TSTP Solution File: SET654+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET654+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 : n010.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 10:56:48 EDT 2023

% Result   : Theorem 4.20s 2.21s
% Output   : CNFRefutation 4.81s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   33
% Syntax   : Number of formulae    :   49 (   8 unt;  28 typ;   0 def)
%            Number of atoms       :   62 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   65 (  24   ~;  22   |;   2   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   33 (  22   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   23 (  23 usr;   6 con; 0-2 aty)
%            Number of variables   :   40 (;  40   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ subset > member > ilf_type > relation_like > empty > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > binary_relation_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(range_of,type,
    range_of: $i > $i ).

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

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

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

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

tff(binary_relation_type,type,
    binary_relation_type: $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_269,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(D,B))
                   => ( subset(B,C)
                     => ilf_type(E,relation_type(D,C)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_relset_1_16) ).

tff(f_252,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p22) ).

tff(f_54,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,relation_type(B,C))
             => ( subset(domain_of(D),B)
                & subset(range_of(D),C) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p2) ).

tff(f_41,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,set_type)
             => ( ( subset(B,C)
                  & subset(C,D) )
               => subset(B,D) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p1) ).

tff(f_70,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(D,B))
                 => ( subset(range_of(E),C)
                   => ilf_type(E,relation_type(D,C)) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',p3) ).

tff(c_82,plain,
    ~ ilf_type('#skF_13',relation_type('#skF_12','#skF_11')),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_86,plain,
    ilf_type('#skF_13',relation_type('#skF_12','#skF_10')),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_80,plain,
    ! [B_125] : ilf_type(B_125,set_type),
    inference(cnfTransformation,[status(thm)],[f_252]) ).

tff(c_4,plain,
    ! [D_14,C_12,B_8] :
      ( subset(range_of(D_14),C_12)
      | ~ ilf_type(D_14,relation_type(B_8,C_12))
      | ~ ilf_type(C_12,set_type)
      | ~ ilf_type(B_8,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_54]) ).

tff(c_240,plain,
    ! [D_172,C_173,B_174] :
      ( subset(range_of(D_172),C_173)
      | ~ ilf_type(D_172,relation_type(B_174,C_173)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_4]) ).

tff(c_246,plain,
    subset(range_of('#skF_13'),'#skF_10'),
    inference(resolution,[status(thm)],[c_86,c_240]) ).

tff(c_84,plain,
    subset('#skF_10','#skF_11'),
    inference(cnfTransformation,[status(thm)],[f_269]) ).

tff(c_2,plain,
    ! [B_1,D_7,C_5] :
      ( subset(B_1,D_7)
      | ~ subset(C_5,D_7)
      | ~ subset(B_1,C_5)
      | ~ ilf_type(D_7,set_type)
      | ~ ilf_type(C_5,set_type)
      | ~ ilf_type(B_1,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_41]) ).

tff(c_211,plain,
    ! [B_163,D_164,C_165] :
      ( subset(B_163,D_164)
      | ~ subset(C_165,D_164)
      | ~ subset(B_163,C_165) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_80,c_2]) ).

tff(c_220,plain,
    ! [B_163] :
      ( subset(B_163,'#skF_11')
      | ~ subset(B_163,'#skF_10') ),
    inference(resolution,[status(thm)],[c_84,c_211]) ).

tff(c_8,plain,
    ! [E_29,D_27,C_23,B_15] :
      ( ilf_type(E_29,relation_type(D_27,C_23))
      | ~ subset(range_of(E_29),C_23)
      | ~ ilf_type(E_29,relation_type(D_27,B_15))
      | ~ ilf_type(D_27,set_type)
      | ~ ilf_type(C_23,set_type)
      | ~ ilf_type(B_15,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_70]) ).

tff(c_1216,plain,
    ! [E_292,D_293,C_294,B_295] :
      ( ilf_type(E_292,relation_type(D_293,C_294))
      | ~ subset(range_of(E_292),C_294)
      | ~ ilf_type(E_292,relation_type(D_293,B_295)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_80,c_80,c_80,c_8]) ).

tff(c_1383,plain,
    ! [E_311,D_312,B_313] :
      ( ilf_type(E_311,relation_type(D_312,'#skF_11'))
      | ~ ilf_type(E_311,relation_type(D_312,B_313))
      | ~ subset(range_of(E_311),'#skF_10') ),
    inference(resolution,[status(thm)],[c_220,c_1216]) ).

tff(c_1391,plain,
    ( ilf_type('#skF_13',relation_type('#skF_12','#skF_11'))
    | ~ subset(range_of('#skF_13'),'#skF_10') ),
    inference(resolution,[status(thm)],[c_86,c_1383]) ).

tff(c_1397,plain,
    ilf_type('#skF_13',relation_type('#skF_12','#skF_11')),
    inference(demodulation,[status(thm),theory(equality)],[c_246,c_1391]) ).

tff(c_1399,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_82,c_1397]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET654+3 : TPTP v8.1.2. Released v2.2.0.
% 0.14/0.14  % 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 : n010.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
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Thu Aug  3 15:56:14 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.20/2.21  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.20/2.21  
% 4.20/2.21  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.81/2.24  
% 4.81/2.24  Inference rules
% 4.81/2.24  ----------------------
% 4.81/2.24  #Ref     : 0
% 4.81/2.24  #Sup     : 282
% 4.81/2.24  #Fact    : 0
% 4.81/2.24  #Define  : 0
% 4.81/2.24  #Split   : 5
% 4.81/2.24  #Chain   : 0
% 4.81/2.24  #Close   : 0
% 4.81/2.24  
% 4.81/2.24  Ordering : KBO
% 4.81/2.24  
% 4.81/2.24  Simplification rules
% 4.81/2.24  ----------------------
% 4.81/2.24  #Subsume      : 99
% 4.81/2.24  #Demod        : 114
% 4.81/2.24  #Tautology    : 49
% 4.81/2.24  #SimpNegUnit  : 11
% 4.81/2.24  #BackRed      : 5
% 4.81/2.24  
% 4.81/2.24  #Partial instantiations: 0
% 4.81/2.24  #Strategies tried      : 1
% 4.81/2.24  
% 4.81/2.24  Timing (in seconds)
% 4.81/2.24  ----------------------
% 4.81/2.24  Preprocessing        : 0.58
% 4.81/2.25  Parsing              : 0.31
% 4.81/2.25  CNF conversion       : 0.05
% 4.81/2.25  Main loop            : 0.60
% 4.81/2.25  Inferencing          : 0.23
% 4.81/2.25  Reduction            : 0.18
% 4.81/2.25  Demodulation         : 0.13
% 4.81/2.25  BG Simplification    : 0.03
% 4.81/2.25  Subsumption          : 0.12
% 4.81/2.25  Abstraction          : 0.02
% 4.81/2.25  MUC search           : 0.00
% 4.81/2.25  Cooper               : 0.00
% 4.81/2.25  Total                : 1.23
% 4.81/2.25  Index Insertion      : 0.00
% 4.81/2.25  Index Deletion       : 0.00
% 4.81/2.25  Index Matching       : 0.00
% 4.81/2.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------