TSTP Solution File: SYO890_16 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYO890_16 : 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 : n026.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 15:45:48 EDT 2023

% Result   : Theorem 0.20s 0.55s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   32 (   5 unt;   8 typ;   0 def)
%            Number of atoms       :   97 (   0 equ)
%            Maximal formula atoms :    7 (   4 avg)
%            Number of connectives :  101 (  36   ~;  23   |;  26   &)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :    8 (   8 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :    9 (   5   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   54 (;  40   !;  14   ?;  33   :)

% 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' ).

tff(func_def_3,type,
    sK2: '$ki_world' > $i ).

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

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

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

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

tff(f39,plain,
    $false,
    inference(subsumption_resolution,[],[f38,f26]) ).

tff(f26,plain,
    '$ki_accessible'('$ki_local_world',sK0),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ! [X1] :
        ( ~ f(sK0,X1)
        | ~ '$ki_exists_in_world_$i'(sK0,X1) )
    & '$ki_accessible'('$ki_local_world',sK0)
    & '$ki_exists_in_world_$i'('$ki_local_world',sK1)
    & ! [X3: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X3)
        | f(X3,sK1) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f16,f18,f17]) ).

tff(f17,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ~ f(X0,X1)
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ~ f(sK0,X1)
          | ~ '$ki_exists_in_world_$i'(sK0,X1) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ( ? [X2] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X2)
        & ! [X3: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X3)
            | f(X3,X2) ) )
   => ( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
      & ! [X3: '$ki_world'] :
          ( ~ '$ki_accessible'('$ki_local_world',X3)
          | f(X3,sK1) ) ) ),
    introduced(choice_axiom,[]) ).

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

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

tff(f10,plain,
    ~ ( ? [X0] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X0)
          & ! [X1: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X1)
             => f(X1,X0) ) )
     => ! [X2: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X2)
         => ? [X3] :
              ( '$ki_exists_in_world_$i'(X2,X3)
              & f(X2,X3) ) ) ),
    inference(pure_predicate_removal,[],[f9]) ).

tff(f9,plain,
    ~ ( ? [X0] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X0)
          & ! [X1: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X1)
             => ( e(X1,X0)
                & f(X1,X0) ) ) )
     => ! [X2: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X2)
         => ? [X3] :
              ( '$ki_exists_in_world_$i'(X2,X3)
              & f(X2,X3) ) ) ),
    inference(rectify,[],[f6]) ).

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

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

tff(f38,plain,
    ~ '$ki_accessible'('$ki_local_world',sK0),
    inference(resolution,[],[f37,f24]) ).

tff(f24,plain,
    ! [X3: '$ki_world'] :
      ( f(X3,sK1)
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f37,plain,
    ~ f(sK0,sK1),
    inference(subsumption_resolution,[],[f34,f26]) ).

tff(f34,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK0)
    | ~ f(sK0,sK1) ),
    inference(resolution,[],[f33,f25]) ).

tff(f25,plain,
    '$ki_exists_in_world_$i'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f19]) ).

tff(f33,plain,
    ! [X0: '$ki_world',X1: $i] :
      ( ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ f(sK0,X1)
      | ~ '$ki_accessible'(X0,sK0) ),
    inference(resolution,[],[f31,f27]) ).

tff(f27,plain,
    ! [X1: $i] :
      ( ~ '$ki_exists_in_world_$i'(sK0,X1)
      | ~ f(sK0,X1) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f31,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
      ( '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'(X2,X0)
      | ~ '$ki_exists_in_world_$i'(X2,X1) ),
    inference(cnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0: '$ki_world',X1,X2: '$ki_world'] :
      ( ~ '$ki_accessible'(X2,X0)
      | ~ '$ki_exists_in_world_$i'(X2,X1)
      | '$ki_exists_in_world_$i'(X0,X1) ),
    inference(rectify,[],[f14]) ).

tff(f14,plain,
    ! [X1: '$ki_world',X0,X2: '$ki_world'] :
      ( ~ '$ki_accessible'(X2,X1)
      | ~ '$ki_exists_in_world_$i'(X2,X0)
      | '$ki_exists_in_world_$i'(X1,X0) ),
    inference(flattening,[],[f13]) ).

tff(f13,plain,
    ! [X1: '$ki_world',X2: '$ki_world',X0] :
      ( '$ki_exists_in_world_$i'(X1,X0)
      | ~ '$ki_exists_in_world_$i'(X2,X0)
      | ~ '$ki_accessible'(X2,X1) ),
    inference(ennf_transformation,[],[f7]) ).

tff(f7,plain,
    ! [X1: '$ki_world',X2: '$ki_world',X0] :
      ( ( '$ki_exists_in_world_$i'(X2,X0)
        & '$ki_accessible'(X2,X1) )
     => '$ki_exists_in_world_$i'(X1,X0) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X3,X1: '$ki_world',X0: '$ki_world'] :
      ( ( '$ki_exists_in_world_$i'(X0,X3)
        & '$ki_accessible'(X0,X1) )
     => '$ki_exists_in_world_$i'(X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO890_16 : TPTP v8.2.0. Released v8.2.0.
% 0.06/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n026.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
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon May 22 13:26:38 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.53  % (4540)dis+1002_1:12_drc=off:fd=preordered:tgt=full:i=99978:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99978Mi)
% 0.20/0.54  % (4551)lrs+10_1:2_br=off:nm=4:ss=included:urr=on:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.54  % (4540)First to succeed.
% 0.20/0.55  % (4541)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)
% 0.20/0.55  % (4540)Refutation found. Thanks to Tanya!
% 0.20/0.55  % SZS status Theorem for theBenchmark
% 0.20/0.55  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.55  % (4540)------------------------------
% 0.20/0.55  % (4540)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55  % (4540)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55  % (4540)Termination reason: Refutation
% 0.20/0.55  
% 0.20/0.55  % (4540)Memory used [KB]: 5884
% 0.20/0.55  % (4540)Time elapsed: 0.129 s
% 0.20/0.55  % (4540)Instructions burned: 2 (million)
% 0.20/0.55  % (4540)------------------------------
% 0.20/0.55  % (4540)------------------------------
% 0.20/0.55  % (4539)Success in time 0.197 s
%------------------------------------------------------------------------------