TSTP Solution File: SYO891_16 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYO891_16 : 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 : n023.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 22 15:45:48 EDT 2023

% Result   : Theorem 1.24s 0.52s
% Output   : Refutation 1.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   32 (   6 unt;   9 typ;   0 def)
%            Number of atoms       :  121 (   0 equ)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :  122 (  34   ~;  26   |;  45   &)
%                                         (   0 <=>;  17  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :   10 (  10 fml;   0 var)
%            Number of types       :    3 (   1 usr)
%            Number of type conns  :   12 (   6   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   5 usr;   2 prp; 0-3 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   73 (;  44   !;  29   ?;  39   :)

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

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

tff(func_def_1,type,
    sK0: '$ki_world' > $i ).

tff(func_def_2,type,
    sK1: ( $i * '$ki_world' ) > $i ).

tff(func_def_4,type,
    sK3: '$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,
    p: ( '$ki_world' * $i ) > $o ).

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

tff(f65,plain,
    $false,
    inference(subsumption_resolution,[],[f62,f59]) ).

tff(f59,plain,
    '$ki_exists_in_world_$i'(sK3,sK2),
    inference(unit_resulting_resolution,[],[f44,f46,f53]) ).

tff(f53,plain,
    ! [X2: '$ki_world',X0: $i,X1: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X1,X0)
      | ~ '$ki_accessible'(X1,X2)
      | '$ki_exists_in_world_$i'(X2,X0) ),
    inference(cnf_transformation,[],[f40]) ).

tff(f40,plain,
    ! [X0,X1: '$ki_world',X2: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X1,X0)
      | ~ '$ki_accessible'(X1,X2)
      | '$ki_exists_in_world_$i'(X2,X0) ),
    inference(rectify,[],[f26]) ).

tff(f26,plain,
    ! [X1,X0: '$ki_world',X2: '$ki_world'] :
      ( ~ '$ki_exists_in_world_$i'(X0,X1)
      | ~ '$ki_accessible'(X0,X2)
      | '$ki_exists_in_world_$i'(X2,X1) ),
    inference(flattening,[],[f25]) ).

tff(f25,plain,
    ! [X1,X2: '$ki_world',X0: '$ki_world'] :
      ( '$ki_exists_in_world_$i'(X2,X1)
      | ~ '$ki_accessible'(X0,X2)
      | ~ '$ki_exists_in_world_$i'(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

tff(f17,plain,
    ! [X1,X2: '$ki_world',X0: '$ki_world'] :
      ( ( '$ki_accessible'(X0,X2)
        & '$ki_exists_in_world_$i'(X0,X1) )
     => '$ki_exists_in_world_$i'(X2,X1) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X0: '$ki_world',X3,X1: '$ki_world'] :
      ( ( '$ki_exists_in_world_$i'(X0,X3)
        & '$ki_accessible'(X0,X1) )
     => '$ki_exists_in_world_$i'(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$ki_exists_in_world_$i_cumul') ).

tff(f46,plain,
    '$ki_exists_in_world_$i'('$ki_local_world',sK2),
    inference(cnf_transformation,[],[f39]) ).

tff(f39,plain,
    ( ! [X0] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | ( qmltpeq(X1,X0,sK1(X0,X1))
              & '$ki_exists_in_world_$i'(X1,sK1(X0,X1)) ) ) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ~ p(X3,X4)
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & '$ki_exists_in_world_$i'('$ki_local_world',sK2)
    & p(sK3,sK2)
    & '$ki_accessible'('$ki_local_world',sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f35,f38,f37,f36]) ).

