TSTP Solution File: TOP001-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : TOP001-2 : 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 : n013.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 11:18:39 EDT 2023

% Result   : Unsatisfiable 6.73s 2.58s
% Output   : CNFRefutation 6.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   25
% Syntax   : Number of formulae    :   53 (  10 unt;  12 typ;   0 def)
%            Number of atoms       :   91 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   97 (  47   ~;  50   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   19 (  10   >;   9   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   2 con; 0-3 aty)
%            Number of variables   :   81 (;  81   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset_sets > equal_sets > element_of_set > element_of_collection > basis > f10 > in_1st_set > f1 > #nlpp > union_of_members > top_of_basis > f > cx

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(in_1st_set,type,
    in_1st_set: ( $i * $i ) > $i ).

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

tff(f10,type,
    f10: ( $i * $i * $i ) > $i ).

tff(f1,type,
    f1: ( $i * $i ) > $i ).

tff(f_93,axiom,
    basis(cx,f),
    file(unknown,unknown) ).

tff(f_51,axiom,
    ! [X,Vf] :
      ( ~ basis(X,Vf)
      | equal_sets(union_of_members(Vf),X) ),
    file(unknown,unknown) ).

tff(f_83,axiom,
    ! [X,Y] :
      ( ~ equal_sets(X,Y)
      | subset_sets(X,Y) ),
    file(unknown,unknown) ).

tff(f_70,axiom,
    ! [X] : subset_sets(X,X),
    file(unknown,unknown) ).

tff(f_87,axiom,
    ! [X,Y] :
      ( subset_sets(X,Y)
      | element_of_set(in_1st_set(X,Y),X) ),
    file(unknown,unknown) ).

tff(f_78,axiom,
    ! [X,Y,U] :
      ( ~ subset_sets(X,Y)
      | ~ element_of_set(U,X)
      | element_of_set(U,Y) ),
    file(unknown,unknown) ).

tff(f_37,axiom,
    ! [U,Vf] :
      ( ~ element_of_set(U,union_of_members(Vf))
      | element_of_collection(f1(Vf,U),Vf) ),
    file(unknown,unknown) ).

tff(f_32,axiom,
    ! [U,Vf] :
      ( ~ element_of_set(U,union_of_members(Vf))
      | element_of_set(U,f1(Vf,U)) ),
    file(unknown,unknown) ).

tff(f_60,axiom,
    ! [U,Vf,X] :
      ( ~ element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(X,U)
      | element_of_set(X,f10(Vf,U,X)) ),
    file(unknown,unknown) ).

tff(f_68,axiom,
    ! [U,Vf,X] :
      ( ~ element_of_collection(U,top_of_basis(Vf))
      | ~ element_of_set(X,U)
      | element_of_collection(f10(Vf,U,X),Vf) ),
    file(unknown,unknown) ).

tff(f_45,axiom,
    ! [U,Vf,Uu1] :
      ( element_of_set(U,union_of_members(Vf))
      | ~ element_of_set(U,Uu1)
      | ~ element_of_collection(Uu1,Vf) ),
    file(unknown,unknown) ).

tff(f_92,axiom,
    ! [X,Y] :
      ( subset_sets(X,Y)
      | ~ element_of_set(in_1st_set(X,Y),Y) ),
    file(unknown,unknown) ).

tff(f_95,axiom,
    ~ subset_sets(union_of_members(top_of_basis(f)),cx),
    file(unknown,unknown) ).

tff(c_24,plain,
    basis(cx,f),
    inference(cnfTransformation,[status(thm)],[f_93]) ).

tff(c_8,plain,
    ! [Vf_9,X_8] :
      ( equal_sets(union_of_members(Vf_9),X_8)
      | ~ basis(X_8,Vf_9) ),
    inference(cnfTransformation,[status(thm)],[f_51]) ).

tff(c_18,plain,
    ! [X_20,Y_21] :
      ( subset_sets(X_20,Y_21)
      | ~ equal_sets(X_20,Y_21) ),
    inference(cnfTransformation,[status(thm)],[f_83]) ).

tff(c_14,plain,
    ! [X_16] : subset_sets(X_16,X_16),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_20,plain,
    ! [X_22,Y_23] :
      ( element_of_set(in_1st_set(X_22,Y_23),X_22)
      | subset_sets(X_22,Y_23) ),
    inference(cnfTransformation,[status(thm)],[f_87]) ).

