TSTP Solution File: SET642+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 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 : n012.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 10:56:47 EDT 2023

% Result   : Theorem 4.39s 2.02s
% Output   : CNFRefutation 4.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   29
% Syntax   : Number of formulae    :   41 (   7 unt;  25 typ;   0 def)
%            Number of atoms       :   44 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   45 (  17   ~;  14   |;   0   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   31 (  20   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   20 (  20 usr;   5 con; 0-2 aty)
%            Number of variables   :   31 (;  31   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > power_set > member_type > set_type > #skF_9 > #skF_5 > #skF_11 > #skF_10 > #skF_13 > #skF_8 > #skF_3 > #skF_2 > #skF_7 > #skF_1 > #skF_6 > #skF_12 > #skF_4

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

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

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

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

tff('#skF_11',type,
    '#skF_11': $i ).

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

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

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

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

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

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

tff('#skF_13',type,
    '#skF_13': $i ).

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_12',type,
    '#skF_12': $i ).

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

tff(f_244,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,set_type)
           => ! [D] :
                ( ilf_type(D,set_type)
               => ! [E] :
                    ( ilf_type(E,relation_type(C,D))
                   => ( subset(B,E)
                     => ilf_type(B,relation_type(C,D)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_4) ).

tff(f_227,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p19) ).

tff(f_42,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ! [E] :
                  ( ilf_type(E,relation_type(C,D))
                 => ( subset(B,E)
                   => subset(B,cross_product(C,D)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

tff(f_55,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ( subset(B,cross_product(C,D))
               => ilf_type(B,relation_type(C,D)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

tff(c_78,plain,
    ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_76,plain,
    subset('#skF_10','#skF_13'),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_72,plain,
    ! [B_116] : ilf_type(B_116,set_type),
    inference(cnfTransformation,[status(thm)],[f_227]) ).

tff(c_2,plain,
    ! [B_1,C_9,D_13,E_15] :
      ( subset(B_1,cross_product(C_9,D_13))
      | ~ subset(B_1,E_15)
      | ~ ilf_type(E_15,relation_type(C_9,D_13))
      | ~ ilf_type(D_13,set_type)
      | ~ ilf_type(C_9,set_type)
      | ~ ilf_type(B_1,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_608,plain,
    ! [B_229,C_230,D_231,E_232] :
      ( subset(B_229,cross_product(C_230,D_231))
      | ~ subset(B_229,E_232)
      | ~ ilf_type(E_232,relation_type(C_230,D_231)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_72,c_72,c_2]) ).

tff(c_656,plain,
    ! [C_244,D_245] :
      ( subset('#skF_10',cross_product(C_244,D_245))
      | ~ ilf_type('#skF_13',relation_type(C_244,D_245)) ),
    inference(resolution,[status(thm)],[c_76,c_608]) ).

tff(c_4,plain,
    ! [B_16,C_20,D_22] :
      ( ilf_type(B_16,relation_type(C_20,D_22))
      | ~ subset(B_16,cross_product(C_20,D_22))
      | ~ ilf_type(D_22,set_type)
      | ~ ilf_type(C_20,set_type)
      | ~ ilf_type(B_16,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_155,plain,
    ! [B_16,C_20,D_22] :
      ( ilf_type(B_16,relation_type(C_20,D_22))
      | ~ subset(B_16,cross_product(C_20,D_22)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_72,c_72,c_72,c_4]) ).

tff(c_709,plain,
    ! [C_251,D_252] :
      ( ilf_type('#skF_10',relation_type(C_251,D_252))
      | ~ ilf_type('#skF_13',relation_type(C_251,D_252)) ),
    inference(resolution,[status(thm)],[c_656,c_155]) ).

tff(c_74,plain,
    ~ ilf_type('#skF_10',relation_type('#skF_11','#skF_12')),
    inference(cnfTransformation,[status(thm)],[f_244]) ).

tff(c_715,plain,
    ~ ilf_type('#skF_13',relation_type('#skF_11','#skF_12')),
    inference(resolution,[status(thm)],[c_709,c_74]) ).

tff(c_720,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_78,c_715]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SET642+3 : TPTP v8.1.2. Released v2.2.0.
% 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
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Thu Aug  3 16:23:37 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 4.39/2.02  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.39/2.03  
% 4.39/2.03  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.39/2.05  
% 4.39/2.05  Inference rules
% 4.39/2.05  ----------------------
% 4.39/2.05  #Ref     : 0
% 4.39/2.05  #Sup     : 116
% 4.39/2.05  #Fact    : 0
% 4.39/2.05  #Define  : 0
% 4.39/2.05  #Split   : 0
% 4.39/2.05  #Chain   : 0
% 4.39/2.05  #Close   : 0
% 4.39/2.05  
% 4.39/2.05  Ordering : KBO
% 4.39/2.05  
% 4.39/2.05  Simplification rules
% 4.39/2.05  ----------------------
% 4.39/2.05  #Subsume      : 19
% 4.39/2.05  #Demod        : 88
% 4.39/2.05  #Tautology    : 33
% 4.39/2.05  #SimpNegUnit  : 7
% 4.39/2.05  #BackRed      : 0
% 4.39/2.05  
% 4.39/2.05  #Partial instantiations: 0
% 4.39/2.05  #Strategies tried      : 1
% 4.39/2.05  
% 4.39/2.05  Timing (in seconds)
% 4.39/2.05  ----------------------
% 4.39/2.06  Preprocessing        : 0.56
% 4.39/2.06  Parsing              : 0.30
% 4.39/2.06  CNF conversion       : 0.05
% 4.39/2.06  Main loop            : 0.44
% 4.39/2.06  Inferencing          : 0.18
% 4.39/2.06  Reduction            : 0.13
% 4.39/2.06  Demodulation         : 0.09
% 4.39/2.06  BG Simplification    : 0.03
% 4.39/2.06  Subsumption          : 0.09
% 4.39/2.06  Abstraction          : 0.02
% 4.39/2.06  MUC search           : 0.00
% 4.39/2.06  Cooper               : 0.00
% 4.39/2.06  Total                : 1.05
% 4.39/2.06  Index Insertion      : 0.00
% 4.39/2.06  Index Deletion       : 0.00
% 4.39/2.06  Index Matching       : 0.00
% 4.39/2.06  BG Taut test         : 0.00
%------------------------------------------------------------------------------