TSTP Solution File: SET009-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n024.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 10:55:29 EDT 2023

% Result   : Unsatisfiable 15.50s 5.89s
% Output   : CNFRefutation 15.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   24
% Syntax   : Number of formulae    :   59 (  13 unt;  11 typ;   0 def)
%            Number of atoms       :  105 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  105 (  48   ~;  57   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   6   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-3 aty)
%            Number of variables   :   78 (;  78   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ difference > subset > member > equal_sets > k > member_of_1_not_of_2 > #nlpp > d > bDd > bDa > b > a

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

tff(f_158,axiom,
    ~ subset(bDa,bDd),
    file(unknown,unknown) ).

tff(f_56,axiom,
    ! [Subset,Superset] :
      ( subset(Subset,Superset)
      | member(member_of_1_not_of_2(Subset,Superset),Subset) ),
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [Subset,Superset] :
      ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
      | subset(Subset,Superset) ),
    file(unknown,unknown) ).

tff(f_79,axiom,
    ! [Set1,Set2] :
      ( ~ subset(Set1,Set2)
      | ~ subset(Set2,Set1)
      | equal_sets(Set2,Set1) ),
    file(unknown,unknown) ).

tff(f_155,axiom,
    difference(b,a,bDa),
    file(unknown,unknown) ).

tff(f_109,axiom,
    ! [Set1,Set2,Difference,Element] :
      ( ~ difference(Set1,Set2,Difference)
      | ~ member(Element,Difference)
      | member(Element,Set1) ),
    file(unknown,unknown) ).

tff(f_66,axiom,
    ! [Subset,Superset] :
      ( ~ equal_sets(Subset,Superset)
      | subset(Subset,Superset) ),
    file(unknown,unknown) ).

tff(f_52,axiom,
    ! [Element,Subset,Superset] :
      ( ~ member(Element,Subset)
      | ~ subset(Subset,Superset)
      | member(Element,Superset) ),
    file(unknown,unknown) ).

tff(f_156,axiom,
    difference(b,d,bDd),
    file(unknown,unknown) ).

tff(f_128,axiom,
    ! [Element,Set1,Set2,Difference] :
      ( ~ member(Element,Set1)
      | ~ difference(Set1,Set2,Difference)
      | member(Element,Difference)
      | member(Element,Set2) ),
    file(unknown,unknown) ).

tff(f_154,axiom,
    subset(d,a),
    file(unknown,unknown) ).

tff(f_71,axiom,
    ! [Superset,Subset] :
      ( ~ equal_sets(Superset,Subset)
      | subset(Subset,Superset) ),
    file(unknown,unknown) ).

tff(f_118,axiom,
    ! [Element,Set1,Set2,A_set] :
      ( ~ member(Element,Set1)
      | ~ member(Element,Set2)
      | ~ difference(A_set,Set1,Set2) ),
    file(unknown,unknown) ).

tff(c_32,plain,
    ~ subset(bDa,bDd),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_44,plain,
    ! [Subset_41,Superset_42] :
      ( member(member_of_1_not_of_2(Subset_41,Superset_42),Subset_41)
      | subset(Subset_41,Superset_42) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_6,plain,
    ! [Subset_6,Superset_7] :
      ( subset(Subset_6,Superset_7)
      | ~ member(member_of_1_not_of_2(Subset_6,Superset_7),Superset_7) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_49,plain,
    ! [Subset_41] : subset(Subset_41,Subset_41),
    inference(resolution,[status(thm)],[c_44,c_6]) ).

tff(c_77,plain,
    ! [Set2_49,Set1_50] :
      ( equal_sets(Set2_49,Set1_50)
      | ~ subset(Set2_49,Set1_50)
      | ~ subset(Set1_50,Set2_49) ),
    inference(cnfTransformation,[status(thm)],[f_79]) ).

tff(c_79,plain,
    ! [Subset_41] :
      ( equal_sets(Subset_41,Subset_41)
      | ~ subset(Subset_41,Subset_41) ),
    inference(resolution,[status(thm)],[c_49,c_77]) ).

tff(c_88,plain,
    ! [Subset_41] : equal_sets(Subset_41,Subset_41),
    inference(demodulation,[status(thm),theory(equality)],[c_49,c_79]) ).

tff(c_28,plain,
    difference(b,a,bDa),
    inference(cnfTransformation,[status(thm)],[f_155]) ).

