TSTP Solution File: KRS256+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : KRS256+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n002.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 07:20:16 EDT 2024

% Result   : Theorem 0.22s 0.46s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   64 (  16 unt;   0 def)
%            Number of atoms       :  166 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :  172 (  70   ~;  53   |;  26   &)
%                                         (  12 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   3 prp; 0-3 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  136 (  97   !;  39   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f4964,plain,
    $false,
    inference(avatar_sat_refutation,[],[f4891,f4903,f4963]) ).

fof(f4963,plain,
    ~ spl97_69,
    inference(avatar_contradiction_clause,[],[f4936]) ).

fof(f4936,plain,
    ( $false
    | ~ spl97_69 ),
    inference(resolution,[],[f4886,f3504]) ).

fof(f3504,plain,
    ~ sP93(not(sK41)),
    inference(resolution,[],[f924,f285]) ).

fof(f285,plain,
    ~ model(sK42,sK41),
    inference(cnf_transformation,[],[f188]) ).

fof(f188,plain,
    ( ~ model(sK42,sK41)
    & model(sK43,sK41) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK41,sK42,sK43])],[f54,f187,f186,f185]) ).

fof(f185,plain,
    ( ? [X0] :
        ( ? [X1] : ~ model(X1,X0)
        & ? [X2] : model(X2,X0) )
   => ( ? [X1] : ~ model(X1,sK41)
      & ? [X2] : model(X2,sK41) ) ),
    introduced(choice_axiom,[]) ).

fof(f186,plain,
    ( ? [X1] : ~ model(X1,sK41)
   => ~ model(sK42,sK41) ),
    introduced(choice_axiom,[]) ).

fof(f187,plain,
    ( ? [X2] : model(X2,sK41)
   => model(sK43,sK41) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ? [X0] :
      ( ? [X1] : ~ model(X1,X0)
      & ? [X2] : model(X2,X0) ),
    inference(rectify,[],[f28]) ).

fof(f28,axiom,
    ? [X9] :
      ( ? [X3] : ~ model(X3,X9)
      & ? [X2] : model(X2,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfiable) ).

fof(f924,plain,
    ! [X0,X1] :
      ( model(X0,X1)
      | ~ sP93(not(X1)) ),
    inference(resolution,[],[f207,f368]) ).

fof(f368,plain,
    ! [X0,X7] :
      ( ~ model(X7,X0)
      | ~ sP93(X0) ),
    inference(general_splitting,[],[f366,f367_D]) ).

fof(f367,plain,
    ! [X0,X1] :
      ( status(X0,X1,esa)
      | ~ sP92(X1)
      | sP93(X0) ),
    inference(cnf_transformation,[],[f367_D]) ).

fof(f367_D,plain,
    ! [X0] :
      ( ! [X1] :
          ( status(X0,X1,esa)
          | ~ sP92(X1) )
    <=> ~ sP93(X0) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP93])]) ).

fof(f366,plain,
    ! [X0,X1,X7] :
      ( status(X0,X1,esa)
      | ~ model(X7,X0)
      | ~ sP92(X1) ),
    inference(general_splitting,[],[f264,f365_D]) ).

fof(f365,plain,
    ! [X1,X6] :
      ( ~ model(X6,X1)
      | sP92(X1) ),
    inference(cnf_transformation,[],[f365_D]) ).

fof(f365_D,plain,
    ! [X1] :
      ( ! [X6] : ~ model(X6,X1)
    <=> ~ sP92(X1) ),
    introduced(general_splitting_component_introduction,[new_symbols(naming,[sP92])]) ).

fof(f264,plain,
    ! [X0,X1,X6,X7] :
      ( status(X0,X1,esa)
      | ~ model(X6,X1)
      | ~ model(X7,X0) ),
    inference(cnf_transformation,[],[f163]) ).

fof(f163,plain,
    ! [X0,X1] :
      ( ( ( ( model(sK32(X0),X0)
            | ! [X3] : ~ model(X3,X1) )
          & ( model(sK33(X1),X1)
            | ! [X5] : ~ model(X5,X0) ) )
        | ~ status(X0,X1,esa) )
      & ( status(X0,X1,esa)
        | ( ( ! [X6] : ~ model(X6,X1)
            | ! [X7] : ~ model(X7,X0) )
          & ( model(sK34(X1),X1)
            | model(sK35(X0),X0) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35])],[f158,f162,f161,f160,f159]) ).

fof(f159,plain,
    ! [X0] :
      ( ? [X2] : model(X2,X0)
     => model(sK32(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f160,plain,
    ! [X1] :
      ( ? [X4] : model(X4,X1)
     => model(sK33(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f161,plain,
    ! [X1] :
      ( ? [X8] : model(X8,X1)
     => model(sK34(X1),X1) ),
    introduced(choice_axiom,[]) ).

