TSTP Solution File: SET577+3 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SET577+3 : TPTP v8.1.2. 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/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n025.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 : Sun May  5 09:07:19 EDT 2024

% Result   : Theorem 0.51s 0.72s
% Output   : Refutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   56 (   3 unt;   0 def)
%            Number of atoms       :  193 (  19 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  219 (  82   ~;  91   |;  31   &)
%                                         (  11 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   74 (  59   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f82,plain,
    $false,
    inference(avatar_sat_refutation,[],[f50,f51,f62,f66,f69,f72,f77,f81]) ).

fof(f81,plain,
    ( spl5_1
    | ~ spl5_4 ),
    inference(avatar_contradiction_clause,[],[f80]) ).

fof(f80,plain,
    ( $false
    | spl5_1
    | ~ spl5_4 ),
    inference(subsumption_resolution,[],[f79,f44]) ).

fof(f44,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),sK0)
    | spl5_1 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl5_1
  <=> member(sK3(sK0,union(sK1,sK2)),sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

fof(f79,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK0)
    | ~ spl5_4 ),
    inference(resolution,[],[f61,f21]) ).

fof(f21,plain,
    ! [X3] :
      ( ~ member(X3,sK1)
      | member(X3,sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f13,plain,
    ( sK0 != union(sK1,sK2)
    & ! [X3] :
        ( ( member(X3,sK0)
          | ( ~ member(X3,sK2)
            & ~ member(X3,sK1) ) )
        & ( member(X3,sK2)
          | member(X3,sK1)
          | ~ member(X3,sK0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f11,f12]) ).

fof(f12,plain,
    ( ? [X0,X1,X2] :
        ( union(X1,X2) != X0
        & ! [X3] :
            ( ( member(X3,X0)
              | ( ~ member(X3,X2)
                & ~ member(X3,X1) ) )
            & ( member(X3,X2)
              | member(X3,X1)
              | ~ member(X3,X0) ) ) )
   => ( sK0 != union(sK1,sK2)
      & ! [X3] :
          ( ( member(X3,sK0)
            | ( ~ member(X3,sK2)
              & ~ member(X3,sK1) ) )
          & ( member(X3,sK2)
            | member(X3,sK1)
            | ~ member(X3,sK0) ) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f11,plain,
    ? [X0,X1,X2] :
      ( union(X1,X2) != X0
      & ! [X3] :
          ( ( member(X3,X0)
            | ( ~ member(X3,X2)
              & ~ member(X3,X1) ) )
          & ( member(X3,X2)
            | member(X3,X1)
            | ~ member(X3,X0) ) ) ),
    inference(flattening,[],[f10]) ).

fof(f10,plain,
    ? [X0,X1,X2] :
      ( union(X1,X2) != X0
      & ! [X3] :
          ( ( member(X3,X0)
            | ( ~ member(X3,X2)
              & ~ member(X3,X1) ) )
          & ( member(X3,X2)
            | member(X3,X1)
            | ~ member(X3,X0) ) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,plain,
    ? [X0,X1,X2] :
      ( union(X1,X2) != X0
      & ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X2)
            | member(X3,X1) ) ) ),
    inference(ennf_transformation,[],[f8]) ).

fof(f8,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ! [X3] :
            ( member(X3,X0)
          <=> ( member(X3,X2)
              | member(X3,X1) ) )
       => union(X1,X2) = X0 ),
    inference(negated_conjecture,[],[f7]) ).

fof(f7,conjecture,
    ! [X0,X1,X2] :
      ( ! [X3] :
          ( member(X3,X0)
        <=> ( member(X3,X2)
            | member(X3,X1) ) )
     => union(X1,X2) = X0 ),
    file('/export/starexec/sandbox/tmp/tmp.c4O1IVKcg5/Vampire---4.8_30579',prove_th18) ).

fof(f61,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK1)
    | ~ spl5_4 ),
    inference(avatar_component_clause,[],[f59]) ).

fof(f59,plain,
    ( spl5_4
  <=> member(sK3(sK0,union(sK1,sK2)),sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

fof(f77,plain,
    ( ~ spl5_1
    | spl5_4
    | spl5_3 ),
    inference(avatar_split_clause,[],[f73,f55,f59,f43]) ).

