TSTP Solution File: SET935+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET935+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/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 : 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 10:57:23 EDT 2023

% Result   : Theorem 13.95s 4.40s
% Output   : CNFRefutation 13.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   70 (  28 unt;  14 typ;   0 def)
%            Number of atoms       :   93 (  20 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   63 (  26   ~;  28   |;   1   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  10   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   4 con; 0-3 aty)
%            Number of variables   :   65 (;  65   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > inclusion_comparable > in > empty > set_union2 > #nlpp > powerset > #skF_4 > #skF_7 > #skF_5 > #skF_6 > #skF_8 > #skF_3 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff('#skF_8',type,
    '#skF_8': $i ).

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

tff(powerset,type,
    powerset: $i > $i ).

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

tff(f_95,negated_conjecture,
    ~ ! [A,B] :
        ( ( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B)) )
       => inclusion_comparable(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t82_zfmisc_1) ).

tff(f_82,axiom,
    ! [A,B] : subset(A,A),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).

tff(f_46,axiom,
    ! [A,B] :
      ( ( B = powerset(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> subset(C,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).

tff(f_33,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_55,axiom,
    ! [A,B,C] :
      ( ( C = set_union2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            | in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).

tff(f_90,axiom,
    ! [A,B] : subset(A,set_union2(A,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_xboole_1) ).

tff(f_39,axiom,
    ! [A,B] :
      ( ( A = B )
    <=> ( subset(A,B)
        & subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_xboole_0) ).

tff(f_61,axiom,
    ! [A,B] :
      ( inclusion_comparable(A,B)
    <=> ( subset(A,B)
        | subset(B,A) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_xboole_0) ).

tff(f_88,axiom,
    ! [A,B] :
      ( inclusion_comparable(A,B)
     => inclusion_comparable(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_r3_xboole_0) ).

tff(c_66,plain,
    ~ inclusion_comparable('#skF_7','#skF_8'),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_58,plain,
    ! [A_26] : subset(A_26,A_26),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_14,plain,
    ! [C_11,A_7] :
      ( in(C_11,powerset(A_7))
      | ~ subset(C_11,A_7) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_4,plain,
    ! [B_4,A_3] : ( set_union2(B_4,A_3) = set_union2(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_68,plain,
    set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset(set_union2('#skF_7','#skF_8')),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_71,plain,
    set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset(set_union2('#skF_8','#skF_7')),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_68]) ).

tff(c_559,plain,
    ! [D_85,B_86,A_87] :
      ( in(D_85,B_86)
      | in(D_85,A_87)
      | ~ in(D_85,set_union2(A_87,B_86)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_3244,plain,
    ! [D_265] :
      ( in(D_265,powerset('#skF_8'))
      | in(D_265,powerset('#skF_7'))
      | ~ in(D_265,powerset(set_union2('#skF_8','#skF_7'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_71,c_559]) ).

tff(c_11351,plain,
    ! [C_750] :
      ( in(C_750,powerset('#skF_8'))
      | in(C_750,powerset('#skF_7'))
      | ~ subset(C_750,set_union2('#skF_8','#skF_7')) ),
    inference(resolution,[status(thm)],[c_14,c_3244]) ).

tff(c_11429,plain,
    ( in(set_union2('#skF_8','#skF_7'),powerset('#skF_8'))
    | in(set_union2('#skF_8','#skF_7'),powerset('#skF_7')) ),
    inference(resolution,[status(thm)],[c_58,c_11351]) ).

tff(c_11518,plain,
    in(set_union2('#skF_8','#skF_7'),powerset('#skF_7')),
    inference(splitLeft,[status(thm)],[c_11429]) ).

tff(c_12,plain,
    ! [C_11,A_7] :
      ( subset(C_11,A_7)
      | ~ in(C_11,powerset(A_7)) ),
    inference(cnfTransformation,[status(thm)],[f_46]) ).

tff(c_11544,plain,
    subset(set_union2('#skF_8','#skF_7'),'#skF_7'),
    inference(resolution,[status(thm)],[c_11518,c_12]) ).

