TSTP Solution File: SET578+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET578+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 : n015.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 10:56:36 EDT 2023

% Result   : Theorem 23.29s 12.62s
% Output   : CNFRefutation 23.50s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   79 (  20 unt;   9 typ;   0 def)
%            Number of atoms       :  148 (  32 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  128 (  50   ~;  67   |;   3   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 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   :  113 (; 113   !;   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_43,axiom,
    ! [B,C] : ( intersection(B,C) = intersection(C,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_intersection) ).

tff(f_73,negated_conjecture,
    ~ ! [B,C,D] :
        ( ! [E] :
            ( member(E,B)
          <=> ( member(E,C)
              & member(E,D) ) )
       => ( B = intersection(C,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th19) ).

tff(f_51,axiom,
    ! [B,C] :
      ( subset(B,C)
    <=> ! [D] :
          ( member(D,B)
         => member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

tff(f_33,axiom,
    ! [B,C,D] :
      ( member(D,intersection(B,C))
    <=> ( member(D,B)
        & member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).

tff(f_40,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ( subset(B,C)
        & subset(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

tff(f_62,axiom,
    ! [B,C] :
      ( ( B = C )
    <=> ! [D] :
          ( member(D,B)
        <=> member(D,C) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).

tff(c_14,plain,
    ! [C_7,B_6] : ( intersection(C_7,B_6) = intersection(B_6,C_7) ),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_36,plain,
    intersection('#skF_5','#skF_6') != '#skF_4',
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_43,plain,
    intersection('#skF_6','#skF_5') != '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_36]) ).

tff(c_20,plain,
    ! [B_8,C_9] :
      ( member('#skF_1'(B_8,C_9),B_8)
      | subset(B_8,C_9) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_40,plain,
    ! [E_20] :
      ( member(E_20,'#skF_6')
      | ~ member(E_20,'#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_181,plain,
    ! [D_48,B_49,C_50] :
      ( member(D_48,intersection(B_49,C_50))
      | ~ member(D_48,C_50)
      | ~ member(D_48,B_49) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_18,plain,
    ! [B_8,C_9] :
      ( ~ member('#skF_1'(B_8,C_9),C_9)
      | subset(B_8,C_9) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_2366,plain,
    ! [B_209,B_210,C_211] :
      ( subset(B_209,intersection(B_210,C_211))
      | ~ member('#skF_1'(B_209,intersection(B_210,C_211)),C_211)
      | ~ member('#skF_1'(B_209,intersection(B_210,C_211)),B_210) ),
    inference(resolution,[status(thm)],[c_181,c_18]) ).

tff(c_2415,plain,
    ! [B_212,B_213] :
      ( ~ member('#skF_1'(B_212,intersection(B_213,B_212)),B_213)
      | subset(B_212,intersection(B_213,B_212)) ),
    inference(resolution,[status(thm)],[c_20,c_2366]) ).

tff(c_2558,plain,
    ! [B_215] :
      ( subset(B_215,intersection('#skF_6',B_215))
      | ~ member('#skF_1'(B_215,intersection('#skF_6',B_215)),'#skF_4') ),
    inference(resolution,[status(thm)],[c_40,c_2415]) ).

tff(c_2582,plain,
    subset('#skF_4',intersection('#skF_6','#skF_4')),
    inference(resolution,[status(thm)],[c_20,c_2558]) ).

tff(c_2597,plain,
    subset('#skF_4',intersection('#skF_4','#skF_6')),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_2582]) ).

tff(c_102,plain,
    ! [D_33,B_34,C_35] :
      ( member(D_33,B_34)
      | ~ member(D_33,intersection(B_34,C_35)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_584,plain,
    ! [B_74,C_75,C_76] :
      ( member('#skF_1'(intersection(B_74,C_75),C_76),B_74)
      | subset(intersection(B_74,C_75),C_76) ),
    inference(resolution,[status(thm)],[c_20,c_102]) ).

tff(c_648,plain,
    ! [B_79,C_80] : subset(intersection(B_79,C_80),B_79),
    inference(resolution,[status(thm)],[c_584,c_18]) ).

