TSTP Solution File: SET914+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET914+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 : n026.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 10:57:19 EDT 2023

% Result   : Theorem 3.81s 1.99s
% Output   : CNFRefutation 3.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   21
% Syntax   : Number of formulae    :   32 (   7 unt;  16 typ;   0 def)
%            Number of atoms       :   31 (   8 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   27 (  12   ~;   7   |;   2   &)
%                                         (   6 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  10   >;  12   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   13 (  13 usr;   6 con; 0-3 aty)
%            Number of variables   :   25 (;  25   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > disjoint > empty > unordered_pair > set_intersection2 > #nlpp > empty_set > #skF_1 > #skF_4 > #skF_7 > #skF_10 > #skF_6 > #skF_5 > #skF_2 > #skF_9 > #skF_8 > #skF_3

%Foreground sorts:

%Background operators:

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

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

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

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

tff('#skF_10',type,
    '#skF_10': $i ).

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

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

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

tff(set_intersection2,type,
    set_intersection2: ( $i * $i ) > $i ).

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

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

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

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

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

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

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

tff(f_81,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( disjoint(unordered_pair(A,B),C)
          & in(A,C) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_zfmisc_1) ).

tff(f_50,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_41,axiom,
    ! [A] :
      ( ( A = empty_set )
    <=> ! [B] : ~ in(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_xboole_0) ).

tff(f_63,axiom,
    ! [A,B] :
      ( disjoint(A,B)
    <=> ( set_intersection2(A,B) = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7_xboole_0) ).

tff(f_59,axiom,
    ! [A,B,C] :
      ( ( C = set_intersection2(A,B) )
    <=> ! [D] :
          ( in(D,C)
        <=> ( in(D,A)
            & in(D,B) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).

tff(c_62,plain,
    in('#skF_8','#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_16,plain,
    ! [D_16,B_12] : in(D_16,unordered_pair(D_16,B_12)),
    inference(cnfTransformation,[status(thm)],[f_50]) ).

tff(c_8,plain,
    ! [B_10] : ~ in(B_10,empty_set),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_64,plain,
    disjoint(unordered_pair('#skF_8','#skF_9'),'#skF_10'),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_187,plain,
    ! [A_44,B_45] :
      ( ( set_intersection2(A_44,B_45) = empty_set )
      | ~ disjoint(A_44,B_45) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_195,plain,
    set_intersection2(unordered_pair('#skF_8','#skF_9'),'#skF_10') = empty_set,
    inference(resolution,[status(thm)],[c_64,c_187]) ).

tff(c_400,plain,
    ! [D_71,A_72,B_73] :
      ( in(D_71,set_intersection2(A_72,B_73))
      | ~ in(D_71,B_73)
      | ~ in(D_71,A_72) ),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_422,plain,
    ! [D_71] :
      ( in(D_71,empty_set)
      | ~ in(D_71,'#skF_10')
      | ~ in(D_71,unordered_pair('#skF_8','#skF_9')) ),
    inference(superposition,[status(thm),theory(equality)],[c_195,c_400]) ).

tff(c_561,plain,
    ! [D_79] :
      ( ~ in(D_79,'#skF_10')
      | ~ in(D_79,unordered_pair('#skF_8','#skF_9')) ),
    inference(negUnitSimplification,[status(thm)],[c_8,c_422]) ).

tff(c_573,plain,
    ~ in('#skF_8','#skF_10'),
    inference(resolution,[status(thm)],[c_16,c_561]) ).

tff(c_583,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_62,c_573]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET914+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13  % 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
% 0.12/0.34  % Computer : n026.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu Aug  3 16:54:47 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 3.81/1.99  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.81/1.99  
% 3.81/1.99  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.81/2.01  
% 3.81/2.01  Inference rules
% 3.81/2.01  ----------------------
% 3.81/2.01  #Ref     : 0
% 3.81/2.01  #Sup     : 128
% 3.81/2.01  #Fact    : 0
% 3.81/2.01  #Define  : 0
% 3.81/2.01  #Split   : 0
% 3.81/2.01  #Chain   : 0
% 3.81/2.01  #Close   : 0
% 3.81/2.01  
% 3.81/2.01  Ordering : KBO
% 3.81/2.01  
% 3.81/2.01  Simplification rules
% 3.81/2.01  ----------------------
% 3.81/2.01  #Subsume      : 25
% 3.81/2.01  #Demod        : 28
% 3.81/2.01  #Tautology    : 70
% 3.81/2.01  #SimpNegUnit  : 7
% 3.81/2.01  #BackRed      : 0
% 3.81/2.01  
% 3.81/2.01  #Partial instantiations: 0
% 3.81/2.01  #Strategies tried      : 1
% 3.81/2.01  
% 3.81/2.01  Timing (in seconds)
% 3.81/2.01  ----------------------
% 3.81/2.02  Preprocessing        : 0.52
% 3.81/2.02  Parsing              : 0.26
% 3.81/2.02  CNF conversion       : 0.04
% 3.81/2.02  Main loop            : 0.42
% 3.81/2.02  Inferencing          : 0.14
% 3.81/2.02  Reduction            : 0.15
% 3.81/2.02  Demodulation         : 0.11
% 3.81/2.02  BG Simplification    : 0.03
% 3.81/2.02  Subsumption          : 0.09
% 3.81/2.02  Abstraction          : 0.02
% 3.81/2.02  MUC search           : 0.00
% 3.81/2.02  Cooper               : 0.00
% 3.81/2.02  Total                : 0.99
% 3.81/2.02  Index Insertion      : 0.00
% 3.81/2.02  Index Deletion       : 0.00
% 3.81/2.02  Index Matching       : 0.00
% 3.81/2.02  BG Taut test         : 0.00
%------------------------------------------------------------------------------