TSTP Solution File: PLA053_2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -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 : Mon May 22 15:41:23 EDT 2023

% Result   : Theorem 0.18s 0.50s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   51 (  11 unt;  11 typ;   0 def)
%            Number of atoms       :  168 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  186 (  69   ~;  54   |;  41   &)
%                                         (   2 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   11 (  11 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   69 (;  53   !;  16   ?;  38   :)

% 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 ).

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

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

tff(func_def_6,type,
    sK5: '$ki_world' > $i ).

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

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

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

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

tff(pred_def_5,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(f68,plain,
    $false,
    inference(avatar_sat_refutation,[],[f56,f60,f67]) ).

tff(f67,plain,
    ~ spl6_1,
    inference(avatar_contradiction_clause,[],[f66]) ).

tff(f66,plain,
    ( $false
    | ~ spl6_1 ),
    inference(subsumption_resolution,[],[f62,f44]) ).

tff(f44,plain,
    ! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: '$ki_world'] : '$ki_accessible'(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(f62,plain,
    ( ~ '$ki_accessible'(sK1,sK1)
    | ~ spl6_1 ),
    inference(resolution,[],[f52,f36]) ).

tff(f36,plain,
    '$ki_accessible'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f24]) ).

tff(f24,plain,
    ( '$ki_accessible'('$ki_local_world',sK1)
    & ! [X2] :
        ( ~ '$ki_exists_in_world_$i'(sK1,X2)
        | ( ~ defused(sK1,sK2)
          & h(sK1,X2)
          & bomb(sK1,sK2) ) )
    & '$ki_exists_in_world_$i'(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f19,f23,f22]) ).

tff(f22,plain,
    ( ? [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
        & ? [X1] :
            ( ! [X2] :
                ( ~ '$ki_exists_in_world_$i'(X0,X2)
                | ( ~ defused(X0,X1)
                  & h(X0,X2)
                  & bomb(X0,X1) ) )
            & '$ki_exists_in_world_$i'(X0,X1) ) )
   => ( '$ki_accessible'('$ki_local_world',sK1)
      & ? [X1] :
          ( ! [X2] :
              ( ~ '$ki_exists_in_world_$i'(sK1,X2)
              | ( ~ defused(sK1,X1)
                & h(sK1,X2)
                & bomb(sK1,X1) ) )
          & '$ki_exists_in_world_$i'(sK1,X1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f23,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( ~ '$ki_exists_in_world_$i'(sK1,X2)
            | ( ~ defused(sK1,X1)
              & h(sK1,X2)
              & bomb(sK1,X1) ) )
        & '$ki_exists_in_world_$i'(sK1,X1) )
   => ( ! [X2] :
          ( ~ '$ki_exists_in_world_$i'(sK1,X2)
          | ( ~ defused(sK1,sK2)
            & h(sK1,X2)
            & bomb(sK1,sK2) ) )
      & '$ki_exists_in_world_$i'(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ? [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
      & ? [X1] :
          ( ! [X2] :
              ( ~ '$ki_exists_in_world_$i'(X0,X2)
              | ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) ) )
          & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(flattening,[],[f18]) ).

tff(f18,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2] :
              ( ~ '$ki_exists_in_world_$i'(X0,X2)
              | ( ~ defused(X0,X1)
                & bomb(X0,X1)
                & h(X0,X2) ) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ? [X2] :
                ( '$ki_exists_in_world_$i'(X0,X2)
                & ( ( bomb(X0,X1)
                    & h(X0,X2) )
                 => defused(X0,X1) ) ) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ? [X5] :
                ( '$ki_exists_in_world_$i'(X0,X5)
                & ( ( h(X0,X5)
                    & bomb(X0,X1) )
                 => defused(X0,X1) ) ) ) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f7,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ? [X5] :
              ( '$ki_exists_in_world_$i'(X0,X5)
              & ( ( h(X0,X5)
                  & bomb(X0,X1) )
               => defused(X0,X1) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f52,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X0)
        | ~ '$ki_accessible'(X0,sK1) )
    | ~ spl6_1 ),
    inference(avatar_component_clause,[],[f51]) ).

tff(f51,plain,
    ( spl6_1
  <=> ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(X0,sK1)
        | ~ '$ki_accessible'('$ki_local_world',X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

tff(f60,plain,
    ~ spl6_2,
    inference(avatar_contradiction_clause,[],[f59]) ).

tff(f59,plain,
    ( $false
    | ~ spl6_2 ),
    inference(subsumption_resolution,[],[f57,f46]) ).

tff(f46,plain,
    ~ defused(sK1,sK2),
    inference(subsumption_resolution,[],[f35,f43]) ).

tff(f43,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f35,plain,
    ! [X2: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK1,X2)
      | ~ defused(sK1,sK2) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f57,plain,
    ( defused(sK1,sK2)
    | ~ spl6_2 ),
    inference(resolution,[],[f55,f47]) ).