tff(c_8,plain,
    ! [C_5,B_4] :
      ( ( C_5 = B_4 )
      | ~ subset(C_5,B_4)
      | ~ subset(B_4,C_5) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_657,plain,
    ! [B_79,C_80] :
      ( ( intersection(B_79,C_80) = B_79 )
      | ~ subset(B_79,intersection(B_79,C_80)) ),
    inference(resolution,[status(thm)],[c_648,c_8]) ).

tff(c_2939,plain,
    intersection('#skF_4','#skF_6') = '#skF_4',
    inference(resolution,[status(thm)],[c_2597,c_657]) ).

tff(c_113,plain,
    ! [B_34,C_35,C_9] :
      ( member('#skF_1'(intersection(B_34,C_35),C_9),B_34)
      | subset(intersection(B_34,C_35),C_9) ),
    inference(resolution,[status(thm)],[c_20,c_102]) ).

tff(c_42,plain,
    ! [E_20] :
      ( member(E_20,'#skF_5')
      | ~ member(E_20,'#skF_4') ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_90,plain,
    ! [D_30,C_31,B_32] :
      ( member(D_30,C_31)
      | ~ member(D_30,intersection(B_32,C_31)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_101,plain,
    ! [B_32,C_31,C_9] :
      ( member('#skF_1'(intersection(B_32,C_31),C_9),C_31)
      | subset(intersection(B_32,C_31),C_9) ),
    inference(resolution,[status(thm)],[c_20,c_90]) ).

tff(c_8879,plain,
    ! [B_315,C_316,B_317] :
      ( ~ member('#skF_1'(intersection(B_315,C_316),intersection(B_317,C_316)),B_317)
      | subset(intersection(B_315,C_316),intersection(B_317,C_316)) ),
    inference(resolution,[status(thm)],[c_101,c_2366]) ).

tff(c_9221,plain,
    ! [B_322,C_323] :
      ( subset(intersection(B_322,C_323),intersection('#skF_5',C_323))
      | ~ member('#skF_1'(intersection(B_322,C_323),intersection('#skF_5',C_323)),'#skF_4') ),
    inference(resolution,[status(thm)],[c_42,c_8879]) ).

tff(c_9492,plain,
    ! [C_327] : subset(intersection('#skF_4',C_327),intersection('#skF_5',C_327)),
    inference(resolution,[status(thm)],[c_113,c_9221]) ).

tff(c_9543,plain,
    subset('#skF_4',intersection('#skF_5','#skF_6')),
    inference(superposition,[status(thm),theory(equality)],[c_2939,c_9492]) ).

tff(c_9585,plain,
    subset('#skF_4',intersection('#skF_6','#skF_5')),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_9543]) ).

tff(c_656,plain,
    ! [B_6,C_7] : subset(intersection(B_6,C_7),C_7),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_648]) ).

tff(c_150,plain,
    ! [D_40,C_41,B_42] :
      ( member(D_40,C_41)
      | ~ member(D_40,B_42)
      | ~ subset(B_42,C_41) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_157,plain,
    ! [B_8,C_9,C_41] :
      ( member('#skF_1'(B_8,C_9),C_41)
      | ~ subset(B_8,C_41)
      | subset(B_8,C_9) ),
    inference(resolution,[status(thm)],[c_20,c_150]) ).

tff(c_3903,plain,
    ! [B_225,C_226] :
      ( ~ subset(B_225,C_226)
      | subset(B_225,intersection(C_226,B_225)) ),
    inference(resolution,[status(thm)],[c_157,c_2415]) ).

tff(c_773,plain,
    ! [B_91,C_92] :
      ( ( intersection(B_91,C_92) = B_91 )
      | ~ subset(B_91,intersection(B_91,C_92)) ),
    inference(resolution,[status(thm)],[c_648,c_8]) ).

tff(c_779,plain,
    ! [C_7,B_6] :
      ( ( intersection(C_7,B_6) = C_7 )
      | ~ subset(C_7,intersection(B_6,C_7)) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_773]) ).

tff(c_4009,plain,
    ! [B_225,C_226] :
      ( ( intersection(B_225,C_226) = B_225 )
      | ~ subset(B_225,C_226) ),
    inference(resolution,[status(thm)],[c_3903,c_779]) ).

tff(c_9606,plain,
    intersection('#skF_4',intersection('#skF_6','#skF_5')) = '#skF_4',
    inference(resolution,[status(thm)],[c_9585,c_4009]) ).

