TSTP Solution File: SYO889_16 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO889_16 : 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 : n025.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 09:16:07 EDT 2024

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   34 (   6 unt;   9 typ;   0 def)
%            Number of atoms       :  159 (   0 equ)
%            Maximal formula atoms :   13 (   6 avg)
%            Number of connectives :  176 (  60   ~;  49   |;  52   &)
%                                         (   0 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   18 (  18 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   82 (  50   !;  32   ?;  58   :)

% 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' * $i ) > '$ki_world' ).

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

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

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

tff(pred_def_2,type,
    a: ( '$ki_world' * $i ) > $o ).

tff(pred_def_3,type,
    b: ( '$ki_world' * $i ) > $o ).

tff(pred_def_4,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(f53,plain,
    $false,
    inference(subsumption_resolution,[],[f52,f36]) ).

tff(f36,plain,
    '$ki_accessible'(sK1,sK0(sK1,sK2)),
    inference(subsumption_resolution,[],[f34,f23]) ).

tff(f23,plain,
    '$ki_accessible'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f20]) ).

tff(f20,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2: '$ki_world'] :
                ( ~ b(X2,X1)
                | ~ a(X2,X1)
                | ~ '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ( b(sK0(X3,X4),X4)
              & '$ki_accessible'(X3,sK0(X3,X4)) )
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & ! [X8: '$ki_world'] :
        ( a(X8,sK2)
        | ~ '$ki_accessible'(sK1,X8) )
    & '$ki_exists_in_world_$i'(sK1,sK2)
    & '$ki_accessible'('$ki_local_world',sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f16,f19,f18,f17]) ).

tff(f17,plain,
    ! [X3: '$ki_world',X4] :
      ( ? [X5: '$ki_world'] :
          ( b(X5,X4)
          & '$ki_accessible'(X3,X5) )
     => ( b(sK0(X3,X4),X4)
        & '$ki_accessible'(X3,sK0(X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ( ? [X6: '$ki_world'] :
        ( ? [X7] :
            ( ! [X8: '$ki_world'] :
                ( a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            & '$ki_exists_in_world_$i'(X6,X7) )
        & '$ki_accessible'('$ki_local_world',X6) )
   => ( ? [X7] :
          ( ! [X8: '$ki_world'] :
              ( a(X8,X7)
              | ~ '$ki_accessible'(sK1,X8) )
          & '$ki_exists_in_world_$i'(sK1,X7) )
      & '$ki_accessible'('$ki_local_world',sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ( ? [X7] :
        ( ! [X8: '$ki_world'] :
            ( a(X8,X7)
            | ~ '$ki_accessible'(sK1,X8) )
        & '$ki_exists_in_world_$i'(sK1,X7) )
   => ( ! [X8: '$ki_world'] :
          ( a(X8,sK2)
          | ~ '$ki_accessible'(sK1,X8) )
      & '$ki_exists_in_world_$i'(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ( ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2: '$ki_world'] :
                ( ~ b(X2,X1)
                | ~ a(X2,X1)
                | ~ '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ? [X5: '$ki_world'] :
                ( b(X5,X4)
                & '$ki_accessible'(X3,X5) )
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & ? [X6: '$ki_world'] :
        ( ? [X7] :
            ( ! [X8: '$ki_world'] :
                ( a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            & '$ki_exists_in_world_$i'(X6,X7) )
        & '$ki_accessible'('$ki_local_world',X6) ) ),
    inference(rectify,[],[f11]) ).

tff(f11,plain,
    ( ! [X6: '$ki_world'] :
        ( ! [X7] :
            ( ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            | ~ '$ki_exists_in_world_$i'(X6,X7) )
        | ~ '$ki_accessible'('$ki_local_world',X6) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( b(X2,X1)
                & '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X4] :
            ( ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) )
            & '$ki_exists_in_world_$i'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(flattening,[],[f10]) ).

tff(f10,plain,
    ( ! [X6: '$ki_world'] :
        ( ! [X7] :
            ( ! [X8: '$ki_world'] :
                ( ~ b(X8,X7)
                | ~ a(X8,X7)
                | ~ '$ki_accessible'(X6,X8) )
            | ~ '$ki_exists_in_world_$i'(X6,X7) )
        | ~ '$ki_accessible'('$ki_local_world',X6) )
    & ! [X0: '$ki_world'] :
        ( ! [X1] :
            ( ? [X2: '$ki_world'] :
                ( b(X2,X1)
                & '$ki_accessible'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X4] :
            ( ! [X5: '$ki_world'] :
                ( a(X5,X4)
                | ~ '$ki_accessible'(X3,X5) )
            & '$ki_exists_in_world_$i'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(ennf_transformation,[],[f7]) ).

