TSTP Solution File: SET664+3 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SET664+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/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 : n023.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 10:56:50 EDT 2023

% Result   : Theorem 4.23s 2.14s
% Output   : CNFRefutation 4.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   42
% Syntax   : Number of formulae    :   64 (   9 unt;  34 typ;   0 def)
%            Number of atoms       :   78 (  16 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   74 (  26   ~;  25   |;   3   &)
%                                         (   1 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   45 (  27   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   28 (  28 usr;   7 con; 0-3 aty)
%            Number of variables   :   45 (;  45   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ type > subset > member > ilf_type > relation_like > empty > range > domain > relation_type > ordered_pair > cross_product > #nlpp > subset_type > range_of > power_set > member_type > domain_of > set_type > empty_set > binary_relation_type > #skF_9 > #skF_7 > #skF_5 > #skF_11 > #skF_6 > #skF_15 > #skF_3 > #skF_14 > #skF_13 > #skF_10 > #skF_8 > #skF_4 > #skF_2 > #skF_12 > #skF_1

%Foreground sorts:

%Background operators:

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

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

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

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

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

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

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

tff('#skF_15',type,
    '#skF_15': $i ).

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

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

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

tff('#skF_14',type,
    '#skF_14': $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_10',type,
    '#skF_10': ( $i * $i ) > $i ).

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

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

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

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

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

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

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

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

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

tff('#skF_4',type,
    '#skF_4': $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_12',type,
    '#skF_12': $i > $i ).

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

tff(f_350,negated_conjecture,
    ~ ! [B] :
        ( ilf_type(B,set_type)
       => ! [C] :
            ( ilf_type(C,set_type)
           => ! [D] :
                ( ilf_type(D,relation_type(C,B))
               => ( ilf_type(D,relation_type(C,empty_set))
                 => ( D = empty_set ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_relset_1_27) ).

tff(f_336,axiom,
    ! [B] : ilf_type(B,set_type),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p33) ).

tff(f_55,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/sandbox/benchmark/theBenchmark.p',p3) ).

tff(f_33,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( subset(B,empty_set)
       => ( B = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p1) ).

tff(f_81,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ( ! [D] :
                ( ilf_type(D,subset_type(cross_product(B,C)))
               => ilf_type(D,relation_type(B,C)) )
            & ! [E] :
                ( ilf_type(E,relation_type(B,C))
               => ilf_type(E,subset_type(cross_product(B,C))) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p6) ).

tff(f_289,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ! [C] :
          ( ilf_type(C,set_type)
         => ! [D] :
              ( ilf_type(D,subset_type(cross_product(B,C)))
             => relation_like(D) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p28) ).

tff(f_143,axiom,
    ! [B] :
      ( ilf_type(B,set_type)
     => ( ilf_type(B,binary_relation_type)
      <=> ( relation_like(B)
          & ilf_type(B,set_type) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p13) ).

tff(f_42,axiom,
    ! [B] :
      ( ilf_type(B,binary_relation_type)
     => ( ( ( domain_of(B) = empty_set )
          | ( range_of(B) = empty_set ) )
       => ( B = empty_set ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2) ).

tff(c_128,plain,
    empty_set != '#skF_15',
    inference(cnfTransformation,[status(thm)],[f_350]) ).

tff(c_130,plain,
    ilf_type('#skF_15',relation_type('#skF_14',empty_set)),
    inference(cnfTransformation,[status(thm)],[f_350]) ).

tff(c_126,plain,
    ! [B_164] : ilf_type(B_164,set_type),
    inference(cnfTransformation,[status(thm)],[f_336]) ).

tff(c_8,plain,
    ! [D_9,C_7,B_3] :
      ( subset(range_of(D_9),C_7)
      | ~ ilf_type(D_9,relation_type(B_3,C_7))
      | ~ ilf_type(C_7,set_type)
      | ~ ilf_type(B_3,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_55]) ).

tff(c_428,plain,
    ! [D_219,C_220,B_221] :
      ( subset(range_of(D_219),C_220)
      | ~ ilf_type(D_219,relation_type(B_221,C_220)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_8]) ).

tff(c_436,plain,
    subset(range_of('#skF_15'),empty_set),
    inference(resolution,[status(thm)],[c_130,c_428]) ).

tff(c_2,plain,
    ! [B_1] :
      ( ( empty_set = B_1 )
      | ~ subset(B_1,empty_set)
      | ~ ilf_type(B_1,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_33]) ).

tff(c_228,plain,
    ! [B_1] :
      ( ( empty_set = B_1 )
      | ~ subset(B_1,empty_set) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_2]) ).

tff(c_441,plain,
    range_of('#skF_15') = empty_set,
    inference(resolution,[status(thm)],[c_436,c_228]) ).

tff(c_18,plain,
    ! [E_21,B_11,C_17] :
      ( ilf_type(E_21,subset_type(cross_product(B_11,C_17)))
      | ~ ilf_type(E_21,relation_type(B_11,C_17))
      | ~ ilf_type(C_17,set_type)
      | ~ ilf_type(B_11,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_81]) ).