tff(c_348,plain,
    ! [B_65,C_66] :
      ( member('#skF_2'(B_65,C_66),C_66)
      | member('#skF_3'(B_65,C_66),B_65)
      | ( C_66 = B_65 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_6,plain,
    ! [D_3,B_1,C_2] :
      ( member(D_3,B_1)
      | ~ member(D_3,intersection(B_1,C_2)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_1719,plain,
    ! [B_168,C_169,C_170] :
      ( member('#skF_3'(intersection(B_168,C_169),C_170),B_168)
      | member('#skF_2'(intersection(B_168,C_169),C_170),C_170)
      | ( intersection(B_168,C_169) = C_170 ) ),
    inference(resolution,[status(thm)],[c_348,c_6]) ).

tff(c_30,plain,
    ! [B_14,C_15] :
      ( member('#skF_2'(B_14,C_15),C_15)
      | ~ member('#skF_3'(B_14,C_15),C_15)
      | ( C_15 = B_14 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_1817,plain,
    ! [B_173,C_174] :
      ( member('#skF_2'(intersection(B_173,C_174),B_173),B_173)
      | ( intersection(B_173,C_174) = B_173 ) ),
    inference(resolution,[status(thm)],[c_1719,c_30]) ).

tff(c_1837,plain,
    ! [B_6,C_7] :
      ( member('#skF_2'(intersection(B_6,C_7),C_7),C_7)
      | ( intersection(C_7,B_6) = C_7 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_1817]) ).

tff(c_10220,plain,
    ( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
    | ( intersection(intersection('#skF_6','#skF_5'),'#skF_4') = intersection('#skF_6','#skF_5') ) ),
    inference(superposition,[status(thm),theory(equality)],[c_9606,c_1837]) ).

tff(c_10359,plain,
    ( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
    | ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9606,c_14,c_10220]) ).

tff(c_10360,plain,
    member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_43,c_10359]) ).

tff(c_56601,plain,
    member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_6'),
    inference(resolution,[status(thm)],[c_10360,c_6]) ).

tff(c_16,plain,
    ! [D_12,C_9,B_8] :
      ( member(D_12,C_9)
      | ~ member(D_12,B_8)
      | ~ subset(B_8,C_9) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_1249,plain,
    ! [B_137,C_138,C_139] :
      ( member('#skF_3'(B_137,C_138),C_139)
      | ~ subset(B_137,C_139)
      | member('#skF_2'(B_137,C_138),C_138)
      | ( C_138 = B_137 ) ),
    inference(resolution,[status(thm)],[c_348,c_16]) ).

tff(c_1381,plain,
    ! [B_144,C_145] :
      ( ~ subset(B_144,C_145)
      | member('#skF_2'(B_144,C_145),C_145)
      | ( C_145 = B_144 ) ),
    inference(resolution,[status(thm)],[c_1249,c_30]) ).

tff(c_1973,plain,
    ! [B_183,C_184,C_185] :
      ( member('#skF_2'(B_183,C_184),C_185)
      | ~ subset(C_184,C_185)
      | ~ subset(B_183,C_184)
      | ( C_184 = B_183 ) ),
    inference(resolution,[status(thm)],[c_1381,c_16]) ).

tff(c_38,plain,
    ! [E_20] :
      ( member(E_20,'#skF_4')
      | ~ member(E_20,'#skF_6')
      | ~ member(E_20,'#skF_5') ),
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_2031,plain,
    ! [B_183,C_184] :
      ( member('#skF_2'(B_183,C_184),'#skF_4')
      | ~ member('#skF_2'(B_183,C_184),'#skF_6')
      | ~ subset(C_184,'#skF_5')
      | ~ subset(B_183,C_184)
      | ( C_184 = B_183 ) ),
    inference(resolution,[status(thm)],[c_1973,c_38]) ).

tff(c_56605,plain,
    ( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
    | ~ subset(intersection('#skF_6','#skF_5'),'#skF_5')
    | ~ subset('#skF_4',intersection('#skF_6','#skF_5'))
    | ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_56601,c_2031]) ).

tff(c_56610,plain,
    ( member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
    | ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_9585,c_656,c_56605]) ).