tff(c_46,plain,
    ! [U_35,Y_36,X_37] :
      ( element_of_set(U_35,Y_36)
      | ~ element_of_set(U_35,X_37)
      | ~ subset_sets(X_37,Y_36) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_60,plain,
    ! [X_45,Y_46,Y_47] :
      ( element_of_set(in_1st_set(X_45,Y_46),Y_47)
      | ~ subset_sets(X_45,Y_47)
      | subset_sets(X_45,Y_46) ),
    inference(resolution,[status(thm)],[c_20,c_46]) ).

tff(c_4,plain,
    ! [Vf_4,U_3] :
      ( element_of_collection(f1(Vf_4,U_3),Vf_4)
      | ~ element_of_set(U_3,union_of_members(Vf_4)) ),
    inference(cnfTransformation,[status(thm)],[f_37]) ).

tff(c_70,plain,
    ! [Vf_4,X_45,Y_46] :
      ( element_of_collection(f1(Vf_4,in_1st_set(X_45,Y_46)),Vf_4)
      | ~ subset_sets(X_45,union_of_members(Vf_4))
      | subset_sets(X_45,Y_46) ),
    inference(resolution,[status(thm)],[c_60,c_4]) ).

tff(c_2,plain,
    ! [U_1,Vf_2] :
      ( element_of_set(U_1,f1(Vf_2,U_1))
      | ~ element_of_set(U_1,union_of_members(Vf_2)) ),
    inference(cnfTransformation,[status(thm)],[f_32]) ).

tff(c_10,plain,
    ! [X_12,Vf_11,U_10] :
      ( element_of_set(X_12,f10(Vf_11,U_10,X_12))
      | ~ element_of_set(X_12,U_10)
      | ~ element_of_collection(U_10,top_of_basis(Vf_11)) ),
    inference(cnfTransformation,[status(thm)],[f_60]) ).

tff(c_77,plain,
    ! [Vf_50,U_51,X_52] :
      ( element_of_collection(f10(Vf_50,U_51,X_52),Vf_50)
      | ~ element_of_set(X_52,U_51)
      | ~ element_of_collection(U_51,top_of_basis(Vf_50)) ),
    inference(cnfTransformation,[status(thm)],[f_68]) ).

tff(c_6,plain,
    ! [Uu1_7,Vf_6,U_5] :
      ( ~ element_of_collection(Uu1_7,Vf_6)
      | ~ element_of_set(U_5,Uu1_7)
      | element_of_set(U_5,union_of_members(Vf_6)) ),
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_181,plain,
    ! [U_102,Vf_103,U_104,X_105] :
      ( ~ element_of_set(U_102,f10(Vf_103,U_104,X_105))
      | element_of_set(U_102,union_of_members(Vf_103))
      | ~ element_of_set(X_105,U_104)
      | ~ element_of_collection(U_104,top_of_basis(Vf_103)) ),
    inference(resolution,[status(thm)],[c_77,c_6]) ).

tff(c_201,plain,
    ! [X_106,Vf_107,U_108] :
      ( element_of_set(X_106,union_of_members(Vf_107))
      | ~ element_of_set(X_106,U_108)
      | ~ element_of_collection(U_108,top_of_basis(Vf_107)) ),
    inference(resolution,[status(thm)],[c_10,c_181]) ).

tff(c_252,plain,
    ! [U_114,Vf_115,Vf_116] :
      ( element_of_set(U_114,union_of_members(Vf_115))
      | ~ element_of_collection(f1(Vf_116,U_114),top_of_basis(Vf_115))
      | ~ element_of_set(U_114,union_of_members(Vf_116)) ),
    inference(resolution,[status(thm)],[c_2,c_201]) ).

tff(c_3106,plain,
    ! [X_488,Y_489,Vf_490] :
      ( element_of_set(in_1st_set(X_488,Y_489),union_of_members(Vf_490))
      | ~ element_of_set(in_1st_set(X_488,Y_489),union_of_members(top_of_basis(Vf_490)))
      | ~ subset_sets(X_488,union_of_members(top_of_basis(Vf_490)))
      | subset_sets(X_488,Y_489) ),
    inference(resolution,[status(thm)],[c_70,c_252]) ).

tff(c_3158,plain,
    ! [Vf_490,Y_23] :
      ( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_490)),Y_23),union_of_members(Vf_490))
      | ~ subset_sets(union_of_members(top_of_basis(Vf_490)),union_of_members(top_of_basis(Vf_490)))
      | subset_sets(union_of_members(top_of_basis(Vf_490)),Y_23) ),
    inference(resolution,[status(thm)],[c_20,c_3106]) ).

