TSTP Solution File: PLA053_2 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% 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 file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n020.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 02:21:19 EDT 2024

% Result   : Theorem 0.62s 0.77s
% Output   : Refutation 0.62s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   43 (  10 unt;  11 typ;   0 def)
%            Number of atoms       :  155 (   0 equ)
%            Maximal formula atoms :   12 (   4 avg)
%            Number of connectives :  168 (  61   ~;  46   |;  41   &)
%                                         (   0 <=>;  20  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   16 (  16 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   :   65 (  49   !;  16   ?;  35   :)

% 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' > $i ).

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

tff(func_def_5,type,
    sK4: '$ki_world' ).

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(subsumption_resolution,[],[f66,f31]) ).

tff(f31,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/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(f66,plain,
    ~ '$ki_accessible'(sK4,sK4),
    inference(resolution,[],[f62,f40]) ).

tff(f40,plain,
    '$ki_accessible'('$ki_local_world',sK4),
    inference(cnf_transformation,[],[f30]) ).

tff(f30,plain,
    ( ! [X2] :
        ( ( ~ defused(sK4,sK5)
          & h(sK4,X2)
          & bomb(sK4,sK5) )
        | ~ '$ki_exists_in_world_$i'(sK4,X2) )
    & '$ki_exists_in_world_$i'(sK4,sK5)
    & '$ki_accessible'('$ki_local_world',sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f19,f29,f28]) ).

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

tff(f29,plain,
    ( ? [X1] :
        ( ! [X2] :
            ( ( ~ defused(sK4,X1)
              & h(sK4,X2)
              & bomb(sK4,X1) )
            | ~ '$ki_exists_in_world_$i'(sK4,X2) )
        & '$ki_exists_in_world_$i'(sK4,X1) )
   => ( ! [X2] :
          ( ( ~ defused(sK4,sK5)
            & h(sK4,X2)
            & bomb(sK4,sK5) )
          | ~ '$ki_exists_in_world_$i'(sK4,X2) )
      & '$ki_exists_in_world_$i'(sK4,sK5) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,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(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,[],[f12]) ).

tff(f12,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_$i'(X0,X1)
           => ? [X5] :
                ( ( ( h(X0,X5)
                    & bomb(X0,X1) )
                 => defused(X0,X1) )
                & '$ki_exists_in_world_$i'(X0,X5) ) ) ),
    inference(negated_conjecture,[],[f7]) ).

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

tff(f62,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(X0,sK4) ),
    inference(subsumption_resolution,[],[f61,f32]) ).

tff(f32,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_$i'(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f61,plain,
    ! [X0: '$ki_world'] :
      ( ~ '$ki_accessible'(X0,sK4)
      | ~ '$ki_exists_in_world_$i'(X0,sK5)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f60,f46]) ).

tff(f46,plain,
    ! [X2: $i] : h(sK4,X2),
    inference(subsumption_resolution,[],[f43,f32]) ).

tff(f43,plain,
    ! [X2: $i] :
      ( h(sK4,X2)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f60,plain,
    ! [X0: '$ki_world'] :
      ( ~ h(sK4,sK3(X0,sK5))
      | ~ '$ki_accessible'(X0,sK4)
      | ~ '$ki_exists_in_world_$i'(X0,sK5)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f58,f45]) ).

tff(f45,plain,
    ~ defused(sK4,sK5),
    inference(subsumption_resolution,[],[f44,f32]) ).

tff(f44,plain,
    ! [X2: $i] :
      ( ~ defused(sK4,sK5)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f30]) ).

tff(f58,plain,
    ! [X0: '$ki_world'] :
      ( defused(sK4,sK5)
      | ~ h(sK4,sK3(X0,sK5))
      | ~ '$ki_accessible'(X0,sK4)
      | ~ '$ki_exists_in_world_$i'(X0,sK5)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(resolution,[],[f47,f39]) ).

tff(f39,plain,
    ! [X3: '$ki_world',X0: '$ki_world',X1: $i] :
      ( defused(X3,X1)
      | ~ h(X3,sK3(X0,X1))
      | ~ bomb(X3,X1)
      | ~ '$ki_accessible'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ( ! [X3: '$ki_world'] :
                ( defused(X3,X1)
                | ~ h(X3,sK3(X0,X1))
                | ~ bomb(X3,X1)
                | ~ '$ki_accessible'(X0,X3) )
            & '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f17,f26]) ).

tff(f26,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_$i'(X0,X2) )
     => ( ! [X3: '$ki_world'] :
            ( defused(X3,X1)
            | ~ h(X3,sK3(X0,X1))
            | ~ bomb(X3,X1)
            | ~ '$ki_accessible'(X0,X3) )
        & '$ki_exists_in_world_$i'(X0,sK3(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f17,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(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,[],[f11]) ).

tff(f11,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'] :
                  ( '$ki_accessible'(X0,X4)
                 => ( ( h(X4,X5)
                      & bomb(X4,X1) )
                   => defused(X4,X1) ) )
              & '$ki_exists_in_world_$i'(X0,X5) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

tff(f47,plain,
    bomb(sK4,sK5),
    inference(subsumption_resolution,[],[f42,f32]) ).

tff(f42,plain,
    ! [X2: $i] :
      ( bomb(sK4,sK5)
      | ~ '$ki_exists_in_world_$i'(sK4,X2) ),
    inference(cnf_transformation,[],[f30]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.15  % Problem    : PLA053_2 : TPTP v8.2.0. Released v8.2.0.
% 0.13/0.17  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.17/0.39  % Computer : n020.cluster.edu
% 0.17/0.39  % Model    : x86_64 x86_64
% 0.17/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39  % Memory   : 8042.1875MB
% 0.17/0.39  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39  % CPULimit   : 300
% 0.17/0.39  % WCLimit    : 300
% 0.17/0.39  % DateTime   : Sat May 18 13:44:23 EDT 2024
% 0.17/0.40  % CPUTime    : 
% 0.17/0.40  This is a TF0_THM_NEQ_NAR problem
% 0.17/0.40  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.77  % (23625)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2996ds/34Mi)
% 0.62/0.77  % (23627)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2996ds/83Mi)
% 0.62/0.77  % (23626)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2996ds/45Mi)
% 0.62/0.77  % (23628)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2996ds/56Mi)
% 0.62/0.77  % (23625)First to succeed.
% 0.62/0.77  % (23625)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-23620"
% 0.62/0.77  % (23621)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2996ds/34Mi)
% 0.62/0.77  % (23626)Also succeeded, but the first one will report.
% 0.62/0.77  % (23628)Also succeeded, but the first one will report.
% 0.62/0.77  % (23627)Also succeeded, but the first one will report.
% 0.62/0.77  % (23625)Refutation found. Thanks to Tanya!
% 0.62/0.77  % SZS status Theorem for theBenchmark
% 0.62/0.77  % SZS output start Proof for theBenchmark
% See solution above
% 0.62/0.77  % (23625)------------------------------
% 0.62/0.77  % (23625)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.62/0.77  % (23625)Termination reason: Refutation
% 0.62/0.77  
% 0.62/0.77  % (23625)Memory used [KB]: 1045
% 0.62/0.77  % (23625)Time elapsed: 0.002 s
% 0.62/0.77  % (23625)Instructions burned: 4 (million)
% 0.62/0.77  % (23620)Success in time 0.369 s
% 0.62/0.77  % Vampire---4.8 exiting
%------------------------------------------------------------------------------