TSTP Solution File: LCL947_10 by Vampire---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire---4.8
% Problem  : LCL947_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 file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s

% Computer : n024.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 00:24:07 EDT 2024

% Result   : Theorem 0.61s 0.83s
% Output   : Refutation 0.61s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :   61
% Syntax   : Number of formulae    :  113 (  10 unt;  48 typ;   0 def)
%            Number of atoms       :  365 (   0 equ)
%            Maximal formula atoms :    9 (   5 avg)
%            Number of connectives :  365 ( 167   ~; 133   |;  25   &)
%                                         (   4 <=>;  36  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :  102 ( 102 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :  132 (  44   >;  88   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  14 usr;   6 prp; 0-4 aty)
%            Number of functors    :   39 (  39 usr;   3 con; 0-4 aty)
%            Number of variables   :  129 ( 113   !;  16   ?; 105   :)

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

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

tff(func_def_2,type,
    sK3: '$ki_world' ).

tff(func_def_4,type,
    sK5: '$ki_world' ).

tff(func_def_5,type,
    sK6: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_6,type,
    sK7: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_7,type,
    sK8: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_8,type,
    sK9: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_9,type,
    sK10: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_10,type,
    sK11: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_11,type,
    sK12: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_12,type,
    sK13: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_13,type,
    sK14: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_14,type,
    sK15: '$ki_world' > $i ).

tff(func_def_15,type,
    sK16: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_16,type,
    sK17: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_17,type,
    sK18: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_18,type,
    sK19: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_19,type,
    sK20: ( $i * $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_20,type,
    sK21: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_21,type,
    sK22: ( $i * $i * '$ki_world' ) > $i ).

tff(func_def_22,type,
    sK23: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_23,type,
    sK24: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_24,type,
    sK25: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_25,type,
    sK26: ( $i * $i * '$ki_world' ) > $i ).

tff(func_def_26,type,
    sK27: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_27,type,
    sK28: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_28,type,
    sK29: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_29,type,
    sK30: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_30,type,
    sK31: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_31,type,
    sK32: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_32,type,
    sK33: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_33,type,
    sK34: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_34,type,
    sK35: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_35,type,
    sK36: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_36,type,
    sK37: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_37,type,
    sK38: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_38,type,
    sK39: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_39,type,
    sK40: ( $i * $i * '$ki_world' ) > '$ki_world' ).

tff(func_def_40,type,
    sK41: ( $i * $i * '$ki_world' ) > '$ki_world' ).

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

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

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

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

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

tff(pred_def_6,type,
    sP0: ( $i * $i * $i * '$ki_world' ) > $o ).

tff(pred_def_7,type,
    sP1: ( $i * $i * '$ki_world' ) > $o ).

tff(pred_def_8,type,
    sP2: ( $i * $i * '$ki_world' ) > $o ).

tff(f312,plain,
    $false,
    inference(avatar_sat_refutation,[],[f244,f298,f304,f307,f311]) ).

tff(f311,plain,
    ~ spl42_1,
    inference(avatar_contradiction_clause,[],[f310]) ).

tff(f310,plain,
    ( $false
    | ~ spl42_1 ),
    inference(subsumption_resolution,[],[f309,f158]) ).

tff(f158,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/sandbox/benchmark/theBenchmark.p',mrel_reflexive) ).

tff(f309,plain,
    ( ~ '$ki_accessible'(sK3,sK3)
    | ~ spl42_1 ),
    inference(subsumption_resolution,[],[f308,f153]) ).

tff(f153,plain,
    '$ki_accessible'('$ki_local_world',sK3),
    inference(cnf_transformation,[],[f80]) ).

tff(f80,plain,
    ( ~ qmltpeq(sK5,union(sK4,sK4),sK4)
    & '$ki_accessible'(sK3,sK5)
    & '$ki_exists_in_world_$i'(sK3,sK4)
    & '$ki_accessible'('$ki_local_world',sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f40,f79,f78,f77]) ).

