TSTP Solution File: SYO893_11 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYO893_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_sat --cores 0 -t %d %s

% Computer : n006.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 15:45:52 EDT 2023

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   45 (   6 unt;  10 typ;   0 def)
%            Number of atoms       :  176 (   0 equ)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :  228 (  87   ~;  63   |;  57   &)
%                                         (   4 <=>;  15  =>;   0  <=;   2 <~>)
%            Maximal formula depth :   10 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    7 (   6   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   2 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-1 aty)
%            Number of variables   :  104 (;  65   !;  39   ?; 104   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    '$ki_world': $tType ).

tff(func_def_0,type,
    '$ki_local_world': '$ki_world' ).

tff(func_def_1,type,
    sK1: '$ki_world' > '$ki_world' ).

tff(func_def_2,type,
    sK2: '$ki_world' ).

tff(func_def_3,type,
    sK3: '$ki_world' > '$ki_world' ).

tff(func_def_4,type,
    sK4: '$ki_world' > '$ki_world' ).

tff(func_def_5,type,
    sK5: '$ki_world' ).

tff(func_def_6,type,
    sK6: '$ki_world' > '$ki_world' ).

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

tff(pred_def_2,type,
    p: '$ki_world' > $o ).

tff(f49,plain,
    $false,
    inference(subsumption_resolution,[],[f48,f20]) ).

tff(f20,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X0,X1),
    inference(cnf_transformation,[],[f1]) ).

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

tff(f48,plain,
    ! [X0: '$ki_world'] : ~ '$ki_accessible'(sK5,X0),
    inference(subsumption_resolution,[],[f46,f40]) ).

tff(f40,plain,
    ~ sP0,
    inference(subsumption_resolution,[],[f39,f20]) ).

tff(f39,plain,
    ! [X0: '$ki_world'] :
      ( ~ sP0
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f38,f20]) ).

tff(f38,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_accessible'(sK4(X0),sK3(X1))
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ sP0 ),
    inference(duplicate_literal_removal,[],[f37]) ).

tff(f37,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] :
      ( ~ sP0
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ sP0
      | ~ '$ki_accessible'(sK4(X0),sK3(X1)) ),
    inference(resolution,[],[f36,f29]) ).

tff(f29,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( p(X2)
      | ~ sP0
      | ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(sK4(X0),X2) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f19,plain,
    ( ( ~ sP0
      | ! [X0: '$ki_world'] :
          ( ~ '$ki_accessible'('$ki_local_world',X0)
          | ( '$ki_accessible'(X0,sK4(X0))
            & ! [X2: '$ki_world'] :
                ( p(X2)
                | ~ '$ki_accessible'(sK4(X0),X2) ) ) ) )
    & ( sP0
      | ( '$ki_accessible'('$ki_local_world',sK5)
        & ! [X4: '$ki_world'] :
            ( ~ '$ki_accessible'(sK5,X4)
            | ( ~ p(sK6(X4))
              & '$ki_accessible'(X4,sK6(X4)) ) ) ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f15,f18,f17,f16]) ).

tff(f16,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( '$ki_accessible'(X0,X1)
          & ! [X2: '$ki_world'] :
              ( p(X2)
              | ~ '$ki_accessible'(X1,X2) ) )
     => ( '$ki_accessible'(X0,sK4(X0))
        & ! [X2: '$ki_world'] :
            ( p(X2)
            | ~ '$ki_accessible'(sK4(X0),X2) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f17,plain,
    ( ? [X3: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X3)
        & ! [X4: '$ki_world'] :
            ( ~ '$ki_accessible'(X3,X4)
            | ? [X5: '$ki_world'] :
                ( ~ p(X5)
                & '$ki_accessible'(X4,X5) ) ) )
   => ( '$ki_accessible'('$ki_local_world',sK5)
      & ! [X4: '$ki_world'] :
          ( ~ '$ki_accessible'(sK5,X4)
          | ? [X5: '$ki_world'] :
              ( ~ p(X5)
              & '$ki_accessible'(X4,X5) ) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ! [X4: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ~ p(X5)
          & '$ki_accessible'(X4,X5) )
     => ( ~ p(sK6(X4))
        & '$ki_accessible'(X4,sK6(X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f15,plain,
    ( ( ~ sP0
      | ! [X0: '$ki_world'] :
          ( ~ '$ki_accessible'('$ki_local_world',X0)
          | ? [X1: '$ki_world'] :
              ( '$ki_accessible'(X0,X1)
              & ! [X2: '$ki_world'] :
                  ( p(X2)
                  | ~ '$ki_accessible'(X1,X2) ) ) ) )
    & ( sP0
      | ? [X3: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X3)
          & ! [X4: '$ki_world'] :
              ( ~ '$ki_accessible'(X3,X4)
              | ? [X5: '$ki_world'] :
                  ( ~ p(X5)
                  & '$ki_accessible'(X4,X5) ) ) ) ) ),
    inference(rectify,[],[f14]) ).

