TSTP Solution File: SET617+3 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 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 10:56:43 EDT 2023

% Result   : Theorem 3.50s 1.96s
% Output   : CNFRefutation 3.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   35 (  19 unt;  13 typ;   0 def)
%            Number of atoms       :   25 (  23 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   7   ~;   2   |;   1   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   18 (  10   >;   8   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   3 con; 0-2 aty)
%            Number of variables   :   21 (;  21   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > empty > union > symmetric_difference > difference > #nlpp > empty_set > #skF_4 > #skF_3 > #skF_5 > #skF_6 > #skF_2 > #skF_1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_4',type,
    '#skF_4': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_33,axiom,
    ! [B] : ( union(B,empty_set) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).

tff(f_39,axiom,
    ! [B] : ( difference(empty_set,B) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).

tff(f_36,axiom,
    ! [B] : ( difference(B,empty_set) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).

tff(f_30,axiom,
    ! [B,C] : ( symmetric_difference(B,C) = union(difference(B,C),difference(C,B)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).

tff(f_56,axiom,
    ! [B,C] : ( symmetric_difference(B,C) = symmetric_difference(C,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).

tff(f_88,negated_conjecture,
    ~ ! [B] :
        ( ( symmetric_difference(B,empty_set) = B )
        & ( symmetric_difference(empty_set,B) = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).

tff(c_4,plain,
    ! [B_3] : ( union(B_3,empty_set) = B_3 ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_8,plain,
    ! [B_5] : ( difference(empty_set,B_5) = empty_set ),
    inference(cnfTransformation,[status(thm)],[f_39]) ).

tff(c_6,plain,
    ! [B_4] : ( difference(B_4,empty_set) = B_4 ),
    inference(cnfTransformation,[status(thm)],[f_36]) ).

tff(c_558,plain,
    ! [B_89,C_90] : ( union(difference(B_89,C_90),difference(C_90,B_89)) = symmetric_difference(B_89,C_90) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_579,plain,
    ! [B_4] : ( union(B_4,difference(empty_set,B_4)) = symmetric_difference(B_4,empty_set) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_558]) ).

tff(c_591,plain,
    ! [B_4] : ( symmetric_difference(B_4,empty_set) = B_4 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_8,c_579]) ).

tff(c_345,plain,
    ! [B_64,C_65] : ( union(difference(B_64,C_65),difference(C_65,B_64)) = symmetric_difference(B_64,C_65) ),
    inference(cnfTransformation,[status(thm)],[f_30]) ).

tff(c_366,plain,
    ! [B_4] : ( union(B_4,difference(empty_set,B_4)) = symmetric_difference(B_4,empty_set) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_345]) ).

tff(c_378,plain,
    ! [B_4] : ( symmetric_difference(B_4,empty_set) = B_4 ),
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_8,c_366]) ).

tff(c_20,plain,
    ! [C_12,B_11] : ( symmetric_difference(C_12,B_11) = symmetric_difference(B_11,C_12) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_46,plain,
    ( ( symmetric_difference('#skF_6',empty_set) != '#skF_6' )
    | ( symmetric_difference(empty_set,'#skF_5') != '#skF_5' ) ),
    inference(cnfTransformation,[status(thm)],[f_88]) ).

tff(c_47,plain,
    ( ( symmetric_difference('#skF_6',empty_set) != '#skF_6' )
    | ( symmetric_difference('#skF_5',empty_set) != '#skF_5' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_20,c_46]) ).

tff(c_145,plain,
    symmetric_difference('#skF_5',empty_set) != '#skF_5',
    inference(splitLeft,[status(thm)],[c_47]) ).

tff(c_384,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_378,c_145]) ).

tff(c_385,plain,
    symmetric_difference('#skF_6',empty_set) != '#skF_6',
    inference(splitRight,[status(thm)],[c_47]) ).

tff(c_598,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_591,c_385]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : SET617+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % 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
% 0.13/0.35  % Computer : n024.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 16:27:15 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 3.50/1.96  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.50/1.96  
% 3.50/1.96  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.76/1.99  
% 3.76/1.99  Inference rules
% 3.76/1.99  ----------------------
% 3.76/1.99  #Ref     : 0
% 3.76/1.99  #Sup     : 120
% 3.76/1.99  #Fact    : 0
% 3.76/1.99  #Define  : 0
% 3.76/1.99  #Split   : 1
% 3.76/1.99  #Chain   : 0
% 3.76/1.99  #Close   : 0
% 3.76/1.99  
% 3.76/1.99  Ordering : KBO
% 3.76/1.99  
% 3.76/1.99  Simplification rules
% 3.76/1.99  ----------------------
% 3.76/1.99  #Subsume      : 4
% 3.76/1.99  #Demod        : 43
% 3.76/1.99  #Tautology    : 84
% 3.76/1.99  #SimpNegUnit  : 0
% 3.76/1.99  #BackRed      : 2
% 3.76/1.99  
% 3.76/1.99  #Partial instantiations: 0
% 3.76/1.99  #Strategies tried      : 1
% 3.76/1.99  
% 3.76/1.99  Timing (in seconds)
% 3.76/1.99  ----------------------
% 3.76/1.99  Preprocessing        : 0.49
% 3.76/1.99  Parsing              : 0.26
% 3.76/1.99  CNF conversion       : 0.03
% 3.76/1.99  Main loop            : 0.37
% 3.76/1.99  Inferencing          : 0.14
% 3.76/1.99  Reduction            : 0.11
% 3.76/1.99  Demodulation         : 0.09
% 3.76/1.99  BG Simplification    : 0.02
% 3.76/1.99  Subsumption          : 0.07
% 3.76/1.99  Abstraction          : 0.02
% 3.76/1.99  MUC search           : 0.00
% 3.76/1.99  Cooper               : 0.00
% 3.76/1.99  Total                : 0.91
% 3.76/1.99  Index Insertion      : 0.00
% 3.76/1.99  Index Deletion       : 0.00
% 3.76/1.99  Index Matching       : 0.00
% 3.76/1.99  BG Taut test         : 0.00
%------------------------------------------------------------------------------