TSTP Solution File: SET097-7 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n005.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 May 21 03:08:49 EDT 2024

% Result   : Unsatisfiable 0.54s 0.75s
% Output   : Refutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   63 (   8 unt;   0 def)
%            Number of atoms       :  156 (  24 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  167 (  74   ~;  89   |;   0   &)
%                                         (   4 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-2 aty)
%            Number of variables   :   38 (  38   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f506,plain,
    $false,
    inference(avatar_sat_refutation,[],[f272,f299,f301,f313,f403,f505]) ).

fof(f505,plain,
    ( spl0_2
    | ~ spl0_1
    | ~ spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f503,f269,f263,f256,f260]) ).

fof(f260,plain,
    ( spl0_2
  <=> ! [X0] : ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f256,plain,
    ( spl0_1
  <=> member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),x) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f263,plain,
    ( spl0_3
  <=> member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f269,plain,
    ( spl0_4
  <=> subclass(x,singleton(not_subclass_element(x,null_class))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f503,plain,
    ( ! [X0] : ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),X0)
    | ~ spl0_1
    | ~ spl0_3
    | spl0_4 ),
    inference(resolution,[],[f490,f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( member(X0,universal_class)
      | ~ member(X0,X1) ),
    inference(resolution,[],[f1,f4]) ).

fof(f4,axiom,
    ! [X0] : subclass(X0,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',class_elements_are_sets) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subclass_members) ).

fof(f490,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
    | ~ spl0_1
    | ~ spl0_3
    | spl0_4 ),
    inference(subsumption_resolution,[],[f489,f441]) ).

fof(f441,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),singleton(not_subclass_element(x,null_class)))
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f440,f142]) ).

fof(f142,axiom,
    x != singleton(not_subclass_element(x,null_class)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_2) ).

fof(f440,plain,
    ( x = singleton(not_subclass_element(x,null_class))
    | ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),singleton(not_subclass_element(x,null_class)))
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f436,f404]) ).

fof(f404,plain,
    ( member(not_subclass_element(x,null_class),x)
    | ~ spl0_1
    | ~ spl0_3 ),
    inference(forward_demodulation,[],[f257,f382]) ).

fof(f382,plain,
    ( not_subclass_element(x,null_class) = not_subclass_element(singleton(not_subclass_element(x,null_class)),x)
    | ~ spl0_3 ),
    inference(resolution,[],[f265,f125]) ).

fof(f125,axiom,
    ! [X0,X1] :
      ( ~ member(X1,singleton(X0))
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',only_member_in_singleton) ).

fof(f265,plain,
    ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f263]) ).

fof(f257,plain,
    ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),x)
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f436,plain,
    ( ~ member(not_subclass_element(x,null_class),x)
    | x = singleton(not_subclass_element(x,null_class))
    | ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),singleton(not_subclass_element(x,null_class)))
    | ~ spl0_3 ),
    inference(superposition,[],[f101,f382]) ).

fof(f101,axiom,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X1,X0),X0)
      | X0 = X1
      | ~ member(not_subclass_element(X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality4) ).

fof(f489,plain,
    ( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),singleton(not_subclass_element(x,null_class)))
    | ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),universal_class)
    | spl0_4 ),
    inference(resolution,[],[f339,f25]) ).

fof(f25,axiom,
    ! [X0,X4] :
      ( member(X4,complement(X0))
      | member(X4,X0)
      | ~ member(X4,universal_class) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complement2) ).

fof(f339,plain,
    ( ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),complement(singleton(not_subclass_element(x,null_class))))
    | spl0_4 ),
    inference(resolution,[],[f327,f192]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ member(X0,x)
      | ~ member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
    inference(subsumption_resolution,[],[f190,f103]) ).

fof(f103,axiom,
    ! [X4] : ~ member(X4,null_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_of_null_class) ).

fof(f190,plain,
    ! [X0] :
      ( member(X0,null_class)
      | ~ member(X0,x)
      | ~ member(X0,complement(singleton(not_subclass_element(x,null_class)))) ),
    inference(superposition,[],[f23,f153]) ).

fof(f153,plain,
    null_class = intersection(complement(singleton(not_subclass_element(x,null_class))),x),
    inference(resolution,[],[f106,f141]) ).

fof(f141,axiom,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_1) ).

fof(f106,axiom,
    ! [X4] :
      ( member(not_subclass_element(X4,null_class),X4)
      | null_class = X4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',null_class_is_unique) ).

fof(f23,axiom,
    ! [X0,X1,X4] :
      ( member(X4,intersection(X0,X1))
      | ~ member(X4,X1)
      | ~ member(X4,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection3) ).

fof(f327,plain,
    ( member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),x)
    | spl0_4 ),
    inference(resolution,[],[f270,f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(not_subclass_element(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members1) ).

fof(f270,plain,
    ( ~ subclass(x,singleton(not_subclass_element(x,null_class)))
    | spl0_4 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f403,plain,
    ( spl0_1
    | ~ spl0_3 ),
    inference(avatar_contradiction_clause,[],[f402]) ).

fof(f402,plain,
    ( $false
    | spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f401,f143]) ).

fof(f143,axiom,
    null_class != x,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_number_of_elements_in_class_3) ).

fof(f401,plain,
    ( null_class = x
    | spl0_1
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f397,f103]) ).

fof(f397,plain,
    ( member(not_subclass_element(null_class,x),null_class)
    | null_class = x
    | spl0_1
    | ~ spl0_3 ),
    inference(resolution,[],[f385,f98]) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( member(not_subclass_element(X1,X0),X1)
      | member(not_subclass_element(X0,X1),X0)
      | X0 = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality1) ).

