TSTP Solution File: SWC381+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC381+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 : n007.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 04:38:34 EDT 2024

% Result   : Theorem 0.60s 0.79s
% Output   : Refutation 0.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   48 (   5 unt;   0 def)
%            Number of atoms       :  261 (  55 equ)
%            Maximal formula atoms :   18 (   5 avg)
%            Number of connectives :  306 (  93   ~;  81   |; 109   &)
%                                         (   3 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   4 prp; 0-4 aty)
%            Number of functors    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :  111 (  74   !;  37   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f323,plain,
    $false,
    inference(avatar_sat_refutation,[],[f229,f231,f286,f322]) ).

fof(f322,plain,
    ( ~ spl12_1
    | ~ spl12_3 ),
    inference(avatar_contradiction_clause,[],[f321]) ).

fof(f321,plain,
    ( $false
    | ~ spl12_1
    | ~ spl12_3 ),
    inference(resolution,[],[f308,f224]) ).

fof(f224,plain,
    ( sP0(sK5,sK4,sK5,sK4)
    | ~ spl12_1 ),
    inference(avatar_component_clause,[],[f222]) ).

fof(f222,plain,
    ( spl12_1
  <=> sP0(sK5,sK4,sK5,sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f308,plain,
    ( ! [X0,X1] : ~ sP0(sK5,sK4,X0,X1)
    | ~ spl12_1
    | ~ spl12_3 ),
    inference(resolution,[],[f303,f159]) ).

fof(f159,plain,
    ! [X2,X3,X0,X1] :
      ( memberP(X0,sK1(X0,X1))
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f130,plain,
    ! [X0,X1,X2,X3] :
      ( ( memberP(X0,sK1(X0,X1))
        & cons(sK1(X0,X1),nil) = X1
        & ssItem(sK1(X0,X1))
        & ! [X5] :
            ( ~ memberP(X2,X5)
            | cons(X5,nil) != X3
            | ~ ssItem(X5) )
        & neq(X2,nil) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f128,f129]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ? [X4] :
          ( memberP(X0,X4)
          & cons(X4,nil) = X1
          & ssItem(X4) )
     => ( memberP(X0,sK1(X0,X1))
        & cons(sK1(X0,X1),nil) = X1
        & ssItem(sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

fof(f128,plain,
    ! [X0,X1,X2,X3] :
      ( ( ? [X4] :
            ( memberP(X0,X4)
            & cons(X4,nil) = X1
            & ssItem(X4) )
        & ! [X5] :
            ( ~ memberP(X2,X5)
            | cons(X5,nil) != X3
            | ~ ssItem(X5) )
        & neq(X2,nil) )
      | ~ sP0(X0,X1,X2,X3) ),
    inference(rectify,[],[f127]) ).

fof(f127,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( memberP(X3,X4)
            & cons(X4,nil) = X2
            & ssItem(X4) )
        & ! [X5] :
            ( ~ memberP(X1,X5)
            | cons(X5,nil) != X0
            | ~ ssItem(X5) )
        & neq(X1,nil) )
      | ~ sP0(X3,X2,X1,X0) ),
    inference(nnf_transformation,[],[f125]) ).

fof(f125,plain,
    ! [X3,X2,X1,X0] :
      ( ( ? [X4] :
            ( memberP(X3,X4)
            & cons(X4,nil) = X2
            & ssItem(X4) )
        & ! [X5] :
            ( ~ memberP(X1,X5)
            | cons(X5,nil) != X0
            | ~ ssItem(X5) )
        & neq(X1,nil) )
      | ~ sP0(X3,X2,X1,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f303,plain,
    ( ~ memberP(sK5,sK1(sK5,sK4))
    | ~ spl12_1
    | ~ spl12_3 ),
    inference(resolution,[],[f288,f224]) ).

