TSTP Solution File: SET632+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET632+3 : TPTP v8.2.0. Released v2.2.0.
% 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 : n002.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 03:12:34 EDT 2024

% Result   : Theorem 0.73s 0.88s
% Output   : Refutation 0.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   62 (  11 unt;   0 def)
%            Number of atoms       :  184 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  199 (  77   ~;  67   |;  41   &)
%                                         (   7 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  111 (  95   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f232,plain,
    $false,
    inference(avatar_sat_refutation,[],[f155,f165,f231]) ).

fof(f231,plain,
    ~ spl5_7,
    inference(avatar_contradiction_clause,[],[f224]) ).

fof(f224,plain,
    ( $false
    | ~ spl5_7 ),
    inference(resolution,[],[f220,f48]) ).

fof(f48,plain,
    ~ intersect(sK3,sK4),
    inference(resolution,[],[f36,f44]) ).

fof(f44,plain,
    disjoint(sK3,sK4),
    inference(cnf_transformation,[],[f28]) ).

fof(f28,plain,
    ( empty_set != sK2
    & disjoint(sK3,sK4)
    & subset(sK2,sK4)
    & subset(sK2,sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4])],[f16,f27]) ).

fof(f27,plain,
    ( ? [X0,X1,X2] :
        ( empty_set != X0
        & disjoint(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
   => ( empty_set != sK2
      & disjoint(sK3,sK4)
      & subset(sK2,sK4)
      & subset(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f16,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & disjoint(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(flattening,[],[f15]) ).

fof(f15,plain,
    ? [X0,X1,X2] :
      ( empty_set != X0
      & disjoint(X1,X2)
      & subset(X0,X2)
      & subset(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ( disjoint(X1,X2)
          & subset(X0,X2)
          & subset(X0,X1) )
       => empty_set = X0 ),
    inference(negated_conjecture,[],[f9]) ).

fof(f9,conjecture,
    ! [X0,X1,X2] :
      ( ( disjoint(X1,X2)
        & subset(X0,X2)
        & subset(X0,X1) )
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th114) ).

fof(f36,plain,
    ! [X0,X1] :
      ( ~ disjoint(X0,X1)
      | ~ intersect(X0,X1) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ! [X0,X1] :
      ( ~ intersect(X0,X1)
      | ~ disjoint(X0,X1) ),
    inference(ennf_transformation,[],[f11]) ).

fof(f11,plain,
    ! [X0,X1] :
      ( disjoint(X0,X1)
     => ~ intersect(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( disjoint(X0,X1)
    <=> ~ intersect(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjoint_defn) ).

fof(f220,plain,
    ( intersect(sK3,sK4)
    | ~ spl5_7 ),
    inference(resolution,[],[f172,f42]) ).

fof(f42,plain,
    subset(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

fof(f172,plain,
    ( ! [X0] :
        ( ~ subset(sK2,X0)
        | intersect(X0,sK4) )
    | ~ spl5_7 ),
    inference(resolution,[],[f154,f115]) ).

fof(f115,plain,
    ! [X2,X0,X1] :
      ( ~ intersect(X1,X2)
      | intersect(X0,X1)
      | ~ subset(X2,X0) ),
    inference(duplicate_literal_removal,[],[f112]) ).

fof(f112,plain,
    ! [X2,X0,X1] :
      ( intersect(X0,X1)
      | ~ intersect(X1,X2)
      | ~ subset(X2,X0)
      | ~ intersect(X1,X2) ),
    inference(resolution,[],[f86,f56]) ).

fof(f56,plain,
    ! [X2,X0,X1] :
      ( member(sK1(X0,X1),X2)
      | ~ subset(X1,X2)
      | ~ intersect(X0,X1) ),
    inference(resolution,[],[f29,f33]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X1)
      | ~ intersect(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ( member(sK1(X0,X1),X1)
          & member(sK1(X0,X1),X0) )
        | ~ intersect(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f22,f23]) ).

fof(f23,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( member(X3,X1)
          & member(X3,X0) )
     => ( member(sK1(X0,X1),X1)
        & member(sK1(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X3] :
            ( member(X3,X1)
            & member(X3,X0) )
        | ~ intersect(X0,X1) ) ),
    inference(rectify,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ( intersect(X0,X1)
        | ! [X2] :
            ( ~ member(X2,X1)
            | ~ member(X2,X0) ) )
      & ( ? [X2] :
            ( member(X2,X1)
            & member(X2,X0) )
        | ~ intersect(X0,X1) ) ),
    inference(nnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( intersect(X0,X1)
    <=> ? [X2] :
          ( member(X2,X1)
          & member(X2,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersect_defn) ).

fof(f29,plain,
    ! [X3,X0,X1] :
      ( ~ member(X3,X0)
      | member(X3,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f20,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ( ~ member(sK0(X0,X1),X1)
          & member(sK0(X0,X1),X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f18,f19]) ).

fof(f19,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ member(X2,X1)
          & member(X2,X0) )
     => ( ~ member(sK0(X0,X1),X1)
        & member(sK0(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f18,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X3] :
            ( member(X3,X1)
            | ~ member(X3,X0) )
        | ~ subset(X0,X1) ) ),
    inference(rectify,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( subset(X0,X1)
        | ? [X2] :
            ( ~ member(X2,X1)
            & member(X2,X0) ) )
      & ( ! [X2] :
            ( member(X2,X1)
            | ~ member(X2,X0) )
        | ~ subset(X0,X1) ) ),
    inference(nnf_transformation,[],[f12]) ).

fof(f12,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X1)
          | ~ member(X2,X0) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( subset(X0,X1)
    <=> ! [X2] :
          ( member(X2,X0)
         => member(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).