tff(f77,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1] :
            ( ? [X2: '$ki_world'] :
                ( ~ qmltpeq(X2,union(X1,X1),X1)
                & '$ki_accessible'(X0,X2) )
            & '$ki_exists_in_world_$i'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ~ qmltpeq(X2,union(X1,X1),X1)
              & '$ki_accessible'(sK3,X2) )
          & '$ki_exists_in_world_$i'(sK3,X1) )
      & '$ki_accessible'('$ki_local_world',sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f78,plain,
    ( ? [X1] :
        ( ? [X2: '$ki_world'] :
            ( ~ qmltpeq(X2,union(X1,X1),X1)
            & '$ki_accessible'(sK3,X2) )
        & '$ki_exists_in_world_$i'(sK3,X1) )
   => ( ? [X2: '$ki_world'] :
          ( ~ qmltpeq(X2,union(sK4,sK4),sK4)
          & '$ki_accessible'(sK3,X2) )
      & '$ki_exists_in_world_$i'(sK3,sK4) ) ),
    introduced(choice_axiom,[]) ).

tff(f79,plain,
    ( ? [X2: '$ki_world'] :
        ( ~ qmltpeq(X2,union(sK4,sK4),sK4)
        & '$ki_accessible'(sK3,X2) )
   => ( ~ qmltpeq(sK5,union(sK4,sK4),sK4)
      & '$ki_accessible'(sK3,sK5) ) ),
    introduced(choice_axiom,[]) ).

tff(f40,plain,
    ? [X0: '$ki_world'] :
      ( ? [X1] :
          ( ? [X2: '$ki_world'] :
              ( ~ qmltpeq(X2,union(X1,X1),X1)
              & '$ki_accessible'(X0,X2) )
          & '$ki_exists_in_world_$i'(X0,X1) )
      & '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f22]) ).

tff(f22,plain,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X1] :
            ( '$ki_exists_in_world_$i'(X0,X1)
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => qmltpeq(X2,union(X1,X1),X1) ) ) ),
    inference(rectify,[],[f21]) ).

tff(f21,negated_conjecture,
    ~ ! [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
       => ! [X11] :
            ( '$ki_exists_in_world_$i'(X0,X11)
           => ! [X4: '$ki_world'] :
                ( '$ki_accessible'(X0,X4)
               => qmltpeq(X4,union(X11,X11),X11) ) ) ),
    inference(negated_conjecture,[],[f20]) ).

tff(f20,conjecture,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X11] :
          ( '$ki_exists_in_world_$i'(X0,X11)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => qmltpeq(X4,union(X11,X11),X11) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',verify) ).

tff(f308,plain,
    ( ~ '$ki_accessible'('$ki_local_world',sK3)
    | ~ '$ki_accessible'(sK3,sK3)
    | ~ spl42_1 ),
    inference(resolution,[],[f240,f154]) ).

tff(f154,plain,
    '$ki_exists_in_world_$i'(sK3,sK4),
    inference(cnf_transformation,[],[f80]) ).

tff(f240,plain,
    ( ! [X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X1,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X1)
        | ~ '$ki_accessible'(X1,sK3) )
    | ~ spl42_1 ),
    inference(avatar_component_clause,[],[f239]) ).

tff(f239,plain,
    ( spl42_1
  <=> ! [X1: '$ki_world'] :
        ( ~ '$ki_accessible'(X1,sK3)
        | ~ '$ki_accessible'('$ki_local_world',X1)
        | ~ '$ki_exists_in_world_$i'(X1,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl42_1])]) ).

tff(f307,plain,
    ~ spl42_6,
    inference(avatar_contradiction_clause,[],[f306]) ).

tff(f306,plain,
    ( $false
    | ~ spl42_6 ),
    inference(subsumption_resolution,[],[f305,f155]) ).

tff(f155,plain,
    '$ki_accessible'(sK3,sK5),
    inference(cnf_transformation,[],[f80]) ).

tff(f305,plain,
    ( ~ '$ki_accessible'(sK3,sK5)
    | ~ spl42_6 ),
    inference(resolution,[],[f281,f156]) ).

tff(f156,plain,
    ~ qmltpeq(sK5,union(sK4,sK4),sK4),
    inference(cnf_transformation,[],[f80]) ).

tff(f281,plain,
    ( ! [X0: '$ki_world'] :
        ( qmltpeq(X0,union(sK4,sK4),sK4)
        | ~ '$ki_accessible'(sK3,X0) )
    | ~ spl42_6 ),
    inference(avatar_component_clause,[],[f280]) ).

