TSTP Solution File: SET013-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET013-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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 : n019.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 10:55:30 EDT 2023

% Result   : Unsatisfiable 12.00s 4.06s
% Output   : CNFRefutation 12.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   35 (   6 unt;  11 typ;   0 def)
%            Number of atoms       :   47 (   0 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   43 (  20   ~;  23   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   15 (   8   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   52 (;  52   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > equal_sets > equal_elements > union > member_of_1_not_of_2 > intersection > #nlpp > complement > empty_set > bs > as

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(member_of_1_not_of_2,type,
    member_of_1_not_of_2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

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

tff(f_62,axiom,
    ! [Subset,Superset] :
      ( subset(Subset,Superset)
      | member(member_of_1_not_of_2(Subset,Superset),Subset) ),
    file(unknown,unknown) ).

tff(f_115,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,intersection(Xs,Ys))
      | member(X,Ys) ),
    file(unknown,unknown) ).

tff(f_110,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,intersection(Xs,Ys))
      | member(X,Xs) ),
    file(unknown,unknown) ).

tff(f_105,axiom,
    ! [X,Xs,Ys] :
      ( ~ member(X,Xs)
      | ~ member(X,Ys)
      | member(X,intersection(Xs,Ys)) ),
    file(unknown,unknown) ).

tff(f_67,axiom,
    ! [Subset,Superset] :
      ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
      | subset(Subset,Superset) ),
    file(unknown,unknown) ).

tff(f_134,axiom,
    ! [Set1,Set2] :
      ( ~ subset(Set1,Set2)
      | ~ subset(Set2,Set1)
      | equal_sets(Set2,Set1) ),
    file(unknown,unknown) ).

tff(f_169,axiom,
    ~ equal_sets(intersection(as,bs),intersection(bs,as)),
    file(unknown,unknown) ).

tff(c_73,plain,
    ! [Subset_69,Superset_70] :
      ( member(member_of_1_not_of_2(Subset_69,Superset_70),Subset_69)
      | subset(Subset_69,Superset_70) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_24,plain,
    ! [X_28,Ys_30,Xs_29] :
      ( member(X_28,Ys_30)
      | ~ member(X_28,intersection(Xs_29,Ys_30)) ),
    inference(cnfTransformation,[status(thm)],[f_115]) ).

tff(c_91,plain,
    ! [Xs_29,Ys_30,Superset_70] :
      ( member(member_of_1_not_of_2(intersection(Xs_29,Ys_30),Superset_70),Ys_30)
      | subset(intersection(Xs_29,Ys_30),Superset_70) ),
    inference(resolution,[status(thm)],[c_73,c_24]) ).

tff(c_6,plain,
    ! [Subset_5,Superset_6] :
      ( member(member_of_1_not_of_2(Subset_5,Superset_6),Subset_5)
      | subset(Subset_5,Superset_6) ),
    inference(cnfTransformation,[status(thm)],[f_62]) ).

tff(c_102,plain,
    ! [X_76,Xs_77,Ys_78] :
      ( member(X_76,Xs_77)
      | ~ member(X_76,intersection(Xs_77,Ys_78)) ),
    inference(cnfTransformation,[status(thm)],[f_110]) ).

tff(c_107,plain,
    ! [Xs_77,Ys_78,Superset_6] :
      ( member(member_of_1_not_of_2(intersection(Xs_77,Ys_78),Superset_6),Xs_77)
      | subset(intersection(Xs_77,Ys_78),Superset_6) ),
    inference(resolution,[status(thm)],[c_6,c_102]) ).

tff(c_274,plain,
    ! [X_108,Xs_109,Ys_110] :
      ( member(X_108,intersection(Xs_109,Ys_110))
      | ~ member(X_108,Ys_110)
      | ~ member(X_108,Xs_109) ),
    inference(cnfTransformation,[status(thm)],[f_105]) ).

tff(c_8,plain,
    ! [Subset_7,Superset_8] :
      ( subset(Subset_7,Superset_8)
      | ~ member(member_of_1_not_of_2(Subset_7,Superset_8),Superset_8) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_966,plain,
    ! [Subset_183,Xs_184,Ys_185] :
      ( subset(Subset_183,intersection(Xs_184,Ys_185))
      | ~ member(member_of_1_not_of_2(Subset_183,intersection(Xs_184,Ys_185)),Ys_185)
      | ~ member(member_of_1_not_of_2(Subset_183,intersection(Xs_184,Ys_185)),Xs_184) ),
    inference(resolution,[status(thm)],[c_274,c_8]) ).