tff(f7,plain,
    ~ ( ( ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X1] :
                ( '$ki_exists_in_world_$i'(X0,X1)
               => ? [X2: '$ki_world'] :
                    ( b(X2,X1)
                    & '$ki_accessible'(X0,X2) ) ) )
        & ? [X3: '$ki_world'] :
            ( ? [X4] :
                ( ! [X5: '$ki_world'] :
                    ( '$ki_accessible'(X3,X5)
                   => a(X5,X4) )
                & '$ki_exists_in_world_$i'(X3,X4) )
            & '$ki_accessible'('$ki_local_world',X3) ) )
     => ? [X6: '$ki_world'] :
          ( ? [X7] :
              ( ? [X8: '$ki_world'] :
                  ( b(X8,X7)
                  & a(X8,X7)
                  & '$ki_accessible'(X6,X8) )
              & '$ki_exists_in_world_$i'(X6,X7) )
          & '$ki_accessible'('$ki_local_world',X6) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,negated_conjecture,
    ~ ( ( ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ! [X3] :
                ( '$ki_exists_in_world_$i'(X0,X3)
               => ? [X4: '$ki_world'] :
                    ( b(X4,X3)
                    & '$ki_accessible'(X0,X4) ) ) )
        & ? [X0: '$ki_world'] :
            ( ? [X3] :
                ( ! [X4: '$ki_world'] :
                    ( '$ki_accessible'(X0,X4)
                   => a(X4,X3) )
                & '$ki_exists_in_world_$i'(X0,X3) )
            & '$ki_accessible'('$ki_local_world',X0) ) )
     => ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( ? [X4: '$ki_world'] :
                  ( b(X4,X3)
                  & a(X4,X3)
                  & '$ki_accessible'(X0,X4) )
              & '$ki_exists_in_world_$i'(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f5,conjecture,
    ( ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ! [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
             => ? [X4: '$ki_world'] :
                  ( b(X4,X3)
                  & '$ki_accessible'(X0,X4) ) ) )
      & ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( ! [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                 => a(X4,X3) )
              & '$ki_exists_in_world_$i'(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) )
   => ? [X0: '$ki_world'] :
        ( ? [X3] :
            ( ? [X4: '$ki_world'] :
                ( b(X4,X3)
                & a(X4,X3)
                & '$ki_accessible'(X0,X4) )
            & '$ki_exists_in_world_$i'(X0,X3) )
        & '$ki_accessible'('$ki_local_world',X0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f34,plain,
    ( '$ki_accessible'(sK1,sK0(sK1,sK2))
    | ~ '$ki_accessible'('$ki_local_world',sK1) ),
    inference(resolution,[],[f26,f24]) ).

tff(f24,plain,
    '$ki_exists_in_world_$i'(sK1,sK2),
    inference(cnf_transformation,[],[f20]) ).

tff(f26,plain,
    ! [X3: '$ki_world',X4: $i] :
      ( ~ '$ki_exists_in_world_$i'(X3,X4)
      | '$ki_accessible'(X3,sK0(X3,X4))
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f52,plain,
    ~ '$ki_accessible'(sK1,sK0(sK1,sK2)),
    inference(resolution,[],[f51,f44]) ).

tff(f44,plain,
    b(sK0(sK1,sK2),sK2),
    inference(subsumption_resolution,[],[f42,f23]) ).

tff(f42,plain,
    ( b(sK0(sK1,sK2),sK2)
    | ~ '$ki_accessible'('$ki_local_world',sK1) ),
    inference(resolution,[],[f27,f24]) ).

tff(f27,plain,
    ! [X3: '$ki_world',X4: $i] :
      ( ~ '$ki_exists_in_world_$i'(X3,X4)
      | b(sK0(X3,X4),X4)
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f51,plain,
    ! [X0: '$ki_world'] :
      ( ~ b(X0,sK2)
      | ~ '$ki_accessible'(sK1,X0) ),
    inference(subsumption_resolution,[],[f50,f25]) ).

tff(f25,plain,
    ! [X8: '$ki_world'] :
      ( ~ '$ki_accessible'(sK1,X8)
      | a(X8,sK2) ),
    inference(cnf_transformation,[],[f20]) ).

tff(f50,plain,
    ! [X0: '$ki_world'] :
      ( ~ a(X0,sK2)
      | ~ '$ki_accessible'(sK1,X0)
      | ~ b(X0,sK2) ),
    inference(subsumption_resolution,[],[f48,f23]) ).

tff(f48,plain,
    ! [X0: '$ki_world'] :
      ( ~ a(X0,sK2)
      | ~ '$ki_accessible'(sK1,X0)
      | ~ b(X0,sK2)
      | ~ '$ki_accessible'('$ki_local_world',sK1) ),
    inference(resolution,[],[f28,f24]) ).

tff(f28,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ a(X2,X1)
      | ~ '$ki_accessible'(X0,X2)
      | ~ b(X2,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f20]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO889_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 10:28:23 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.13/0.35  % (1504)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37  % (1506)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37  % (1507)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)
% 0.13/0.37  % (1509)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.37  % (1510)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.37  % (1505)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  % (1509)First to succeed.
% 0.13/0.37  TRYING [2,1]
% 0.13/0.37  TRYING [3,1]
% 0.13/0.37  TRYING [1,1]
% 0.13/0.37  TRYING [2,1]
% 0.13/0.37  % (1509)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1504"
% 0.13/0.37  TRYING [3,1]
% 0.13/0.37  TRYING [4,1]
% 0.13/0.37  % (1507)Also succeeded, but the first one will report.
% 0.13/0.37  TRYING [4,1]
% 0.13/0.37  % (1510)Also succeeded, but the first one will report.
% 0.13/0.37  % (1509)Refutation found. Thanks to Tanya!
% 0.13/0.37  % SZS status Theorem for theBenchmark
% 0.13/0.37  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.37  % (1509)------------------------------
% 0.13/0.37  % (1509)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.37  % (1509)Termination reason: Refutation
% 0.13/0.37  
% 0.13/0.37  % (1509)Memory used [KB]: 751
% 0.13/0.37  % (1509)Time elapsed: 0.004 s
% 0.13/0.37  % (1509)Instructions burned: 4 (million)
% 0.13/0.37  % (1504)Success in time 0.009 s
%------------------------------------------------------------------------------