fof(f288,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP0(X0,X1,X2,sK4)
        | ~ memberP(X2,sK1(sK5,sK4)) )
    | ~ spl12_1
    | ~ spl12_3 ),
    inference(subsumption_resolution,[],[f287,f263]) ).

fof(f263,plain,
    ( ssItem(sK1(sK5,sK4))
    | ~ spl12_3 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f262,plain,
    ( spl12_3
  <=> ssItem(sK1(sK5,sK4)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f287,plain,
    ( ! [X2,X0,X1] :
        ( ~ sP0(X0,X1,X2,sK4)
        | ~ ssItem(sK1(sK5,sK4))
        | ~ memberP(X2,sK1(sK5,sK4)) )
    | ~ spl12_1 ),
    inference(superposition,[],[f210,f247]) ).

fof(f247,plain,
    ( sK4 = cons(sK1(sK5,sK4),nil)
    | ~ spl12_1 ),
    inference(resolution,[],[f158,f224]) ).

fof(f158,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | cons(sK1(X0,X1),nil) = X1 ),
    inference(cnf_transformation,[],[f130]) ).

fof(f210,plain,
    ! [X2,X0,X1,X5] :
      ( ~ sP0(X0,X1,X2,cons(X5,nil))
      | ~ ssItem(X5)
      | ~ memberP(X2,X5) ),
    inference(equality_resolution,[],[f156]) ).

fof(f156,plain,
    ! [X2,X3,X0,X1,X5] :
      ( ~ memberP(X2,X5)
      | cons(X5,nil) != X3
      | ~ ssItem(X5)
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f286,plain,
    ( ~ spl12_1
    | spl12_3 ),
    inference(avatar_contradiction_clause,[],[f285]) ).

fof(f285,plain,
    ( $false
    | ~ spl12_1
    | spl12_3 ),
    inference(resolution,[],[f281,f224]) ).

fof(f281,plain,
    ( ! [X0,X1] : ~ sP0(sK5,sK4,X0,X1)
    | spl12_3 ),
    inference(resolution,[],[f264,f157]) ).

fof(f157,plain,
    ! [X2,X3,X0,X1] :
      ( ssItem(sK1(X0,X1))
      | ~ sP0(X0,X1,X2,X3) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f264,plain,
    ( ~ ssItem(sK1(sK5,sK4))
    | spl12_3 ),
    inference(avatar_component_clause,[],[f262]) ).

fof(f231,plain,
    spl12_2,
    inference(avatar_split_clause,[],[f230,f226]) ).

fof(f226,plain,
    ( spl12_2
  <=> neq(sK5,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f230,plain,
    neq(sK5,nil),
    inference(subsumption_resolution,[],[f207,f155]) ).

fof(f155,plain,
    ! [X2,X3,X0,X1] :
      ( ~ sP0(X0,X1,X2,X3)
      | neq(X2,nil) ),
    inference(cnf_transformation,[],[f130]) ).

fof(f207,plain,
    ( neq(sK5,nil)
    | sP0(sK5,sK4,sK5,sK4) ),
    inference(definition_unfolding,[],[f166,f164,f164,f165]) ).

fof(f165,plain,
    sK2 = sK4,
    inference(cnf_transformation,[],[f135]) ).

fof(f135,plain,
    ( ( ( ~ neq(sK5,nil)
        & neq(sK3,nil) )
      | sP0(sK5,sK4,sK3,sK2) )
    & sK2 = sK4
    & sK3 = sK5
    & ssList(sK5)
    & ssList(sK4)
    & ssList(sK3)
    & ssList(sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5])],[f126,f134,f133,f132,f131]) ).