fof(f55,plain,
    ( spl5_3
  <=> member(sK3(sK0,union(sK1,sK2)),sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

fof(f73,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK1)
    | ~ member(sK3(sK0,union(sK1,sK2)),sK0)
    | spl5_3 ),
    inference(resolution,[],[f56,f20]) ).

fof(f20,plain,
    ! [X3] :
      ( member(X3,sK2)
      | member(X3,sK1)
      | ~ member(X3,sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f56,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),sK2)
    | spl5_3 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f72,plain,
    ( ~ spl5_3
    | spl5_2 ),
    inference(avatar_split_clause,[],[f68,f47,f55]) ).

fof(f47,plain,
    ( spl5_2
  <=> member(sK3(sK0,union(sK1,sK2)),union(sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

fof(f68,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),sK2)
    | spl5_2 ),
    inference(resolution,[],[f48,f31]) ).

fof(f31,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(flattening,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( ( member(X2,union(X0,X1))
        | ( ~ member(X2,X1)
          & ~ member(X2,X0) ) )
      & ( member(X2,X1)
        | member(X2,X0)
        | ~ member(X2,union(X0,X1)) ) ),
    inference(nnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( member(X2,union(X0,X1))
    <=> ( member(X2,X1)
        | member(X2,X0) ) ),
    file('/export/starexec/sandbox/tmp/tmp.c4O1IVKcg5/Vampire---4.8_30579',union_defn) ).

fof(f48,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),union(sK1,sK2))
    | spl5_2 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f69,plain,
    ( ~ spl5_4
    | spl5_2 ),
    inference(avatar_split_clause,[],[f67,f47,f59]) ).

fof(f67,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),sK1)
    | spl5_2 ),
    inference(resolution,[],[f48,f30]) ).

fof(f30,plain,
    ! [X2,X0,X1] :
      ( member(X2,union(X0,X1))
      | ~ member(X2,X0) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f66,plain,
    ( spl5_1
    | ~ spl5_3 ),
    inference(avatar_split_clause,[],[f63,f55,f43]) ).

fof(f63,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK0)
    | ~ spl5_3 ),
    inference(resolution,[],[f57,f22]) ).

fof(f22,plain,
    ! [X3] :
      ( ~ member(X3,sK2)
      | member(X3,sK0) ),
    inference(cnf_transformation,[],[f13]) ).

fof(f57,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK2)
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f62,plain,
    ( spl5_3
    | spl5_4
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f53,f47,f59,f55]) ).

fof(f53,plain,
    ( member(sK3(sK0,union(sK1,sK2)),sK1)
    | member(sK3(sK0,union(sK1,sK2)),sK2)
    | ~ spl5_2 ),
    inference(resolution,[],[f49,f29]) ).

fof(f29,plain,
    ! [X2,X0,X1] :
      ( ~ member(X2,union(X0,X1))
      | member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[],[f19]) ).

fof(f49,plain,
    ( member(sK3(sK0,union(sK1,sK2)),union(sK1,sK2))
    | ~ spl5_2 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f51,plain,
    ( ~ spl5_1
    | ~ spl5_2 ),
    inference(avatar_split_clause,[],[f41,f47,f43]) ).

fof(f41,plain,
    ( ~ member(sK3(sK0,union(sK1,sK2)),union(sK1,sK2))
    | ~ member(sK3(sK0,union(sK1,sK2)),sK0) ),
    inference(resolution,[],[f35,f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f27,f34]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
    <=> X0 = X1 ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ4_eqProxy])]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ member(sK3(X0,X1),X1)
      | ~ member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ( ( ~ member(sK3(X0,X1),X1)
            | ~ member(sK3(X0,X1),X0) )
          & ( member(sK3(X0,X1),X1)
            | member(sK3(X0,X1),X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f15,f16]) ).

fof(f16,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ( ~ member(X2,X1)
            | ~ member(X2,X0) )
          & ( member(X2,X1)
            | member(X2,X0) ) )
     => ( ( ~ member(sK3(X0,X1),X1)
          | ~ member(sK3(X0,X1),X0) )
        & ( member(sK3(X0,X1),X1)
          | member(sK3(X0,X1),X0) ) ) ),
    introduced(choice_axiom,[]) ).

