TSTP Solution File: SWC406+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC406+1 : TPTP v8.1.2. 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 : n020.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 : Wed May  1 04:01:57 EDT 2024

% Result   : Theorem 0.60s 0.76s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   23 (   9 unt;   0 def)
%            Number of atoms       :  324 (  60 equ)
%            Maximal formula atoms :   44 (  14 avg)
%            Number of connectives :  425 ( 124   ~; 104   |; 173   &)
%                                         (   0 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  10 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   94 (  42   !;  52   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f248,plain,
    $false,
    inference(subsumption_resolution,[],[f247,f164]) ).

fof(f164,plain,
    ssItem(sK4),
    inference(cnf_transformation,[],[f134]) ).

fof(f134,plain,
    ( ~ memberP(sK1,sK4)
    & memberP(sK0,sK4)
    & ssItem(sK4)
    & ! [X5] :
        ( ( ( ( ! [X6] :
                  ( ~ leq(X6,X5)
                  | ~ memberP(sK3,X6)
                  | X5 = X6
                  | ~ ssItem(X6) )
              & memberP(sK3,X5) )
            | ~ memberP(sK2,X5) )
          & ( ~ memberP(sK3,X5)
            | ( sK5(X5) != X5
              & leq(sK5(X5),X5)
              & memberP(sK3,sK5(X5))
              & ssItem(sK5(X5)) )
            | memberP(sK2,X5) ) )
        | ~ ssItem(X5) )
    & sK0 = sK2
    & sK1 = sK3
    & ssList(sK3)
    & ssList(sK2)
    & ssList(sK1)
    & ssList(sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f100,f133,f132,f131,f130,f129,f128]) ).

fof(f128,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ~ memberP(X1,X4)
                        & memberP(X0,X4)
                        & ssItem(X4) )
                    & ! [X5] :
                        ( ( ( ( ! [X6] :
                                  ( ~ leq(X6,X5)
                                  | ~ memberP(X3,X6)
                                  | X5 = X6
                                  | ~ ssItem(X6) )
                              & memberP(X3,X5) )
                            | ~ memberP(X2,X5) )
                          & ( ~ memberP(X3,X5)
                            | ? [X7] :
                                ( X5 != X7
                                & leq(X7,X5)
                                & memberP(X3,X7)
                                & ssItem(X7) )
                            | memberP(X2,X5) ) )
                        | ~ ssItem(X5) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(sK0,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & sK0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