fof(f131,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | sP0(X3,X2,X1,X0) )
                    & X0 = X2
                    & X1 = X3
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP0(X3,X2,X1,sK2) )
                  & sK2 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f132,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | sP0(X3,X2,X1,sK2) )
                & sK2 = X2
                & X1 = X3
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK3,nil) )
                | sP0(X3,X2,sK3,sK2) )
              & sK2 = X2
              & sK3 = X3
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

fof(f133,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK3,nil) )
              | sP0(X3,X2,sK3,sK2) )
            & sK2 = X2
            & sK3 = X3
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK3,nil) )
            | sP0(X3,sK4,sK3,sK2) )
          & sK2 = sK4
          & sK3 = X3
          & ssList(X3) )
      & ssList(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f134,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK3,nil) )
          | sP0(X3,sK4,sK3,sK2) )
        & sK2 = sK4
        & sK3 = X3
        & ssList(X3) )
   => ( ( ( ~ neq(sK5,nil)
          & neq(sK3,nil) )
        | sP0(sK5,sK4,sK3,sK2) )
      & sK2 = sK4
      & sK3 = sK5
      & ssList(sK5) ) ),
    introduced(choice_axiom,[]) ).

fof(f126,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | sP0(X3,X2,X1,X0) )
                  & X0 = X2
                  & X1 = X3
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(definition_folding,[],[f100,f125]) ).

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

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

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

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

fof(f164,plain,
    sK3 = sK5,
    inference(cnf_transformation,[],[f135]) ).

fof(f166,plain,
    ( neq(sK3,nil)
    | sP0(sK5,sK4,sK3,sK2) ),
    inference(cnf_transformation,[],[f135]) ).

fof(f229,plain,
    ( spl12_1
    | ~ spl12_2 ),
    inference(avatar_split_clause,[],[f206,f226,f222]) ).

fof(f206,plain,
    ( ~ neq(sK5,nil)
    | sP0(sK5,sK4,sK5,sK4) ),
    inference(definition_unfolding,[],[f167,f164,f165]) ).

fof(f167,plain,
    ( ~ neq(sK5,nil)
    | sP0(sK5,sK4,sK3,sK2) ),
    inference(cnf_transformation,[],[f135]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14  % Problem    : SWC381+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.16  % 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
% 0.14/0.37  % Computer : n007.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Sun May 19 02:46:08 EDT 2024
% 0.14/0.37  % CPUTime    : 
% 0.14/0.37  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.38  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
% 0.60/0.78  % (20188)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 (2995ds/34Mi)
% 0.60/0.78  % (20190)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.60/0.78  % (20189)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 (2995ds/51Mi)
% 0.60/0.78  % (20192)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 (2995ds/34Mi)
% 0.60/0.78  % (20194)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 (2995ds/83Mi)
% 0.60/0.78  % (20193)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.60/0.78  % (20191)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.60/0.79  % (20193)Refutation not found, incomplete strategy% (20193)------------------------------
% 0.60/0.79  % (20193)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (20193)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79  
% 0.60/0.79  % (20193)Memory used [KB]: 1153
% 0.60/0.79  % (20193)Time elapsed: 0.004 s
% 0.60/0.79  % (20193)Instructions burned: 5 (million)
% 0.60/0.79  % (20193)------------------------------
% 0.60/0.79  % (20193)------------------------------
% 0.60/0.79  % (20190)First to succeed.
% 0.60/0.79  % (20190)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20187"
% 0.60/0.79  % (20190)Refutation found. Thanks to Tanya!
% 0.60/0.79  % SZS status Theorem for theBenchmark
% 0.60/0.79  % SZS output start Proof for theBenchmark
% See solution above
% 0.60/0.79  % (20190)------------------------------
% 0.60/0.79  % (20190)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79  % (20190)Termination reason: Refutation
% 0.60/0.79  
% 0.60/0.79  % (20190)Memory used [KB]: 1185
% 0.60/0.79  % (20190)Time elapsed: 0.005 s
% 0.60/0.79  % (20190)Instructions burned: 11 (million)
% 0.60/0.79  % (20187)Success in time 0.409 s
% 0.60/0.79  % Vampire---4.8 exiting
%------------------------------------------------------------------------------