TSTP Solution File: PLA053_2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---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_sat --cores 0 -t %d %s

% Computer : n021.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 15:41:24 EDT 2023

% Result   : Theorem 0.19s 0.51s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   44 (   9 unt;  11 typ;   0 def)
%            Number of atoms       :  164 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  181 (  69   ~;  51   |;  41   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   19 (  19 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   14 (   8   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   6 usr;   2 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   67 (;  51   !;  16   ?;  36   :)

% 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_3,type,
    sK2: '$ki_world' ).

tff(func_def_5,type,
    sK4: ( '$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(f76,plain,
    $false,
    inference(resolution,[],[f74,f34]) ).

tff(f34,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(f74,plain,
    ~ '$ki_accessible'(sK2,sK2),
    inference(resolution,[],[f62,f45]) ).

tff(f45,plain,
    ! [X0: $i,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ! [X0,X1: '$ki_world'] : '$ki_exists_in_world_$i'(X1,X0),
    inference(rectify,[],[f2]) ).

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

tff(f62,plain,
    ! [X0: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK2,X0)
      | ~ '$ki_accessible'(sK2,sK2) ),
    inference(resolution,[],[f54,f39]) ).

tff(f39,plain,
    ! [X2: $i] :
      ( bomb(sK2,sK3)
      | ~ '$ki_exists_in_world_$i'(sK2,X2) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,plain,
    ( '$ki_accessible'('$ki_local_world',sK2)
    & '$ki_exists_in_world_$i'(sK2,sK3)
    & ! [X2] :
        ( ~ '$ki_exists_in_world_$i'(sK2,X2)
        | ( bomb(sK2,sK3)
          & h(sK2,X2)
          & ~ defused(sK2,sK3) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f19,f26,f25]) ).

tff(f25,plain,
    ( ? [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
        & ? [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
            & ! [X2] :
                ( ~ '$ki_exists_in_world_$i'(X0,X2)
                | ( bomb(X0,X1)
                  & h(X0,X2)
                  & ~ defused(X0,X1) ) ) ) )
   => ( '$ki_accessible'('$ki_local_world',sK2)
      & ? [X1] :
          ( '$ki_exists_in_world_$i'(sK2,X1)
          & ! [X2] :
              ( ~ '$ki_exists_in_world_$i'(sK2,X2)
              | ( bomb(sK2,X1)
                & h(sK2,X2)
                & ~ defused(sK2,X1) ) ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ( ? [X1] :
        ( '$ki_exists_in_world_$i'(sK2,X1)
        & ! [X2] :
            ( ~ '$ki_exists_in_world_$i'(sK2,X2)
            | ( bomb(sK2,X1)
              & h(sK2,X2)
              & ~ defused(sK2,X1) ) ) )
   => ( '$ki_exists_in_world_$i'(sK2,sK3)
      & ! [X2] :
          ( ~ '$ki_exists_in_world_$i'(sK2,X2)
          | ( bomb(sK2,sK3)
            & h(sK2,X2)
            & ~ defused(sK2,sK3) ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,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(flattening,[],[f18]) ).

tff(f18,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2] :
              ( ( ~ defused(X0,X1)
                & h(X0,X2)
                & bomb(X0,X1) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ? [X2] :
                ( ( ( h(X0,X2)
                    & bomb(X0,X1) )
                 => defused(X0,X1) )
                & '$ki_exists_in_world_$i'(X0,X2) ) ) ),
    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(f54,plain,
    ( ~ bomb(sK2,sK3)
    | ~ '$ki_accessible'(sK2,sK2) ),
    inference(resolution,[],[f53,f41]) ).

tff(f41,plain,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f27]) ).

tff(f53,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ bomb(sK2,sK3)
      | ~ '$ki_accessible'(X0,sK2) ),
    inference(resolution,[],[f51,f45]) ).

tff(f51,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X0,sK3)
      | ~ '$ki_accessible'(X0,sK2)
      | ~ bomb(sK2,sK3)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(resolution,[],[f49,f45]) ).

tff(f49,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(sK2,sK4(X0,sK3))
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_exists_in_world_$i'(X0,sK3)
      | ~ bomb(sK2,sK3)
      | ~ '$ki_accessible'(X0,sK2) ),
    inference(resolution,[],[f48,f38]) ).

tff(f38,plain,
    ! [X2: $i] :
      ( h(sK2,X2)
      | ~ '$ki_exists_in_world_$i'(sK2,X2) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f48,plain,
    ! [X0: '$ki_world'] :
      ( ~ h(sK2,sK4(X0,sK3))
      | ~ '$ki_exists_in_world_$i'(X0,sK3)
      | ~ bomb(sK2,sK3)
      | ~ '$ki_accessible'(X0,sK2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(resolution,[],[f43,f46]) ).

tff(f46,plain,
    ~ defused(sK2,sK3),
    inference(resolution,[],[f45,f37]) ).

tff(f37,plain,
    ! [X2: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK2,X2)
      | ~ defused(sK2,sK3) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f43,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( defused(X3,X1)
      | ~ bomb(X3,X1)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ h(X3,sK4(X0,X1))
      | ~ '$ki_accessible'(X0,X3)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f29]) ).

tff(f29,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ( ! [X3: '$ki_world'] :
                ( ~ '$ki_accessible'(X0,X3)
                | ~ h(X3,sK4(X0,X1))
                | ~ bomb(X3,X1)
                | defused(X3,X1) )
            & '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f17,f28]) ).

tff(f28,plain,
    ! [X0: '$ki_world',X1] :
      ( ? [X2] :
          ( ! [X3: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X3)
              | ~ h(X3,X2)
              | ~ bomb(X3,X1)
              | defused(X3,X1) )
          & '$ki_exists_in_world_$i'(X0,X2) )
     => ( ! [X3: '$ki_world'] :
            ( ~ '$ki_accessible'(X0,X3)
            | ~ h(X3,sK4(X0,X1))
            | ~ bomb(X3,X1)
            | defused(X3,X1) )
        & '$ki_exists_in_world_$i'(X0,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ? [X2] :
              ( ! [X3: '$ki_world'] :
                  ( ~ '$ki_accessible'(X0,X3)
                  | ~ h(X3,X2)
                  | ~ bomb(X3,X1)
                  | defused(X3,X1) )
              & '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f16]) ).

tff(f16,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_$i'(X0,X1)
         => ? [X5] :
              ( ! [X4: '$ki_world'] :
                  ( '$ki_accessible'(X0,X4)
                 => ( ( bomb(X4,X1)
                      & h(X4,X5) )
                   => defused(X4,X1) ) )
              & '$ki_exists_in_world_$i'(X0,X5) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % 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 22 12:25:15 EDT 2023
% 0.13/0.35  % CPUTime    : 
% 0.19/0.51  % (19987)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51  % (19995)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51  % (19979)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51  % (19979)First to succeed.
% 0.19/0.51  % (19992)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.51  % (19979)Refutation found. Thanks to Tanya!
% 0.19/0.51  % SZS status Theorem for theBenchmark
% 0.19/0.51  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51  % (19979)------------------------------
% 0.19/0.51  % (19979)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51  % (19979)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51  % (19979)Termination reason: Refutation
% 0.19/0.51  
% 0.19/0.51  % (19979)Memory used [KB]: 895
% 0.19/0.51  % (19979)Time elapsed: 0.104 s
% 0.19/0.51  % (19979)Instructions burned: 3 (million)
% 0.19/0.51  % (19979)------------------------------
% 0.19/0.51  % (19979)------------------------------
% 0.19/0.51  % (19969)Success in time 0.155 s
%------------------------------------------------------------------------------