tff(c_88,plain,
    ! [B_39,A_40] : ( set_union2(B_39,A_40) = set_union2(A_40,B_39) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_64,plain,
    ! [A_32,B_33] : subset(A_32,set_union2(A_32,B_33)),
    inference(cnfTransformation,[status(thm)],[f_90]) ).

tff(c_103,plain,
    ! [A_40,B_39] : subset(A_40,set_union2(B_39,A_40)),
    inference(superposition,[status(thm),theory(equality)],[c_88,c_64]) ).

tff(c_342,plain,
    ! [B_69,A_70] :
      ( ( B_69 = A_70 )
      | ~ subset(B_69,A_70)
      | ~ subset(A_70,B_69) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_355,plain,
    ! [B_39,A_40] :
      ( ( set_union2(B_39,A_40) = A_40 )
      | ~ subset(set_union2(B_39,A_40),A_40) ),
    inference(resolution,[status(thm)],[c_103,c_342]) ).

tff(c_11607,plain,
    set_union2('#skF_8','#skF_7') = '#skF_7',
    inference(resolution,[status(thm)],[c_11544,c_355]) ).

tff(c_159,plain,
    set_union2(powerset('#skF_8'),powerset('#skF_7')) = powerset(set_union2('#skF_8','#skF_7')),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_71]) ).

tff(c_712,plain,
    ! [A_97,B_98] :
      ( ( set_union2(A_97,B_98) = A_97 )
      | ~ subset(set_union2(A_97,B_98),A_97) ),
    inference(resolution,[status(thm)],[c_64,c_342]) ).

tff(c_726,plain,
    ( ( set_union2(powerset('#skF_7'),powerset('#skF_8')) = powerset('#skF_7') )
    | ~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')) ),
    inference(superposition,[status(thm),theory(equality)],[c_71,c_712]) ).

tff(c_743,plain,
    ( ( powerset(set_union2('#skF_8','#skF_7')) = powerset('#skF_7') )
    | ~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_159,c_4,c_726]) ).

tff(c_10884,plain,
    ~ subset(powerset(set_union2('#skF_8','#skF_7')),powerset('#skF_7')),
    inference(splitLeft,[status(thm)],[c_743]) ).

tff(c_11633,plain,
    ~ subset(powerset('#skF_7'),powerset('#skF_7')),
    inference(demodulation,[status(thm),theory(equality)],[c_11607,c_10884]) ).

tff(c_11740,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_58,c_11633]) ).

tff(c_11741,plain,
    in(set_union2('#skF_8','#skF_7'),powerset('#skF_8')),
    inference(splitRight,[status(thm)],[c_11429]) ).

tff(c_11768,plain,
    subset(set_union2('#skF_8','#skF_7'),'#skF_8'),
    inference(resolution,[status(thm)],[c_11741,c_12]) ).

tff(c_1231,plain,
    ! [B_131,A_132] :
      ( ( set_union2(B_131,A_132) = A_132 )
      | ~ subset(set_union2(B_131,A_132),A_132) ),
    inference(resolution,[status(thm)],[c_103,c_342]) ).

tff(c_1251,plain,
    ! [B_4,A_3] :
      ( ( set_union2(B_4,A_3) = A_3 )
      | ~ subset(set_union2(A_3,B_4),A_3) ),
    inference(superposition,[status(thm),theory(equality)],[c_4,c_1231]) ).

tff(c_11790,plain,
    set_union2('#skF_7','#skF_8') = '#skF_8',
    inference(resolution,[status(thm)],[c_11768,c_1251]) ).

tff(c_240,plain,
    ! [A_55,B_56] :
      ( ~ subset(A_55,B_56)
      | inclusion_comparable(A_55,B_56) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_255,plain,
    ! [A_32,B_33] : inclusion_comparable(A_32,set_union2(A_32,B_33)),
    inference(resolution,[status(thm)],[c_64,c_240]) ).

tff(c_12048,plain,
    inclusion_comparable('#skF_7','#skF_8'),
    inference(superposition,[status(thm),theory(equality)],[c_11790,c_255]) ).

tff(c_12118,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_66,c_12048]) ).

tff(c_12119,plain,
    powerset(set_union2('#skF_8','#skF_7')) = powerset('#skF_7'),
    inference(splitRight,[status(thm)],[c_743]) ).