fof(f15,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X3] :
            ( ( member(X3,X0)
              | ~ member(X3,X1) )
            & ( member(X3,X1)
              | ~ member(X3,X0) ) )
        | X0 != X1 ) ),
    inference(rectify,[],[f14]) ).

fof(f14,plain,
    ! [X0,X1] :
      ( ( X0 = X1
        | ? [X2] :
            ( ( ~ member(X2,X1)
              | ~ member(X2,X0) )
            & ( member(X2,X1)
              | member(X2,X0) ) ) )
      & ( ! [X2] :
            ( ( member(X2,X0)
              | ~ member(X2,X1) )
            & ( member(X2,X1)
              | ~ member(X2,X0) ) )
        | X0 != X1 ) ),
    inference(nnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X1] :
      ( X0 = X1
    <=> ! [X2] :
          ( member(X2,X0)
        <=> member(X2,X1) ) ),
    file('/export/starexec/sandbox/tmp/tmp.c4O1IVKcg5/Vampire---4.8_30579',equal_member_defn) ).

fof(f35,plain,
    ~ sQ4_eqProxy(sK0,union(sK1,sK2)),
    inference(equality_proxy_replacement,[],[f23,f34]) ).

fof(f23,plain,
    sK0 != union(sK1,sK2),
    inference(cnf_transformation,[],[f13]) ).

fof(f50,plain,
    ( spl5_1
    | spl5_2 ),
    inference(avatar_split_clause,[],[f40,f47,f43]) ).

fof(f40,plain,
    ( member(sK3(sK0,union(sK1,sK2)),union(sK1,sK2))
    | member(sK3(sK0,union(sK1,sK2)),sK0) ),
    inference(resolution,[],[f35,f37]) ).

fof(f37,plain,
    ! [X0,X1] :
      ( sQ4_eqProxy(X0,X1)
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(equality_proxy_replacement,[],[f26,f34]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( X0 = X1
      | member(sK3(X0,X1),X1)
      | member(sK3(X0,X1),X0) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.13/0.32  % Computer : n025.cluster.edu
% 0.13/0.32  % Model    : x86_64 x86_64
% 0.13/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32  % Memory   : 8042.1875MB
% 0.13/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32  % CPULimit   : 300
% 0.13/0.32  % WCLimit    : 300
% 0.13/0.32  % DateTime   : Fri May  3 16:28:52 EDT 2024
% 0.13/0.32  % CPUTime    : 
% 0.13/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.13/0.32  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/tmp/tmp.c4O1IVKcg5/Vampire---4.8_30579
% 0.51/0.71  % (30697)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.51/0.71  % (30690)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 Vampire---4 for (2996ds/34Mi)
% 0.51/0.71  % (30692)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.51/0.71  % (30693)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.51/0.71  % (30691)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 Vampire---4 for (2996ds/51Mi)
% 0.51/0.71  % (30694)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 Vampire---4 for (2996ds/34Mi)
% 0.51/0.71  % (30695)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.51/0.71  % (30697)First to succeed.
% 0.51/0.71  % (30696)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 Vampire---4 for (2996ds/83Mi)
% 0.51/0.72  % (30697)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30689"
% 0.51/0.72  % (30697)Refutation found. Thanks to Tanya!
% 0.51/0.72  % SZS status Theorem for Vampire---4
% 0.51/0.72  % SZS output start Proof for Vampire---4
% See solution above
% 0.51/0.72  % (30697)------------------------------
% 0.51/0.72  % (30697)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.51/0.72  % (30697)Termination reason: Refutation
% 0.51/0.72  
% 0.51/0.72  % (30697)Memory used [KB]: 993
% 0.51/0.72  % (30697)Time elapsed: 0.003 s
% 0.51/0.72  % (30697)Instructions burned: 5 (million)
% 0.51/0.72  % (30689)Success in time 0.387 s
% 0.51/0.72  % Vampire---4.8 exiting
%------------------------------------------------------------------------------