TSTP Solution File: SET872+1 by Beagle---0.9.51

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%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : n005.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 10:57:15 EDT 2023

% Result   : Theorem 3.15s 1.85s
% Output   : CNFRefutation 3.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   28 (   6 unt;  14 typ;   0 def)
%            Number of atoms       :   26 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   17 (   5   ~;   6   |;   0   &)
%                                         (   5 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   20 (  10   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   4 con; 0-3 aty)
%            Number of variables   :   22 (;  22   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > unordered_pair > #nlpp > singleton > #skF_4 > #skF_7 > #skF_6 > #skF_9 > #skF_8 > #skF_3 > #skF_2 > #skF_1 > #skF_5

%Foreground sorts:

%Background operators:

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

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

tff('#skF_4',type,
    '#skF_4': ( $i * $i * $i ) > $i ).

tff('#skF_7',type,
    '#skF_7': $i ).

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

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

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

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

tff('#skF_9',type,
    '#skF_9': $i ).

tff('#skF_8',type,
    '#skF_8': $i ).

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

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

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

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

tff(f_66,negated_conjecture,
    ~ ! [A,B] : subset(singleton(A),unordered_pair(A,B)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_zfmisc_1) ).

tff(f_49,axiom,
    ! [A,B,C] :
      ( ( C = unordered_pair(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( ( D = A )
            | ( D = B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).

tff(f_56,axiom,
    ! [A,B] :
      ( subset(A,B)
    <=> ! [C] :
          ( in(C,A)
         => in(C,B) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).

tff(f_40,axiom,
    ! [A,B] :
      ( ( B = singleton(A) )
    <=> ! [C] :
          ( in(C,B)
        <=> ( C = A ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tarski) ).

tff(c_48,plain,
    ~ subset(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')),
    inference(cnfTransformation,[status(thm)],[f_66]) ).

tff(c_22,plain,
    ! [D_15,B_11] : in(D_15,unordered_pair(D_15,B_11)),
    inference(cnfTransformation,[status(thm)],[f_49]) ).

tff(c_133,plain,
    ! [A_40,B_41] :
      ( in('#skF_5'(A_40,B_41),A_40)
      | subset(A_40,B_41) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_6,plain,
    ! [C_9,A_5] :
      ( ( C_9 = A_5 )
      | ~ in(C_9,singleton(A_5)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_241,plain,
    ! [A_65,B_66] :
      ( ( '#skF_5'(singleton(A_65),B_66) = A_65 )
      | subset(singleton(A_65),B_66) ),
    inference(resolution,[status(thm)],[c_133,c_6]) ).

tff(c_249,plain,
    '#skF_5'(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')) = '#skF_8',
    inference(resolution,[status(thm)],[c_241,c_48]) ).

tff(c_38,plain,
    ! [A_16,B_17] :
      ( ~ in('#skF_5'(A_16,B_17),B_17)
      | subset(A_16,B_17) ),
    inference(cnfTransformation,[status(thm)],[f_56]) ).

tff(c_256,plain,
    ( ~ in('#skF_8',unordered_pair('#skF_8','#skF_9'))
    | subset(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')) ),
    inference(superposition,[status(thm),theory(equality)],[c_249,c_38]) ).

tff(c_264,plain,
    subset(singleton('#skF_8'),unordered_pair('#skF_8','#skF_9')),
    inference(demodulation,[status(thm),theory(equality)],[c_22,c_256]) ).

tff(c_266,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_48,c_264]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET872+1 : TPTP v8.1.2. Released v3.2.0.
% 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
% 0.15/0.36  % Computer : n005.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 16:33:12 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 3.15/1.85  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.15/1.85  
% 3.15/1.85  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.15/1.88  
% 3.15/1.88  Inference rules
% 3.15/1.88  ----------------------
% 3.15/1.88  #Ref     : 0
% 3.15/1.88  #Sup     : 51
% 3.15/1.88  #Fact    : 0
% 3.15/1.88  #Define  : 0
% 3.15/1.88  #Split   : 0
% 3.15/1.88  #Chain   : 0
% 3.15/1.88  #Close   : 0
% 3.15/1.88  
% 3.15/1.88  Ordering : KBO
% 3.15/1.88  
% 3.15/1.88  Simplification rules
% 3.15/1.88  ----------------------
% 3.15/1.88  #Subsume      : 11
% 3.15/1.88  #Demod        : 9
% 3.15/1.88  #Tautology    : 22
% 3.15/1.88  #SimpNegUnit  : 2
% 3.15/1.88  #BackRed      : 0
% 3.15/1.88  
% 3.15/1.88  #Partial instantiations: 0
% 3.15/1.88  #Strategies tried      : 1
% 3.15/1.88  
% 3.15/1.88  Timing (in seconds)
% 3.15/1.88  ----------------------
% 3.34/1.88  Preprocessing        : 0.48
% 3.34/1.88  Parsing              : 0.24
% 3.34/1.88  CNF conversion       : 0.04
% 3.34/1.88  Main loop            : 0.29
% 3.34/1.88  Inferencing          : 0.10
% 3.34/1.88  Reduction            : 0.10
% 3.34/1.88  Demodulation         : 0.07
% 3.34/1.88  BG Simplification    : 0.02
% 3.34/1.88  Subsumption          : 0.07
% 3.34/1.88  Abstraction          : 0.01
% 3.34/1.88  MUC search           : 0.00
% 3.34/1.88  Cooper               : 0.00
% 3.34/1.88  Total                : 0.81
% 3.34/1.88  Index Insertion      : 0.00
% 3.34/1.88  Index Deletion       : 0.00
% 3.34/1.88  Index Matching       : 0.00
% 3.34/1.88  BG Taut test         : 0.00
%------------------------------------------------------------------------------