tff(c_373,plain,
    ! [D_71,B_72,A_73] :
      ( ~ in(D_71,B_72)
      | in(D_71,set_union2(A_73,B_72)) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_382,plain,
    ! [D_71] :
      ( ~ in(D_71,powerset('#skF_8'))
      | in(D_71,powerset(set_union2('#skF_8','#skF_7'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_71,c_373]) ).

tff(c_13549,plain,
    ! [D_766] :
      ( ~ in(D_766,powerset('#skF_8'))
      | in(D_766,powerset('#skF_7')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_12119,c_382]) ).

tff(c_13858,plain,
    ! [D_767] :
      ( subset(D_767,'#skF_7')
      | ~ in(D_767,powerset('#skF_8')) ),
    inference(resolution,[status(thm)],[c_13549,c_12]) ).

tff(c_14063,plain,
    ! [C_768] :
      ( subset(C_768,'#skF_7')
      | ~ subset(C_768,'#skF_8') ),
    inference(resolution,[status(thm)],[c_14,c_13858]) ).

tff(c_46,plain,
    ! [A_18,B_19] :
      ( ~ subset(A_18,B_19)
      | inclusion_comparable(A_18,B_19) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_14307,plain,
    ! [C_769] :
      ( inclusion_comparable(C_769,'#skF_7')
      | ~ subset(C_769,'#skF_8') ),
    inference(resolution,[status(thm)],[c_14063,c_46]) ).

tff(c_14364,plain,
    inclusion_comparable('#skF_8','#skF_7'),
    inference(resolution,[status(thm)],[c_58,c_14307]) ).

tff(c_62,plain,
    ! [B_31,A_30] :
      ( inclusion_comparable(B_31,A_30)
      | ~ inclusion_comparable(A_30,B_31) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_14410,plain,
    inclusion_comparable('#skF_7','#skF_8'),
    inference(resolution,[status(thm)],[c_14364,c_62]) ).

tff(c_14414,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_66,c_14410]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET935+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/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 : 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 16:05:13 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 13.95/4.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.95/4.40  
% 13.95/4.40  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.95/4.43  
% 13.95/4.43  Inference rules
% 13.95/4.43  ----------------------
% 13.95/4.43  #Ref     : 0
% 13.95/4.43  #Sup     : 3403
% 13.95/4.43  #Fact    : 40
% 13.95/4.43  #Define  : 0
% 13.95/4.43  #Split   : 10
% 13.95/4.43  #Chain   : 0
% 13.95/4.43  #Close   : 0
% 13.95/4.43  
% 13.95/4.43  Ordering : KBO
% 13.95/4.43  
% 13.95/4.43  Simplification rules
% 13.95/4.43  ----------------------
% 13.95/4.43  #Subsume      : 1428
% 13.95/4.43  #Demod        : 1337
% 13.95/4.43  #Tautology    : 180
% 13.95/4.43  #SimpNegUnit  : 5
% 13.95/4.43  #BackRed      : 210
% 13.95/4.43  
% 13.95/4.43  #Partial instantiations: 0
% 13.95/4.43  #Strategies tried      : 1
% 13.95/4.43  
% 13.95/4.43  Timing (in seconds)
% 13.95/4.43  ----------------------
% 13.95/4.44  Preprocessing        : 0.51
% 13.95/4.44  Parsing              : 0.26
% 13.95/4.44  CNF conversion       : 0.04
% 13.95/4.44  Main loop            : 2.82
% 13.95/4.44  Inferencing          : 0.78
% 14.24/4.44  Reduction            : 1.01
% 14.24/4.44  Demodulation         : 0.71
% 14.24/4.44  BG Simplification    : 0.07
% 14.24/4.44  Subsumption          : 0.76
% 14.24/4.44  Abstraction          : 0.07
% 14.24/4.44  MUC search           : 0.00
% 14.24/4.44  Cooper               : 0.00
% 14.24/4.44  Total                : 3.38
% 14.24/4.44  Index Insertion      : 0.00
% 14.24/4.44  Index Deletion       : 0.00
% 14.24/4.44  Index Matching       : 0.00
% 14.24/4.44  BG Taut test         : 0.00
%------------------------------------------------------------------------------