tff(c_3174,plain,
    ! [Vf_491,Y_492] :
      ( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_491)),Y_492),union_of_members(Vf_491))
      | subset_sets(union_of_members(top_of_basis(Vf_491)),Y_492) ),
    inference(demodulation,[status(thm),theory(equality)],[c_14,c_3158]) ).

tff(c_16,plain,
    ! [U_19,Y_18,X_17] :
      ( element_of_set(U_19,Y_18)
      | ~ element_of_set(U_19,X_17)
      | ~ subset_sets(X_17,Y_18) ),
    inference(cnfTransformation,[status(thm)],[f_78]) ).

tff(c_3474,plain,
    ! [Vf_502,Y_503,Y_504] :
      ( element_of_set(in_1st_set(union_of_members(top_of_basis(Vf_502)),Y_503),Y_504)
      | ~ subset_sets(union_of_members(Vf_502),Y_504)
      | subset_sets(union_of_members(top_of_basis(Vf_502)),Y_503) ),
    inference(resolution,[status(thm)],[c_3174,c_16]) ).

tff(c_22,plain,
    ! [X_24,Y_25] :
      ( ~ element_of_set(in_1st_set(X_24,Y_25),Y_25)
      | subset_sets(X_24,Y_25) ),
    inference(cnfTransformation,[status(thm)],[f_92]) ).

tff(c_3550,plain,
    ! [Vf_505,Y_506] :
      ( ~ subset_sets(union_of_members(Vf_505),Y_506)
      | subset_sets(union_of_members(top_of_basis(Vf_505)),Y_506) ),
    inference(resolution,[status(thm)],[c_3474,c_22]) ).

tff(c_26,plain,
    ~ subset_sets(union_of_members(top_of_basis(f)),cx),
    inference(cnfTransformation,[status(thm)],[f_95]) ).

tff(c_3602,plain,
    ~ subset_sets(union_of_members(f),cx),
    inference(resolution,[status(thm)],[c_3550,c_26]) ).

tff(c_3620,plain,
    ~ equal_sets(union_of_members(f),cx),
    inference(resolution,[status(thm)],[c_18,c_3602]) ).

tff(c_3623,plain,
    ~ basis(cx,f),
    inference(resolution,[status(thm)],[c_8,c_3620]) ).

tff(c_3627,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_24,c_3623]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : TOP001-2 : TPTP v8.1.2. Released v1.0.0.
% 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
% 0.14/0.34  % Computer : n013.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 17:42:18 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 6.73/2.58  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.73/2.59  
% 6.73/2.59  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.92/2.62  
% 6.92/2.62  Inference rules
% 6.92/2.62  ----------------------
% 6.92/2.62  #Ref     : 0
% 6.92/2.62  #Sup     : 925
% 6.92/2.62  #Fact    : 0
% 6.92/2.62  #Define  : 0
% 6.92/2.62  #Split   : 0
% 6.92/2.62  #Chain   : 0
% 6.92/2.62  #Close   : 0
% 6.92/2.62  
% 6.92/2.62  Ordering : KBO
% 6.92/2.62  
% 6.92/2.62  Simplification rules
% 6.92/2.62  ----------------------
% 6.92/2.62  #Subsume      : 125
% 6.92/2.62  #Demod        : 5
% 6.92/2.62  #Tautology    : 2
% 6.92/2.62  #SimpNegUnit  : 0
% 6.92/2.62  #BackRed      : 0
% 6.92/2.62  
% 6.92/2.62  #Partial instantiations: 0
% 6.92/2.62  #Strategies tried      : 1
% 6.92/2.62  
% 6.92/2.62  Timing (in seconds)
% 6.92/2.62  ----------------------
% 6.92/2.62  Preprocessing        : 0.41
% 6.92/2.62  Parsing              : 0.23
% 6.92/2.62  CNF conversion       : 0.02
% 6.92/2.62  Main loop            : 1.18
% 6.92/2.62  Inferencing          : 0.41
% 6.92/2.62  Reduction            : 0.24
% 6.92/2.62  Demodulation         : 0.15
% 6.92/2.62  BG Simplification    : 0.03
% 6.92/2.62  Subsumption          : 0.42
% 6.92/2.62  Abstraction          : 0.04
% 6.92/2.62  MUC search           : 0.00
% 6.92/2.62  Cooper               : 0.00
% 6.92/2.62  Total                : 1.64
% 6.92/2.62  Index Insertion      : 0.00
% 6.92/2.62  Index Deletion       : 0.00
% 6.92/2.62  Index Matching       : 0.00
% 6.92/2.62  BG Taut test         : 0.00
%------------------------------------------------------------------------------