TSTP Solution File: NLP266_23 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n007.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 01:05:44 EDT 2024

% Result   : Theorem 0.15s 0.38s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   32
% Syntax   : Number of formulae    :   88 (  12 unt;  18 typ;   0 def)
%            Number of atoms       :  478 (   0 equ)
%            Maximal formula atoms :   20 (   6 avg)
%            Number of connectives :  529 ( 202   ~; 185   |;  98   &)
%                                         (   0 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (  10 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of FOOLs       :   81 (  81 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   45 (  15   >;  30   *;   0   +;   0  <<)
%            Number of predicates  :   13 (  12 usr;   4 prp; 0-5 aty)
%            Number of functors    :    8 (   8 usr;   2 con; 0-5 aty)
%            Number of variables   :  310 ( 259   !;  51   ?; 193   :)

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

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

tff(func_def_3,type,
    sK1: ( $i * $i * $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_4,type,
    sK2: ( $i * $i * $i * $i * '$ki_world' ) > $i ).

tff(func_def_5,type,
    sK3: '$ki_world' ).

tff(func_def_6,type,
    sK4: ( $i * $i ) > '$ki_world' ).

tff(func_def_7,type,
    sK5: ( '$ki_world' * $i * $i * $i ) > $i ).

tff(func_def_8,type,
    sK6: '$ki_world' > $i ).

tff(func_def_9,type,
    sK7: '$ki_world' > $i ).

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

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

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

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

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

tff(pred_def_6,type,
    entry_box: ( '$ki_world' * $i ) > $o ).

tff(pred_def_7,type,
    userid: ( '$ki_world' * $i * $i ) > $o ).

tff(pred_def_8,type,
    '$ki_exists_in_world_$i': ( '$ki_world' * $i ) > $o ).

tff(pred_def_9,type,
    sP0: ( $i * $i * $i * $i * '$ki_world' ) > $o ).

tff(f82,plain,
    $false,
    inference(resolution,[],[f81,f70]) ).

tff(f70,plain,
    ! [X2: $i,X0: '$ki_world',X1: $i] : sP0(sK8,sK6(X0),X1,X2,sK3),
    inference(subsumption_resolution,[],[f69,f59]) ).

tff(f59,plain,
    ! [X1: '$ki_world'] : number(X1,sK8,one),
    inference(subsumption_resolution,[],[f57,f53]) ).

tff(f53,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/sandbox2/benchmark/theBenchmark.p',mrel_universal) ).

tff(f57,plain,
    ! [X1: '$ki_world'] :
      ( number(X1,sK8,one)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,plain,
    ( ! [X1: '$ki_world'] :
        ( ( number(X1,sK8,one)
          & entry_box(X1,sK8) )
        | ~ '$ki_accessible'('$ki_local_world',X1) )
    & '$ki_exists_in_world_$i'('$ki_local_world',sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f20,f38]) ).

tff(f38,plain,
    ( ? [X0] :
        ( ! [X1: '$ki_world'] :
            ( ( number(X1,X0,one)
              & entry_box(X1,X0) )
            | ~ '$ki_accessible'('$ki_local_world',X1) )
        & '$ki_exists_in_world_$i'('$ki_local_world',X0) )
   => ( ! [X1: '$ki_world'] :
          ( ( number(X1,sK8,one)
            & entry_box(X1,sK8) )
          | ~ '$ki_accessible'('$ki_local_world',X1) )
      & '$ki_exists_in_world_$i'('$ki_local_world',sK8) ) ),
    introduced(choice_axiom,[]) ).

tff(f20,plain,
    ? [X0] :
      ( ! [X1: '$ki_world'] :
          ( ( number(X1,X0,one)
            & entry_box(X1,X0) )
          | ~ '$ki_accessible'('$ki_local_world',X1) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f14]) ).

tff(f14,plain,
    ? [X0] :
      ( ! [X1: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X1)
         => ( number(X1,X0,one)
            & entry_box(X1,X0) ) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X0) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ? [X5] :
      ( ! [X0: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X0)
         => ( number(X0,X5,one)
            & entry_box(X0,X5) ) )
      & '$ki_exists_in_world_$i'('$ki_local_world',X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).

tff(f69,plain,
    ! [X2: $i,X0: '$ki_world',X1: $i] :
      ( ~ number(sK4(sK6(X0),sK8),sK8,one)
      | sP0(sK8,sK6(X0),X1,X2,sK3) ),
    inference(resolution,[],[f68,f58]) ).

