TSTP Solution File: SET012-4 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET012-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n008.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 5.61s 2.55s
% Output   : CNFRefutation 6.01s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   45 (  14 unt;   9 typ;   0 def)
%            Number of atoms       :   75 (  20 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   67 (  28   ~;  39   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   4   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   30 (;  30   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ member > little_set > f1 > #nlpp > complement > universal_set > empty_set > cs > bs > as

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(bs,type,
    bs: $i ).

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

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

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

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

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

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

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

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

tff(f_75,axiom,
    as != cs,
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [X,Y] :
      ( little_set(f1(X,Y))
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_73,axiom,
    complement(bs) = cs,
    file(unknown,unknown) ).

tff(f_72,axiom,
    complement(as) = bs,
    file(unknown,unknown) ).

tff(f_61,axiom,
    ! [Z,X] :
      ( member(Z,complement(X))
      | ~ little_set(Z)
      | member(Z,X) ),
    file(unknown,unknown) ).

tff(f_39,axiom,
    ! [X,Y] :
      ( member(f1(X,Y),X)
      | member(f1(X,Y),Y)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_54,axiom,
    ! [Z,X] :
      ( ~ member(Z,complement(X))
      | ~ member(Z,X) ),
    file(unknown,unknown) ).

tff(f_47,axiom,
    ! [X,Y] :
      ( ~ member(f1(X,Y),X)
      | ~ member(f1(X,Y),Y)
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(c_22,plain,
    cs != as,
    inference(cnfTransformation,[status(thm)],[f_75]) ).

tff(c_4,plain,
    ! [Y_4,X_3] :
      ( ( Y_4 = X_3 )
      | little_set(f1(X_3,Y_4)) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_20,plain,
    complement(bs) = cs,
    inference(cnfTransformation,[status(thm)],[f_73]) ).

tff(c_18,plain,
    complement(as) = bs,
    inference(cnfTransformation,[status(thm)],[f_72]) ).

tff(c_47,plain,
    ! [Z_24,X_25] :
      ( member(Z_24,X_25)
      | ~ little_set(Z_24)
      | member(Z_24,complement(X_25)) ),
    inference(cnfTransformation,[status(thm)],[f_61]) ).

tff(c_56,plain,
    ! [Z_24] :
      ( member(Z_24,as)
      | ~ little_set(Z_24)
      | member(Z_24,bs) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_47]) ).

tff(c_136,plain,
    ! [Y_32,X_33] :
      ( ( Y_32 = X_33 )
      | member(f1(X_33,Y_32),Y_32)
      | member(f1(X_33,Y_32),X_33) ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_10,plain,
    ! [Z_9,X_10] :
      ( ~ member(Z_9,X_10)
      | ~ member(Z_9,complement(X_10)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_390,plain,
    ! [X_40,X_41] :
      ( ~ member(f1(X_40,complement(X_41)),X_41)
      | ( complement(X_41) = X_40 )
      | member(f1(X_40,complement(X_41)),X_40) ),
    inference(resolution,[status(thm)],[c_136,c_10]) ).

tff(c_396,plain,
    ! [X_40] :
      ( ( complement(bs) = X_40 )
      | member(f1(X_40,complement(bs)),X_40)
      | member(f1(X_40,complement(bs)),as)
      | ~ little_set(f1(X_40,complement(bs))) ),
    inference(resolution,[status(thm)],[c_56,c_390]) ).

tff(c_412,plain,
    ! [X_40] :
      ( ( cs = X_40 )
      | member(f1(X_40,cs),X_40)
      | member(f1(X_40,cs),as)
      | ~ little_set(f1(X_40,cs)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_20,c_20,c_20,c_396]) ).

tff(c_2652,plain,
    ( ( cs = as )
    | ~ little_set(f1(as,cs))
    | member(f1(as,cs),as) ),
    inference(factorization,[status(thm),theory(equality)],[c_412]) ).

tff(c_2655,plain,
    ( ~ little_set(f1(as,cs))
    | member(f1(as,cs),as) ),
    inference(negUnitSimplification,[status(thm)],[c_22,c_2652]) ).

tff(c_2707,plain,
    ~ little_set(f1(as,cs)),
    inference(splitLeft,[status(thm)],[c_2655]) ).

tff(c_2710,plain,
    cs = as,
    inference(resolution,[status(thm)],[c_4,c_2707]) ).

tff(c_2714,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_22,c_2710]) ).