tff(f280,plain,
    ( spl42_6
  <=> ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(sK3,X0)
        | qmltpeq(X0,union(sK4,sK4),sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl42_6])]) ).

tff(f304,plain,
    ( spl42_5
    | spl42_6
    | ~ spl42_2 ),
    inference(avatar_split_clause,[],[f303,f242,f280,f277]) ).

tff(f277,plain,
    ( spl42_5
  <=> ! [X2: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_accessible'(X1,sK3)
        | ~ '$ki_accessible'('$ki_local_world',X2)
        | ~ '$ki_exists_in_world_$i'(X2,sK4)
        | ~ '$ki_accessible'(X2,X1)
        | ~ '$ki_exists_in_world_$i'(X1,sK4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl42_5])]) ).

tff(f242,plain,
    ( spl42_2
  <=> ! [X0: '$ki_world'] :
        ( ~ subset(sK9(sK4,sK4,X0),sK4,sK4)
        | ~ '$ki_accessible'(X0,sK5)
        | ~ '$ki_accessible'(sK3,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl42_2])]) ).

tff(f303,plain,
    ( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_accessible'(sK3,X0)
        | qmltpeq(X0,union(sK4,sK4),sK4)
        | ~ '$ki_accessible'(X1,sK3)
        | ~ '$ki_exists_in_world_$i'(X1,sK4)
        | ~ '$ki_accessible'(X2,X1)
        | ~ '$ki_exists_in_world_$i'(X2,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X2) )
    | ~ spl42_2 ),
    inference(subsumption_resolution,[],[f283,f158]) ).

tff(f283,plain,
    ( ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_accessible'(sK3,sK3)
        | ~ '$ki_accessible'(sK3,X0)
        | qmltpeq(X0,union(sK4,sK4),sK4)
        | ~ '$ki_accessible'(X1,sK3)
        | ~ '$ki_exists_in_world_$i'(X1,sK4)
        | ~ '$ki_accessible'(X2,X1)
        | ~ '$ki_exists_in_world_$i'(X2,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X2) )
    | ~ spl42_2 ),
    inference(resolution,[],[f275,f166]) ).

tff(f166,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( '$ki_accessible'(X4,sK9(X1,X3,X4))
      | ~ '$ki_accessible'(X4,X5)
      | qmltpeq(X5,union(X1,X3),X3)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f88]) ).

tff(f88,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( qmltpeq(X5,union(X1,X3),X3)
                          | ~ '$ki_accessible'(X4,X5) )
                      | ( ~ subset(sK9(X1,X3,X4),X1,X3)
                        & '$ki_accessible'(X4,sK9(X1,X3,X4)) )
                      | ~ '$ki_accessible'(X2,X4) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f86,f87]) ).

tff(f87,plain,
    ! [X1,X3,X4: '$ki_world'] :
      ( ? [X6: '$ki_world'] :
          ( ~ subset(X6,X1,X3)
          & '$ki_accessible'(X4,X6) )
     => ( ~ subset(sK9(X1,X3,X4),X1,X3)
        & '$ki_accessible'(X4,sK9(X1,X3,X4)) ) ),
    introduced(choice_axiom,[]) ).

tff(f86,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X5: '$ki_world'] :
                          ( qmltpeq(X5,union(X1,X3),X3)
                          | ~ '$ki_accessible'(X4,X5) )
                      | ? [X6: '$ki_world'] :
                          ( ~ subset(X6,X1,X3)
                          & '$ki_accessible'(X4,X6) )
                      | ~ '$ki_accessible'(X2,X4) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(rectify,[],[f47]) ).

tff(f47,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X6: '$ki_world'] :
                          ( qmltpeq(X6,union(X1,X3),X3)
                          | ~ '$ki_accessible'(X4,X6) )
                      | ? [X5: '$ki_world'] :
                          ( ~ subset(X5,X1,X3)
                          & '$ki_accessible'(X4,X5) )
                      | ~ '$ki_accessible'(X2,X4) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(flattening,[],[f46]) ).