tff(f58,plain,
    ! [X1: '$ki_world'] : entry_box(X1,sK8),
    inference(subsumption_resolution,[],[f56,f53]) ).

tff(f56,plain,
    ! [X1: '$ki_world'] :
      ( entry_box(X1,sK8)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f68,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i] :
      ( ~ entry_box(sK4(sK6(X0),X1),X1)
      | ~ number(sK4(sK6(X0),X1),X1,one)
      | sP0(X1,sK6(X0),X2,X3,sK3) ),
    inference(resolution,[],[f67,f63]) ).

tff(f63,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] : userid(X2,u,sK6(X0)),
    inference(subsumption_resolution,[],[f62,f53]) ).

tff(f62,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( userid(X2,u,sK6(X0))
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f50,f53]) ).

tff(f50,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( userid(X2,u,sK6(X0))
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f35,plain,
    ! [X0: '$ki_world'] :
      ( ( ! [X2: '$ki_world'] :
            ( ( string(X2,sK6(X0))
              & userid(X2,u,sK6(X0)) )
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_exists_in_world_$i'(X0,sK6(X0)) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f19,f34]) ).

tff(f34,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( ( string(X2,X1)
                & userid(X2,u,X1) )
              | ~ '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
     => ( ! [X2: '$ki_world'] :
            ( ( string(X2,sK6(X0))
              & userid(X2,u,sK6(X0)) )
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_exists_in_world_$i'(X0,sK6(X0)) ) ),
    introduced(choice_axiom,[]) ).

tff(f19,plain,
    ! [X0: '$ki_world'] :
      ( ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( ( string(X2,X1)
                & userid(X2,u,X1) )
              | ~ '$ki_accessible'(X0,X2) )
          & '$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'('$ki_local_world',X0)
     => ? [X1] :
          ( ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ( string(X2,X1)
                & userid(X2,u,X1) ) )
          & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X3] :
          ( ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ( string(X4,X3)
                & userid(X4,u,X3) ) )
          & '$ki_exists_in_world_$i'(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).

tff(f67,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( ~ userid(sK4(X1,X2),u,X1)
      | ~ number(sK4(X1,X2),X2,one)
      | ~ entry_box(sK4(X1,X2),X2)
      | sP0(X2,X1,X3,X4,sK3) ),
    inference(subsumption_resolution,[],[f66,f54]) ).

tff(f54,plain,
    ! [X0: '$ki_world',X1: $i] : '$ki_exists_in_world_$i'(X0,X1),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ! [X0: '$ki_world',X1] : '$ki_exists_in_world_$i'(X0,X1),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X0: '$ki_world',X2] : '$ki_exists_in_world_$i'(X0,X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_const') ).

tff(f66,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( sP0(X2,X1,X3,X4,sK3)
      | ~ number(sK4(X1,X2),X2,one)
      | ~ entry_box(sK4(X1,X2),X2)
      | ~ userid(sK4(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK3,X1) ),
    inference(subsumption_resolution,[],[f65,f54]) ).

tff(f65,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( sP0(X2,X1,X3,X4,sK3)
      | ~ number(sK4(X1,X2),X2,one)
      | ~ entry_box(sK4(X1,X2),X2)
      | ~ userid(sK4(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK3,X2)
      | ~ '$ki_exists_in_world_$i'(sK3,X1) ),
    inference(subsumption_resolution,[],[f64,f54]) ).

tff(f64,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( sP0(X2,X1,X3,X4,sK3)
      | ~ number(sK4(X1,X2),X2,one)
      | ~ entry_box(sK4(X1,X2),X2)
      | ~ userid(sK4(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK3,X3)
      | ~ '$ki_exists_in_world_$i'(sK3,X2)
      | ~ '$ki_exists_in_world_$i'(sK3,X1) ),
    inference(subsumption_resolution,[],[f46,f54]) ).

tff(f46,plain,
    ! [X2: $i,X3: $i,X1: $i,X4: $i] :
      ( sP0(X2,X1,X3,X4,sK3)
      | ~ number(sK4(X1,X2),X2,one)
      | ~ entry_box(sK4(X1,X2),X2)
      | ~ userid(sK4(X1,X2),u,X1)
      | ~ '$ki_exists_in_world_$i'(sK3,X4)
      | ~ '$ki_exists_in_world_$i'(sK3,X3)
      | ~ '$ki_exists_in_world_$i'(sK3,X2)
      | ~ '$ki_exists_in_world_$i'(sK3,X1) ),
    inference(cnf_transformation,[],[f31]) ).

