TSTP Solution File: SYO900_11 by Vampire-SAT---4.8

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%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n018.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 09:16:10 EDT 2024

% Result   : Theorem 0.12s 0.35s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   26 (   5 unt;   9 typ;   0 def)
%            Number of atoms       :  105 (   0 equ)
%            Maximal formula atoms :   10 (   6 avg)
%            Number of connectives :  120 (  32   ~;  16   |;  44   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   56 (  36   !;  20   ?;  56   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    '$ki_world': $tType ).

tff(func_def_0,type,
    '$ki_local_world': '$ki_world' ).

tff(func_def_1,type,
    sK0: '$ki_world' ).

tff(func_def_2,type,
    sK1: '$ki_world' ).

tff(func_def_3,type,
    sK2: '$ki_world' ).

tff(func_def_4,type,
    sK3: '$ki_world' ).

tff(pred_def_1,type,
    '$ki_accessible': ( '$ki_world' * '$ki_world' ) > $o ).

tff(pred_def_2,type,
    p: '$ki_world' > $o ).

tff(pred_def_3,type,
    q: '$ki_world' > $o ).

tff(f23,plain,
    $false,
    inference(resolution,[],[f22,f20]) ).

tff(f20,plain,
    ~ p(sK1),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,plain,
    ( ~ p(sK1)
    & '$ki_accessible'(sK0,sK1)
    & ! [X2: '$ki_world'] :
        ( q(X2)
        | ~ '$ki_accessible'(sK0,X2) )
    & '$ki_accessible'('$ki_local_world',sK0)
    & ~ q(sK3)
    & '$ki_accessible'(sK2,sK3)
    & ! [X5: '$ki_world'] :
        ( p(X5)
        | ~ '$ki_accessible'(sK2,X5) )
    & '$ki_accessible'('$ki_local_world',sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f7,f11,f10,f9,f8]) ).

tff(f8,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( ~ p(X1)
            & '$ki_accessible'(X0,X1) )
        & ! [X2: '$ki_world'] :
            ( q(X2)
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1: '$ki_world'] :
          ( ~ p(X1)
          & '$ki_accessible'(sK0,X1) )
      & ! [X2: '$ki_world'] :
          ( q(X2)
          | ~ '$ki_accessible'(sK0,X2) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f9,plain,
    ( ? [X1: '$ki_world'] :
        ( ~ p(X1)
        & '$ki_accessible'(sK0,X1) )
   => ( ~ p(sK1)
      & '$ki_accessible'(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f10,plain,
    ( ? [X3: '$ki_world'] :
        ( ? [X4: '$ki_world'] :
            ( ~ q(X4)
            & '$ki_accessible'(X3,X4) )
        & ! [X5: '$ki_world'] :
            ( p(X5)
            | ~ '$ki_accessible'(X3,X5) )
        & '$ki_accessible'('$ki_local_world',X3) )
   => ( ? [X4: '$ki_world'] :
          ( ~ q(X4)
          & '$ki_accessible'(sK2,X4) )
      & ! [X5: '$ki_world'] :
          ( p(X5)
          | ~ '$ki_accessible'(sK2,X5) )
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ( ? [X4: '$ki_world'] :
        ( ~ q(X4)
        & '$ki_accessible'(sK2,X4) )
   => ( ~ q(sK3)
      & '$ki_accessible'(sK2,sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f7,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( ~ p(X1)
            & '$ki_accessible'(X0,X1) )
        & ! [X2: '$ki_world'] :
            ( q(X2)
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X4: '$ki_world'] :
            ( ~ q(X4)
            & '$ki_accessible'(X3,X4) )
        & ! [X5: '$ki_world'] :
            ( p(X5)
            | ~ '$ki_accessible'(X3,X5) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X2: '$ki_world'] :
            ( ~ p(X2)
            & '$ki_accessible'(X0,X2) )
        & ! [X1: '$ki_world'] :
            ( q(X1)
            | ~ '$ki_accessible'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X5: '$ki_world'] :
            ( ~ q(X5)
            & '$ki_accessible'(X3,X5) )
        & ! [X4: '$ki_world'] :
            ( p(X4)
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(flattening,[],[f5]) ).