tff(c_56611,plain,
    member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4'),
    inference(negUnitSimplification,[status(thm)],[c_43,c_56610]) ).

tff(c_32,plain,
    ! [B_14,C_15] :
      ( ~ member('#skF_2'(B_14,C_15),B_14)
      | member('#skF_3'(B_14,C_15),B_14)
      | ( C_15 = B_14 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_4,plain,
    ! [D_3,C_2,B_1] :
      ( member(D_3,C_2)
      | ~ member(D_3,intersection(B_1,C_2)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_10306,plain,
    ! [D_3] :
      ( member(D_3,intersection('#skF_6','#skF_5'))
      | ~ member(D_3,'#skF_4') ),
    inference(superposition,[status(thm),theory(equality)],[c_9606,c_4]) ).

tff(c_28,plain,
    ! [B_14,C_15] :
      ( ~ member('#skF_2'(B_14,C_15),B_14)
      | ~ member('#skF_3'(B_14,C_15),C_15)
      | ( C_15 = B_14 ) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_57335,plain,
    ( ~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5'))
    | ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_56611,c_28]) ).

tff(c_57343,plain,
    ~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),intersection('#skF_6','#skF_5')),
    inference(negUnitSimplification,[status(thm)],[c_43,c_57335]) ).

tff(c_66963,plain,
    ~ member('#skF_3'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4'),
    inference(resolution,[status(thm)],[c_10306,c_57343]) ).

tff(c_67013,plain,
    ( ~ member('#skF_2'('#skF_4',intersection('#skF_6','#skF_5')),'#skF_4')
    | ( intersection('#skF_6','#skF_5') = '#skF_4' ) ),
    inference(resolution,[status(thm)],[c_32,c_66963]) ).

tff(c_67055,plain,
    intersection('#skF_6','#skF_5') = '#skF_4',
    inference(demodulation,[status(thm),theory(equality)],[c_56611,c_67013]) ).

tff(c_67057,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_43,c_67055]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % 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
% 0.15/0.35  % Computer : n015.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 16:39:14 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 23.29/12.62  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.29/12.62  
% 23.29/12.62  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.50/12.66  
% 23.50/12.66  Inference rules
% 23.50/12.66  ----------------------
% 23.50/12.66  #Ref     : 0
% 23.50/12.66  #Sup     : 16553
% 23.50/12.66  #Fact    : 0
% 23.50/12.66  #Define  : 0
% 23.50/12.66  #Split   : 12
% 23.50/12.66  #Chain   : 0
% 23.50/12.66  #Close   : 0
% 23.50/12.66  
% 23.50/12.66  Ordering : KBO
% 23.50/12.66  
% 23.50/12.66  Simplification rules
% 23.50/12.66  ----------------------
% 23.50/12.66  #Subsume      : 4956
% 23.50/12.66  #Demod        : 23288
% 23.50/12.66  #Tautology    : 4496
% 23.50/12.66  #SimpNegUnit  : 271
% 23.50/12.66  #BackRed      : 17
% 23.50/12.66  
% 23.50/12.66  #Partial instantiations: 0
% 23.50/12.66  #Strategies tried      : 1
% 23.50/12.66  
% 23.50/12.66  Timing (in seconds)
% 23.50/12.66  ----------------------
% 23.50/12.66  Preprocessing        : 0.51
% 23.50/12.66  Parsing              : 0.27
% 23.50/12.66  CNF conversion       : 0.04
% 23.50/12.66  Main loop            : 11.00
% 23.50/12.66  Inferencing          : 1.48
% 23.50/12.66  Reduction            : 5.19
% 23.50/12.66  Demodulation         : 4.40
% 23.50/12.66  BG Simplification    : 0.12
% 23.50/12.66  Subsumption          : 3.71
% 23.50/12.66  Abstraction          : 0.16
% 23.50/12.66  MUC search           : 0.00
% 23.50/12.67  Cooper               : 0.00
% 23.50/12.67  Total                : 11.57
% 23.50/12.67  Index Insertion      : 0.00
% 23.50/12.67  Index Deletion       : 0.00
% 23.50/12.67  Index Matching       : 0.00
% 23.50/12.67  BG Taut test         : 0.00
%------------------------------------------------------------------------------