tff(f31,plain,
    ( ! [X1] :
        ( ! [X2] :
            ( ! [X3] :
                ( ! [X4] :
                    ( sP0(X2,X1,X3,X4,sK3)
                    | ( ( ~ number(sK4(X1,X2),X2,one)
                        | ~ entry_box(sK4(X1,X2),X2)
                        | ~ userid(sK4(X1,X2),u,X1) )
                      & '$ki_accessible'(sK3,sK4(X1,X2)) )
                    | ~ '$ki_exists_in_world_$i'(sK3,X4) )
                | ~ '$ki_exists_in_world_$i'(sK3,X3) )
            | ~ '$ki_exists_in_world_$i'(sK3,X2) )
        | ~ '$ki_exists_in_world_$i'(sK3,X1) )
    & '$ki_accessible'('$ki_local_world',sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4])],[f28,f30,f29]) ).

tff(f29,plain,
    ( ? [X0: '$ki_world'] :
        ( ! [X1] :
            ( ! [X2] :
                ( ! [X3] :
                    ( ! [X4] :
                        ( sP0(X2,X1,X3,X4,X0)
                        | ? [X5: '$ki_world'] :
                            ( ( ~ number(X5,X2,one)
                              | ~ entry_box(X5,X2)
                              | ~ userid(X5,u,X1) )
                            & '$ki_accessible'(X0,X5) )
                        | ~ '$ki_exists_in_world_$i'(X0,X4) )
                    | ~ '$ki_exists_in_world_$i'(X0,X3) )
                | ~ '$ki_exists_in_world_$i'(X0,X2) )
            | ~ '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( sP0(X2,X1,X3,X4,sK3)
                      | ? [X5: '$ki_world'] :
                          ( ( ~ number(X5,X2,one)
                            | ~ entry_box(X5,X2)
                            | ~ userid(X5,u,X1) )
                          & '$ki_accessible'(sK3,X5) )
                      | ~ '$ki_exists_in_world_$i'(sK3,X4) )
                  | ~ '$ki_exists_in_world_$i'(sK3,X3) )
              | ~ '$ki_exists_in_world_$i'(sK3,X2) )
          | ~ '$ki_exists_in_world_$i'(sK3,X1) )
      & '$ki_accessible'('$ki_local_world',sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X1,X2] :
      ( ? [X5: '$ki_world'] :
          ( ( ~ number(X5,X2,one)
            | ~ entry_box(X5,X2)
            | ~ userid(X5,u,X1) )
          & '$ki_accessible'(sK3,X5) )
     => ( ( ~ number(sK4(X1,X2),X2,one)
          | ~ entry_box(sK4(X1,X2),X2)
          | ~ userid(sK4(X1,X2),u,X1) )
        & '$ki_accessible'(sK3,sK4(X1,X2)) ) ),
    introduced(choice_axiom,[]) ).

tff(f28,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( sP0(X2,X1,X3,X4,X0)
                      | ? [X5: '$ki_world'] :
                          ( ( ~ number(X5,X2,one)
                            | ~ entry_box(X5,X2)
                            | ~ userid(X5,u,X1) )
                          & '$ki_accessible'(X0,X5) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(rectify,[],[f22]) ).

tff(f22,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( sP0(X2,X1,X3,X4,X0)
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(X0,X7) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(definition_folding,[],[f16,f21]) ).

tff(f21,plain,
    ! [X2,X1,X3,X4,X0: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ? [X6] :
              ( ~ in(X5,X1,X2,X6)
              & do(X5,X4,X3,X6)
              & '$ki_exists_in_world_$i'(X5,X6) )
          & '$ki_accessible'(X0,X5) )
      | ~ sP0(X2,X1,X3,X4,X0) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

tff(f16,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ? [X5: '$ki_world'] :
                          ( ? [X6] :
                              ( ~ in(X5,X1,X2,X6)
                              & do(X5,X4,X3,X6)
                              & '$ki_exists_in_world_$i'(X5,X6) )
                          & '$ki_accessible'(X0,X5) )
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(X0,X7) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f15]) ).

