TSTP Solution File: SET881+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET881+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 : n001.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 10:57:16 EDT 2023

% Result   : Theorem 2.06s 1.58s
% Output   : CNFRefutation 2.06s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   23 (   8 unt;  12 typ;   0 def)
%            Number of atoms       :   16 (  10 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   10 (   5   ~;   2   |;   0   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   14 (   7   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-3 aty)
%            Number of variables   :   16 (;  16   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ in > empty > unordered_pair > set_difference > #nlpp > singleton > empty_set > #skF_1 > #skF_5 > #skF_6 > #skF_3 > #skF_2 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_42,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_47,axiom,
    ! [A,B] :
      ( ( set_difference(singleton(A),B) = empty_set )
    <=> in(A,B) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l36_zfmisc_1) ).

tff(f_33,axiom,
    ! [A,B] : ( unordered_pair(A,B) = unordered_pair(B,A) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).

tff(f_55,negated_conjecture,
    ~ ! [A,B] : ( set_difference(singleton(A),unordered_pair(A,B)) = empty_set ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_zfmisc_1) ).

tff(c_8,plain,
    ! [D_10,A_5] : in(D_10,unordered_pair(A_5,D_10)),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_109,plain,
    ! [A_27,B_28] :
      ( ( set_difference(singleton(A_27),B_28) = empty_set )
      | ~ in(A_27,B_28) ),
    inference(cnfTransformation,[status(thm)],[f_47]) ).

tff(c_4,plain,
    ! [B_4,A_3] : ( unordered_pair(B_4,A_3) = unordered_pair(A_3,B_4) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_34,plain,
    set_difference(singleton('#skF_5'),unordered_pair('#skF_5','#skF_6')) != empty_set,
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_35,plain,
    set_difference(singleton('#skF_5'),unordered_pair('#skF_6','#skF_5')) != empty_set,
    inference(demodulation,[status(thm),theory(equality)],[c_4,c_34]) ).

tff(c_118,plain,
    ~ in('#skF_5',unordered_pair('#skF_6','#skF_5')),
    inference(superposition,[status(thm),theory(equality)],[c_109,c_35]) ).

tff(c_127,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_8,c_118]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET881+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
% 0.14/0.35  % Computer : n001.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % 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 17:05:25 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 2.06/1.58  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.06/1.58  
% 2.06/1.58  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 2.06/1.60  
% 2.06/1.60  Inference rules
% 2.06/1.60  ----------------------
% 2.06/1.60  #Ref     : 0
% 2.06/1.60  #Sup     : 22
% 2.06/1.60  #Fact    : 0
% 2.06/1.60  #Define  : 0
% 2.06/1.60  #Split   : 0
% 2.06/1.60  #Chain   : 0
% 2.06/1.60  #Close   : 0
% 2.06/1.60  
% 2.06/1.60  Ordering : KBO
% 2.06/1.60  
% 2.06/1.60  Simplification rules
% 2.06/1.60  ----------------------
% 2.06/1.61  #Subsume      : 4
% 2.06/1.61  #Demod        : 6
% 2.06/1.61  #Tautology    : 14
% 2.06/1.61  #SimpNegUnit  : 0
% 2.06/1.61  #BackRed      : 0
% 2.06/1.61  
% 2.06/1.61  #Partial instantiations: 0
% 2.06/1.61  #Strategies tried      : 1
% 2.06/1.61  
% 2.06/1.61  Timing (in seconds)
% 2.06/1.61  ----------------------
% 2.55/1.61  Preprocessing        : 0.43
% 2.55/1.61  Parsing              : 0.23
% 2.55/1.61  CNF conversion       : 0.03
% 2.55/1.61  Main loop            : 0.19
% 2.55/1.61  Inferencing          : 0.06
% 2.55/1.61  Reduction            : 0.07
% 2.55/1.61  Demodulation         : 0.05
% 2.55/1.61  BG Simplification    : 0.01
% 2.55/1.61  Subsumption          : 0.05
% 2.55/1.61  Abstraction          : 0.01
% 2.55/1.61  MUC search           : 0.00
% 2.55/1.61  Cooper               : 0.00
% 2.55/1.61  Total                : 0.67
% 2.55/1.61  Index Insertion      : 0.00
% 2.55/1.61  Index Deletion       : 0.00
% 2.55/1.61  Index Matching       : 0.00
% 2.55/1.61  BG Taut test         : 0.00
%------------------------------------------------------------------------------