tff(f5,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X2: '$ki_world'] :
            ( ~ p(X2)
            & '$ki_accessible'(X0,X2) )
        & ! [X1: '$ki_world'] :
            ( q(X1)
            | ~ '$ki_accessible'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X5: '$ki_world'] :
            ( ~ q(X5)
            & '$ki_accessible'(X3,X5) )
        & ! [X4: '$ki_world'] :
            ( p(X4)
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(ennf_transformation,[],[f4]) ).

tff(f4,plain,
    ~ ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( ! [X1: '$ki_world'] :
                ( '$ki_accessible'(X0,X1)
               => q(X1) )
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => p(X2) ) ) )
      | ! [X3: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X3)
         => ( ! [X4: '$ki_world'] :
                ( '$ki_accessible'(X3,X4)
               => p(X4) )
           => ! [X5: '$ki_world'] :
                ( '$ki_accessible'(X3,X5)
               => q(X5) ) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => q(X2) )
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => p(X2) ) ) )
      | ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => p(X2) )
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => q(X2) ) ) ) ),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    ( ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => q(X2) )
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => p(X2) ) ) )
    | ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => p(X2) )
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => q(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f22,plain,
    ! [X5: '$ki_world'] : p(X5),
    inference(subsumption_resolution,[],[f14,f21]) ).

tff(f21,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).

tff(f14,plain,
    ! [X5: '$ki_world'] :
      ( p(X5)
      | ~ '$ki_accessible'(sK2,X5) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n018.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon May 20 09:56:37 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (2249)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.35  % (2255)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.12/0.35  % (2254)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.12/0.35  % (2251)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.35  % (2253)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.12/0.35  % (2252)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)
% 0.12/0.35  % (2256)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)
% 0.12/0.35  Detected minimum model sizes of [1,1]
% 0.12/0.35  Detected minimum model sizes of [1]
% 0.12/0.35  Detected minimum model sizes of [1,1]
% 0.12/0.35  Detected maximum model sizes of [2,2]
% 0.12/0.35  Detected maximum model sizes of [5]
% 0.12/0.35  Detected maximum model sizes of [2,2]
% 0.12/0.35  % (2254)Also succeeded, but the first one will report.
% 0.12/0.35  % (2252)Also succeeded, but the first one will report.
% 0.12/0.35  % (2255)First to succeed.
% 0.12/0.35  % (2250)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.12/0.35  TRYING [1]
% 0.12/0.35  TRYING [1,1]
% 0.12/0.35  TRYING [1,1]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  TRYING [2,2]
% 0.12/0.35  TRYING [2,2]
% 0.12/0.35  % (2255)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2249"
% 0.12/0.35  Cannot enumerate next child to try in an incomplete setup
% 0.12/0.35  % (2251)Refutation not found, incomplete strategy% (2251)------------------------------
% 0.12/0.35  % (2251)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (2251)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.35  
% 0.12/0.35  % (2251)Memory used [KB]: 725
% 0.12/0.35  % (2251)Time elapsed: 0.003 s
% 0.12/0.35  % (2251)Instructions burned: 2 (million)
% 0.12/0.35  Cannot enumerate next child to try in an incomplete setup
% 0.12/0.35  TRYING [3]
% 0.12/0.35  % (2253)Refutation not found, incomplete strategy% (2253)------------------------------
% 0.12/0.35  % (2253)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (2253)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.35  
% 0.12/0.35  % (2253)Memory used [KB]: 726
% 0.12/0.35  % (2253)Time elapsed: 0.003 s
% 0.12/0.35  % (2253)Instructions burned: 2 (million)
% 0.12/0.35  % (2251)------------------------------
% 0.12/0.35  % (2251)------------------------------
% 0.12/0.35  % (2253)------------------------------
% 0.12/0.35  % (2253)------------------------------
% 0.12/0.35  TRYING [4]
% 0.12/0.35  Detected minimum model sizes of [1]
% 0.12/0.35  Detected maximum model sizes of [5]
% 0.12/0.35  % (2255)Refutation found. Thanks to Tanya!
% 0.12/0.35  % SZS status Theorem for theBenchmark
% 0.12/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.35  % (2255)------------------------------
% 0.12/0.35  % (2255)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.35  % (2255)Termination reason: Refutation
% 0.12/0.35  
% 0.12/0.35  % (2255)Memory used [KB]: 732
% 0.12/0.35  % (2255)Time elapsed: 0.003 s
% 0.12/0.35  % (2255)Instructions burned: 3 (million)
% 0.12/0.35  % (2249)Success in time 0.017 s
%------------------------------------------------------------------------------