tff(f15,plain,
    ? [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ! [X4] :
                      ( ? [X5: '$ki_world'] :
                          ( ? [X6] :
                              ( ~ in(X5,X1,X2,X6)
                              & do(X5,X4,X3,X6)
                              & '$ki_exists_in_world_$i'(X5,X6) )
                          & '$ki_accessible'(X0,X5) )
                      | ? [X7: '$ki_world'] :
                          ( ( ~ number(X7,X2,one)
                            | ~ entry_box(X7,X2)
                            | ~ userid(X7,u,X1) )
                          & '$ki_accessible'(X0,X7) )
                      | ~ '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f9]) ).

tff(f9,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X1] :
            ( ? [X2] :
                ( ? [X3] :
                    ( ? [X4] :
                        ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X0,X5)
                           => ! [X6] :
                                ( '$ki_exists_in_world_$i'(X5,X6)
                               => ( do(X5,X4,X3,X6)
                                 => in(X5,X1,X2,X6) ) ) )
                        & ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X0,X7)
                           => ( number(X7,X2,one)
                              & entry_box(X7,X2)
                              & userid(X7,u,X1) ) )
                        & '$ki_exists_in_world_$i'(X0,X4) )
                    & '$ki_exists_in_world_$i'(X0,X3) )
                & '$ki_exists_in_world_$i'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) ) ),
    inference(rectify,[],[f8]) ).

tff(f8,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ? [X3] :
            ( ? [X5] :
                ( ? [X7] :
                    ( ? [X6] :
                        ( ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ! [X8] :
                                ( '$ki_exists_in_world_$i'(X4,X8)
                               => ( do(X4,X6,X7,X8)
                                 => in(X4,X3,X5,X8) ) ) )
                        & ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ( number(X4,X5,one)
                              & entry_box(X4,X5)
                              & userid(X4,u,X3) ) )
                        & '$ki_exists_in_world_$i'(X0,X6) )
                    & '$ki_exists_in_world_$i'(X0,X7) )
                & '$ki_exists_in_world_$i'(X0,X5) )
            & '$ki_exists_in_world_$i'(X0,X3) ) ),
    inference(negated_conjecture,[],[f7]) ).

tff(f7,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ? [X3] :
          ( ? [X5] :
              ( ? [X7] :
                  ( ? [X6] :
                      ( ! [X4: '$ki_world'] :
                          ( '$ki_accessible'(X0,X4)
                         => ! [X8] :
                              ( '$ki_exists_in_world_$i'(X4,X8)
                             => ( do(X4,X6,X7,X8)
                               => in(X4,X3,X5,X8) ) ) )
                      & ! [X4: '$ki_world'] :
                          ( '$ki_accessible'(X0,X4)
                         => ( number(X4,X5,one)
                            & entry_box(X4,X5)
                            & userid(X4,u,X3) ) )
                      & '$ki_exists_in_world_$i'(X0,X6) )
                  & '$ki_exists_in_world_$i'(X0,X7) )
              & '$ki_exists_in_world_$i'(X0,X5) )
          & '$ki_exists_in_world_$i'(X0,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f81,plain,
    ! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] : ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3),
    inference(duplicate_literal_removal,[],[f80]) ).

tff(f80,plain,
    ! [X2: $i,X3: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3)
      | ~ sP0(sK8,sK6(X0),sK5(X1,X2,sK6(X0),sK8),X2,X3) ),
    inference(resolution,[],[f79,f43]) ).

tff(f43,plain,
    ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: '$ki_world'] :
      ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f27,plain,
    ! [X0,X1,X2,X3,X4: '$ki_world'] :
      ( ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
        & do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
        & '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),sK2(X0,X1,X2,X3,X4))
        & '$ki_accessible'(X4,sK1(X0,X1,X2,X3,X4)) )
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f24,f26,f25]) ).

tff(f25,plain,
    ! [X0,X1,X2,X3,X4: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ? [X6] :
              ( ~ in(X5,X1,X0,X6)
              & do(X5,X3,X2,X6)
              & '$ki_exists_in_world_$i'(X5,X6) )
          & '$ki_accessible'(X4,X5) )
     => ( ? [X6] :
            ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,X6)
            & do(sK1(X0,X1,X2,X3,X4),X3,X2,X6)
            & '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),X6) )
        & '$ki_accessible'(X4,sK1(X0,X1,X2,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f26,plain,
    ! [X0,X1,X2,X3,X4: '$ki_world'] :
      ( ? [X6] :
          ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,X6)
          & do(sK1(X0,X1,X2,X3,X4),X3,X2,X6)
          & '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),X6) )
     => ( ~ in(sK1(X0,X1,X2,X3,X4),X1,X0,sK2(X0,X1,X2,X3,X4))
        & do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
        & '$ki_exists_in_world_$i'(sK1(X0,X1,X2,X3,X4),sK2(X0,X1,X2,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f24,plain,
    ! [X0,X1,X2,X3,X4: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ? [X6] :
              ( ~ in(X5,X1,X0,X6)
              & do(X5,X3,X2,X6)
              & '$ki_exists_in_world_$i'(X5,X6) )
          & '$ki_accessible'(X4,X5) )
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(rectify,[],[f23]) ).