tff(f46,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( ! [X3] :
                  ( ! [X4: '$ki_world'] :
                      ( ! [X6: '$ki_world'] :
                          ( qmltpeq(X6,union(X1,X3),X3)
                          | ~ '$ki_accessible'(X4,X6) )
                      | ? [X5: '$ki_world'] :
                          ( ~ subset(X5,X1,X3)
                          & '$ki_accessible'(X4,X5) )
                      | ~ '$ki_accessible'(X2,X4) )
                  | ~ '$ki_exists_in_world_$i'(X2,X3) )
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f25]) ).

tff(f25,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => ! [X3] :
                  ( '$ki_exists_in_world_$i'(X2,X3)
                 => ! [X4: '$ki_world'] :
                      ( '$ki_accessible'(X2,X4)
                     => ( ! [X5: '$ki_world'] :
                            ( '$ki_accessible'(X4,X5)
                           => subset(X5,X1,X3) )
                       => ! [X6: '$ki_world'] :
                            ( '$ki_accessible'(X4,X6)
                           => qmltpeq(X6,union(X1,X3),X3) ) ) ) ) ) ) ),
    inference(rectify,[],[f13]) ).

tff(f13,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X11] :
          ( '$ki_exists_in_world_$i'(X0,X11)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => ! [X12] :
                  ( '$ki_exists_in_world_$i'(X4,X12)
                 => ! [X6: '$ki_world'] :
                      ( '$ki_accessible'(X4,X6)
                     => ( ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X6,X7)
                           => subset(X7,X11,X12) )
                       => ! [X7: '$ki_world'] :
                            ( '$ki_accessible'(X6,X7)
                           => qmltpeq(X7,union(X11,X12),X12) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_union) ).

tff(f275,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(X0,sK9(sK4,sK4,sK3))
        | ~ '$ki_accessible'(sK3,X0) )
    | ~ spl42_2 ),
    inference(resolution,[],[f273,f157]) ).

tff(f157,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_accessible'(X0,X1) ),
    inference(cnf_transformation,[],[f42]) ).

tff(f42,plain,
    ! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
      ( '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_accessible'(X0,X1) ),
    inference(flattening,[],[f41]) ).

tff(f41,plain,
    ! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
      ( '$ki_accessible'(X0,X2)
      | ~ '$ki_accessible'(X1,X2)
      | ~ '$ki_accessible'(X0,X1) ),
    inference(ennf_transformation,[],[f2]) ).

tff(f2,axiom,
    ! [X0: '$ki_world',X1: '$ki_world',X2: '$ki_world'] :
      ( ( '$ki_accessible'(X1,X2)
        & '$ki_accessible'(X0,X1) )
     => '$ki_accessible'(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',mrel_transitive) ).

tff(f273,plain,
    ( ~ '$ki_accessible'(sK3,sK9(sK4,sK4,sK3))
    | ~ spl42_2 ),
    inference(subsumption_resolution,[],[f272,f153]) ).

tff(f272,plain,
    ( ~ '$ki_accessible'(sK3,sK9(sK4,sK4,sK3))
    | ~ '$ki_accessible'('$ki_local_world',sK3)
    | ~ spl42_2 ),
    inference(resolution,[],[f254,f154]) ).

tff(f254,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK4)
        | ~ '$ki_accessible'(X0,sK9(sK4,sK4,sK3))
        | ~ '$ki_accessible'('$ki_local_world',X0) )
    | ~ spl42_2 ),
    inference(resolution,[],[f249,f218]) ).

tff(f218,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: $i] :
      ( subset(X2,X1,X1)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f65]) ).

tff(f65,plain,
    ! [X0: '$ki_world'] :
      ( ! [X1] :
          ( ! [X2: '$ki_world'] :
              ( subset(X2,X1,X1)
              | ~ '$ki_accessible'(X0,X2) )
          | ~ '$ki_exists_in_world_$i'(X0,X1) )
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(ennf_transformation,[],[f36]) ).

tff(f36,plain,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X1] :
          ( '$ki_exists_in_world_$i'(X0,X1)
         => ! [X2: '$ki_world'] :
              ( '$ki_accessible'(X0,X2)
             => subset(X2,X1,X1) ) ) ),
    inference(rectify,[],[f18]) ).