tff(f36,plain,
    ! [X0,X1: '$ki_world'] :
      ( ? [X2] :
          ( qmltpeq(X1,X0,X2)
          & '$ki_exists_in_world_$i'(X1,X2) )
     => ( qmltpeq(X1,X0,sK1(X0,X1))
        & '$ki_exists_in_world_$i'(X1,sK1(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f37,plain,
    ( ? [X5] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X5)
        & ? [X6: '$ki_world'] :
            ( p(X6,X5)
            & '$ki_accessible'('$ki_local_world',X6) ) )
   => ( '$ki_exists_in_world_$i'('$ki_local_world',sK2)
      & ? [X6: '$ki_world'] :
          ( p(X6,sK2)
          & '$ki_accessible'('$ki_local_world',X6) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f38,plain,
    ( ? [X6: '$ki_world'] :
        ( p(X6,sK2)
        & '$ki_accessible'('$ki_local_world',X6) )
   => ( p(sK3,sK2)
      & '$ki_accessible'('$ki_local_world',sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f35,plain,
    ( ! [X0] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | ? [X2] :
                ( qmltpeq(X1,X0,X2)
                & '$ki_exists_in_world_$i'(X1,X2) ) ) )
    & ! [X3: '$ki_world'] :
        ( ! [X4] :
            ( ~ p(X3,X4)
            | ~ '$ki_exists_in_world_$i'(X3,X4) )
        | ~ '$ki_accessible'('$ki_local_world',X3) )
    & ? [X5] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X5)
        & ? [X6: '$ki_world'] :
            ( p(X6,X5)
            & '$ki_accessible'('$ki_local_world',X6) ) ) ),
    inference(rectify,[],[f28]) ).

tff(f28,plain,
    ( ! [X0] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | ? [X2] :
                ( qmltpeq(X1,X0,X2)
                & '$ki_exists_in_world_$i'(X1,X2) ) ) )
    & ! [X5: '$ki_world'] :
        ( ! [X6] :
            ( ~ p(X5,X6)
            | ~ '$ki_exists_in_world_$i'(X5,X6) )
        | ~ '$ki_accessible'('$ki_local_world',X5) )
    & ? [X3] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
        & ? [X4: '$ki_world'] :
            ( p(X4,X3)
            & '$ki_accessible'('$ki_local_world',X4) ) ) ),
    inference(flattening,[],[f27]) ).

tff(f27,plain,
    ( ! [X5: '$ki_world'] :
        ( ! [X6] :
            ( ~ p(X5,X6)
            | ~ '$ki_exists_in_world_$i'(X5,X6) )
        | ~ '$ki_accessible'('$ki_local_world',X5) )
    & ? [X3] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
        & ? [X4: '$ki_world'] :
            ( p(X4,X3)
            & '$ki_accessible'('$ki_local_world',X4) ) )
    & ! [X0] :
        ( ~ '$ki_exists_in_world_$i'('$ki_local_world',X0)
        | ! [X1: '$ki_world'] :
            ( ~ '$ki_accessible'('$ki_local_world',X1)
            | ? [X2] :
                ( qmltpeq(X1,X0,X2)
                & '$ki_exists_in_world_$i'(X1,X2) ) ) ) ),
    inference(ennf_transformation,[],[f11]) ).

tff(f11,plain,
    ~ ( ! [X0] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X0)
         => ! [X1: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X1)
             => ? [X2] :
                  ( qmltpeq(X1,X0,X2)
                  & '$ki_exists_in_world_$i'(X1,X2) ) ) )
     => ( ? [X3] :
            ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
            & ? [X4: '$ki_world'] :
                ( p(X4,X3)
                & '$ki_accessible'('$ki_local_world',X4) ) )
       => ? [X5: '$ki_world'] :
            ( ? [X6] :
                ( '$ki_exists_in_world_$i'(X5,X6)
                & p(X5,X6) )
            & '$ki_accessible'('$ki_local_world',X5) ) ) ),
    inference(rectify,[],[f10]) ).

tff(f10,negated_conjecture,
    ~ ( ! [X3] :
          ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
         => ! [X0: '$ki_world'] :
              ( '$ki_accessible'('$ki_local_world',X0)
             => ? [X4] :
                  ( qmltpeq(X0,X3,X4)
                  & '$ki_exists_in_world_$i'(X0,X4) ) ) )
     => ( ? [X3] :
            ( ? [X0: '$ki_world'] :
                ( p(X0,X3)
                & '$ki_accessible'('$ki_local_world',X0) )
            & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
       => ? [X0: '$ki_world'] :
            ( ? [X3] :
                ( '$ki_exists_in_world_$i'(X0,X3)
                & p(X0,X3) )
            & '$ki_accessible'('$ki_local_world',X0) ) ) ),
    inference(negated_conjecture,[],[f9]) ).

