TSTP Solution File: SWC001+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% 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 : 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 04:35:29 EDT 2024

% Result   : Theorem 0.47s 0.64s
% Output   : Refutation 0.47s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   44 (   5 unt;   0 def)
%            Number of atoms       :  329 (  30 equ)
%            Maximal formula atoms :   36 (   7 avg)
%            Number of connectives :  418 ( 133   ~; 130   |; 131   &)
%                                         (   4 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   66 (  28   !;  38   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f300,plain,
    $false,
    inference(avatar_sat_refutation,[],[f263,f264,f269,f270,f285,f299]) ).

fof(f299,plain,
    ( ~ spl17_1
    | spl17_2
    | ~ spl17_4 ),
    inference(avatar_contradiction_clause,[],[f298]) ).

fof(f298,plain,
    ( $false
    | ~ spl17_1
    | spl17_2
    | ~ spl17_4 ),
    inference(subsumption_resolution,[],[f297,f268]) ).

fof(f268,plain,
    ( ssItem(sK4)
    | ~ spl17_4 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f266,plain,
    ( spl17_4
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).

fof(f297,plain,
    ( ~ ssItem(sK4)
    | ~ spl17_1
    | spl17_2 ),
    inference(subsumption_resolution,[],[f295,f258]) ).

fof(f258,plain,
    ( ~ memberP(sK2,sK4)
    | spl17_2 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f256,plain,
    ( spl17_2
  <=> memberP(sK2,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).

fof(f295,plain,
    ( memberP(sK2,sK4)
    | ~ ssItem(sK4)
    | ~ spl17_1 ),
    inference(resolution,[],[f165,f253]) ).

fof(f253,plain,
    ( memberP(sK3,sK4)
    | ~ spl17_1 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f252,plain,
    ( spl17_1
  <=> memberP(sK3,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).

fof(f165,plain,
    ! [X5] :
      ( ~ memberP(sK3,X5)
      | memberP(sK2,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f131,plain,
    ( ( ~ duplicatefreeP(sK0)
      | ( ( ~ memberP(sK0,sK4)
          | ~ memberP(sK1,sK4) )
        & ( memberP(sK0,sK4)
          | memberP(sK1,sK4) )
        & ssItem(sK4) ) )
    & ! [X5] :
        ( ( ( ~ memberP(sK3,X5)
            | memberP(sK2,X5) )
          & ( ~ memberP(sK2,X5)
            | memberP(sK3,X5) ) )
        | ~ ssItem(X5) )
    & duplicatefreeP(sK2)
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f100,f130,f129,f128,f127,f126]) ).

