TSTP Solution File: SEU165+2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : 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 10:57:52 EDT 2023

% Result   : Theorem 19.87s 7.50s
% Output   : CNFRefutation 19.90s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   55
% Syntax   : Number of formulae    :  107 (  36 unt;  53 typ;   0 def)
%            Number of atoms       :   80 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   60 (  34   ~;  22   |;   2   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   2 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   96 (  42   >;  54   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   48 (  48 usr;  11 con; 0-4 aty)
%            Number of variables   :   28 (;  28   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > proper_subset > in > disjoint > empty > unordered_pair > set_union2 > set_intersection2 > set_difference > ordered_pair > cartesian_product2 > #nlpp > union > singleton > powerset > empty_set > #skF_13 > #skF_33 > #skF_24 > #skF_37 > #skF_35 > #skF_17 > #skF_6 > #skF_31 > #skF_25 > #skF_18 > #skF_20 > #skF_22 > #skF_12 > #skF_38 > #skF_15 > #skF_26 > #skF_23 > #skF_19 > #skF_11 > #skF_36 > #skF_32 > #skF_7 > #skF_9 > #skF_30 > #skF_3 > #skF_29 > #skF_28 > #skF_2 > #skF_27 > #skF_8 > #skF_14 > #skF_1 > #skF_16 > #skF_21 > #skF_5 > #skF_4 > #skF_10 > #skF_34

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_13',type,
    '#skF_13': ( $i * $i * $i ) > $i ).

tff('#skF_33',type,
    '#skF_33': $i ).

tff('#skF_24',type,
    '#skF_24': ( $i * $i * $i ) > $i ).

tff('#skF_37',type,
    '#skF_37': ( $i * $i ) > $i ).

tff('#skF_35',type,
    '#skF_35': ( $i * $i ) > $i ).

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

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

tff('#skF_17',type,
    '#skF_17': ( $i * $i * $i ) > $i ).

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

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

tff('#skF_31',type,
    '#skF_31': $i ).

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

tff('#skF_25',type,
    '#skF_25': $i ).

tff('#skF_18',type,
    '#skF_18': ( $i * $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': ( $i * $i ) > $i ).

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

tff('#skF_22',type,
    '#skF_22': ( $i * $i * $i ) > $i ).

tff('#skF_12',type,
    '#skF_12': ( $i * $i * $i ) > $i ).

tff('#skF_38',type,
    '#skF_38': ( $i * $i ) > $i ).

tff('#skF_15',type,
    '#skF_15': ( $i * $i * $i * $i ) > $i ).

tff('#skF_26',type,
    '#skF_26': $i ).

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

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

tff('#skF_23',type,
    '#skF_23': ( $i * $i * $i ) > $i ).

tff('#skF_19',type,
    '#skF_19': ( $i * $i ) > $i ).

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

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

tff('#skF_11',type,
    '#skF_11': ( $i * $i * $i ) > $i ).

tff('#skF_36',type,
    '#skF_36': ( $i * $i ) > $i ).

tff('#skF_32',type,
    '#skF_32': $i ).

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

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

tff('#skF_9',type,
    '#skF_9': ( $i * $i * $i ) > $i ).

tff('#skF_30',type,
    '#skF_30': $i ).

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

tff('#skF_29',type,
    '#skF_29': $i ).

tff('#skF_28',type,
    '#skF_28': $i ).

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

tff('#skF_27',type,
    '#skF_27': $i ).

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

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

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

tff(cartesian_product2,type,
    cartesian_product2: ( $i * $i ) > $i ).

tff('#skF_14',type,
    '#skF_14': ( $i * $i * $i * $i ) > $i ).

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

tff('#skF_16',type,
    '#skF_16': ( $i * $i ) > $i ).

tff('#skF_21',type,
    '#skF_21': ( $i * $i ) > $i ).

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

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

tff('#skF_10',type,
    '#skF_10': ( $i * $i * $i ) > $i ).

tff('#skF_34',type,
    '#skF_34': $i ).

tff(f_236,negated_conjecture,
    ~ ! [A,B,C,D] :
        ( in(ordered_pair(A,B),cartesian_product2(C,D))
      <=> ( in(A,C)
          & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).

tff(f_218,lemma,
    ! [A,B,C,D] :
      ( in(ordered_pair(A,B),cartesian_product2(C,D))
    <=> ( in(A,C)
        & in(B,D) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l55_zfmisc_1) ).

tff(c_262,plain,
    ( in('#skF_27','#skF_29')
    | in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')) ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_9351,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitLeft,[status(thm)],[c_262]) ).

tff(c_260,plain,
    ( in('#skF_28','#skF_30')
    | in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')) ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_526,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitLeft,[status(thm)],[c_260]) ).