tff(c_796,plain,
    ! [E_263,B_264,C_265] :
      ( ilf_type(E_263,subset_type(cross_product(B_264,C_265)))
      | ~ ilf_type(E_263,relation_type(B_264,C_265)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_18]) ).

tff(c_116,plain,
    ! [D_135,B_129,C_133] :
      ( relation_like(D_135)
      | ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133)))
      | ~ ilf_type(C_133,set_type)
      | ~ ilf_type(B_129,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_289]) ).

tff(c_148,plain,
    ! [D_135,B_129,C_133] :
      ( relation_like(D_135)
      | ~ ilf_type(D_135,subset_type(cross_product(B_129,C_133))) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_126,c_116]) ).

tff(c_810,plain,
    ! [E_268,B_269,C_270] :
      ( relation_like(E_268)
      | ~ ilf_type(E_268,relation_type(B_269,C_270)) ),
    inference(resolution,[status(thm)],[c_796,c_148]) ).

tff(c_821,plain,
    relation_like('#skF_15'),
    inference(resolution,[status(thm)],[c_130,c_810]) ).

tff(c_48,plain,
    ! [B_61] :
      ( ilf_type(B_61,binary_relation_type)
      | ~ relation_like(B_61)
      | ~ ilf_type(B_61,set_type) ),
    inference(cnfTransformation,[status(thm)],[f_143]) ).

tff(c_206,plain,
    ! [B_61] :
      ( ilf_type(B_61,binary_relation_type)
      | ~ relation_like(B_61) ),
    inference(demodulation,[status(thm),theory(equality)],[c_126,c_48]) ).

tff(c_317,plain,
    ! [B_193] :
      ( ( range_of(B_193) != empty_set )
      | ( empty_set = B_193 )
      | ~ ilf_type(B_193,binary_relation_type) ),
    inference(cnfTransformation,[status(thm)],[f_42]) ).

tff(c_324,plain,
    ! [B_61] :
      ( ( range_of(B_61) != empty_set )
      | ( empty_set = B_61 )
      | ~ relation_like(B_61) ),
    inference(resolution,[status(thm)],[c_206,c_317]) ).

tff(c_825,plain,
    ( ( range_of('#skF_15') != empty_set )
    | ( empty_set = '#skF_15' ) ),
    inference(resolution,[status(thm)],[c_821,c_324]) ).

tff(c_831,plain,
    empty_set = '#skF_15',
    inference(demodulation,[status(thm),theory(equality)],[c_441,c_825]) ).

tff(c_833,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_128,c_831]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SET664+3 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14  % 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
% 0.14/0.35  % Computer : n023.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 16:49:07 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 4.23/2.14  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.23/2.14  
% 4.23/2.14  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.89/2.17  
% 4.89/2.17  Inference rules
% 4.89/2.17  ----------------------
% 4.89/2.17  #Ref     : 0
% 4.89/2.17  #Sup     : 124
% 4.89/2.17  #Fact    : 2
% 4.89/2.17  #Define  : 0
% 4.89/2.17  #Split   : 2
% 4.89/2.17  #Chain   : 0
% 4.89/2.17  #Close   : 0
% 4.89/2.17  
% 4.89/2.17  Ordering : KBO
% 4.89/2.17  
% 4.89/2.17  Simplification rules
% 4.89/2.17  ----------------------
% 4.89/2.17  #Subsume      : 12
% 4.89/2.17  #Demod        : 105
% 4.89/2.17  #Tautology    : 55
% 4.89/2.17  #SimpNegUnit  : 6
% 4.89/2.17  #BackRed      : 1
% 4.89/2.17  
% 4.89/2.17  #Partial instantiations: 0
% 4.89/2.17  #Strategies tried      : 1
% 4.89/2.17  
% 4.89/2.17  Timing (in seconds)
% 4.89/2.17  ----------------------
% 4.89/2.17  Preprocessing        : 0.65
% 4.89/2.17  Parsing              : 0.33
% 4.89/2.17  CNF conversion       : 0.06
% 4.89/2.17  Main loop            : 0.47
% 4.89/2.17  Inferencing          : 0.16
% 4.89/2.17  Reduction            : 0.15
% 4.89/2.17  Demodulation         : 0.11
% 4.89/2.17  BG Simplification    : 0.04
% 4.89/2.17  Subsumption          : 0.08
% 4.89/2.17  Abstraction          : 0.02
% 4.89/2.17  MUC search           : 0.00
% 4.89/2.17  Cooper               : 0.00
% 4.89/2.17  Total                : 1.16
% 4.89/2.17  Index Insertion      : 0.00
% 4.89/2.17  Index Deletion       : 0.00
% 4.89/2.17  Index Matching       : 0.00
% 4.89/2.17  BG Taut test         : 0.00
%------------------------------------------------------------------------------