tff(f23,plain,
    ! [X2,X1,X3,X4,X0: '$ki_world'] :
      ( ? [X5: '$ki_world'] :
          ( ? [X6] :
              ( ~ in(X5,X1,X2,X6)
              & do(X5,X4,X3,X6)
              & '$ki_exists_in_world_$i'(X5,X6) )
          & '$ki_accessible'(X0,X5) )
      | ~ sP0(X2,X1,X3,X4,X0) ),
    inference(nnf_transformation,[],[f21]) ).

tff(f79,plain,
    ! [X2: '$ki_world',X3: $i,X0: $i,X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( in(sK1(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5),sK6(X4),sK8,sK2(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5))
      | ~ sP0(X0,X1,sK5(X2,X3,sK6(X4),sK8),X3,X5) ),
    inference(resolution,[],[f78,f42]) ).

tff(f42,plain,
    ! [X2: $i,X3: $i,X0: $i,X1: $i,X4: '$ki_world'] :
      ( do(sK1(X0,X1,X2,X3,X4),X3,X2,sK2(X0,X1,X2,X3,X4))
      | ~ sP0(X0,X1,X2,X3,X4) ),
    inference(cnf_transformation,[],[f27]) ).

tff(f78,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: '$ki_world',X4: '$ki_world'] :
      ( ~ do(X0,X3,sK5(X4,X3,sK6(X1),sK8),X2)
      | in(X0,sK6(X1),sK8,X2) ),
    inference(resolution,[],[f77,f61]) ).

tff(f61,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] : string(X2,sK6(X0)),
    inference(subsumption_resolution,[],[f60,f53]) ).

tff(f60,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( string(X2,sK6(X0))
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f51,f53]) ).

tff(f51,plain,
    ! [X2: '$ki_world',X0: '$ki_world'] :
      ( string(X2,sK6(X0))
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f35]) ).

tff(f77,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: $i] :
      ( ~ string(X2,X3)
      | in(X0,X3,sK8,X4)
      | ~ do(X0,X1,sK5(X2,X1,X3,sK8),X4) ),
    inference(resolution,[],[f76,f58]) ).

tff(f76,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( ~ entry_box(X0,X3)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | in(X5,X2,X3,X6)
      | ~ string(X0,X2) ),
    inference(subsumption_resolution,[],[f75,f53]) ).

tff(f75,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f74,f54]) ).

tff(f74,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f73,f54]) ).

tff(f73,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f72,f54]) ).

tff(f72,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f71,f53]) ).

tff(f71,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ '$ki_accessible'(X0,X5)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(subsumption_resolution,[],[f48,f54]) ).

tff(f48,plain,
    ! [X2: $i,X3: $i,X0: '$ki_world',X1: $i,X6: $i,X5: '$ki_world'] :
      ( in(X5,X2,X3,X6)
      | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
      | ~ '$ki_exists_in_world_$i'(X5,X6)
      | ~ '$ki_accessible'(X0,X5)
      | ~ entry_box(X0,X3)
      | ~ string(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X3)
      | ~ '$ki_exists_in_world_$i'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f33]) ).

tff(f33,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ! [X5: '$ki_world'] :
                        ( ! [X6] :
                            ( in(X5,X2,X3,X6)
                            | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
                            | ~ '$ki_exists_in_world_$i'(X5,X6) )
                        | ~ '$ki_accessible'(X0,X5) )
                    & '$ki_exists_in_world_$i'(X0,sK5(X0,X1,X2,X3)) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f18,f32]) ).