fof(f162,plain,
    ! [X0] :
      ( ? [X9] : model(X9,X0)
     => model(sK35(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f158,plain,
    ! [X0,X1] :
      ( ( ( ( ? [X2] : model(X2,X0)
            | ! [X3] : ~ model(X3,X1) )
          & ( ? [X4] : model(X4,X1)
            | ! [X5] : ~ model(X5,X0) ) )
        | ~ status(X0,X1,esa) )
      & ( status(X0,X1,esa)
        | ( ( ! [X6] : ~ model(X6,X1)
            | ! [X7] : ~ model(X7,X0) )
          & ( ? [X8] : model(X8,X1)
            | ? [X9] : model(X9,X0) ) ) ) ),
    inference(rectify,[],[f157]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( ( ( ( ? [X2] : model(X2,X0)
            | ! [X3] : ~ model(X3,X1) )
          & ( ? [X3] : model(X3,X1)
            | ! [X2] : ~ model(X2,X0) ) )
        | ~ status(X0,X1,esa) )
      & ( status(X0,X1,esa)
        | ( ( ! [X3] : ~ model(X3,X1)
            | ! [X2] : ~ model(X2,X0) )
          & ( ? [X3] : model(X3,X1)
            | ? [X2] : model(X2,X0) ) ) ) ),
    inference(nnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0,X1] :
      ( ( ? [X2] : model(X2,X0)
      <=> ? [X3] : model(X3,X1) )
    <=> status(X0,X1,esa) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',esa) ).

fof(f207,plain,
    ! [X0,X1] :
      ( model(X0,not(X1))
      | model(X0,X1) ),
    inference(cnf_transformation,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ( model(X0,X1)
        | model(X0,not(X1)) )
      & ( ~ model(X0,not(X1))
        | ~ model(X0,X1) ) ),
    inference(nnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1] :
      ( model(X0,X1)
    <=> ~ model(X0,not(X1)) ),
    inference(rectify,[],[f26]) ).

fof(f26,axiom,
    ! [X8,X9] :
      ( model(X8,X9)
    <=> ~ model(X8,not(X9)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).

fof(f4886,plain,
    ( ! [X0] : sP93(X0)
    | ~ spl97_69 ),
    inference(avatar_component_clause,[],[f4885]) ).

fof(f4885,plain,
    ( spl97_69
  <=> ! [X0] : sP93(X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_69])]) ).

fof(f4903,plain,
    spl97_70,
    inference(avatar_contradiction_clause,[],[f4892]) ).

fof(f4892,plain,
    ( $false
    | spl97_70 ),
    inference(resolution,[],[f4890,f726]) ).

fof(f726,plain,
    sP92(sK45),
    inference(resolution,[],[f365,f287]) ).

fof(f287,plain,
    ! [X1] : model(X1,sK45),
    inference(cnf_transformation,[],[f192]) ).

fof(f192,plain,
    ! [X1] : model(X1,sK45),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK45])],[f56,f191]) ).

fof(f191,plain,
    ( ? [X0] :
      ! [X1] : model(X1,X0)
   => ! [X1] : model(X1,sK45) ),
    introduced(choice_axiom,[]) ).

fof(f56,plain,
    ? [X0] :
    ! [X1] : model(X1,X0),
    inference(rectify,[],[f27]) ).

fof(f27,axiom,
    ? [X9] :
    ! [X8] : model(X8,X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).

fof(f4890,plain,
    ( ~ sP92(sK45)
    | spl97_70 ),
    inference(avatar_component_clause,[],[f4888]) ).

fof(f4888,plain,
    ( spl97_70
  <=> sP92(sK45) ),
    introduced(avatar_definition,[new_symbols(naming,[spl97_70])]) ).

fof(f4891,plain,
    ( spl97_69
    | ~ spl97_70 ),
    inference(avatar_split_clause,[],[f4879,f4888,f4885]) ).

fof(f4879,plain,
    ! [X0] :
      ( ~ sP92(sK45)
      | sP93(X0) ),
    inference(resolution,[],[f4875,f367]) ).

fof(f4875,plain,
    ! [X0] : ~ status(X0,sK45,esa),
    inference(resolution,[],[f2010,f1503]) ).

fof(f1503,plain,
    ! [X0] : status(X0,sK45,thm),
    inference(resolution,[],[f273,f287]) ).