tff(f18,axiom,
    ! [X0: '$ki_world'] :
      ( '$ki_accessible'('$ki_local_world',X0)
     => ! [X11] :
          ( '$ki_exists_in_world_$i'(X0,X11)
         => ! [X4: '$ki_world'] :
              ( '$ki_accessible'(X0,X4)
             => subset(X4,X11,X11) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).

tff(f249,plain,
    ( ~ subset(sK9(sK4,sK4,sK3),sK4,sK4)
    | ~ spl42_2 ),
    inference(subsumption_resolution,[],[f247,f158]) ).

tff(f247,plain,
    ( ~ subset(sK9(sK4,sK4,sK3),sK4,sK4)
    | ~ '$ki_accessible'(sK3,sK3)
    | ~ spl42_2 ),
    inference(resolution,[],[f243,f155]) ).

tff(f243,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'(X0,sK5)
        | ~ subset(sK9(sK4,sK4,X0),sK4,sK4)
        | ~ '$ki_accessible'(sK3,X0) )
    | ~ spl42_2 ),
    inference(avatar_component_clause,[],[f242]) ).

tff(f298,plain,
    ~ spl42_5,
    inference(avatar_contradiction_clause,[],[f297]) ).

tff(f297,plain,
    ( $false
    | ~ spl42_5 ),
    inference(subsumption_resolution,[],[f296,f158]) ).

tff(f296,plain,
    ( ~ '$ki_accessible'(sK3,sK3)
    | ~ spl42_5 ),
    inference(duplicate_literal_removal,[],[f295]) ).

tff(f295,plain,
    ( ~ '$ki_accessible'(sK3,sK3)
    | ~ '$ki_accessible'(sK3,sK3)
    | ~ spl42_5 ),
    inference(resolution,[],[f293,f154]) ).

tff(f293,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X0,sK4)
        | ~ '$ki_accessible'(sK3,X0)
        | ~ '$ki_accessible'(X0,sK3) )
    | ~ spl42_5 ),
    inference(subsumption_resolution,[],[f292,f153]) ).

tff(f292,plain,
    ( ! [X0: '$ki_world'] :
        ( ~ '$ki_accessible'('$ki_local_world',sK3)
        | ~ '$ki_accessible'(X0,sK3)
        | ~ '$ki_accessible'(sK3,X0)
        | ~ '$ki_exists_in_world_$i'(X0,sK4) )
    | ~ spl42_5 ),
    inference(resolution,[],[f278,f154]) ).

tff(f278,plain,
    ( ! [X2: '$ki_world',X1: '$ki_world'] :
        ( ~ '$ki_exists_in_world_$i'(X2,sK4)
        | ~ '$ki_accessible'('$ki_local_world',X2)
        | ~ '$ki_accessible'(X1,sK3)
        | ~ '$ki_accessible'(X2,X1)
        | ~ '$ki_exists_in_world_$i'(X1,sK4) )
    | ~ spl42_5 ),
    inference(avatar_component_clause,[],[f277]) ).

tff(f244,plain,
    ( spl42_1
    | spl42_2 ),
    inference(avatar_split_clause,[],[f237,f242,f239]) ).

tff(f237,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] :
      ( ~ subset(sK9(sK4,sK4,X0),sK4,sK4)
      | ~ '$ki_accessible'(sK3,X0)
      | ~ '$ki_accessible'(X0,sK5)
      | ~ '$ki_accessible'(X1,sK3)
      | ~ '$ki_exists_in_world_$i'(X1,sK4)
      | ~ '$ki_accessible'('$ki_local_world',X1) ),
    inference(resolution,[],[f236,f154]) ).

tff(f236,plain,
    ! [X2: '$ki_world',X0: '$ki_world',X1: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X1,sK4)
      | ~ subset(sK9(sK4,sK4,X0),sK4,sK4)
      | ~ '$ki_accessible'(X1,X0)
      | ~ '$ki_accessible'(X0,sK5)
      | ~ '$ki_accessible'(X2,X1)
      | ~ '$ki_exists_in_world_$i'(X2,sK4)
      | ~ '$ki_accessible'('$ki_local_world',X2) ),
    inference(resolution,[],[f167,f156]) ).