fof(f129,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ? [X4] :
                    ( ~ memberP(X1,X4)
                    & memberP(sK0,X4)
                    & ssItem(X4) )
                & ! [X5] :
                    ( ( ( ( ! [X6] :
                              ( ~ leq(X6,X5)
                              | ~ memberP(X3,X6)
                              | X5 = X6
                              | ~ ssItem(X6) )
                          & memberP(X3,X5) )
                        | ~ memberP(X2,X5) )
                      & ( ~ memberP(X3,X5)
                        | ? [X7] :
                            ( X5 != X7
                            & leq(X7,X5)
                            & memberP(X3,X7)
                            & ssItem(X7) )
                        | memberP(X2,X5) ) )
                    | ~ ssItem(X5) )
                & sK0 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ? [X4] :
                  ( ~ memberP(sK1,X4)
                  & memberP(sK0,X4)
                  & ssItem(X4) )
              & ! [X5] :
                  ( ( ( ( ! [X6] :
                            ( ~ leq(X6,X5)
                            | ~ memberP(X3,X6)
                            | X5 = X6
                            | ~ ssItem(X6) )
                        & memberP(X3,X5) )
                      | ~ memberP(X2,X5) )
                    & ( ~ memberP(X3,X5)
                      | ? [X7] :
                          ( X5 != X7
                          & leq(X7,X5)
                          & memberP(X3,X7)
                          & ssItem(X7) )
                      | memberP(X2,X5) ) )
                  | ~ ssItem(X5) )
              & sK0 = X2
              & sK1 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ? [X4] :
                ( ~ memberP(sK1,X4)
                & memberP(sK0,X4)
                & ssItem(X4) )
            & ! [X5] :
                ( ( ( ( ! [X6] :
                          ( ~ leq(X6,X5)
                          | ~ memberP(X3,X6)
                          | X5 = X6
                          | ~ ssItem(X6) )
                      & memberP(X3,X5) )
                    | ~ memberP(X2,X5) )
                  & ( ~ memberP(X3,X5)
                    | ? [X7] :
                        ( X5 != X7
                        & leq(X7,X5)
                        & memberP(X3,X7)
                        & ssItem(X7) )
                    | memberP(X2,X5) ) )
                | ~ ssItem(X5) )
            & sK0 = X2
            & sK1 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ? [X4] :
              ( ~ memberP(sK1,X4)
              & memberP(sK0,X4)
              & ssItem(X4) )
          & ! [X5] :
              ( ( ( ( ! [X6] :
                        ( ~ leq(X6,X5)
                        | ~ memberP(X3,X6)
                        | X5 = X6
                        | ~ ssItem(X6) )
                    & memberP(X3,X5) )
                  | ~ memberP(sK2,X5) )
                & ( ~ memberP(X3,X5)
                  | ? [X7] :
                      ( X5 != X7
                      & leq(X7,X5)
                      & memberP(X3,X7)
                      & ssItem(X7) )
                  | memberP(sK2,X5) ) )
              | ~ ssItem(X5) )
          & sK0 = sK2
          & sK1 = X3
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ( ? [X3] :
        ( ? [X4] :
            ( ~ memberP(sK1,X4)
            & memberP(sK0,X4)
            & ssItem(X4) )
        & ! [X5] :
            ( ( ( ( ! [X6] :
                      ( ~ leq(X6,X5)
                      | ~ memberP(X3,X6)
                      | X5 = X6
                      | ~ ssItem(X6) )
                  & memberP(X3,X5) )
                | ~ memberP(sK2,X5) )
              & ( ~ memberP(X3,X5)
                | ? [X7] :
                    ( X5 != X7
                    & leq(X7,X5)
                    & memberP(X3,X7)
                    & ssItem(X7) )
                | memberP(sK2,X5) ) )
            | ~ ssItem(X5) )
        & sK0 = sK2
        & sK1 = X3
        & ssList(X3) )
   => ( ? [X4] :
          ( ~ memberP(sK1,X4)
          & memberP(sK0,X4)
          & ssItem(X4) )
      & ! [X5] :
          ( ( ( ( ! [X6] :
                    ( ~ leq(X6,X5)
                    | ~ memberP(sK3,X6)
                    | X5 = X6
                    | ~ ssItem(X6) )
                & memberP(sK3,X5) )
              | ~ memberP(sK2,X5) )
            & ( ~ memberP(sK3,X5)
              | ? [X7] :
                  ( X5 != X7
                  & leq(X7,X5)
                  & memberP(sK3,X7)
                  & ssItem(X7) )
              | memberP(sK2,X5) ) )
          | ~ ssItem(X5) )
      & sK0 = sK2
      & sK1 = sK3
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X4] :
        ( ~ memberP(sK1,X4)
        & memberP(sK0,X4)
        & ssItem(X4) )
   => ( ~ memberP(sK1,sK4)
      & memberP(sK0,sK4)
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ! [X5] :
      ( ? [X7] :
          ( X5 != X7
          & leq(X7,X5)
          & memberP(sK3,X7)
          & ssItem(X7) )
     => ( sK5(X5) != X5
        & leq(sK5(X5),X5)
        & memberP(sK3,sK5(X5))
        & ssItem(sK5(X5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f100,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(X0,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(flattening,[],[f99]) ).

fof(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ? [X4] :
                      ( ~ memberP(X1,X4)
                      & memberP(X0,X4)
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( ( ( ! [X6] :
                                ( ~ leq(X6,X5)
                                | ~ memberP(X3,X6)
                                | X5 = X6
                                | ~ ssItem(X6) )
                            & memberP(X3,X5) )
                          | ~ memberP(X2,X5) )
                        & ( ~ memberP(X3,X5)
                          | ? [X7] :
                              ( X5 != X7
                              & leq(X7,X5)
                              & memberP(X3,X7)
                              & ssItem(X7) )
                          | memberP(X2,X5) ) )
                      | ~ ssItem(X5) )
                  & 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)
                   => ( ! [X4] :
                          ( ssItem(X4)
                         => ( memberP(X1,X4)
                            | ~ memberP(X0,X4) ) )
                      | ? [X5] :
                          ( ( ( ( ? [X6] :
                                    ( leq(X6,X5)
                                    & memberP(X3,X6)
                                    & X5 != X6
                                    & ssItem(X6) )
                                | ~ memberP(X3,X5) )
                              & memberP(X2,X5) )
                            | ( memberP(X3,X5)
                              & ! [X7] :
                                  ( ssItem(X7)
                                 => ( X5 = X7
                                    | ~ leq(X7,X5)
                                    | ~ memberP(X3,X7) ) )
                              & ~ memberP(X2,X5) ) )
                          & ssItem(X5) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(rectify,[],[f97]) ).

