TSTP Solution File: DAT334_21 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT334_21 : 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 : n003.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 05:06:25 EDT 2024

% Result   : Theorem 0.16s 0.33s
% Output   : Refutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   36 (   4 unt;   9 typ;   0 def)
%            Number of atoms       :  116 (   0 equ)
%            Maximal formula atoms :    6 (   4 avg)
%            Number of connectives :   73 (  23   ~;  16   |;  25   &)
%                                         (   2 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   39 (  39 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   12 (  11 usr;   9 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :   24 (  15   !;   9   ?;  13   :)

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

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

tff(func_def_7,type,
    sK0: '$ki_world' ).

tff(func_def_8,type,
    sK1: '$ki_world' > $i ).

tff(func_def_9,type,
    sK2: '$ki_world' > '$ki_world' ).

tff(func_def_10,type,
    sK3: '$ki_world' > $i ).

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

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

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

tff(f48,plain,
    $false,
    inference(avatar_sat_refutation,[],[f41,f45,f47]) ).

tff(f47,plain,
    spl4_2,
    inference(avatar_contradiction_clause,[],[f46]) ).

tff(f46,plain,
    ( $false
    | spl4_2 ),
    inference(resolution,[],[f40,f22]) ).

tff(f22,plain,
    '$ki_accessible'('$ki_local_world',sK0),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,plain,
    ( ! [X1] :
        ( ~ teach(sK0,X1,cs)
        | ~ '$ki_exists_in_world_$i'(sK0,X1) )
    & '$ki_accessible'('$ki_local_world',sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f14]) ).

tff(f14,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ teach(X0,X1,cs)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ~ teach(sK0,X1,cs)
          | ~ '$ki_exists_in_world_$i'(sK0,X1) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f10,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ~ teach(X0,X1,cs)
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f7]) ).

tff(f7,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X2] :
            ( teach(X0,X2,cs)
            & '$ki_exists_in_world_$i'(X0,X2) ) ),
    inference(negated_conjecture,[],[f5]) ).

tff(f5,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X2] :
          ( teach(X0,X2,cs)
          & '$ki_exists_in_world_$i'(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f40,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK0)
    | spl4_2 ),
    inference(avatar_component_clause,[],[f38]) ).

tff(f38,plain,
    ( spl4_2
  <=> '$ki_accessible'('$ki_local_world',sK0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

tff(f45,plain,
    spl4_1,
    inference(avatar_contradiction_clause,[],[f44]) ).

tff(f44,plain,
    ( $false
    | spl4_1 ),
    inference(resolution,[],[f42,f22]) ).

tff(f42,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK0)
    | spl4_1 ),
    inference(resolution,[],[f36,f25]) ).

tff(f25,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_exists_in_world_$i'(X0,sK1(X0))
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & teach(X0,sK1(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK1(X0))
        & teach(X0,john,math) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f16]) ).

tff(f16,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( teach(X0,X1,cs)
          & '$ki_exists_in_world_$i'(X0,X1) )
     => ( teach(X0,sK1(X0),cs)
        & '$ki_exists_in_world_$i'(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ! [X0: '$ki_world'] :
      ( ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) )
        & teach(X0,john,math) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f8]) ).

tff(f8,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X1] :
            ( teach(X0,X1,cs)
            & '$ki_exists_in_world_$i'(X0,X1) )
        & teach(X0,john,math) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ( teach(X0,sue,psych)
        & teach(X0,mary,psych)
        & ? [X2] :
            ( teach(X0,X2,cs)
            & '$ki_exists_in_world_$i'(X0,X2) )
        & teach(X0,john,math) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',db) ).

tff(f36,plain,
    ( ~ '$ki_exists_in_world_$i'(sK0,sK1(sK0))
    | spl4_1 ),
    inference(avatar_component_clause,[],[f34]) ).

tff(f34,plain,
    ( spl4_1
  <=> '$ki_exists_in_world_$i'(sK0,sK1(sK0)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

tff(f41,plain,
    ( ~ spl4_1
    | ~ spl4_2 ),
    inference(avatar_split_clause,[],[f32,f38,f34]) ).

tff(f32,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK0)
    | ~ '$ki_exists_in_world_$i'(sK0,sK1(sK0)) ),
    inference(resolution,[],[f26,f23]) ).

tff(f23,plain,
    ! [X1: $i] :
      ( ~ teach(sK0,X1,cs)
      | ~ '$ki_exists_in_world_$i'(sK0,X1) ),
    inference(cnf_transformation,[],[f15]) ).

tff(f26,plain,
    ! [X0: '$ki_world'] :
      ( teach(X0,sK1(X0),cs)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f17]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem    : DAT334_21 : TPTP v8.2.0. Released v8.2.0.
% 0.10/0.11  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31  % Computer : n003.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit   : 300
% 0.10/0.31  % WCLimit    : 300
% 0.10/0.31  % DateTime   : Fri May  3 13:03:20 EDT 2024
% 0.10/0.31  % CPUTime    : 
% 0.10/0.32  % (16448)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.33  % (16451)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)
% 0.16/0.33  % (16450)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.16/0.33  % (16456)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)
% 0.16/0.33  % (16454)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.16/0.33  % (16452)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.16/0.33  % (16455)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.16/0.33  % (16449)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.16/0.33  TRYING [1,1,1]
% 0.16/0.33  TRYING [1,1]
% 0.16/0.33  TRYING [1,1,1]
% 0.16/0.33  % (16454)Also succeeded, but the first one will report.
% 0.16/0.33  % (16451)First to succeed.
% 0.16/0.33  % (16455)Also succeeded, but the first one will report.
% 0.16/0.33  TRYING [2,1,1]
% 0.16/0.33  TRYING [2,1,1]
% 0.16/0.33  TRYING [2,1]
% 0.16/0.33  TRYING [1,1]
% 0.16/0.33  TRYING [1,2,2]
% 0.16/0.33  TRYING [1,2,2]
% 0.16/0.33  TRYING [1,2]
% 0.16/0.33  TRYING [2,1]
% 0.16/0.33  TRYING [2,2,2]
% 0.16/0.33  TRYING [2,2,2]
% 0.16/0.33  TRYING [2,2]
% 0.16/0.33  % (16451)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16448"
% 0.16/0.33  TRYING [1,2]
% 0.16/0.33  TRYING [2,3,3]
% 0.16/0.33  TRYING [2,3,3]
% 0.16/0.33  TRYING [2,2]
% 0.16/0.33  TRYING [1,3]
% 0.16/0.33  % (16451)Refutation found. Thanks to Tanya!
% 0.16/0.33  % SZS status Theorem for theBenchmark
% 0.16/0.33  % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33  % (16451)------------------------------
% 0.16/0.33  % (16451)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.33  % (16451)Termination reason: Refutation
% 0.16/0.33  
% 0.16/0.33  % (16451)Memory used [KB]: 749
% 0.16/0.33  % (16451)Time elapsed: 0.004 s
% 0.16/0.33  % (16451)Instructions burned: 3 (million)
% 0.16/0.33  % (16448)Success in time 0.016 s
%------------------------------------------------------------------------------