TSTP Solution File: SET018-1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET018-1 : 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/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 : n020.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 10:55:33 EDT 2023

% Result   : Unsatisfiable 3.51s 1.98s
% Output   : CNFRefutation 3.65s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   65 (  45 unt;   8 typ;   0 def)
%            Number of atoms       :   75 (  47 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   31 (  13   ~;  18   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   4   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   38 (;  38   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ member > unordered_pair > ordered_pair > #nlpp > singleton_set > r2 > r1 > m2 > m1

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(m2,type,
    m2: $i ).

tff(r1,type,
    r1: $i ).

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

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

tff(r2,type,
    r2: $i ).

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

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

tff(m1,type,
    m1: $i ).

tff(f_45,axiom,
    r1 != r2,
    file(unknown,unknown) ).

tff(f_43,axiom,
    ordered_pair(m1,r1) = ordered_pair(m2,r2),
    file(unknown,unknown) ).

tff(f_42,axiom,
    ! [X,Y] : ( ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)) ),
    file(unknown,unknown) ).

tff(f_31,axiom,
    ! [X,Y] : member(X,unordered_pair(X,Y)),
    file(unknown,unknown) ).

tff(f_40,axiom,
    ! [X,Y,Z] :
      ( ~ member(X,unordered_pair(Y,Z))
      | ( X = Y )
      | ( X = Z ) ),
    file(unknown,unknown) ).

tff(f_24,axiom,
    ! [X] : member(X,singleton_set(X)),
    file(unknown,unknown) ).

tff(f_29,axiom,
    ! [X,Y] :
      ( ~ member(X,singleton_set(Y))
      | ( X = Y ) ),
    file(unknown,unknown) ).

tff(f_33,axiom,
    ! [Y,X] : member(Y,unordered_pair(X,Y)),
    file(unknown,unknown) ).

tff(c_16,plain,
    r2 != r1,
    inference(cnfTransformation,[status(thm)],[f_45]) ).

tff(c_14,plain,
    ordered_pair(m2,r2) = ordered_pair(m1,r1),
    inference(cnfTransformation,[status(thm)],[f_43]) ).

tff(c_41,plain,
    ! [X_23,Y_24] : ( unordered_pair(singleton_set(X_23),unordered_pair(X_23,Y_24)) = ordered_pair(X_23,Y_24) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_6,plain,
    ! [X_4,Y_5] : member(X_4,unordered_pair(X_4,Y_5)),
    inference(cnfTransformation,[status(thm)],[f_31]) ).

tff(c_65,plain,
    ! [X_25,Y_26] : member(singleton_set(X_25),ordered_pair(X_25,Y_26)),
    inference(superposition,[status(thm),theory(equality)],[c_41,c_6]) ).

tff(c_68,plain,
    member(singleton_set(m2),ordered_pair(m1,r1)),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_65]) ).

tff(c_10,plain,
    ! [Z_10,X_8,Y_9] :
      ( ( Z_10 = X_8 )
      | ( Y_9 = X_8 )
      | ~ member(X_8,unordered_pair(Y_9,Z_10)) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_83,plain,
    ! [X_31,Y_32,X_33] :
      ( ( unordered_pair(X_31,Y_32) = X_33 )
      | ( singleton_set(X_31) = X_33 )
      | ~ member(X_33,ordered_pair(X_31,Y_32)) ),
    inference(superposition,[status(thm),theory(equality)],[c_41,c_10]) ).

tff(c_112,plain,
    ( ( unordered_pair(m1,r1) = singleton_set(m2) )
    | ( singleton_set(m2) = singleton_set(m1) ) ),
    inference(resolution,[status(thm)],[c_68,c_83]) ).

tff(c_147,plain,
    singleton_set(m2) = singleton_set(m1),
    inference(splitLeft,[status(thm)],[c_112]) ).

tff(c_2,plain,
    ! [X_1] : member(X_1,singleton_set(X_1)),
    inference(cnfTransformation,[status(thm)],[f_24]) ).

tff(c_169,plain,
    member(m2,singleton_set(m1)),
    inference(superposition,[status(thm),theory(equality)],[c_147,c_2]) ).