tff(c_2715,plain,
    member(f1(as,cs),as),
    inference(splitRight,[status(thm)],[c_2655]) ).

tff(c_2716,plain,
    little_set(f1(as,cs)),
    inference(splitRight,[status(thm)],[c_2655]) ).

tff(c_59,plain,
    ! [Z_24] :
      ( member(Z_24,bs)
      | ~ little_set(Z_24)
      | member(Z_24,cs) ),
    inference(superposition,[status(thm),theory(equality)],[c_20,c_47]) ).

tff(c_81,plain,
    ! [Y_29,X_30] :
      ( ( Y_29 = X_30 )
      | ~ member(f1(X_30,Y_29),Y_29)
      | ~ member(f1(X_30,Y_29),X_30) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_95,plain,
    ! [X_30] :
      ( ( cs = X_30 )
      | ~ member(f1(X_30,cs),X_30)
      | member(f1(X_30,cs),bs)
      | ~ little_set(f1(X_30,cs)) ),
    inference(resolution,[status(thm)],[c_59,c_81]) ).

tff(c_2724,plain,
    ( ( cs = as )
    | member(f1(as,cs),bs)
    | ~ little_set(f1(as,cs)) ),
    inference(resolution,[status(thm)],[c_2715,c_95]) ).

tff(c_2730,plain,
    ( ( cs = as )
    | member(f1(as,cs),bs) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2716,c_2724]) ).

tff(c_2731,plain,
    member(f1(as,cs),bs),
    inference(negUnitSimplification,[status(thm)],[c_22,c_2730]) ).

tff(c_39,plain,
    ! [Z_21,X_22] :
      ( ~ member(Z_21,X_22)
      | ~ member(Z_21,complement(X_22)) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_42,plain,
    ! [Z_21] :
      ( ~ member(Z_21,as)
      | ~ member(Z_21,bs) ),
    inference(superposition,[status(thm),theory(equality)],[c_18,c_39]) ).

tff(c_2804,plain,
    ~ member(f1(as,cs),as),
    inference(resolution,[status(thm)],[c_2731,c_42]) ).

tff(c_2814,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2715,c_2804]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET012-4 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.00/0.14  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n008.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 16:47:03 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 5.61/2.55  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.61/2.56  
% 5.61/2.56  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.01/2.59  
% 6.01/2.59  Inference rules
% 6.01/2.59  ----------------------
% 6.01/2.59  #Ref     : 0
% 6.01/2.59  #Sup     : 549
% 6.01/2.59  #Fact    : 8
% 6.01/2.59  #Define  : 0
% 6.01/2.59  #Split   : 22
% 6.01/2.59  #Chain   : 0
% 6.01/2.59  #Close   : 0
% 6.01/2.59  
% 6.01/2.59  Ordering : KBO
% 6.01/2.59  
% 6.01/2.59  Simplification rules
% 6.01/2.59  ----------------------
% 6.01/2.59  #Subsume      : 202
% 6.01/2.59  #Demod        : 712
% 6.01/2.59  #Tautology    : 152
% 6.01/2.59  #SimpNegUnit  : 69
% 6.01/2.59  #BackRed      : 152
% 6.01/2.59  
% 6.01/2.59  #Partial instantiations: 0
% 6.01/2.59  #Strategies tried      : 1
% 6.01/2.59  
% 6.01/2.59  Timing (in seconds)
% 6.01/2.59  ----------------------
% 6.05/2.59  Preprocessing        : 0.48
% 6.05/2.59  Parsing              : 0.26
% 6.05/2.59  CNF conversion       : 0.02
% 6.05/2.59  Main loop            : 0.90
% 6.05/2.59  Inferencing          : 0.33
% 6.05/2.59  Reduction            : 0.28
% 6.05/2.59  Demodulation         : 0.19
% 6.05/2.59  BG Simplification    : 0.03
% 6.05/2.59  Subsumption          : 0.20
% 6.05/2.59  Abstraction          : 0.03
% 6.05/2.59  MUC search           : 0.00
% 6.05/2.59  Cooper               : 0.00
% 6.05/2.59  Total                : 1.43
% 6.05/2.59  Index Insertion      : 0.00
% 6.05/2.59  Index Deletion       : 0.00
% 6.05/2.59  Index Matching       : 0.00
% 6.05/2.59  BG Taut test         : 0.00
%------------------------------------------------------------------------------