tff(f47,plain,
    bomb(sK1,sK2),
    inference(subsumption_resolution,[],[f33,f43]) ).

tff(f33,plain,
    ! [X2: $i] :
      ( bomb(sK1,sK2)
      | ~ '$ki_exists_in_world_$i'(sK1,X2) ),
    inference(cnf_transformation,[],[f24]) ).

tff(f55,plain,
    ( ! [X1: $i] :
        ( ~ bomb(sK1,X1)
        | defused(sK1,X1) )
    | ~ spl6_2 ),
    inference(avatar_component_clause,[],[f54]) ).

tff(f54,plain,
    ( spl6_2
  <=> ! [X1] :
        ( ~ bomb(sK1,X1)
        | defused(sK1,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

tff(f56,plain,
    ( spl6_1
    | spl6_2 ),
    inference(avatar_split_clause,[],[f49,f54,f51]) ).

tff(f49,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( ~ bomb(sK1,X1)
      | ~ '$ki_accessible'(X0,sK1)
      | defused(sK1,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f48,f43]) ).

tff(f48,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ bomb(sK1,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(X0,sK1)
      | defused(sK1,X1) ),
    inference(resolution,[],[f45,f37]) ).

tff(f37,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( ~ h(X3,sK3(X0,X1))
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ bomb(X3,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | defused(X3,X1)
      | ~ '$ki_accessible'(X0,X3) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ( '$ki_exists_in_world_$i'(X0,sK3(X0,X1))
            & ! [X3: '$ki_world'] :
                ( ~ h(X3,sK3(X0,X1))
                | ~ bomb(X3,X1)
                | ~ '$ki_accessible'(X0,X3)
                | defused(X3,X1) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f16,f25]) ).

tff(f25,plain,
    ! [X0: '$ki_world',X1] :
      ( ? [X2] :
          ( '$ki_exists_in_world_$i'(X0,X2)
          & ! [X3: '$ki_world'] :
              ( ~ h(X3,X2)
              | ~ bomb(X3,X1)
              | ~ '$ki_accessible'(X0,X3)
              | defused(X3,X1) ) )
     => ( '$ki_exists_in_world_$i'(X0,sK3(X0,X1))
        & ! [X3: '$ki_world'] :
            ( ~ h(X3,sK3(X0,X1))
            | ~ bomb(X3,X1)
            | ~ '$ki_accessible'(X0,X3)
            | defused(X3,X1) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( '$ki_exists_in_world_$i'(X0,X2)
              & ! [X3: '$ki_world'] :
                  ( ~ h(X3,X2)
                  | ~ bomb(X3,X1)
                  | ~ '$ki_accessible'(X0,X3)
                  | defused(X3,X1) ) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f15]) ).

tff(f15,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( defused(X3,X1)
                  | ~ h(X3,X2)
                  | ~ bomb(X3,X1)
                  | ~ '$ki_accessible'(X0,X3) )
              & '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f10]) ).

tff(f10,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( '$ki_accessible'(X0,X3)
                 => ( ( h(X3,X2)
                      & bomb(X3,X1) )
                   => defused(X3,X1) ) )
              & '$ki_exists_in_world_$i'(X0,X2) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ? [X5] :
              ( '$ki_exists_in_world_$i'(X0,X5)
              & ! [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                 => ( ( bomb(X4,X1)
                      & h(X4,X5) )
                   => defused(X4,X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

tff(f45,plain,
    ! [X2: $i] : h(sK1,X2),
    inference(subsumption_resolution,[],[f34,f43]) ).

tff(f34,plain,
    ! [X2: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK1,X2)
      | h(sK1,X2) ),
    inference(cnf_transformation,[],[f24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.03/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.12/0.33  % Computer : n028.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 22 12:39:22 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.18/0.49  % (14560)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.18/0.49  % (14568)lrs+10_1:1_br=off:sos=on:ss=axioms:st=2.0:urr=on:i=33:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/33Mi)
% 0.18/0.50  % (14576)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.18/0.50  % (14560)First to succeed.
% 0.18/0.50  TRYING [1]
% 0.18/0.50  % (14560)Refutation found. Thanks to Tanya!
% 0.18/0.50  % SZS status Theorem for theBenchmark
% 0.18/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.50  % (14560)------------------------------
% 0.18/0.50  % (14560)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.18/0.50  % (14560)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.18/0.50  % (14560)Termination reason: Refutation
% 0.18/0.50  
% 0.18/0.50  % (14560)Memory used [KB]: 5884
% 0.18/0.50  % (14560)Time elapsed: 0.101 s
% 0.18/0.50  % (14560)Instructions burned: 1 (million)
% 0.18/0.50  % (14560)------------------------------
% 0.18/0.50  % (14560)------------------------------
% 0.18/0.50  % (14558)Success in time 0.162 s
%------------------------------------------------------------------------------