tff(f9,conjecture,
    ( ! [X3] :
        ( '$ki_exists_in_world_$i'('$ki_local_world',X3)
       => ! [X0: '$ki_world'] :
            ( '$ki_accessible'('$ki_local_world',X0)
           => ? [X4] :
                ( qmltpeq(X0,X3,X4)
                & '$ki_exists_in_world_$i'(X0,X4) ) ) )
   => ( ? [X3] :
          ( ? [X0: '$ki_world'] :
              ( p(X0,X3)
              & '$ki_accessible'('$ki_local_world',X0) )
          & '$ki_exists_in_world_$i'('$ki_local_world',X3) )
     => ? [X0: '$ki_world'] :
          ( ? [X3] :
              ( '$ki_exists_in_world_$i'(X0,X3)
              & p(X0,X3) )
          & '$ki_accessible'('$ki_local_world',X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',verify) ).

tff(f44,plain,
    '$ki_accessible'('$ki_local_world',sK3),
    inference(cnf_transformation,[],[f39]) ).

tff(f62,plain,
    ~ '$ki_exists_in_world_$i'(sK3,sK2),
    inference(unit_resulting_resolution,[],[f45,f44,f47]) ).

tff(f47,plain,
    ! [X3: '$ki_world',X4: $i] :
      ( ~ '$ki_exists_in_world_$i'(X3,X4)
      | ~ p(X3,X4)
      | ~ '$ki_accessible'('$ki_local_world',X3) ),
    inference(cnf_transformation,[],[f39]) ).

tff(f45,plain,
    p(sK3,sK2),
    inference(cnf_transformation,[],[f39]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO891_16 : 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 : n023.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 13:27:57 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (8464)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.51  % (8463)dis+1002_1:1_aac=none:bd=off:sac=on:sos=on:spb=units:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 1.24/0.52  % (8471)lrs+10_1:1_ep=R:lcm=predicate:lma=on:sos=all:spb=goal:ss=included:i=12:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/12Mi)
% 1.24/0.52  % (8480)dis-10_3:2_amm=sco:ep=RS:fsr=off:nm=10:sd=2:sos=on:ss=axioms:st=3.0:i=11:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/11Mi)
% 1.24/0.52  % (8464)First to succeed.
% 1.24/0.52  % (8463)Instruction limit reached!
% 1.24/0.52  % (8463)------------------------------
% 1.24/0.52  % (8463)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.24/0.52  % (8463)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.24/0.52  % (8463)Termination reason: Unknown
% 1.24/0.52  % (8463)Termination phase: Saturation
% 1.24/0.52  
% 1.24/0.52  % (8463)Memory used [KB]: 5884
% 1.24/0.52  % (8463)Time elapsed: 0.105 s
% 1.24/0.52  % (8463)Instructions burned: 3 (million)
% 1.24/0.52  % (8463)------------------------------
% 1.24/0.52  % (8463)------------------------------
% 1.24/0.52  % (8464)Refutation found. Thanks to Tanya!
% 1.24/0.52  % SZS status Theorem for theBenchmark
% 1.24/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 1.24/0.52  % (8464)------------------------------
% 1.24/0.52  % (8464)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.24/0.52  % (8464)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.24/0.52  % (8464)Termination reason: Refutation
% 1.24/0.52  
% 1.24/0.52  % (8464)Memory used [KB]: 5884
% 1.24/0.52  % (8464)Time elapsed: 0.112 s
% 1.24/0.52  % (8464)Instructions burned: 1 (million)
% 1.24/0.52  % (8464)------------------------------
% 1.24/0.52  % (8464)------------------------------
% 1.24/0.52  % (8457)Success in time 0.165 s
%------------------------------------------------------------------------------