fof(f126,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ~ duplicatefreeP(X0)
                      | ? [X4] :
                          ( ( ~ memberP(X0,X4)
                            | ~ memberP(X1,X4) )
                          & ( memberP(X0,X4)
                            | memberP(X1,X4) )
                          & ssItem(X4) ) )
                    & ! [X5] :
                        ( ( ( ~ memberP(X3,X5)
                            | memberP(X2,X5) )
                          & ( ~ memberP(X2,X5)
                            | memberP(X3,X5) ) )
                        | ~ ssItem(X5) )
                    & duplicatefreeP(X2)
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(sK0)
                    | ? [X4] :
                        ( ( ~ memberP(sK0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(sK0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(X2)
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f127,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ~ duplicatefreeP(sK0)
                  | ? [X4] :
                      ( ( ~ memberP(sK0,X4)
                        | ~ memberP(X1,X4) )
                      & ( memberP(sK0,X4)
                        | memberP(X1,X4) )
                      & ssItem(X4) ) )
                & ! [X5] :
                    ( ( ( ~ memberP(X3,X5)
                        | memberP(X2,X5) )
                      & ( ~ memberP(X2,X5)
                        | memberP(X3,X5) ) )
                    | ~ ssItem(X5) )
                & duplicatefreeP(X2)
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ~ duplicatefreeP(sK0)
                | ? [X4] :
                    ( ( ~ memberP(sK0,X4)
                      | ~ memberP(sK1,X4) )
                    & ( memberP(sK0,X4)
                      | memberP(sK1,X4) )
                    & ssItem(X4) ) )
              & ! [X5] :
                  ( ( ( ~ memberP(X3,X5)
                      | memberP(X2,X5) )
                    & ( ~ memberP(X2,X5)
                      | memberP(X3,X5) ) )
                  | ~ ssItem(X5) )
              & duplicatefreeP(X2)
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ~ duplicatefreeP(sK0)
              | ? [X4] :
                  ( ( ~ memberP(sK0,X4)
                    | ~ memberP(sK1,X4) )
                  & ( memberP(sK0,X4)
                    | memberP(sK1,X4) )
                  & ssItem(X4) ) )
            & ! [X5] :
                ( ( ( ~ memberP(X3,X5)
                    | memberP(X2,X5) )
                  & ( ~ memberP(X2,X5)
                    | memberP(X3,X5) ) )
                | ~ ssItem(X5) )
            & duplicatefreeP(X2)
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ~ duplicatefreeP(sK0)
            | ? [X4] :
                ( ( ~ memberP(sK0,X4)
                  | ~ memberP(sK1,X4) )
                & ( memberP(sK0,X4)
                  | memberP(sK1,X4) )
                & ssItem(X4) ) )
          & ! [X5] :
              ( ( ( ~ memberP(X3,X5)
                  | memberP(sK2,X5) )
                & ( ~ memberP(sK2,X5)
                  | memberP(X3,X5) ) )
              | ~ ssItem(X5) )
          & duplicatefreeP(sK2)
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ? [X3] :
        ( ( ~ duplicatefreeP(sK0)
          | ? [X4] :
              ( ( ~ memberP(sK0,X4)
                | ~ memberP(sK1,X4) )
              & ( memberP(sK0,X4)
                | memberP(sK1,X4) )
              & ssItem(X4) ) )
        & ! [X5] :
            ( ( ( ~ memberP(X3,X5)
                | memberP(sK2,X5) )
              & ( ~ memberP(sK2,X5)
                | memberP(X3,X5) ) )
            | ~ ssItem(X5) )
        & duplicatefreeP(sK2)
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ( ~ duplicatefreeP(sK0)
        | ? [X4] :
            ( ( ~ memberP(sK0,X4)
              | ~ memberP(sK1,X4) )
            & ( memberP(sK0,X4)
              | memberP(sK1,X4) )
            & ssItem(X4) ) )
      & ! [X5] :
          ( ( ( ~ memberP(sK3,X5)
              | memberP(sK2,X5) )
            & ( ~ memberP(sK2,X5)
              | memberP(sK3,X5) ) )
          | ~ ssItem(X5) )
      & duplicatefreeP(sK2)
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X4] :
        ( ( ~ memberP(sK0,X4)
          | ~ memberP(sK1,X4) )
        & ( memberP(sK0,X4)
          | memberP(sK1,X4) )
        & ssItem(X4) )
   => ( ( ~ memberP(sK0,sK4)
        | ~ memberP(sK1,sK4) )
      & ( memberP(sK0,sK4)
        | memberP(sK1,sK4) )
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(X0)
                    | ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ~ duplicatefreeP(X0)
                    | ? [X4] :
                        ( ( ~ memberP(X0,X4)
                          | ~ memberP(X1,X4) )
                        & ( memberP(X0,X4)
                          | memberP(X1,X4) )
                        & ssItem(X4) ) )
                  & ! [X5] :
                      ( ( ( ~ memberP(X3,X5)
                          | memberP(X2,X5) )
                        & ( ~ memberP(X2,X5)
                          | memberP(X3,X5) ) )
                      | ~ ssItem(X5) )
                  & duplicatefreeP(X2)
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( duplicatefreeP(X0)
                        & ! [X4] :
                            ( ssItem(X4)
                           => ( ( memberP(X0,X4)
                                & memberP(X1,X4) )
                              | ( ~ memberP(X0,X4)
                                & ~ memberP(X1,X4) ) ) ) )
                      | ? [X5] :
                          ( ( ( memberP(X3,X5)
                              & ~ memberP(X2,X5) )
                            | ( memberP(X2,X5)
                              & ~ memberP(X3,X5) ) )
                          & ssItem(X5) )
                      | ~ duplicatefreeP(X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( duplicatefreeP(X0)
                        & ! [X5] :
                            ( ssItem(X5)
                           => ( ( memberP(X0,X5)
                                & memberP(X1,X5) )
                              | ( ~ memberP(X0,X5)
                                & ~ memberP(X1,X5) ) ) ) )
                      | ? [X4] :
                          ( ( ( memberP(X3,X4)
                              & ~ memberP(X2,X4) )
                            | ( memberP(X2,X4)
                              & ~ memberP(X3,X4) ) )
                          & ssItem(X4) )
                      | ~ duplicatefreeP(X2)
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ( duplicatefreeP(X0)
                      & ! [X5] :
                          ( ssItem(X5)
                         => ( ( memberP(X0,X5)
                              & memberP(X1,X5) )
                            | ( ~ memberP(X0,X5)
                              & ~ memberP(X1,X5) ) ) ) )
                    | ? [X4] :
                        ( ( ( memberP(X3,X4)
                            & ~ memberP(X2,X4) )
                          | ( memberP(X2,X4)
                            & ~ memberP(X3,X4) ) )
                        & ssItem(X4) )
                    | ~ duplicatefreeP(X2)
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(f285,plain,
    ( spl17_1
    | ~ spl17_2
    | ~ spl17_4 ),
    inference(avatar_contradiction_clause,[],[f284]) ).

