TSTP Solution File: SYO901_11 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYO901_11 : 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 : n012.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 15:45:49 EDT 2023

% Result   : Theorem 0.19s 0.50s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   51 (   4 unt;   8 typ;   0 def)
%            Number of atoms       :  183 (   0 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  212 (  72   ~;  72   |;  38   &)
%                                         (  11 <=>;  18  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    8 (   7 usr;   5 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :   68 (;  51   !;  17   ?;  68   :)

% 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_2,type,
    sK1: '$ki_world' ).

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,
    p: '$ki_world' > $o ).

tff(pred_def_3,type,
    q: '$ki_world' > $o ).

tff(f61,plain,
    $false,
    inference(avatar_sat_refutation,[],[f31,f40,f49,f51,f53,f60]) ).

tff(f60,plain,
    ( ~ spl3_1
    | spl3_3 ),
    inference(avatar_contradiction_clause,[],[f59]) ).

tff(f59,plain,
    ( $false
    | ~ spl3_1
    | spl3_3 ),
    inference(subsumption_resolution,[],[f54,f27]) ).

tff(f27,plain,
    ( ! [X4: '$ki_world'] : q(X4)
    | ~ spl3_1 ),
    inference(avatar_component_clause,[],[f26]) ).

tff(f26,plain,
    ( spl3_1
  <=> ! [X4: '$ki_world'] : q(X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).

tff(f54,plain,
    ( ~ q(sK2)
    | spl3_3 ),
    inference(unit_resulting_resolution,[],[f35,f42]) ).

tff(f42,plain,
    ! [X0: '$ki_world'] :
      ( ~ q(X0)
      | p(X0) ),
    inference(subsumption_resolution,[],[f20,f22]) ).

tff(f22,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(rectify,[],[f1]) ).

tff(f1,axiom,
    ! [X1: '$ki_world',X0: '$ki_world'] : '$ki_accessible'(X0,X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_universal) ).

tff(f20,plain,
    ! [X0: '$ki_world'] :
      ( p(X0)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ q(X0) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,plain,
    ( ! [X0: '$ki_world'] :
        ( ( ( q(X0)
            | ~ p(X0) )
          & ( p(X0)
            | ~ q(X0) ) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & '$ki_accessible'('$ki_local_world',sK0)
    & ( ( '$ki_accessible'(sK0,sK1)
        & ~ q(sK1) )
      | ( '$ki_accessible'(sK0,sK2)
        & ~ p(sK2) ) )
    & ( ! [X4: '$ki_world'] :
          ( ~ '$ki_accessible'(sK0,X4)
          | q(X4) )
      | ! [X5: '$ki_world'] :
          ( ~ '$ki_accessible'(sK0,X5)
          | p(X5) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).

