TSTP Solution File: SWC097+1 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : SWC097+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 : n028.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 04:36:12 EDT 2024

% Result   : Theorem 0.56s 0.76s
% Output   : Refutation 0.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   39 (   5 unt;   1 typ;   0 def)
%            Number of atoms       :  515 (  64 equ)
%            Maximal formula atoms :   26 (  13 avg)
%            Number of connectives :  275 (  81   ~;  63   |; 106   &)
%                                         (   5 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :  283 ( 283 fml;   0 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   1   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;  11 prp; 0-3 aty)
%            Number of functors    :    0 (   0 usr;   0 con; --- aty)
%            Number of variables   :   73 (  34   !;  38   ?;   8   :)
%                                         (   1  !>;   0  ?*;   0  @-;   0  @+)

% Comments : 
%------------------------------------------------------------------------------
tff(pred_def_20,type,
    sQ9_eqProxy: 
      !>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).

tff(f256,plain,
    $false,
    inference(avatar_sat_refutation,[],[f229,f234,f238,f242,f255]) ).

tff(f255,plain,
    ( ~ spl10_1
    | ~ spl10_3
    | ~ spl10_4 ),
    inference(avatar_contradiction_clause,[],[f254]) ).

tff(f254,plain,
    ( $false
    | ~ spl10_1
    | ~ spl10_3
    | ~ spl10_4 ),
    inference(subsumption_resolution,[],[f253,f233]) ).

tff(f233,plain,
    ( ssItem(sK4)
    | ~ spl10_3 ),
    inference(avatar_component_clause,[],[f231]) ).

tff(f231,plain,
    ( spl10_3
  <=> ssItem(sK4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).

tff(f253,plain,
    ( ~ ssItem(sK4)
    | ~ spl10_1
    | ~ spl10_4 ),
    inference(resolution,[],[f237,f224]) ).

tff(f224,plain,
    ( sQ9_eqProxy($i,sK3,app(sK2,cons(sK4,nil)))
    | ~ spl10_1 ),
    inference(avatar_component_clause,[],[f222]) ).

tff(f222,plain,
    ( spl10_1
  <=> sQ9_eqProxy($i,sK3,app(sK2,cons(sK4,nil))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).

tff(f237,plain,
    ( ! [X5: $i] :
        ( ~ sQ9_eqProxy($i,sK3,app(sK2,cons(X5,nil)))
        | ~ ssItem(X5) )
    | ~ spl10_4 ),
    inference(avatar_component_clause,[],[f236]) ).

tff(f236,plain,
    ( spl10_4
  <=> ! [X5] :
        ( ~ sQ9_eqProxy($i,sK3,app(sK2,cons(X5,nil)))
        | ~ ssItem(X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).

tff(f242,plain,
    spl10_2,
    inference(avatar_split_clause,[],[f220,f226]) ).

tff(f226,plain,
    ( spl10_2
  <=> neq(sK3,nil) ),
    introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).

tff(f220,plain,
    neq(sK3,nil),
    inference(duplicate_literal_removal,[],[f183]) ).

tff(f183,plain,
    ( neq(sK3,nil)
    | neq(sK3,nil) ),
    inference(definition_unfolding,[],[f143,f141,f141]) ).

tff(f141,plain,
    sK1 = sK3,
    inference(cnf_transformation,[],[f126]) ).

tff(f126,plain,
    ( ( ( ~ neq(sK3,nil)
        & neq(sK1,nil) )
      | ( ( sK3 = app(sK2,cons(sK4,nil)) )
        & ssItem(sK4)
        & ! [X5] :
            ( ( app(sK0,cons(X5,nil)) != sK1 )
            | ~ ssItem(X5) )
        & neq(sK1,nil) ) )
    & ( 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,f125,f124,f123,f122,f121]) ).