fof(f86,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK1(X1,X2),X0)
      | intersect(X0,X1)
      | ~ intersect(X1,X2) ),
    inference(resolution,[],[f34,f32]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( member(sK1(X0,X1),X0)
      | ~ intersect(X0,X1) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,X1)
      | intersect(X0,X1)
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f24]) ).

fof(f154,plain,
    ( intersect(sK4,sK2)
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f152]) ).

fof(f152,plain,
    ( spl5_7
  <=> intersect(sK4,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

fof(f165,plain,
    ~ spl5_5,
    inference(avatar_contradiction_clause,[],[f164]) ).

fof(f164,plain,
    ( $false
    | ~ spl5_5 ),
    inference(trivial_inequality_removal,[],[f157]) ).

fof(f157,plain,
    ( sK2 != sK2
    | ~ spl5_5 ),
    inference(superposition,[],[f45,f145]) ).

fof(f145,plain,
    ( empty_set = sK2
    | ~ spl5_5 ),
    inference(avatar_component_clause,[],[f143]) ).

fof(f143,plain,
    ( spl5_5
  <=> empty_set = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

fof(f45,plain,
    empty_set != sK2,
    inference(cnf_transformation,[],[f28]) ).

fof(f155,plain,
    ( spl5_5
    | spl5_7 ),
    inference(avatar_split_clause,[],[f136,f152,f143]) ).

fof(f136,plain,
    ( intersect(sK4,sK2)
    | empty_set = sK2 ),
    inference(resolution,[],[f121,f43]) ).

fof(f43,plain,
    subset(sK2,sK4),
    inference(cnf_transformation,[],[f28]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | intersect(X0,X1)
      | empty_set = X1 ),
    inference(resolution,[],[f103,f60]) ).

fof(f60,plain,
    ! [X0] :
      ( ~ subset(X0,empty_set)
      | empty_set = X0 ),
    inference(resolution,[],[f39,f49]) ).

fof(f49,plain,
    ! [X0] : subset(empty_set,X0),
    inference(resolution,[],[f30,f35]) ).

fof(f35,plain,
    ! [X0] : ~ member(X0,empty_set),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ member(X0,empty_set),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',empty_set_defn) ).

fof(f30,plain,
    ! [X0,X1] :
      ( member(sK0(X0,X1),X0)
      | subset(X0,X1) ),
    inference(cnf_transformation,[],[f20]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ subset(X1,X0)
      | X0 = X1
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f26]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(flattening,[],[f25]) ).

fof(f25,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ~ subset(X1,X0)
        | ~ subset(X0,X1) )
      & ( ( subset(X1,X0)
          & subset(X0,X1) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ( subset(X1,X0)
        & subset(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( subset(X1,X2)
      | intersect(X0,X1)
      | ~ subset(X1,X0) ),
    inference(duplicate_literal_removal,[],[f102]) ).

fof(f102,plain,
    ! [X2,X0,X1] :
      ( intersect(X0,X1)
      | subset(X1,X2)
      | ~ subset(X1,X0)
      | subset(X1,X2) ),
    inference(resolution,[],[f85,f54]) ).

fof(f54,plain,
    ! [X2,X0,X1] :
      ( member(sK0(X0,X1),X2)
      | ~ subset(X0,X2)
      | subset(X0,X1) ),
    inference(resolution,[],[f29,f30]) ).

fof(f85,plain,
    ! [X2,X0,X1] :
      ( ~ member(sK0(X1,X2),X0)
      | intersect(X0,X1)
      | subset(X1,X2) ),
    inference(resolution,[],[f34,f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SET632+3 : TPTP v8.2.0. Released v2.2.0.
% 0.07/0.14  % 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
% 0.15/0.36  % Computer : n002.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Mon May 20 12:21:38 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.36  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
% 0.71/0.87  % (29513)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2994ds/78Mi)
% 0.71/0.87  % (29511)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 (2994ds/34Mi)
% 0.71/0.87  % (29514)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2994ds/33Mi)
% 0.71/0.87  % (29512)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2994ds/51Mi)
% 0.71/0.87  % (29515)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 (2994ds/34Mi)
% 0.71/0.87  % (29516)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2994ds/45Mi)
% 0.71/0.87  % (29517)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 (2994ds/83Mi)
% 0.73/0.87  % (29515)Refutation not found, incomplete strategy% (29515)------------------------------
% 0.73/0.87  % (29515)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.73/0.87  % (29515)Termination reason: Refutation not found, incomplete strategy
% 0.73/0.87  
% 0.73/0.87  % (29515)Memory used [KB]: 971
% 0.73/0.87  % (29515)Time elapsed: 0.003 s
% 0.73/0.87  % (29515)Instructions burned: 2 (million)
% 0.73/0.87  % (29515)------------------------------
% 0.73/0.87  % (29515)------------------------------
% 0.73/0.87  % (29518)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 (2994ds/56Mi)
% 0.73/0.88  % (29512)First to succeed.
% 0.73/0.88  % (29512)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-29510"
% 0.73/0.88  % (29519)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2994ds/55Mi)
% 0.73/0.88  % (29512)Refutation found. Thanks to Tanya!
% 0.73/0.88  % SZS status Theorem for theBenchmark
% 0.73/0.88  % SZS output start Proof for theBenchmark
% See solution above
% 0.73/0.88  % (29512)------------------------------
% 0.73/0.88  % (29512)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.73/0.88  % (29512)Termination reason: Refutation
% 0.73/0.88  
% 0.73/0.88  % (29512)Memory used [KB]: 1085
% 0.73/0.88  % (29512)Time elapsed: 0.006 s
% 0.73/0.88  % (29512)Instructions burned: 8 (million)
% 0.73/0.88  % (29510)Success in time 0.507 s
% 0.73/0.88  % Vampire---4.8 exiting
%------------------------------------------------------------------------------