tff(f9,plain,
    ( ? [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
        & ( ? [X2: '$ki_world'] :
              ( '$ki_accessible'(X1,X2)
              & ~ q(X2) )
          | ? [X3: '$ki_world'] :
              ( '$ki_accessible'(X1,X3)
              & ~ p(X3) ) )
        & ( ! [X4: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X4)
              | q(X4) )
          | ! [X5: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X5)
              | p(X5) ) ) )
   => ( '$ki_accessible'('$ki_local_world',sK0)
      & ( ? [X2: '$ki_world'] :
            ( '$ki_accessible'(sK0,X2)
            & ~ q(X2) )
        | ? [X3: '$ki_world'] :
            ( '$ki_accessible'(sK0,X3)
            & ~ p(X3) ) )
      & ( ! [X4: '$ki_world'] :
            ( ~ '$ki_accessible'(sK0,X4)
            | q(X4) )
        | ! [X5: '$ki_world'] :
            ( ~ '$ki_accessible'(sK0,X5)
            | p(X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f10,plain,
    ( ? [X2: '$ki_world'] :
        ( '$ki_accessible'(sK0,X2)
        & ~ q(X2) )
   => ( '$ki_accessible'(sK0,sK1)
      & ~ q(sK1) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ( ? [X3: '$ki_world'] :
        ( '$ki_accessible'(sK0,X3)
        & ~ p(X3) )
   => ( '$ki_accessible'(sK0,sK2)
      & ~ p(sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f8,plain,
    ( ! [X0: '$ki_world'] :
        ( ( ( q(X0)
            | ~ p(X0) )
          & ( p(X0)
            | ~ q(X0) ) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
        & ( ? [X2: '$ki_world'] :
              ( '$ki_accessible'(X1,X2)
              & ~ q(X2) )
          | ? [X3: '$ki_world'] :
              ( '$ki_accessible'(X1,X3)
              & ~ p(X3) ) )
        & ( ! [X4: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X4)
              | q(X4) )
          | ! [X5: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X5)
              | p(X5) ) ) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,plain,
    ( ! [X0: '$ki_world'] :
        ( ( ( q(X0)
            | ~ p(X0) )
          & ( p(X0)
            | ~ q(X0) ) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
        & ( ? [X3: '$ki_world'] :
              ( '$ki_accessible'(X1,X3)
              & ~ q(X3) )
          | ? [X2: '$ki_world'] :
              ( '$ki_accessible'(X1,X2)
              & ~ p(X2) ) )
        & ( ! [X3: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X3)
              | q(X3) )
          | ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X2)
              | p(X2) ) ) ) ),
    inference(flattening,[],[f6]) ).

tff(f6,plain,
    ( ! [X0: '$ki_world'] :
        ( ( ( q(X0)
            | ~ p(X0) )
          & ( p(X0)
            | ~ q(X0) ) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
        & ( ? [X3: '$ki_world'] :
              ( '$ki_accessible'(X1,X3)
              & ~ q(X3) )
          | ? [X2: '$ki_world'] :
              ( '$ki_accessible'(X1,X2)
              & ~ p(X2) ) )
        & ( ! [X3: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X3)
              | q(X3) )
          | ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X2)
              | p(X2) ) ) ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f5,plain,
    ( ! [X0: '$ki_world'] :
        ( ( q(X0)
        <=> p(X0) )
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    & ? [X1: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X1)
        & ( ! [X2: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X2)
              | p(X2) )
        <~> ! [X3: '$ki_world'] :
              ( ~ '$ki_accessible'(X1,X3)
              | q(X3) ) ) ) ),
    inference(ennf_transformation,[],[f4]) ).

tff(f4,plain,
    ~ ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( q(X0)
          <=> p(X0) ) )
     => ! [X1: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X1)
         => ( ! [X3: '$ki_world'] :
                ( '$ki_accessible'(X1,X3)
               => q(X3) )
          <=> ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X1,X2)
               => p(X2) ) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( q(X0)
          <=> p(X0) ) )
     => ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => p(X2) )
          <=> ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => q(X2) ) ) ) ),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    ( ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ( q(X0)
        <=> p(X0) ) )
   => ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => p(X2) )
        <=> ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => q(X2) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f35,plain,
    ( ~ p(sK2)
    | spl3_3 ),
    inference(avatar_component_clause,[],[f33]) ).

tff(f33,plain,
    ( spl3_3
  <=> p(sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_3])]) ).

tff(f53,plain,
    ( ~ spl3_1
    | spl3_4 ),
    inference(avatar_contradiction_clause,[],[f52]) ).

tff(f52,plain,
    ( $false
    | ~ spl3_1
    | spl3_4 ),
    inference(subsumption_resolution,[],[f39,f27]) ).

tff(f39,plain,
    ( ~ q(sK1)
    | spl3_4 ),
    inference(avatar_component_clause,[],[f37]) ).

tff(f37,plain,
    ( spl3_4
  <=> q(sK1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).