tff(c_12521,plain,
    ! [Xs_729,Ys_730,Xs_731] :
      ( ~ member(member_of_1_not_of_2(intersection(Xs_729,Ys_730),intersection(Xs_731,Xs_729)),Xs_731)
      | subset(intersection(Xs_729,Ys_730),intersection(Xs_731,Xs_729)) ),
    inference(resolution,[status(thm)],[c_107,c_966]) ).

tff(c_12642,plain,
    ! [Xs_29,Ys_30] : subset(intersection(Xs_29,Ys_30),intersection(Ys_30,Xs_29)),
    inference(resolution,[status(thm)],[c_91,c_12521]) ).

tff(c_12652,plain,
    ! [Xs_732,Ys_733] : subset(intersection(Xs_732,Ys_733),intersection(Ys_733,Xs_732)),
    inference(resolution,[status(thm)],[c_91,c_12521]) ).

tff(c_30,plain,
    ! [Set2_36,Set1_35] :
      ( equal_sets(Set2_36,Set1_35)
      | ~ subset(Set2_36,Set1_35)
      | ~ subset(Set1_35,Set2_36) ),
    inference(cnfTransformation,[status(thm)],[f_134]) ).

tff(c_12666,plain,
    ! [Xs_732,Ys_733] :
      ( equal_sets(intersection(Xs_732,Ys_733),intersection(Ys_733,Xs_732))
      | ~ subset(intersection(Ys_733,Xs_732),intersection(Xs_732,Ys_733)) ),
    inference(resolution,[status(thm)],[c_12652,c_30]) ).

tff(c_12674,plain,
    ! [Xs_732,Ys_733] : equal_sets(intersection(Xs_732,Ys_733),intersection(Ys_733,Xs_732)),
    inference(demodulation,[status(thm),theory(equality)],[c_12642,c_12666]) ).

tff(c_44,plain,
    ~ equal_sets(intersection(as,bs),intersection(bs,as)),
    inference(cnfTransformation,[status(thm)],[f_169]) ).

tff(c_12698,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_12674,c_44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET013-1 : TPTP v8.1.2. Bugfixed v2.1.0.
% 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
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 16:31:01 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 12.00/4.06  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.00/4.07  
% 12.00/4.07  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.16/4.10  
% 12.16/4.10  Inference rules
% 12.16/4.10  ----------------------
% 12.16/4.10  #Ref     : 0
% 12.16/4.10  #Sup     : 2858
% 12.16/4.10  #Fact    : 4
% 12.16/4.10  #Define  : 0
% 12.16/4.10  #Split   : 4
% 12.16/4.10  #Chain   : 0
% 12.16/4.10  #Close   : 0
% 12.16/4.10  
% 12.16/4.10  Ordering : KBO
% 12.16/4.10  
% 12.16/4.10  Simplification rules
% 12.16/4.10  ----------------------
% 12.16/4.10  #Subsume      : 352
% 12.16/4.10  #Demod        : 546
% 12.16/4.10  #Tautology    : 514
% 12.16/4.10  #SimpNegUnit  : 116
% 12.16/4.10  #BackRed      : 1
% 12.16/4.10  
% 12.16/4.10  #Partial instantiations: 0
% 12.16/4.10  #Strategies tried      : 1
% 12.16/4.10  
% 12.16/4.10  Timing (in seconds)
% 12.16/4.10  ----------------------
% 12.16/4.11  Preprocessing        : 0.46
% 12.16/4.11  Parsing              : 0.25
% 12.16/4.11  CNF conversion       : 0.03
% 12.16/4.11  Main loop            : 2.57
% 12.16/4.11  Inferencing          : 0.76
% 12.16/4.11  Reduction            : 0.90
% 12.16/4.11  Demodulation         : 0.68
% 12.16/4.11  BG Simplification    : 0.05
% 12.16/4.11  Subsumption          : 0.69
% 12.16/4.11  Abstraction          : 0.05
% 12.16/4.11  MUC search           : 0.00
% 12.16/4.11  Cooper               : 0.00
% 12.16/4.11  Total                : 3.08
% 12.16/4.11  Index Insertion      : 0.00
% 12.16/4.11  Index Deletion       : 0.00
% 12.16/4.11  Index Matching       : 0.00
% 12.16/4.11  BG Taut test         : 0.00
%------------------------------------------------------------------------------