tff(c_4,plain,
    ! [Y_3,X_2] :
      ( ( Y_3 = X_2 )
      | ~ member(X_2,singleton_set(Y_3)) ),
    inference(cnfTransformation,[status(thm)],[f_29]) ).

tff(c_177,plain,
    m2 = m1,
    inference(resolution,[status(thm)],[c_169,c_4]) ).

tff(c_8,plain,
    ! [Y_6,X_7] : member(Y_6,unordered_pair(X_7,Y_6)),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_69,plain,
    ! [X_27,Y_28] : member(unordered_pair(X_27,Y_28),ordered_pair(X_27,Y_28)),
    inference(superposition,[status(thm),theory(equality)],[c_41,c_8]) ).

tff(c_75,plain,
    member(unordered_pair(m2,r2),ordered_pair(m1,r1)),
    inference(superposition,[status(thm),theory(equality)],[c_14,c_69]) ).

tff(c_109,plain,
    ( ( unordered_pair(m2,r2) = unordered_pair(m1,r1) )
    | ( unordered_pair(m2,r2) = singleton_set(m1) ) ),
    inference(resolution,[status(thm)],[c_75,c_83]) ).

tff(c_243,plain,
    ( ( unordered_pair(m1,r2) = unordered_pair(m1,r1) )
    | ( unordered_pair(m1,r2) = singleton_set(m1) ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_177,c_177,c_109]) ).

tff(c_244,plain,
    unordered_pair(m1,r2) = singleton_set(m1),
    inference(splitLeft,[status(thm)],[c_243]) ).

tff(c_267,plain,
    member(r2,singleton_set(m1)),
    inference(superposition,[status(thm),theory(equality)],[c_244,c_8]) ).

tff(c_278,plain,
    r2 = m1,
    inference(resolution,[status(thm)],[c_267,c_4]) ).

tff(c_282,plain,
    r1 != m1,
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_16]) ).

tff(c_181,plain,
    ordered_pair(m1,r2) = ordered_pair(m1,r1),
    inference(demodulation,[status(thm),theory(equality)],[c_177,c_14]) ).

tff(c_281,plain,
    ordered_pair(m1,r1) = ordered_pair(m1,m1),
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_181]) ).

tff(c_56,plain,
    ! [X_23,Y_24] : member(unordered_pair(X_23,Y_24),ordered_pair(X_23,Y_24)),
    inference(superposition,[status(thm),theory(equality)],[c_41,c_8]) ).

tff(c_354,plain,
    member(unordered_pair(m1,r1),ordered_pair(m1,m1)),
    inference(superposition,[status(thm),theory(equality)],[c_281,c_56]) ).

tff(c_280,plain,
    unordered_pair(m1,m1) = singleton_set(m1),
    inference(demodulation,[status(thm),theory(equality)],[c_278,c_244]) ).

tff(c_12,plain,
    ! [X_11,Y_12] : ( unordered_pair(singleton_set(X_11),unordered_pair(X_11,Y_12)) = ordered_pair(X_11,Y_12) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_326,plain,
    unordered_pair(singleton_set(m1),singleton_set(m1)) = ordered_pair(m1,m1),
    inference(superposition,[status(thm),theory(equality)],[c_280,c_12]) ).

tff(c_425,plain,
    ! [X_39] :
      ( ( singleton_set(m1) = X_39 )
      | ( singleton_set(m1) = X_39 )
      | ~ member(X_39,ordered_pair(m1,m1)) ),
    inference(superposition,[status(thm),theory(equality)],[c_326,c_10]) ).

tff(c_437,plain,
    unordered_pair(m1,r1) = singleton_set(m1),
    inference(resolution,[status(thm)],[c_354,c_425]) ).

tff(c_465,plain,
    member(r1,singleton_set(m1)),
    inference(superposition,[status(thm),theory(equality)],[c_437,c_8]) ).

tff(c_476,plain,
    r1 = m1,
    inference(resolution,[status(thm)],[c_465,c_4]) ).

tff(c_480,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_282,c_476]) ).

tff(c_481,plain,
    unordered_pair(m1,r2) = unordered_pair(m1,r1),
    inference(splitRight,[status(thm)],[c_243]) ).