tff(f51,plain,
    ( ~ spl3_2
    | spl3_3 ),
    inference(avatar_contradiction_clause,[],[f50]) ).

tff(f50,plain,
    ( $false
    | ~ spl3_2
    | spl3_3 ),
    inference(subsumption_resolution,[],[f35,f30]) ).

tff(f30,plain,
    ( ! [X5: '$ki_world'] : p(X5)
    | ~ spl3_2 ),
    inference(avatar_component_clause,[],[f29]) ).

tff(f29,plain,
    ( spl3_2
  <=> ! [X5: '$ki_world'] : p(X5) ),
    introduced(avatar_definition,[new_symbols(naming,[spl3_2])]) ).

tff(f49,plain,
    ( ~ spl3_2
    | spl3_4 ),
    inference(avatar_contradiction_clause,[],[f48]) ).

tff(f48,plain,
    ( $false
    | ~ spl3_2
    | spl3_4 ),
    inference(subsumption_resolution,[],[f43,f30]) ).

tff(f43,plain,
    ( ~ p(sK1)
    | spl3_4 ),
    inference(unit_resulting_resolution,[],[f39,f41]) ).

tff(f41,plain,
    ! [X0: '$ki_world'] :
      ( ~ p(X0)
      | q(X0) ),
    inference(subsumption_resolution,[],[f21,f22]) ).

tff(f21,plain,
    ! [X0: '$ki_world'] :
      ( ~ p(X0)
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | q(X0) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f40,plain,
    ( ~ spl3_3
    | ~ spl3_4 ),
    inference(avatar_split_clause,[],[f15,f37,f33]) ).

tff(f15,plain,
    ( ~ q(sK1)
    | ~ p(sK2) ),
    inference(cnf_transformation,[],[f12]) ).

tff(f31,plain,
    ( spl3_1
    | spl3_2 ),
    inference(avatar_split_clause,[],[f24,f29,f26]) ).

tff(f24,plain,
    ! [X4: '$ki_world',X5: '$ki_world'] :
      ( p(X5)
      | q(X4) ),
    inference(subsumption_resolution,[],[f23,f22]) ).

tff(f23,plain,
    ! [X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'(sK0,X4)
      | q(X4)
      | p(X5) ),
    inference(subsumption_resolution,[],[f14,f22]) ).

tff(f14,plain,
    ! [X4: '$ki_world',X5: '$ki_world'] :
      ( ~ '$ki_accessible'(sK0,X5)
      | p(X5)
      | ~ '$ki_accessible'(sK0,X4)
      | q(X4) ),
    inference(cnf_transformation,[],[f12]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO901_11 : 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_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n012.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 13:08:44 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.49  % (21061)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)
% 0.19/0.49  % (21057)dis+21_1:1_av=off:sos=on:sp=frequency:ss=included:to=lpo:i=15:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/15Mi)
% 0.19/0.49  % (21053)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)
% 0.19/0.50  % (21066)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (21069)fmb+10_1:1_nm=2:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.50  % (21061)First to succeed.
% 0.19/0.50  % (21056)lrs+10_1:1024_nm=0:nwc=5.0:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50  % (21057)Also succeeded, but the first one will report.
% 0.19/0.50  % (21061)Refutation found. Thanks to Tanya!
% 0.19/0.50  % SZS status Theorem for theBenchmark
% 0.19/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.50  % (21061)------------------------------
% 0.19/0.50  % (21061)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (21061)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (21061)Termination reason: Refutation
% 0.19/0.50  
% 0.19/0.50  % (21061)Memory used [KB]: 5884
% 0.19/0.50  % (21061)Time elapsed: 0.095 s
% 0.19/0.50  % (21061)Instructions burned: 2 (million)
% 0.19/0.50  % (21061)------------------------------
% 0.19/0.50  % (21061)------------------------------
% 0.19/0.50  % (21049)Success in time 0.15 s
%------------------------------------------------------------------------------