fof(f97,negated_conjecture,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ! [X6] :
                          ( ssItem(X6)
                         => ( memberP(X1,X6)
                            | ~ memberP(X0,X6) ) )
                      | ? [X4] :
                          ( ( ( ( ? [X5] :
                                    ( leq(X5,X4)
                                    & memberP(X3,X5)
                                    & X4 != X5
                                    & ssItem(X5) )
                                | ~ memberP(X3,X4) )
                              & memberP(X2,X4) )
                            | ( memberP(X3,X4)
                              & ! [X5] :
                                  ( ssItem(X5)
                                 => ( X4 = X5
                                    | ~ leq(X5,X4)
                                    | ~ memberP(X3,X5) ) )
                              & ~ memberP(X2,X4) ) )
                          & ssItem(X4) )
                      | X0 != X2
                      | X1 != X3 ) ) ) ) ),
    inference(negated_conjecture,[],[f96]) ).

fof(f96,conjecture,
    ! [X0] :
      ( ssList(X0)
     => ! [X1] :
          ( ssList(X1)
         => ! [X2] :
              ( ssList(X2)
             => ! [X3] :
                  ( ssList(X3)
                 => ( ! [X6] :
                        ( ssItem(X6)
                       => ( memberP(X1,X6)
                          | ~ memberP(X0,X6) ) )
                    | ? [X4] :
                        ( ( ( ( ? [X5] :
                                  ( leq(X5,X4)
                                  & memberP(X3,X5)
                                  & X4 != X5
                                  & ssItem(X5) )
                              | ~ memberP(X3,X4) )
                            & memberP(X2,X4) )
                          | ( memberP(X3,X4)
                            & ! [X5] :
                                ( ssItem(X5)
                               => ( X4 = X5
                                  | ~ leq(X5,X4)
                                  | ~ memberP(X3,X5) ) )
                            & ~ memberP(X2,X4) ) )
                        & ssItem(X4) )
                    | X0 != X2
                    | X1 != X3 ) ) ) ) ),
    file('/export/starexec/sandbox/tmp/tmp.Soz3J947Kh/Vampire---4.8_22481',co1) ).

fof(f247,plain,
    ~ ssItem(sK4),
    inference(subsumption_resolution,[],[f246,f204]) ).

fof(f204,plain,
    ~ memberP(sK3,sK4),
    inference(definition_unfolding,[],[f166,f156]) ).

fof(f156,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f134]) ).

fof(f166,plain,
    ~ memberP(sK1,sK4),
    inference(cnf_transformation,[],[f134]) ).

fof(f246,plain,
    ( memberP(sK3,sK4)
    | ~ ssItem(sK4) ),
    inference(resolution,[],[f162,f205]) ).

fof(f205,plain,
    memberP(sK2,sK4),
    inference(definition_unfolding,[],[f165,f157]) ).

fof(f157,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f134]) ).

fof(f165,plain,
    memberP(sK0,sK4),
    inference(cnf_transformation,[],[f134]) ).

fof(f162,plain,
    ! [X5] :
      ( ~ memberP(sK2,X5)
      | memberP(sK3,X5)
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f134]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem    : SWC406+1 : TPTP v8.1.2. Released v2.4.0.
% 0.04/0.15  % 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
% 0.15/0.36  % Computer : n020.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   : Tue Apr 30 18:18:02 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.15/0.37  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.Soz3J947Kh/Vampire---4.8_22481
% 0.59/0.76  % (22738)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)
% 0.59/0.76  % (22737)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)
% 0.59/0.76  % (22731)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)
% 0.59/0.76  % (22733)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.59/0.76  % (22734)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)
% 0.59/0.76  % (22732)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)
% 0.59/0.76  % (22735)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)
% 0.59/0.76  % (22736)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)
% 0.59/0.76  % (22738)First to succeed.
% 0.59/0.76  % (22734)Also succeeded, but the first one will report.
% 0.60/0.76  % (22738)Refutation found. Thanks to Tanya!
% 0.60/0.76  % SZS status Theorem for Vampire---4
% 0.60/0.76  % SZS output start Proof for Vampire---4
% See solution above
% 0.60/0.76  % (22738)------------------------------
% 0.60/0.76  % (22738)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.60/0.76  % (22738)Termination reason: Refutation
% 0.60/0.76  
% 0.60/0.76  % (22738)Memory used [KB]: 1154
% 0.60/0.76  % (22738)Time elapsed: 0.003 s
% 0.60/0.76  % (22738)Instructions burned: 7 (million)
% 0.60/0.76  % (22738)------------------------------
% 0.60/0.76  % (22738)------------------------------
% 0.60/0.76  % (22727)Success in time 0.391 s
% 0.60/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------