tff(f14,plain,
    ( ( ~ sP0
      | ! [X0: '$ki_world'] :
          ( ~ '$ki_accessible'('$ki_local_world',X0)
          | ? [X1: '$ki_world'] :
              ( '$ki_accessible'(X0,X1)
              & ! [X2: '$ki_world'] :
                  ( p(X2)
                  | ~ '$ki_accessible'(X1,X2) ) ) ) )
    & ( sP0
      | ? [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
          & ! [X1: '$ki_world'] :
              ( ~ '$ki_accessible'(X0,X1)
              | ? [X2: '$ki_world'] :
                  ( ~ p(X2)
                  & '$ki_accessible'(X1,X2) ) ) ) ) ),
    inference(nnf_transformation,[],[f7]) ).

tff(f7,plain,
    ( ? [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
        & ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'(X0,X1)
            | ? [X2: '$ki_world'] :
                ( ~ p(X2)
                & '$ki_accessible'(X1,X2) ) ) )
  <~> sP0 ),
    inference(definition_folding,[],[f5,f6]) ).

tff(f6,plain,
    ( sP0
  <=> ? [X3: '$ki_world'] :
        ( ! [X4: '$ki_world'] :
            ( ? [X5: '$ki_world'] :
                ( ~ p(X5)
                & '$ki_accessible'(X4,X5) )
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f5,plain,
    ( ? [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
        & ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'(X0,X1)
            | ? [X2: '$ki_world'] :
                ( ~ p(X2)
                & '$ki_accessible'(X1,X2) ) ) )
  <~> ? [X3: '$ki_world'] :
        ( ! [X4: '$ki_world'] :
            ( ? [X5: '$ki_world'] :
                ( ~ p(X5)
                & '$ki_accessible'(X4,X5) )
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) ) ),
    inference(ennf_transformation,[],[f4]) ).

tff(f4,plain,
    ~ ( ? [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
          & ! [X1: '$ki_world'] :
              ( '$ki_accessible'(X0,X1)
             => ? [X2: '$ki_world'] :
                  ( ~ p(X2)
                  & '$ki_accessible'(X1,X2) ) ) )
    <=> ~ ! [X3: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X3)
           => ? [X4: '$ki_world'] :
                ( '$ki_accessible'(X3,X4)
                & ! [X5: '$ki_world'] :
                    ( '$ki_accessible'(X4,X5)
                   => p(X5) ) ) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,negated_conjecture,
    ~ ( ? [X0: '$ki_world'] :
          ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ? [X3: '$ki_world'] :
                  ( ~ p(X3)
                  & '$ki_accessible'(X2,X3) ) )
          & '$ki_accessible'('$ki_local_world',X0) )
    <=> ~ ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ? [X2: '$ki_world'] :
                ( ! [X3: '$ki_world'] :
                    ( '$ki_accessible'(X2,X3)
                   => p(X3) )
                & '$ki_accessible'(X0,X2) ) ) ),
    inference(negated_conjecture,[],[f2]) ).

tff(f2,conjecture,
    ( ? [X0: '$ki_world'] :
        ( ! [X2: '$ki_world'] :
            ( '$ki_accessible'(X0,X2)
           => ? [X3: '$ki_world'] :
                ( ~ p(X3)
                & '$ki_accessible'(X2,X3) ) )
        & '$ki_accessible'('$ki_local_world',X0) )
  <=> ~ ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ? [X2: '$ki_world'] :
              ( ! [X3: '$ki_world'] :
                  ( '$ki_accessible'(X2,X3)
                 => p(X3) )
              & '$ki_accessible'(X0,X2) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f36,plain,
    ! [X4: '$ki_world'] :
      ( ~ p(sK3(X4))
      | ~ sP0 ),
    inference(subsumption_resolution,[],[f23,f20]) ).

tff(f23,plain,
    ! [X4: '$ki_world'] :
      ( ~ p(sK3(X4))
      | ~ '$ki_accessible'(sK2,X4)
      | ~ sP0 ),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ( ( sP0
      | ! [X0: '$ki_world'] :
          ( ( ! [X2: '$ki_world'] :
                ( p(X2)
                | ~ '$ki_accessible'(sK1(X0),X2) )
            & '$ki_accessible'(X0,sK1(X0)) )
          | ~ '$ki_accessible'('$ki_local_world',X0) ) )
    & ( ( ! [X4: '$ki_world'] :
            ( ( ~ p(sK3(X4))
              & '$ki_accessible'(X4,sK3(X4)) )
            | ~ '$ki_accessible'(sK2,X4) )
        & '$ki_accessible'('$ki_local_world',sK2) )
      | ~ sP0 ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f9,f12,f11,f10]) ).

tff(f10,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1: '$ki_world'] :
          ( ! [X2: '$ki_world'] :
              ( p(X2)
              | ~ '$ki_accessible'(X1,X2) )
          & '$ki_accessible'(X0,X1) )
     => ( ! [X2: '$ki_world'] :
            ( p(X2)
            | ~ '$ki_accessible'(sK1(X0),X2) )
        & '$ki_accessible'(X0,sK1(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f11,plain,
    ( ? [X3: '$ki_world'] :
        ( ! [X4: '$ki_world'] :
            ( ? [X5: '$ki_world'] :
                ( ~ p(X5)
                & '$ki_accessible'(X4,X5) )
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) )
   => ( ! [X4: '$ki_world'] :
          ( ? [X5: '$ki_world'] :
              ( ~ p(X5)
              & '$ki_accessible'(X4,X5) )
          | ~ '$ki_accessible'(sK2,X4) )
      & '$ki_accessible'('$ki_local_world',sK2) ) ),
    introduced(choice_axiom,[]) ).