tff(c_254,plain,
    ( in('#skF_28','#skF_30')
    | ~ in('#skF_32','#skF_34')
    | ~ in('#skF_31','#skF_33') ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_402,plain,
    ~ in('#skF_31','#skF_33'),
    inference(splitLeft,[status(thm)],[c_254]) ).

tff(c_607,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitLeft,[status(thm)],[c_262]) ).

tff(c_8901,plain,
    ! [A_706,C_707,B_708,D_709] :
      ( in(A_706,C_707)
      | ~ in(ordered_pair(A_706,B_708),cartesian_product2(C_707,D_709)) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_8904,plain,
    in('#skF_31','#skF_33'),
    inference(resolution,[status(thm)],[c_607,c_8901]) ).

tff(c_8908,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_402,c_8904]) ).

tff(c_8910,plain,
    ~ in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_262]) ).

tff(c_9267,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_526,c_8910]) ).

tff(c_9269,plain,
    ~ in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_260]) ).

tff(c_9737,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9351,c_9269]) ).

tff(c_9738,plain,
    in('#skF_27','#skF_29'),
    inference(splitRight,[status(thm)],[c_262]) ).

tff(c_9268,plain,
    in('#skF_28','#skF_30'),
    inference(splitRight,[status(thm)],[c_260]) ).

tff(c_24690,plain,
    ! [A_1452,B_1453,C_1454,D_1455] :
      ( in(ordered_pair(A_1452,B_1453),cartesian_product2(C_1454,D_1455))
      | ~ in(B_1453,D_1455)
      | ~ in(A_1452,C_1454) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_258,plain,
    ( ~ in(ordered_pair('#skF_27','#skF_28'),cartesian_product2('#skF_29','#skF_30'))
    | in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')) ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_9886,plain,
    ~ in(ordered_pair('#skF_27','#skF_28'),cartesian_product2('#skF_29','#skF_30')),
    inference(splitLeft,[status(thm)],[c_258]) ).

tff(c_24706,plain,
    ( ~ in('#skF_28','#skF_30')
    | ~ in('#skF_27','#skF_29') ),
    inference(resolution,[status(thm)],[c_24690,c_9886]) ).

tff(c_24723,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_9738,c_9268,c_24706]) ).

tff(c_24724,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_258]) ).

tff(c_24986,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24724,c_9269]) ).

tff(c_24988,plain,
    in('#skF_31','#skF_33'),
    inference(splitRight,[status(thm)],[c_254]) ).

tff(c_256,plain,
    ( in('#skF_27','#skF_29')
    | ~ in('#skF_32','#skF_34')
    | ~ in('#skF_31','#skF_33') ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_25050,plain,
    ( in('#skF_27','#skF_29')
    | ~ in('#skF_32','#skF_34') ),
    inference(demodulation,[status(thm),theory(equality)],[c_24988,c_256]) ).

tff(c_25051,plain,
    ~ in('#skF_32','#skF_34'),
    inference(splitLeft,[status(thm)],[c_25050]) ).

tff(c_25117,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitLeft,[status(thm)],[c_260]) ).

tff(c_32285,plain,
    ! [B_1905,D_1906,A_1907,C_1908] :
      ( in(B_1905,D_1906)
      | ~ in(ordered_pair(A_1907,B_1905),cartesian_product2(C_1908,D_1906)) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_32288,plain,
    in('#skF_32','#skF_34'),
    inference(resolution,[status(thm)],[c_25117,c_32285]) ).

tff(c_32292,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_25051,c_32288]) ).

tff(c_32294,plain,
    ~ in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_260]) ).

tff(c_32321,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitLeft,[status(thm)],[c_262]) ).

tff(c_32713,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32294,c_32321]) ).

tff(c_32714,plain,
    in('#skF_27','#skF_29'),
    inference(splitRight,[status(thm)],[c_262]) ).

tff(c_32293,plain,
    in('#skF_28','#skF_30'),
    inference(splitRight,[status(thm)],[c_260]) ).

tff(c_47280,plain,
    ! [A_2567,B_2568,C_2569,D_2570] :
      ( in(ordered_pair(A_2567,B_2568),cartesian_product2(C_2569,D_2570))
      | ~ in(B_2568,D_2570)
      | ~ in(A_2567,C_2569) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_32853,plain,
    ~ in(ordered_pair('#skF_27','#skF_28'),cartesian_product2('#skF_29','#skF_30')),
    inference(splitLeft,[status(thm)],[c_258]) ).

tff(c_47296,plain,
    ( ~ in('#skF_28','#skF_30')
    | ~ in('#skF_27','#skF_29') ),
    inference(resolution,[status(thm)],[c_47280,c_32853]) ).