tff(f121,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ( ( ~ neq(X3,nil)
                        & neq(X1,nil) )
                      | ( ? [X4] :
                            ( ( app(X2,cons(X4,nil)) = X3 )
                            & ssItem(X4) )
                        & ! [X5] :
                            ( ( app(X0,cons(X5,nil)) != X1 )
                            | ~ ssItem(X5) )
                        & neq(X1,nil) ) )
                    & ( X0 = X2 )
                    & ( X1 = X3 )
                    & ssList(X3) )
                & ssList(X2) )
            & ssList(X1) )
        & ssList(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ( app(X2,cons(X4,nil)) = X3 )
                          & ssItem(X4) )
                      & ! [X5] :
                          ( ( app(sK0,cons(X5,nil)) != X1 )
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & ( sK0 = X2 )
                  & ( X1 = X3 )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f122,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ? [X3] :
                ( ( ( ~ neq(X3,nil)
                    & neq(X1,nil) )
                  | ( ? [X4] :
                        ( ( app(X2,cons(X4,nil)) = X3 )
                        & ssItem(X4) )
                    & ! [X5] :
                        ( ( app(sK0,cons(X5,nil)) != X1 )
                        | ~ ssItem(X5) )
                    & neq(X1,nil) ) )
                & ( sK0 = X2 )
                & ( X1 = X3 )
                & ssList(X3) )
            & ssList(X2) )
        & ssList(X1) )
   => ( ? [X2] :
          ( ? [X3] :
              ( ( ( ~ neq(X3,nil)
                  & neq(sK1,nil) )
                | ( ? [X4] :
                      ( ( app(X2,cons(X4,nil)) = X3 )
                      & ssItem(X4) )
                  & ! [X5] :
                      ( ( app(sK0,cons(X5,nil)) != sK1 )
                      | ~ ssItem(X5) )
                  & neq(sK1,nil) ) )
              & ( sK0 = X2 )
              & ( sK1 = X3 )
              & ssList(X3) )
          & ssList(X2) )
      & ssList(sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f123,plain,
    ( ? [X2] :
        ( ? [X3] :
            ( ( ( ~ neq(X3,nil)
                & neq(sK1,nil) )
              | ( ? [X4] :
                    ( ( app(X2,cons(X4,nil)) = X3 )
                    & ssItem(X4) )
                & ! [X5] :
                    ( ( app(sK0,cons(X5,nil)) != sK1 )
                    | ~ ssItem(X5) )
                & neq(sK1,nil) ) )
            & ( sK0 = X2 )
            & ( sK1 = X3 )
            & ssList(X3) )
        & ssList(X2) )
   => ( ? [X3] :
          ( ( ( ~ neq(X3,nil)
              & neq(sK1,nil) )
            | ( ? [X4] :
                  ( ( app(sK2,cons(X4,nil)) = X3 )
                  & ssItem(X4) )
              & ! [X5] :
                  ( ( app(sK0,cons(X5,nil)) != sK1 )
                  | ~ ssItem(X5) )
              & neq(sK1,nil) ) )
          & ( sK0 = sK2 )
          & ( sK1 = X3 )
          & ssList(X3) )
      & ssList(sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f124,plain,
    ( ? [X3] :
        ( ( ( ~ neq(X3,nil)
            & neq(sK1,nil) )
          | ( ? [X4] :
                ( ( app(sK2,cons(X4,nil)) = X3 )
                & ssItem(X4) )
            & ! [X5] :
                ( ( app(sK0,cons(X5,nil)) != sK1 )
                | ~ ssItem(X5) )
            & neq(sK1,nil) ) )
        & ( sK0 = sK2 )
        & ( sK1 = X3 )
        & ssList(X3) )
   => ( ( ( ~ neq(sK3,nil)
          & neq(sK1,nil) )
        | ( ? [X4] :
              ( ( app(sK2,cons(X4,nil)) = sK3 )
              & ssItem(X4) )
          & ! [X5] :
              ( ( app(sK0,cons(X5,nil)) != sK1 )
              | ~ ssItem(X5) )
          & neq(sK1,nil) ) )
      & ( sK0 = sK2 )
      & ( sK1 = sK3 )
      & ssList(sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f125,plain,
    ( ? [X4] :
        ( ( app(sK2,cons(X4,nil)) = sK3 )
        & ssItem(X4) )
   => ( ( sK3 = app(sK2,cons(sK4,nil)) )
      & ssItem(sK4) ) ),
    introduced(choice_axiom,[]) ).

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

tff(f99,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ? [X3] :
                  ( ( ( ~ neq(X3,nil)
                      & neq(X1,nil) )
                    | ( ? [X4] :
                          ( ( app(X2,cons(X4,nil)) = X3 )
                          & ssItem(X4) )
                      & ! [X5] :
                          ( ( app(X0,cons(X5,nil)) != X1 )
                          | ~ ssItem(X5) )
                      & neq(X1,nil) ) )
                  & ( X0 = X2 )
                  & ( X1 = X3 )
                  & ssList(X3) )
              & ssList(X2) )
          & ssList(X1) )
      & ssList(X0) ),
    inference(ennf_transformation,[],[f98]) ).

tff(f98,plain,
    ~ ! [X0] :
        ( ssList(X0)
       => ! [X1] :
            ( ssList(X1)
           => ! [X2] :
                ( ssList(X2)
               => ! [X3] :
                    ( ssList(X3)
                   => ( ( ( neq(X3,nil)
                          | ~ neq(X1,nil) )
                        & ( ! [X4] :
                              ( ssItem(X4)
                             => ( app(X2,cons(X4,nil)) != X3 ) )
                          | ? [X5] :
                              ( ( app(X0,cons(X5,nil)) = X1 )
                              & ssItem(X5) )
                          | ~ neq(X1,nil) ) )
                      | ( X0 != X2 )
                      | ( X1 != X3 ) ) ) ) ) ),
    inference(rectify,[],[f97]) ).

