TSTP Solution File: SYO888_10 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYO888_10 : 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 : n023.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 15:45:51 EDT 2023

% Result   : Theorem 0.17s 0.46s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   41 (  10 unt;   9 typ;   0 def)
%            Number of atoms       :  161 (   0 equ)
%            Maximal formula atoms :   12 (   5 avg)
%            Number of connectives :  162 (  54   ~;  43   |;  31   &)
%                                         (   2 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of FOOLs       :   21 (  21 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   11 (   6   >;   5   *;   0   +;   0  <<)
%            Number of predicates  :    9 (   8 usr;   4 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-1 aty)
%            Number of variables   :   54 (;  44   !;  10   ?;  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' > $i ).

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

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

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

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

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

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

tff(f72,plain,
    $false,
    inference(avatar_sat_refutation,[],[f37,f67,f71]) ).

tff(f71,plain,
    ~ spl3_1,
    inference(avatar_contradiction_clause,[],[f70]) ).

tff(f70,plain,
    ( $false
    | ~ spl3_1 ),
    inference(subsumption_resolution,[],[f68,f25]) ).

tff(f25,plain,
    ~ h(sK2,sK1),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ! [X0] :
        ( ~ f('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | g(X1,X0) ) )
    & '$ki_exists_in_world_$i'('$ki_local_world',sK1)
    & '$ki_accessible'('$ki_local_world',sK2)
    & ~ h(sK2,sK1)
    & f('$ki_local_world',sK1)
    & ! [X4] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
        | ! [X5: '$ki_world'] :
            ( h(X5,X4)
            | ~ '$ki_accessible'('$ki_local_world',X5) )
        | ~ g('$ki_local_world',X4) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f16,f18,f17]) ).

tff(f17,plain,
    ( ? [X2] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X2)
        & ? [X3: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X3)
            & ~ h(X3,X2) )
        & f('$ki_local_world',X2) )
   => ( '$ki_exists_in_world_$i'('$ki_local_world',sK1)
      & ? [X3: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X3)
          & ~ h(X3,sK1) )
      & f('$ki_local_world',sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ( ? [X3: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X3)
        & ~ h(X3,sK1) )
   => ( '$ki_accessible'('$ki_local_world',sK2)
      & ~ h(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f16,plain,
    ( ! [X0] :
        ( ~ f('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | g(X1,X0) ) )
    & ? [X2] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X2)
        & ? [X3: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X3)
            & ~ h(X3,X2) )
        & f('$ki_local_world',X2) )
    & ! [X4] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
        | ! [X5: '$ki_world'] :
            ( h(X5,X4)
            | ~ '$ki_accessible'('$ki_local_world',X5) )
        | ~ g('$ki_local_world',X4) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,plain,
    ( ! [X2] :
        ( ~ f('$ki_local_world',X2)
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X2)
        | ! [X3: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X3)
            | g(X3,X2) ) )
    & ? [X4] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X4)
        & ? [X5: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X5)
            & ~ h(X5,X4) )
        & f('$ki_local_world',X4) )
    & ! [X0] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( h(X1,X0)
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        | ~ g('$ki_local_world',X0) ) ),
    inference(flattening,[],[f9]) ).

tff(f9,plain,
    ( ? [X4] :
        ( ? [X5: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X5)
            & ~ h(X5,X4) )
        & f('$ki_local_world',X4)
        & '$ki_exists_in_world_$i'('$ki_local_world',X4) )
    & ! [X2] :
        ( ! [X3: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X3)
            | g(X3,X2) )
        | ~ f('$ki_local_world',X2)
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X2) )
    & ! [X0] :
        ( ! [X1: '$ki_world'] :
            ( h(X1,X0)
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        | ~ g('$ki_local_world',X0)
        | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0) ) ),
    inference(ennf_transformation,[],[f6]) ).

tff(f6,plain,
    ~ ( ( ! [X2] :
            ( '$ki_exists_in_world_$i'('$ki_local_world',X2)
           => ( f('$ki_local_world',X2)
             => ! [X3: '$ki_world'] :
                  ( '$ki_accessible'('$ki_local_world',X3)
                 => g(X3,X2) ) ) )
        & ! [X0] :
            ( '$ki_exists_in_world_$i'('$ki_local_world',X0)
           => ( g('$ki_local_world',X0)
             => ! [X1: '$ki_world'] :
                  ( '$ki_accessible'('$ki_local_world',X1)
                 => h(X1,X0) ) ) ) )
     => ! [X4] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X4)
         => ( f('$ki_local_world',X4)
           => ! [X5: '$ki_world'] :
                ( '$ki_accessible'('$ki_local_world',X5)
               => h(X5,X4) ) ) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,negated_conjecture,
    ~ ( ( ! [X3] :
            ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
           => ( g('$ki_local_world',X3)
             => ! [X0: '$ki_world'] :
                  ( '$ki_accessible'('$ki_local_world',X0)
                 => h(X0,X3) ) ) )
        & ! [X3] :
            ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
           => ( f('$ki_local_world',X3)
             => ! [X0: '$ki_world'] :
                  ( '$ki_accessible'('$ki_local_world',X0)
                 => g(X0,X3) ) ) ) )
     => ! [X3] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
         => ( f('$ki_local_world',X3)
           => ! [X0: '$ki_world'] :
                ( '$ki_accessible'('$ki_local_world',X0)
               => h(X0,X3) ) ) ) ),
    inference(negated_conjecture,[],[f4]) ).