tff(c_4,plain,
    ! [Subset_4,Superset_5] :
      ( member(member_of_1_not_of_2(Subset_4,Superset_5),Subset_4)
      | subset(Subset_4,Superset_5) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_92,plain,
    ! [Element_51,Set1_52,Difference_53,Set2_54] :
      ( member(Element_51,Set1_52)
      | ~ member(Element_51,Difference_53)
      | ~ difference(Set1_52,Set2_54,Difference_53) ),
    inference(cnfTransformation,[status(thm)],[f_109]) ).

tff(c_446,plain,
    ! [Subset_99,Superset_100,Set1_101,Set2_102] :
      ( member(member_of_1_not_of_2(Subset_99,Superset_100),Set1_101)
      | ~ difference(Set1_101,Set2_102,Subset_99)
      | subset(Subset_99,Superset_100) ),
    inference(resolution,[status(thm)],[c_4,c_92]) ).

tff(c_453,plain,
    ! [Superset_103] :
      ( member(member_of_1_not_of_2(bDa,Superset_103),b)
      | subset(bDa,Superset_103) ),
    inference(resolution,[status(thm)],[c_28,c_446]) ).

tff(c_8,plain,
    ! [Subset_8,Superset_9] :
      ( subset(Subset_8,Superset_9)
      | ~ equal_sets(Subset_8,Superset_9) ),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_51,plain,
    ! [Element_44,Superset_45,Subset_46] :
      ( member(Element_44,Superset_45)
      | ~ subset(Subset_46,Superset_45)
      | ~ member(Element_44,Subset_46) ),
    inference(cnfTransformation,[status(thm)],[f_52]) ).

tff(c_61,plain,
    ! [Element_44,Superset_9,Subset_8] :
      ( member(Element_44,Superset_9)
      | ~ member(Element_44,Subset_8)
      | ~ equal_sets(Subset_8,Superset_9) ),
    inference(resolution,[status(thm)],[c_8,c_51]) ).

tff(c_464,plain,
    ! [Superset_103,Superset_9] :
      ( member(member_of_1_not_of_2(bDa,Superset_103),Superset_9)
      | ~ equal_sets(b,Superset_9)
      | subset(bDa,Superset_103) ),
    inference(resolution,[status(thm)],[c_453,c_61]) ).

tff(c_30,plain,
    difference(b,d,bDd),
    inference(cnfTransformation,[status(thm)],[f_156]) ).

tff(c_129,plain,
    ! [Element_63,Set2_64,Difference_65,Set1_66] :
      ( member(Element_63,Set2_64)
      | member(Element_63,Difference_65)
      | ~ difference(Set1_66,Set2_64,Difference_65)
      | ~ member(Element_63,Set1_66) ),
    inference(cnfTransformation,[status(thm)],[f_128]) ).

tff(c_137,plain,
    ! [Element_68] :
      ( member(Element_68,d)
      | member(Element_68,bDd)
      | ~ member(Element_68,b) ),
    inference(resolution,[status(thm)],[c_30,c_129]) ).

tff(c_26,plain,
    subset(d,a),
    inference(cnfTransformation,[status(thm)],[f_154]) ).

tff(c_63,plain,
    ! [Element_44] :
      ( member(Element_44,a)
      | ~ member(Element_44,d) ),
    inference(resolution,[status(thm)],[c_26,c_51]) ).

tff(c_281,plain,
    ! [Element_83] :
      ( member(Element_83,a)
      | member(Element_83,bDd)
      | ~ member(Element_83,b) ),
    inference(resolution,[status(thm)],[c_137,c_63]) ).

tff(c_39529,plain,
    ! [Subset_682] :
      ( subset(Subset_682,bDd)
      | member(member_of_1_not_of_2(Subset_682,bDd),a)
      | ~ member(member_of_1_not_of_2(Subset_682,bDd),b) ),
    inference(resolution,[status(thm)],[c_281,c_6]) ).

tff(c_39565,plain,
    ( member(member_of_1_not_of_2(bDa,bDd),a)
    | ~ equal_sets(b,b)
    | subset(bDa,bDd) ),
    inference(resolution,[status(thm)],[c_464,c_39529]) ).

tff(c_39614,plain,
    ( member(member_of_1_not_of_2(bDa,bDd),a)
    | subset(bDa,bDd) ),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_39565]) ).

tff(c_39615,plain,
    member(member_of_1_not_of_2(bDa,bDd),a),
    inference(negUnitSimplification,[status(thm)],[c_32,c_39614]) ).