fof(f284,plain,
    ( $false
    | spl17_1
    | ~ spl17_2
    | ~ spl17_4 ),
    inference(subsumption_resolution,[],[f283,f268]) ).

fof(f283,plain,
    ( ~ ssItem(sK4)
    | spl17_1
    | ~ spl17_2 ),
    inference(subsumption_resolution,[],[f278,f257]) ).

fof(f257,plain,
    ( memberP(sK2,sK4)
    | ~ spl17_2 ),
    inference(avatar_component_clause,[],[f256]) ).

fof(f278,plain,
    ( ~ memberP(sK2,sK4)
    | ~ ssItem(sK4)
    | spl17_1 ),
    inference(resolution,[],[f164,f254]) ).

fof(f254,plain,
    ( ~ memberP(sK3,sK4)
    | spl17_1 ),
    inference(avatar_component_clause,[],[f252]) ).

fof(f164,plain,
    ! [X5] :
      ( memberP(sK3,X5)
      | ~ memberP(sK2,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f270,plain,
    spl17_3,
    inference(avatar_split_clause,[],[f163,f260]) ).

fof(f260,plain,
    ( spl17_3
  <=> duplicatefreeP(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).

fof(f163,plain,
    duplicatefreeP(sK2),
    inference(cnf_transformation,[],[f131]) ).

fof(f269,plain,
    ( spl17_4
    | ~ spl17_3 ),
    inference(avatar_split_clause,[],[f215,f260,f266]) ).

fof(f215,plain,
    ( ~ duplicatefreeP(sK2)
    | ssItem(sK4) ),
    inference(definition_unfolding,[],[f166,f162]) ).

fof(f162,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f131]) ).

fof(f166,plain,
    ( ~ duplicatefreeP(sK0)
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f264,plain,
    ( spl17_1
    | spl17_2
    | ~ spl17_3 ),
    inference(avatar_split_clause,[],[f214,f260,f256,f252]) ).

fof(f214,plain,
    ( ~ duplicatefreeP(sK2)
    | memberP(sK2,sK4)
    | memberP(sK3,sK4) ),
    inference(definition_unfolding,[],[f167,f162,f162,f161]) ).

fof(f161,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f131]) ).

fof(f167,plain,
    ( ~ duplicatefreeP(sK0)
    | memberP(sK0,sK4)
    | memberP(sK1,sK4) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f263,plain,
    ( ~ spl17_1
    | ~ spl17_2
    | ~ spl17_3 ),
    inference(avatar_split_clause,[],[f213,f260,f256,f252]) ).

fof(f213,plain,
    ( ~ duplicatefreeP(sK2)
    | ~ memberP(sK2,sK4)
    | ~ memberP(sK3,sK4) ),
    inference(definition_unfolding,[],[f168,f162,f162,f161]) ).

fof(f168,plain,
    ( ~ duplicatefreeP(sK0)
    | ~ memberP(sK0,sK4)
    | ~ memberP(sK1,sK4) ),
    inference(cnf_transformation,[],[f131]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10  % Problem    : SWC001+1 : TPTP v8.2.0. Released v2.4.0.
% 0.08/0.11  % 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
% 0.11/0.32  % Computer : n005.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sun May 19 03:13:23 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.11/0.32  This is a FOF_THM_RFO_SEQ problem
% 0.11/0.32  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/benchmark/theBenchmark.p
% 0.47/0.64  % (29384)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)
% 0.47/0.64  % (29379)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.47/0.64  % (29377)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)
% 0.47/0.64  % (29378)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 (2996ds/51Mi)
% 0.47/0.64  % (29381)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)
% 0.47/0.64  % (29382)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)
% 0.47/0.64  % (29380)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)
% 0.47/0.64  % (29383)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)
% 0.47/0.64  % (29384)First to succeed.
% 0.47/0.64  % (29384)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-29376"
% 0.47/0.64  % (29384)Refutation found. Thanks to Tanya!
% 0.47/0.64  % SZS status Theorem for theBenchmark
% 0.47/0.64  % SZS output start Proof for theBenchmark
% See solution above
% 0.47/0.64  % (29384)------------------------------
% 0.47/0.64  % (29384)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.47/0.64  % (29384)Termination reason: Refutation
% 0.47/0.64  
% 0.47/0.64  % (29384)Memory used [KB]: 1181
% 0.47/0.64  % (29384)Time elapsed: 0.003 s
% 0.47/0.64  % (29384)Instructions burned: 7 (million)
% 0.47/0.64  % (29376)Success in time 0.313 s
% 0.47/0.64  % Vampire---4.8 exiting
%------------------------------------------------------------------------------