fof(f273,plain,
    ! [X0,X1] :
      ( ~ model(sK38(X0,X1),X1)
      | status(X0,X1,thm) ),
    inference(cnf_transformation,[],[f175]) ).

fof(f175,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ( ~ model(sK38(X0,X1),X1)
          & model(sK38(X0,X1),X0) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK38])],[f173,f174]) ).

fof(f174,plain,
    ! [X0,X1] :
      ( ? [X3] :
          ( ~ model(X3,X1)
          & model(X3,X0) )
     => ( ~ model(sK38(X0,X1),X1)
        & model(sK38(X0,X1),X0) ) ),
    introduced(choice_axiom,[]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X3] :
            ( ~ model(X3,X1)
            & model(X3,X0) ) ) ),
    inference(rectify,[],[f172]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( ( ! [X2] :
            ( model(X2,X1)
            | ~ model(X2,X0) )
        | ~ status(X0,X1,thm) )
      & ( status(X0,X1,thm)
        | ? [X2] :
            ( ~ model(X2,X1)
            & model(X2,X0) ) ) ),
    inference(nnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( model(X2,X1)
          | ~ model(X2,X0) )
    <=> status(X0,X1,thm) ),
    inference(ennf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0,X1] :
      ( ! [X2] :
          ( model(X2,X0)
         => model(X2,X1) )
    <=> status(X0,X1,thm) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).

fof(f2010,plain,
    ! [X0,X1] :
      ( ~ status(X0,X1,thm)
      | ~ status(X0,X1,esa) ),
    inference(resolution,[],[f281,f205]) ).

fof(f205,plain,
    ~ mighta(esa,thm),
    inference(cnf_transformation,[],[f35]) ).

fof(f35,plain,
    ~ mighta(esa,thm),
    inference(flattening,[],[f34]) ).

fof(f34,negated_conjecture,
    ~ mighta(esa,thm),
    inference(negated_conjecture,[],[f33]) ).

fof(f33,conjecture,
    mighta(esa,thm),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta_esa_thm) ).

fof(f281,plain,
    ! [X2,X3,X0,X1] :
      ( mighta(X0,X1)
      | ~ status(X2,X3,X1)
      | ~ status(X2,X3,X0) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( mighta(X0,X1)
      | ! [X2,X3] :
          ( ~ status(X2,X3,X1)
          | ~ status(X2,X3,X0) ) ),
    inference(ennf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
     => mighta(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ? [X2,X3] :
          ( status(X2,X3,X1)
          & status(X2,X3,X0) )
    <=> mighta(X0,X1) ),
    inference(rectify,[],[f20]) ).

fof(f20,axiom,
    ! [X6,X7] :
      ( ? [X0,X1] :
          ( status(X0,X1,X7)
          & status(X0,X1,X6) )
    <=> mighta(X6,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : KRS256+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n002.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   : Fri May  3 19:53:53 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (10762)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (10764)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (10765)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.38  % (10763)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (10766)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38  % (10767)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38  % (10768)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38  % (10769)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [1]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [2]
% 0.22/0.39  TRYING [1,1,1]
% 0.22/0.39  TRYING [1,1,1]
% 0.22/0.39  TRYING [2,1,2]
% 0.22/0.39  TRYING [2,1,2]
% 0.22/0.39  TRYING [3]
% 0.22/0.39  TRYING [2,2,2]
% 0.22/0.40  TRYING [3]
% 0.22/0.40  TRYING [2,2,2]
% 0.22/0.40  TRYING [3,3,2]
% 0.22/0.40  TRYING [3,3,2]
% 0.22/0.40  TRYING [4]
% 0.22/0.41  TRYING [4]
% 0.22/0.41  TRYING [4,4,2]
% 0.22/0.41  TRYING [4,4,2]
% 0.22/0.43  TRYING [5]
% 0.22/0.44  TRYING [4,4,3]
% 0.22/0.45  TRYING [4,4,3]
% 0.22/0.46  TRYING [5]
% 0.22/0.46  % (10765)First to succeed.
% 0.22/0.46  % (10765)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-10762"
% 0.22/0.46  % (10765)Refutation found. Thanks to Tanya!
% 0.22/0.46  % SZS status Theorem for theBenchmark
% 0.22/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.46  % (10765)------------------------------
% 0.22/0.46  % (10765)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.22/0.46  % (10765)Termination reason: Refutation
% 0.22/0.46  
% 0.22/0.46  % (10765)Memory used [KB]: 1885
% 0.22/0.46  % (10765)Time elapsed: 0.077 s
% 0.22/0.46  % (10765)Instructions burned: 119 (million)
% 0.22/0.46  % (10762)Success in time 0.096 s
%------------------------------------------------------------------------------