tff(f167,plain,
    ! [X2: '$ki_world',X3: $i,X0: '$ki_world',X1: $i,X4: '$ki_world',X5: '$ki_world'] :
      ( qmltpeq(X5,union(X1,X3),X3)
      | ~ '$ki_accessible'(X4,X5)
      | ~ subset(sK9(X1,X3,X4),X1,X3)
      | ~ '$ki_accessible'(X2,X4)
      | ~ '$ki_exists_in_world_$i'(X2,X3)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'('$ki_local_world',X0) ),
    inference(cnf_transformation,[],[f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem    : LCL947_10 : TPTP v8.2.0. Released v8.2.0.
% 0.12/0.15  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36  % Computer : n024.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit   : 300
% 0.14/0.36  % WCLimit    : 300
% 0.14/0.36  % DateTime   : Mon May 20 01:50:07 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  This is a TF0_THM_NEQ_NAR problem
% 0.14/0.36  Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.61/0.81  % (4222)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on theBenchmark for (2995ds/56Mi)
% 0.61/0.81  % (4215)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on theBenchmark for (2995ds/34Mi)
% 0.61/0.81  % (4216)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on theBenchmark for (2995ds/51Mi)
% 0.61/0.81  % (4221)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on theBenchmark for (2995ds/83Mi)
% 0.61/0.82  % (4220)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on theBenchmark for (2995ds/45Mi)
% 0.61/0.82  % (4218)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on theBenchmark for (2995ds/33Mi)
% 0.61/0.82  % (4220)Refutation not found, incomplete strategy% (4220)------------------------------
% 0.61/0.82  % (4220)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.82  % (4220)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.82  
% 0.61/0.82  % (4220)Memory used [KB]: 1114
% 0.61/0.82  % (4220)Time elapsed: 0.006 s
% 0.61/0.82  % (4220)Instructions burned: 5 (million)
% 0.61/0.82  % (4220)------------------------------
% 0.61/0.82  % (4220)------------------------------
% 0.61/0.82  % (4219)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on theBenchmark for (2995ds/34Mi)
% 0.61/0.82  % (4217)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on theBenchmark for (2995ds/78Mi)
% 0.61/0.82  % (4223)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on theBenchmark for (2995ds/55Mi)
% 0.61/0.83  % (4218)Refutation not found, incomplete strategy% (4218)------------------------------
% 0.61/0.83  % (4218)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.83  % (4218)Termination reason: Refutation not found, incomplete strategy
% 0.61/0.83  
% 0.61/0.83  % (4218)Memory used [KB]: 1210
% 0.61/0.83  % (4218)Time elapsed: 0.009 s
% 0.61/0.83  % (4218)Instructions burned: 14 (million)
% 0.61/0.83  % (4218)------------------------------
% 0.61/0.83  % (4218)------------------------------
% 0.61/0.83  % (4222)Instruction limit reached!
% 0.61/0.83  % (4222)------------------------------
% 0.61/0.83  % (4222)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.83  % (4222)Termination reason: Unknown
% 0.61/0.83  % (4222)Termination phase: Saturation
% 0.61/0.83  
% 0.61/0.83  % (4222)Memory used [KB]: 1476
% 0.61/0.83  % (4222)Time elapsed: 0.024 s
% 0.61/0.83  % (4222)Instructions burned: 57 (million)
% 0.61/0.83  % (4222)------------------------------
% 0.61/0.83  % (4222)------------------------------
% 0.61/0.83  % (4217)First to succeed.
% 0.61/0.83  % (4224)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on theBenchmark for (2995ds/50Mi)
% 0.61/0.83  % (4217)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4214"
% 0.61/0.83  % (4217)Refutation found. Thanks to Tanya!
% 0.61/0.83  % SZS status Theorem for theBenchmark
% 0.61/0.83  % SZS output start Proof for theBenchmark
% See solution above
% 0.61/0.84  % (4217)------------------------------
% 0.61/0.84  % (4217)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.61/0.84  % (4217)Termination reason: Refutation
% 0.61/0.84  
% 0.61/0.84  % (4217)Memory used [KB]: 1345
% 0.61/0.84  % (4217)Time elapsed: 0.013 s
% 0.61/0.84  % (4217)Instructions burned: 20 (million)
% 0.61/0.84  % (4214)Success in time 0.464 s
% 0.61/0.84  % Vampire---4.8 exiting
%------------------------------------------------------------------------------