  
% 119.65/94.30  Ordering : KBO
% 119.65/94.30  
% 119.65/94.30  Simplification rules
% 119.65/94.30  ----------------------
% 119.65/94.30  #Subsume      : 22637
% 119.65/94.30  #Demod        : 47193
% 119.65/94.30  #Tautology    : 18311
% 119.65/94.30  #SimpNegUnit  : 72
% 119.65/94.30  #BackRed      : 529
% 119.65/94.30  
% 119.65/94.30  #Partial instantiations: 0
% 119.65/94.30  #Strategies tried      : 1
% 119.65/94.30  
% 119.65/94.30  Timing (in seconds)
% 119.65/94.30  ----------------------
% 119.65/94.30  Preprocessing        : 0.46
% 119.65/94.30  Parsing              : 0.24
% 119.65/94.30  CNF conversion       : 0.03
% 119.65/94.30  Main loop            : 92.79
% 119.65/94.30  Inferencing          : 5.71
% 119.65/94.30  Reduction            : 39.19
% 119.65/94.30  Demodulation         : 34.43
% 119.65/94.30  BG Simplification    : 0.41
% 119.65/94.30  Subsumption          : 41.25
% 119.65/94.30  Abstraction          : 0.71
% 119.65/94.30  MUC search           : 0.00
% 119.65/94.30  Cooper               : 0.00
% 119.65/94.31  Total                : 93.30
% 119.65/94.31  Index Insertion      : 0.00
% 119.65/94.31  Index Deletion       : 0.00
% 119.65/94.31  Index Matching       : 0.00
% 119.65/94.31  BG Taut test         : 0.00
%------------------------------------------------------------------------------