tff(c_47313,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_32714,c_32293,c_47296]) ).

tff(c_47314,plain,
    in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_258]) ).

tff(c_32715,plain,
    ~ in(ordered_pair('#skF_31','#skF_32'),cartesian_product2('#skF_33','#skF_34')),
    inference(splitRight,[status(thm)],[c_262]) ).

tff(c_47785,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_47314,c_32715]) ).

tff(c_47786,plain,
    in('#skF_27','#skF_29'),
    inference(splitRight,[status(thm)],[c_25050]) ).

tff(c_47787,plain,
    in('#skF_32','#skF_34'),
    inference(splitRight,[status(thm)],[c_25050]) ).

tff(c_24987,plain,
    ( ~ in('#skF_32','#skF_34')
    | in('#skF_28','#skF_30') ),
    inference(splitRight,[status(thm)],[c_254]) ).

tff(c_48206,plain,
    in('#skF_28','#skF_30'),
    inference(demodulation,[status(thm),theory(equality)],[c_47787,c_24987]) ).

tff(c_62715,plain,
    ! [A_3220,B_3221,C_3222,D_3223] :
      ( in(ordered_pair(A_3220,B_3221),cartesian_product2(C_3222,D_3223))
      | ~ in(B_3221,D_3223)
      | ~ in(A_3220,C_3222) ),
    inference(cnfTransformation,[status(thm)],[f_218]) ).

tff(c_252,plain,
    ( ~ in(ordered_pair('#skF_27','#skF_28'),cartesian_product2('#skF_29','#skF_30'))
    | ~ in('#skF_32','#skF_34')
    | ~ in('#skF_31','#skF_33') ),
    inference(cnfTransformation,[status(thm)],[f_236]) ).

tff(c_48014,plain,
    ~ in(ordered_pair('#skF_27','#skF_28'),cartesian_product2('#skF_29','#skF_30')),
    inference(demodulation,[status(thm),theory(equality)],[c_24988,c_47787,c_252]) ).

tff(c_62733,plain,
    ( ~ in('#skF_28','#skF_30')
    | ~ in('#skF_27','#skF_29') ),
    inference(resolution,[status(thm)],[c_62715,c_48014]) ).

tff(c_62746,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_47786,c_48206,c_62733]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU165+2 : TPTP v8.1.2. Released v3.3.0.
% 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 : n009.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
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 11:51:23 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 19.87/7.50  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.90/7.50  
% 19.90/7.50  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.90/7.53  
% 19.90/7.53  Inference rules
% 19.90/7.53  ----------------------
% 19.90/7.53  #Ref     : 22
% 19.90/7.53  #Sup     : 15392
% 19.90/7.53  #Fact    : 0
% 19.90/7.53  #Define  : 0
% 19.90/7.53  #Split   : 45
% 19.90/7.53  #Chain   : 0
% 19.90/7.53  #Close   : 0
% 19.90/7.53  
% 19.90/7.53  Ordering : KBO
% 19.90/7.53  
% 19.90/7.53  Simplification rules
% 19.90/7.53  ----------------------
% 19.90/7.53  #Subsume      : 5932
% 19.90/7.53  #Demod        : 3331
% 19.90/7.53  #Tautology    : 4508
% 19.90/7.53  #SimpNegUnit  : 261
% 19.90/7.53  #BackRed      : 23
% 19.90/7.53  
% 19.90/7.53  #Partial instantiations: 0
% 19.90/7.53  #Strategies tried      : 1
% 19.90/7.53  
% 19.90/7.53  Timing (in seconds)
% 19.90/7.53  ----------------------
% 19.90/7.54  Preprocessing        : 0.75
% 19.90/7.54  Parsing              : 0.35
% 19.90/7.54  CNF conversion       : 0.08
% 19.90/7.54  Main loop            : 5.73
% 19.90/7.54  Inferencing          : 1.43
% 19.90/7.54  Reduction            : 2.34
% 19.90/7.54  Demodulation         : 1.55
% 19.90/7.54  BG Simplification    : 0.11
% 19.90/7.54  Subsumption          : 1.44
% 19.90/7.54  Abstraction          : 0.11
% 19.90/7.54  MUC search           : 0.00
% 19.90/7.54  Cooper               : 0.00
% 19.90/7.54  Total                : 6.53
% 19.90/7.54  Index Insertion      : 0.00
% 19.90/7.54  Index Deletion       : 0.00
% 19.90/7.54  Index Matching       : 0.00
% 19.90/7.54  BG Taut test         : 0.00
%------------------------------------------------------------------------------