tff(c_507,plain,
    member(r2,unordered_pair(m1,r1)),
    inference(superposition,[status(thm),theory(equality)],[c_481,c_8]) ).

tff(c_518,plain,
    ( ( r2 = r1 )
    | ( r2 = m1 ) ),
    inference(resolution,[status(thm)],[c_507,c_10]) ).

tff(c_521,plain,
    r2 = m1,
    inference(negUnitSimplification,[status(thm)],[c_16,c_518]) ).

tff(c_525,plain,
    r1 != m1,
    inference(demodulation,[status(thm),theory(equality)],[c_521,c_16]) ).

tff(c_501,plain,
    ! [X_8] :
      ( ( r2 = X_8 )
      | ( m1 = X_8 )
      | ~ member(X_8,unordered_pair(m1,r1)) ),
    inference(superposition,[status(thm),theory(equality)],[c_481,c_10]) ).

tff(c_532,plain,
    ! [X_40] :
      ( ( m1 = X_40 )
      | ( m1 = X_40 )
      | ~ member(X_40,unordered_pair(m1,r1)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_521,c_501]) ).

tff(c_540,plain,
    r1 = m1,
    inference(resolution,[status(thm)],[c_8,c_532]) ).

tff(c_546,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_525,c_525,c_540]) ).

tff(c_547,plain,
    unordered_pair(m1,r1) = singleton_set(m2),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_564,plain,
    member(m1,singleton_set(m2)),
    inference(superposition,[status(thm),theory(equality)],[c_547,c_6]) ).

tff(c_575,plain,
    m2 = m1,
    inference(resolution,[status(thm)],[c_564,c_4]) ).

tff(c_548,plain,
    singleton_set(m2) != singleton_set(m1),
    inference(splitRight,[status(thm)],[c_112]) ).

tff(c_585,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_575,c_548]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14  % Problem  : SET018-1 : TPTP v8.1.2. Released v1.0.0.
% 0.14/0.15  % 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
% 0.14/0.36  % Computer : n020.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 17:01:22 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 3.51/1.98  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.51/1.99  
% 3.51/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.65/2.02  
% 3.65/2.02  Inference rules
% 3.65/2.02  ----------------------
% 3.65/2.02  #Ref     : 0
% 3.65/2.02  #Sup     : 141
% 3.65/2.02  #Fact    : 0
% 3.65/2.02  #Define  : 0
% 3.65/2.02  #Split   : 2
% 3.65/2.02  #Chain   : 0
% 3.65/2.02  #Close   : 0
% 3.65/2.02  
% 3.65/2.02  Ordering : KBO
% 3.65/2.02  
% 3.65/2.02  Simplification rules
% 3.65/2.02  ----------------------
% 3.65/2.02  #Subsume      : 5
% 3.65/2.02  #Demod        : 129
% 3.65/2.02  #Tautology    : 91
% 3.65/2.02  #SimpNegUnit  : 3
% 3.65/2.02  #BackRed      : 29
% 3.65/2.02  
% 3.65/2.02  #Partial instantiations: 0
% 3.65/2.02  #Strategies tried      : 1
% 3.65/2.02  
% 3.65/2.02  Timing (in seconds)
% 3.65/2.02  ----------------------
% 3.65/2.03  Preprocessing        : 0.43
% 3.65/2.03  Parsing              : 0.23
% 3.65/2.03  CNF conversion       : 0.02
% 3.65/2.03  Main loop            : 0.42
% 3.65/2.03  Inferencing          : 0.16
% 3.65/2.03  Reduction            : 0.13
% 3.65/2.03  Demodulation         : 0.09
% 3.65/2.03  BG Simplification    : 0.02
% 3.65/2.03  Subsumption          : 0.08
% 3.65/2.03  Abstraction          : 0.02
% 3.65/2.03  MUC search           : 0.00
% 3.65/2.03  Cooper               : 0.00
% 3.65/2.03  Total                : 0.91
% 3.65/2.03  Index Insertion      : 0.00
% 3.65/2.03  Index Deletion       : 0.00
% 3.65/2.03  Index Matching       : 0.00
% 3.65/2.03  BG Taut test         : 0.00
%------------------------------------------------------------------------------