tff(f4,conjecture,
    ( ( ! [X3] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
         => ( g('$ki_local_world',X3)
           => ! [X0: '$ki_world'] :
                ( '$ki_accessible'('$ki_local_world',X0)
               => h(X0,X3) ) ) )
      & ! [X3] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
         => ( f('$ki_local_world',X3)
           => ! [X0: '$ki_world'] :
                ( '$ki_accessible'('$ki_local_world',X0)
               => g(X0,X3) ) ) ) )
   => ! [X3] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
       => ( f('$ki_local_world',X3)
         => ! [X0: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X0)
             => h(X0,X3) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f68,plain,
    ( h(sK2,sK1)
    | ~ spl3_1 ),
    inference(resolution,[],[f32,f26]) ).

tff(f26,plain,
    '$ki_accessible'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f19]) ).

tff(f32,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X0)
        | h(X0,sK1) )
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f31]) ).

tff(f31,plain,
    ( spl3_1
  <=> ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',X0)
        | h(X0,sK1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f67,plain,
    spl3_2,
    inference(avatar_contradiction_clause,[],[f66]) ).

tff(f66,plain,
    ( $false
    | spl3_2 ),
    inference(subsumption_resolution,[],[f65,f36]) ).

tff(f36,plain,
    ( ~ g('$ki_local_world',sK1)
    | spl3_2 ),
    inference(avatar_component_clause,[],[f34]) ).

tff(f34,plain,
    ( spl3_2
  <=> g('$ki_local_world',sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f65,plain,
    g('$ki_local_world',sK1),
    inference(subsumption_resolution,[],[f64,f27]) ).

tff(f27,plain,
    '$ki_exists_in_world_$i'('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f19]) ).

tff(f64,plain,
    ( ~ '$ki_exists_in_world_$i'('$ki_local_world',sK1)
    | g('$ki_local_world',sK1) ),
    inference(resolution,[],[f48,f24]) ).

tff(f24,plain,
    f('$ki_local_world',sK1),
    inference(cnf_transformation,[],[f19]) ).

tff(f48,plain,
    ! [X1: $i] :
      ( ~ f('$ki_local_world',X1)
      | ~ '$ki_exists_in_world_$i'('$ki_local_world',X1)
      | g('$ki_local_world',X1) ),
    inference(resolution,[],[f28,f21]) ).

tff(f21,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(f28,plain,
    ! [X0: $i,X1: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X1)
      | ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
      | g(X1,X0)
      | ~ f('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f37,plain,
    ( spl3_1
    | ~ spl3_2 ),
    inference(avatar_split_clause,[],[f29,f34,f31]) ).

tff(f29,plain,
    ! [X0: '$ki_world'] :
      ( ~ g('$ki_local_world',sK1)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | h(X0,sK1) ),
    inference(resolution,[],[f23,f27]) ).

tff(f23,plain,
    ! [X4: $i,X5: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X4)
      | ~ g('$ki_local_world',X4)
      | ~ '$ki_accessible'('$ki_local_world',X5)
      | h(X5,X4) ),
    inference(cnf_transformation,[],[f19]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11  % Problem    : SYO888_10 : TPTP v8.2.0. Released v8.2.0.
% 0.04/0.12  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.31  % Computer : n023.cluster.edu
% 0.12/0.31  % Model    : x86_64 x86_64
% 0.12/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31  % Memory   : 8042.1875MB
% 0.12/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31  % CPULimit   : 300
% 0.12/0.31  % WCLimit    : 300
% 0.12/0.31  % DateTime   : Mon May 22 13:27:12 EDT 2023
% 0.12/0.32  % CPUTime    : 
% 0.17/0.45  % (4995)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.17/0.46  % (5012)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.17/0.46  % (4995)First to succeed.
% 0.17/0.46  % (4995)Refutation found. Thanks to Tanya!
% 0.17/0.46  % SZS status Theorem for theBenchmark
% 0.17/0.46  % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46  % (4995)------------------------------
% 0.17/0.46  % (4995)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.17/0.46  % (4995)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.17/0.46  % (4995)Termination reason: Refutation
% 0.17/0.46  
% 0.17/0.46  % (4995)Memory used [KB]: 5373
% 0.17/0.46  % (4995)Time elapsed: 0.082 s
% 0.17/0.46  % (4995)Instructions burned: 2 (million)
% 0.17/0.46  % (4995)------------------------------
% 0.17/0.46  % (4995)------------------------------
% 0.17/0.46  % (4986)Success in time 0.135 s
%------------------------------------------------------------------------------