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

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

tff(f143,plain,
    ( neq(sK1,nil)
    | neq(sK1,nil) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f238,plain,
    ( spl10_4
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f192,f226,f236]) ).

tff(f192,plain,
    ! [X5: $i] :
      ( ~ neq(sK3,nil)
      | ~ sQ9_eqProxy($i,sK3,app(sK2,cons(X5,nil)))
      | ~ ssItem(X5) ),
    inference(equality_proxy_replacement,[],[f178,f190]) ).

tff(f190,plain,
    ! [X0: $tType,X2: X0,X1: X0] :
      ( sQ9_eqProxy(X0,X1,X2)
    <=> ( X1 = X2 ) ),
    introduced(equality_proxy_definition,[new_symbols(naming,[sQ9_eqProxy])]) ).

tff(f178,plain,
    ! [X5: $i] :
      ( ~ neq(sK3,nil)
      | ( sK3 != app(sK2,cons(X5,nil)) )
      | ~ ssItem(X5) ),
    inference(definition_unfolding,[],[f148,f142,f141]) ).

tff(f142,plain,
    sK0 = sK2,
    inference(cnf_transformation,[],[f126]) ).

tff(f148,plain,
    ! [X5: $i] :
      ( ~ neq(sK3,nil)
      | ( app(sK0,cons(X5,nil)) != sK1 )
      | ~ ssItem(X5) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f234,plain,
    ( spl10_3
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f149,f226,f231]) ).

tff(f149,plain,
    ( ~ neq(sK3,nil)
    | ssItem(sK4) ),
    inference(cnf_transformation,[],[f126]) ).

tff(f229,plain,
    ( spl10_1
    | ~ spl10_2 ),
    inference(avatar_split_clause,[],[f191,f226,f222]) ).

tff(f191,plain,
    ( ~ neq(sK3,nil)
    | sQ9_eqProxy($i,sK3,app(sK2,cons(sK4,nil))) ),
    inference(equality_proxy_replacement,[],[f150,f190]) ).

tff(f150,plain,
    ( ~ neq(sK3,nil)
    | ( sK3 = app(sK2,cons(sK4,nil)) ) ),
    inference(cnf_transformation,[],[f126]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem    : SWC097+1 : TPTP v8.2.0. Released v2.4.0.
% 0.13/0.15  % 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
% 0.14/0.35  % Computer : n028.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Sun May 19 03:53:38 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a FOF_THM_RFO_SEQ problem
% 0.14/0.36  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
% 0.56/0.75  % (30362)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)
% 0.56/0.75  % (30358)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2996ds/78Mi)
% 0.56/0.75  % (30356)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)
% 0.56/0.75  % (30357)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)
% 0.56/0.75  % (30359)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)
% 0.56/0.75  % (30360)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)
% 0.56/0.75  % (30361)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)
% 0.56/0.76  % (30356)First to succeed.
% 0.56/0.76  % (30358)Also succeeded, but the first one will report.
% 0.56/0.76  % (30361)Also succeeded, but the first one will report.
% 0.56/0.76  % (30356)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-30352"
% 0.56/0.76  % (30359)Also succeeded, but the first one will report.
% 0.56/0.76  % (30356)Refutation found. Thanks to Tanya!
% 0.56/0.76  % SZS status Theorem for theBenchmark
% 0.56/0.76  % SZS output start Proof for theBenchmark
% See solution above
% 0.56/0.76  % (30356)------------------------------
% 0.56/0.76  % (30356)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.56/0.76  % (30356)Termination reason: Refutation
% 0.56/0.76  
% 0.56/0.76  % (30356)Memory used [KB]: 1159
% 0.56/0.76  % (30356)Time elapsed: 0.005 s
% 0.56/0.76  % (30356)Instructions burned: 6 (million)
% 0.56/0.76  % (30352)Success in time 0.388 s
% 0.56/0.76  % Vampire---4.8 exiting
%------------------------------------------------------------------------------