tff(f12,plain,
    ! [X4: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ~ p(X5)
          & '$ki_accessible'(X4,X5) )
     => ( ~ p(sK3(X4))
        & '$ki_accessible'(X4,sK3(X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f9,plain,
    ( ( sP0
      | ! [X0: '$ki_world'] :
          ( ? [X1: '$ki_world'] :
              ( ! [X2: '$ki_world'] :
                  ( p(X2)
                  | ~ '$ki_accessible'(X1,X2) )
              & '$ki_accessible'(X0,X1) )
          | ~ '$ki_accessible'('$ki_local_world',X0) ) )
    & ( ? [X3: '$ki_world'] :
          ( ! [X4: '$ki_world'] :
              ( ? [X5: '$ki_world'] :
                  ( ~ p(X5)
                  & '$ki_accessible'(X4,X5) )
              | ~ '$ki_accessible'(X3,X4) )
          & '$ki_accessible'('$ki_local_world',X3) )
      | ~ sP0 ) ),
    inference(rectify,[],[f8]) ).

tff(f8,plain,
    ( ( sP0
      | ! [X3: '$ki_world'] :
          ( ? [X4: '$ki_world'] :
              ( ! [X5: '$ki_world'] :
                  ( p(X5)
                  | ~ '$ki_accessible'(X4,X5) )
              & '$ki_accessible'(X3,X4) )
          | ~ '$ki_accessible'('$ki_local_world',X3) ) )
    & ( ? [X3: '$ki_world'] :
          ( ! [X4: '$ki_world'] :
              ( ? [X5: '$ki_world'] :
                  ( ~ p(X5)
                  & '$ki_accessible'(X4,X5) )
              | ~ '$ki_accessible'(X3,X4) )
          & '$ki_accessible'('$ki_local_world',X3) )
      | ~ sP0 ) ),
    inference(nnf_transformation,[],[f6]) ).

tff(f46,plain,
    ! [X0: '$ki_world'] :
      ( sP0
      | ~ '$ki_accessible'(sK5,X0) ),
    inference(resolution,[],[f45,f27]) ).

tff(f27,plain,
    ! [X4: '$ki_world'] :
      ( ~ p(sK6(X4))
      | sP0
      | ~ '$ki_accessible'(sK5,X4) ),
    inference(cnf_transformation,[],[f19]) ).

tff(f45,plain,
    ! [X2: '$ki_world'] : p(X2),
    inference(subsumption_resolution,[],[f44,f40]) ).

tff(f44,plain,
    ! [X2: '$ki_world'] :
      ( sP0
      | p(X2) ),
    inference(subsumption_resolution,[],[f43,f20]) ).

tff(f43,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( p(X2)
      | ~ '$ki_accessible'(sK1(X0),X2)
      | sP0 ),
    inference(subsumption_resolution,[],[f25,f20]) ).

tff(f25,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( ~ '$ki_accessible'('$ki_local_world',X0)
      | ~ '$ki_accessible'(sK1(X0),X2)
      | sP0
      | p(X2) ),
    inference(cnf_transformation,[],[f13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SYO893_11 : 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_sat --cores 0 -t %d %s
% 0.12/0.33  % Computer : n006.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Mon May 22 13:08:05 EDT 2023
% 0.12/0.33  % CPUTime    : 
% 0.19/0.42  % (10882)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.19/0.42  TRYING [1]
% 0.19/0.42  TRYING [2]
% 0.19/0.43  % (10898)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 (3000ds/498Mi)
% 0.19/0.43  TRYING [3]
% 0.19/0.43  TRYING [4]
% 0.19/0.43  TRYING [5]
% 0.19/0.43  TRYING [6]
% 0.19/0.43  TRYING [7]
% 0.19/0.44  % (10890)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/68Mi)
% 0.19/0.44  TRYING [8]
% 0.19/0.44  % (10898)First to succeed.
% 0.19/0.44  TRYING [9]
% 0.19/0.45  % (10898)Refutation found. Thanks to Tanya!
% 0.19/0.45  % SZS status Theorem for theBenchmark
% 0.19/0.45  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.45  % (10898)------------------------------
% 0.19/0.45  % (10898)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.45  % (10898)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.45  % (10898)Termination reason: Refutation
% 0.19/0.45  
% 0.19/0.45  % (10898)Memory used [KB]: 895
% 0.19/0.45  % (10898)Time elapsed: 0.070 s
% 0.19/0.45  % (10898)Instructions burned: 1 (million)
% 0.19/0.45  % (10898)------------------------------
% 0.19/0.45  % (10898)------------------------------
% 0.19/0.45  % (10875)Success in time 0.104 s
%------------------------------------------------------------------------------