tff(f32,plain,
    ! [X0: '$ki_world',X1,X2,X3] :
      ( ? [X4] :
          ( ! [X5: '$ki_world'] :
              ( ! [X6] :
                  ( in(X5,X2,X3,X6)
                  | ~ do(X5,X1,X4,X6)
                  | ~ '$ki_exists_in_world_$i'(X5,X6) )
              | ~ '$ki_accessible'(X0,X5) )
          & '$ki_exists_in_world_$i'(X0,X4) )
     => ( ! [X5: '$ki_world'] :
            ( ! [X6] :
                ( in(X5,X2,X3,X6)
                | ~ do(X5,X1,sK5(X0,X1,X2,X3),X6)
                | ~ '$ki_exists_in_world_$i'(X5,X6) )
            | ~ '$ki_accessible'(X0,X5) )
        & '$ki_exists_in_world_$i'(X0,sK5(X0,X1,X2,X3)) ) ),
    introduced(choice_axiom,[]) ).

tff(f18,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ? [X4] :
                      ( ! [X5: '$ki_world'] :
                          ( ! [X6] :
                              ( in(X5,X2,X3,X6)
                              | ~ do(X5,X1,X4,X6)
                              | ~ '$ki_exists_in_world_$i'(X5,X6) )
                          | ~ '$ki_accessible'(X0,X5) )
                      & '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f17]) ).

tff(f17,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ? [X4] :
                      ( ! [X5: '$ki_world'] :
                          ( ! [X6] :
                              ( in(X5,X2,X3,X6)
                              | ~ do(X5,X1,X4,X6)
                              | ~ '$ki_exists_in_world_$i'(X5,X6) )
                          | ~ '$ki_accessible'(X0,X5) )
                      & '$ki_exists_in_world_$i'(X0,X4) )
                  | ~ entry_box(X0,X3)
                  | ~ string(X0,X2)
                  | ~ '$ki_exists_in_world_$i'(X0,X3) )
              | ~ '$ki_exists_in_world_$i'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f10]) ).

tff(f10,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2] :
              ( '$ki_exists_in_world_$i'(X0,X2)
             => ! [X3] :
                  ( '$ki_exists_in_world_$i'(X0,X3)
                 => ( ( entry_box(X0,X3)
                      & string(X0,X2) )
                   => ? [X4] :
                        ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X0,X5)
                           => ! [X6] :
                                ( '$ki_exists_in_world_$i'(X5,X6)
                               => ( do(X5,X1,X4,X6)
                                 => in(X5,X2,X3,X6) ) ) )
                        & '$ki_exists_in_world_$i'(X0,X4) ) ) ) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X6] :
          ( '$ki_exists_in_world_$i'(X0,X6)
         => ! [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
             => ! [X5] :
                  ( '$ki_exists_in_world_$i'(X0,X5)
                 => ( ( entry_box(X0,X5)
                      & string(X0,X3) )
                   => ? [X7] :
                        ( ! [X4: '$ki_world'] :
                            ( '$ki_accessible'(X0,X4)
                           => ! [X8] :
                                ( '$ki_exists_in_world_$i'(X4,X8)
                               => ( do(X4,X6,X7,X8)
                                 => in(X4,X3,X5,X8) ) ) )
                        & '$ki_exists_in_world_$i'(X0,X7) ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : NLP266_23 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n007.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun May 19 22:12:08 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.36  % (21990)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (21991)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (21992)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38  % (21993)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.15/0.38  % (21994)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.15/0.38  % (21996)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.15/0.38  % (21997)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.15/0.38  % (21995)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.15/0.38  % (21996)First to succeed.
% 0.15/0.38  % (21995)Also succeeded, but the first one will report.
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  TRYING [2,1]
% 0.15/0.38  TRYING [1,1]
% 0.15/0.38  Detected minimum model sizes of [1,1,1,1]
% 0.15/0.38  Detected maximum model sizes of [max,max,1,max]
% 0.15/0.38  TRYING [1,1,1,1]
% 0.15/0.38  TRYING [2,1]
% 0.15/0.38  TRYING [1,2]
% 0.15/0.38  % (21996)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21990"
% 0.15/0.38  TRYING [2,1,1,1]
% 0.15/0.38  TRYING [1,2]
% 0.15/0.38  TRYING [3,1,1,1]
% 0.15/0.38  % (21996)Refutation found. Thanks to Tanya!
% 0.15/0.38  % SZS status Theorem for theBenchmark
% 0.15/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.38  % (21996)------------------------------
% 0.15/0.38  % (21996)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.38  % (21996)Termination reason: Refutation
% 0.15/0.38  
% 0.15/0.38  % (21996)Memory used [KB]: 816
% 0.15/0.38  % (21996)Time elapsed: 0.006 s
% 0.15/0.38  % (21996)Instructions burned: 8 (million)
% 0.15/0.38  % (21990)Success in time 0.022 s
%------------------------------------------------------------------------------