TSTP Solution File: SET904+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET904+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/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 : n016.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 10:57:18 EDT 2023

% Result   : Theorem 2.82s 1.70s
% Output   : CNFRefutation 2.82s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   20 (   7 unt;   9 typ;   0 def)
%            Number of atoms       :   15 (   2 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    8 (   4   ~;   2   |;   0   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   12 (;  12   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > in > empty > set_union2 > #nlpp > singleton > #skF_2 > #skF_3 > #skF_1 > #skF_4

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

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

tff(set_union2,type,
    set_union2: ( $i * $i ) > $i ).

tff(f_59,negated_conjecture,
    ~ ! [A,B] :
        ( subset(set_union2(singleton(A),B),B)
       => in(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_zfmisc_1) ).

tff(f_40,axiom,
    ! [A,B] : ( set_union2(A,B) = set_union2(B,A) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).

tff(f_63,axiom,
    ! [A,B] :
      ( subset(set_union2(singleton(A),B),B)
     => in(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l21_zfmisc_1) ).

tff(c_18,plain,
    ~ in('#skF_3','#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_6,plain,
    ! [B_6,A_5] : ( set_union2(B_6,A_5) = set_union2(A_5,B_6) ),
    inference(cnfTransformation,[status(thm)],[f_40]) ).

tff(c_20,plain,
    subset(set_union2(singleton('#skF_3'),'#skF_4'),'#skF_4'),
    inference(cnfTransformation,[status(thm)],[f_59]) ).

tff(c_23,plain,
    subset(set_union2('#skF_4',singleton('#skF_3')),'#skF_4'),
    inference(demodulation,[status(thm),theory(equality)],[c_6,c_20]) ).

tff(c_88,plain,
    ! [A_25,B_26] :
      ( in(A_25,B_26)
      | ~ subset(set_union2(singleton(A_25),B_26),B_26) ),
    inference(cnfTransformation,[status(thm)],[f_63]) ).

tff(c_108,plain,
    ! [A_29,B_30] :
      ( in(A_29,B_30)
      | ~ subset(set_union2(B_30,singleton(A_29)),B_30) ),
    inference(superposition,[status(thm),theory(equality)],[c_6,c_88]) ).

tff(c_111,plain,
    in('#skF_3','#skF_4'),
    inference(resolution,[status(thm)],[c_23,c_108]) ).

tff(c_127,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_18,c_111]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET904+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/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
% 0.15/0.35  % Computer : n016.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 16:56:22 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 2.82/1.70  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.82/1.71  
% 2.82/1.71  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.82/1.74  
% 2.82/1.74  Inference rules
% 2.82/1.74  ----------------------
% 2.82/1.74  #Ref     : 0
% 2.82/1.74  #Sup     : 24
% 2.82/1.74  #Fact    : 0
% 2.82/1.74  #Define  : 0
% 2.82/1.74  #Split   : 0
% 2.82/1.74  #Chain   : 0
% 2.82/1.74  #Close   : 0
% 2.82/1.74  
% 2.82/1.74  Ordering : KBO
% 2.82/1.74  
% 2.82/1.74  Simplification rules
% 2.82/1.74  ----------------------
% 2.82/1.74  #Subsume      : 4
% 2.82/1.74  #Demod        : 2
% 2.82/1.74  #Tautology    : 12
% 2.82/1.74  #SimpNegUnit  : 1
% 2.82/1.74  #BackRed      : 0
% 2.82/1.74  
% 2.82/1.74  #Partial instantiations: 0
% 2.82/1.74  #Strategies tried      : 1
% 2.82/1.74  
% 2.82/1.74  Timing (in seconds)
% 2.82/1.74  ----------------------
% 2.82/1.74  Preprocessing        : 0.44
% 2.82/1.74  Parsing              : 0.24
% 2.82/1.74  CNF conversion       : 0.03
% 2.82/1.74  Main loop            : 0.22
% 2.82/1.74  Inferencing          : 0.08
% 2.82/1.74  Reduction            : 0.06
% 2.82/1.74  Demodulation         : 0.05
% 2.82/1.74  BG Simplification    : 0.01
% 2.82/1.74  Subsumption          : 0.05
% 2.82/1.74  Abstraction          : 0.01
% 2.82/1.74  MUC search           : 0.00
% 2.82/1.74  Cooper               : 0.00
% 2.82/1.74  Total                : 0.71
% 2.82/1.74  Index Insertion      : 0.00
% 2.82/1.74  Index Deletion       : 0.00
% 2.82/1.74  Index Matching       : 0.00
% 2.82/1.74  BG Taut test         : 0.00
%------------------------------------------------------------------------------