fof(f385,plain,
    ( ~ member(not_subclass_element(x,null_class),x)
    | spl0_1
    | ~ spl0_3 ),
    inference(backward_demodulation,[],[f258,f382]) ).

fof(f258,plain,
    ( ~ member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),x)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f313,plain,
    ~ spl0_4,
    inference(avatar_contradiction_clause,[],[f312]) ).

fof(f312,plain,
    ( $false
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f311,f142]) ).

fof(f311,plain,
    ( x = singleton(not_subclass_element(x,null_class))
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f308,f143]) ).

fof(f308,plain,
    ( null_class = x
    | x = singleton(not_subclass_element(x,null_class))
    | ~ spl0_4 ),
    inference(resolution,[],[f271,f140]) ).

fof(f140,axiom,
    ! [X0,X1] :
      ( ~ subclass(X0,singleton(X1))
      | null_class = X0
      | singleton(X1) = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_subsets_of_singleton) ).

fof(f271,plain,
    ( subclass(x,singleton(not_subclass_element(x,null_class)))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f269]) ).

fof(f301,plain,
    ( spl0_3
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f300,f260,f263]) ).

fof(f300,plain,
    ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class)))
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f291,f142]) ).

fof(f291,plain,
    ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class)))
    | x = singleton(not_subclass_element(x,null_class))
    | ~ spl0_2 ),
    inference(resolution,[],[f261,f98]) ).

fof(f261,plain,
    ( ! [X0] : ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),X0)
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f260]) ).

fof(f299,plain,
    ( ~ spl0_1
    | ~ spl0_2 ),
    inference(avatar_split_clause,[],[f298,f260,f256]) ).

fof(f298,plain,
    ( ~ member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),x)
    | ~ spl0_2 ),
    inference(subsumption_resolution,[],[f290,f142]) ).

fof(f290,plain,
    ( x = singleton(not_subclass_element(x,null_class))
    | ~ member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),x)
    | ~ spl0_2 ),
    inference(resolution,[],[f261,f100]) ).

fof(f100,axiom,
    ! [X0,X1] :
      ( member(not_subclass_element(X0,X1),X0)
      | X0 = X1
      | ~ member(not_subclass_element(X1,X0),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equality3) ).

fof(f272,plain,
    ( spl0_4
    | spl0_2
    | spl0_3 ),
    inference(avatar_split_clause,[],[f267,f263,f260,f269]) ).

fof(f267,plain,
    ! [X0] :
      ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class)))
      | ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),X0)
      | subclass(x,singleton(not_subclass_element(x,null_class))) ),
    inference(subsumption_resolution,[],[f251,f142]) ).

fof(f251,plain,
    ! [X0] :
      ( member(not_subclass_element(singleton(not_subclass_element(x,null_class)),x),singleton(not_subclass_element(x,null_class)))
      | x = singleton(not_subclass_element(x,null_class))
      | ~ member(not_subclass_element(x,singleton(not_subclass_element(x,null_class))),X0)
      | subclass(x,singleton(not_subclass_element(x,null_class))) ),
    inference(resolution,[],[f232,f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ~ member(not_subclass_element(X0,X1),X1)
      | subclass(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',not_subclass_members2) ).

fof(f232,plain,
    ! [X0,X1] :
      ( member(not_subclass_element(x,X0),singleton(not_subclass_element(x,null_class)))
      | member(not_subclass_element(X0,x),X0)
      | x = X0
      | ~ member(not_subclass_element(x,X0),X1) ),
    inference(resolution,[],[f211,f163]) ).

fof(f211,plain,
    ! [X0] :
      ( ~ member(not_subclass_element(x,X0),universal_class)
      | member(not_subclass_element(X0,x),X0)
      | member(not_subclass_element(x,X0),singleton(not_subclass_element(x,null_class)))
      | x = X0 ),
    inference(resolution,[],[f209,f25]) ).

fof(f209,plain,
    ! [X0] :
      ( ~ member(not_subclass_element(x,X0),complement(singleton(not_subclass_element(x,null_class))))
      | x = X0
      | member(not_subclass_element(X0,x),X0) ),
    inference(resolution,[],[f98,f192]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.13  % Problem    : SET097-7 : TPTP v8.2.0. Bugfixed v2.1.0.
% 0.06/0.14  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.35  % Computer : n005.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 12:49:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.13/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.54/0.73  % (23962)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.54/0.73  % (23963)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2996ds/33Mi)
% 0.54/0.73  % (23964)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.54/0.73  % (23965)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.54/0.73  % (23966)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.54/0.73  % (23967)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.54/0.73  % (23960)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.54/0.74  % (23962)First to succeed.
% 0.54/0.74  % (23962)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-23959"
% 0.54/0.75  % (23962)Refutation found. Thanks to Tanya!
% 0.54/0.75  % SZS status Unsatisfiable for theBenchmark
% 0.54/0.75  % SZS output start Proof for theBenchmark
% See solution above
% 0.54/0.75  % (23962)------------------------------
% 0.54/0.75  % (23962)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.54/0.75  % (23962)Termination reason: Refutation
% 0.54/0.75  
% 0.54/0.75  % (23962)Memory used [KB]: 1220
% 0.54/0.75  % (23962)Time elapsed: 0.012 s
% 0.54/0.75  % (23962)Instructions burned: 28 (million)
% 0.54/0.75  % (23959)Success in time 0.386 s
% 0.54/0.75  % Vampire---4.8 exiting
%------------------------------------------------------------------------------