tff(c_10,plain,
    ! [Subset_11,Superset_10] :
      ( subset(Subset_11,Superset_10)
      | ~ equal_sets(Superset_10,Subset_11) ),
    inference(cnfTransformation,[status(thm)],[f_71]) ).

tff(c_230,plain,
    ! [Element_76,Superset_77,Subset_78] :
      ( member(Element_76,Superset_77)
      | ~ member(Element_76,Subset_78)
      | ~ equal_sets(Superset_77,Subset_78) ),
    inference(resolution,[status(thm)],[c_10,c_51]) ).

tff(c_656,plain,
    ! [Subset_122,Superset_123,Superset_124] :
      ( member(member_of_1_not_of_2(Subset_122,Superset_123),Superset_124)
      | ~ equal_sets(Superset_124,Subset_122)
      | subset(Subset_122,Superset_123) ),
    inference(resolution,[status(thm)],[c_4,c_230]) ).

tff(c_109,plain,
    ! [A_set_56,Set1_57,Set2_58,Element_59] :
      ( ~ difference(A_set_56,Set1_57,Set2_58)
      | ~ member(Element_59,Set2_58)
      | ~ member(Element_59,Set1_57) ),
    inference(cnfTransformation,[status(thm)],[f_118]) ).

tff(c_114,plain,
    ! [Element_59] :
      ( ~ member(Element_59,bDa)
      | ~ member(Element_59,a) ),
    inference(resolution,[status(thm)],[c_28,c_109]) ).

tff(c_701,plain,
    ! [Subset_122,Superset_123] :
      ( ~ member(member_of_1_not_of_2(Subset_122,Superset_123),a)
      | ~ equal_sets(bDa,Subset_122)
      | subset(Subset_122,Superset_123) ),
    inference(resolution,[status(thm)],[c_656,c_114]) ).

tff(c_39680,plain,
    ( ~ equal_sets(bDa,bDa)
    | subset(bDa,bDd) ),
    inference(resolution,[status(thm)],[c_39615,c_701]) ).

tff(c_39734,plain,
    subset(bDa,bDd),
    inference(demodulation,[status(thm),theory(equality)],[c_88,c_39680]) ).

tff(c_39736,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_32,c_39734]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : SET009-1 : TPTP v8.1.2. Released v1.0.0.
% 0.08/0.14  % 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
% 0.14/0.35  % Computer : n024.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 16:27:30 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 15.50/5.89  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 15.54/5.90  
% 15.54/5.90  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.61/5.94  
% 15.61/5.94  Inference rules
% 15.61/5.94  ----------------------
% 15.61/5.94  #Ref     : 0
% 15.61/5.94  #Sup     : 9266
% 15.61/5.94  #Fact    : 30
% 15.61/5.94  #Define  : 0
% 15.61/5.94  #Split   : 27
% 15.61/5.94  #Chain   : 0
% 15.61/5.94  #Close   : 0
% 15.61/5.94  
% 15.61/5.94  Ordering : KBO
% 15.61/5.94  
% 15.61/5.94  Simplification rules
% 15.61/5.94  ----------------------
% 15.61/5.94  #Subsume      : 5653
% 15.61/5.94  #Demod        : 2235
% 15.61/5.94  #Tautology    : 627
% 15.61/5.94  #SimpNegUnit  : 672
% 15.61/5.94  #BackRed      : 8
% 15.61/5.94  
% 15.61/5.94  #Partial instantiations: 0
% 15.61/5.94  #Strategies tried      : 1
% 15.61/5.94  
% 15.61/5.94  Timing (in seconds)
% 15.61/5.94  ----------------------
% 15.61/5.94  Preprocessing        : 0.48
% 15.61/5.94  Parsing              : 0.27
% 15.61/5.94  CNF conversion       : 0.02
% 15.61/5.94  Main loop            : 4.27
% 15.61/5.94  Inferencing          : 1.08
% 15.61/5.94  Reduction            : 1.16
% 15.61/5.94  Demodulation         : 0.71
% 15.61/5.94  BG Simplification    : 0.06
% 15.61/5.94  Subsumption          : 1.68
% 15.61/5.94  Abstraction          : 0.09
% 15.61/5.94  MUC search           : 0.00
% 15.61/5.94  Cooper               : 0.00
% 15.61/5.94  Total                : 4.81
% 15.61/5.94  Index Insertion      : 0.00
% 15.61/5.94  Index Deletion       : 0.00
% 15.61/5.94  Index Matching       : 0.00
% 15.61/5.94  BG Taut test         : 0.00
%------------------------------------------------------------------------------