TSTP Solution File: SYO900_11 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SYO900_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 : n021.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 0.49s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   27 (   6 unt;   9 typ;   0 def)
%            Number of atoms       :  106 (   0 equ)
%            Maximal formula atoms :   10 (   5 avg)
%            Number of connectives :  120 (  32   ~;  16   |;  44   &)
%                                         (   0 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   6 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   1 usr)
%            Number of type conns  :    4 (   3   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   5 con; 0-0 aty)
%            Number of variables   :   58 (;  38   !;  20   ?;  58   :)

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

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

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

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

tff(func_def_3,type,
    sK2: '$ki_world' ).

tff(func_def_4,type,
    sK3: '$ki_world' ).

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

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

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

tff(f27,plain,
    $false,
    inference(resolution,[],[f25,f22]) ).

tff(f22,plain,
    ~ q(sK1),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ( ~ q(sK1)
    & '$ki_accessible'(sK0,sK1)
    & ! [X2: '$ki_world'] :
        ( p(X2)
        | ~ '$ki_accessible'(sK0,X2) )
    & '$ki_accessible'('$ki_local_world',sK0)
    & '$ki_accessible'('$ki_local_world',sK2)
    & ! [X4: '$ki_world'] :
        ( q(X4)
        | ~ '$ki_accessible'(sK2,X4) )
    & '$ki_accessible'(sK2,sK3)
    & ~ p(sK3) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f12,f11,f10,f9]) ).

tff(f9,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( ~ q(X1)
            & '$ki_accessible'(X0,X1) )
        & ! [X2: '$ki_world'] :
            ( p(X2)
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_accessible'('$ki_local_world',X0) )
   => ( ? [X1: '$ki_world'] :
          ( ~ q(X1)
          & '$ki_accessible'(sK0,X1) )
      & ! [X2: '$ki_world'] :
          ( p(X2)
          | ~ '$ki_accessible'(sK0,X2) )
      & '$ki_accessible'('$ki_local_world',sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f10,plain,
    ( ? [X1: '$ki_world'] :
        ( ~ q(X1)
        & '$ki_accessible'(sK0,X1) )
   => ( ~ q(sK1)
      & '$ki_accessible'(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

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

tff(f12,plain,
    ( ? [X5: '$ki_world'] :
        ( '$ki_accessible'(sK2,X5)
        & ~ p(X5) )
   => ( '$ki_accessible'(sK2,sK3)
      & ~ p(sK3) ) ),
    introduced(choice_axiom,[]) ).

tff(f8,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X1: '$ki_world'] :
            ( ~ q(X1)
            & '$ki_accessible'(X0,X1) )
        & ! [X2: '$ki_world'] :
            ( p(X2)
            | ~ '$ki_accessible'(X0,X2) )
        & '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X3)
        & ! [X4: '$ki_world'] :
            ( q(X4)
            | ~ '$ki_accessible'(X3,X4) )
        & ? [X5: '$ki_world'] :
            ( '$ki_accessible'(X3,X5)
            & ~ p(X5) ) ) ),
    inference(rectify,[],[f6]) ).

tff(f6,plain,
    ( ? [X3: '$ki_world'] :
        ( ? [X5: '$ki_world'] :
            ( ~ q(X5)
            & '$ki_accessible'(X3,X5) )
        & ! [X4: '$ki_world'] :
            ( p(X4)
            | ~ '$ki_accessible'(X3,X4) )
        & '$ki_accessible'('$ki_local_world',X3) )
    & ? [X0: '$ki_world'] :
        ( '$ki_accessible'('$ki_local_world',X0)
        & ! [X1: '$ki_world'] :
            ( q(X1)
            | ~ '$ki_accessible'(X0,X1) )
        & ? [X2: '$ki_world'] :
            ( '$ki_accessible'(X0,X2)
            & ~ p(X2) ) ) ),
    inference(flattening,[],[f5]) ).

tff(f5,plain,
    ( ? [X0: '$ki_world'] :
        ( ? [X2: '$ki_world'] :
            ( '$ki_accessible'(X0,X2)
            & ~ p(X2) )
        & ! [X1: '$ki_world'] :
            ( q(X1)
            | ~ '$ki_accessible'(X0,X1) )
        & '$ki_accessible'('$ki_local_world',X0) )
    & ? [X3: '$ki_world'] :
        ( ? [X5: '$ki_world'] :
            ( ~ q(X5)
            & '$ki_accessible'(X3,X5) )
        & ! [X4: '$ki_world'] :
            ( p(X4)
            | ~ '$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'] :
                ( '$ki_accessible'(X0,X1)
               => q(X1) )
           => ! [X2: '$ki_world'] :
                ( '$ki_accessible'(X0,X2)
               => p(X2) ) ) )
      | ! [X3: '$ki_world'] :
          ( '$ki_accessible'('$ki_local_world',X3)
         => ( ! [X4: '$ki_world'] :
                ( '$ki_accessible'(X3,X4)
               => p(X4) )
           => ! [X5: '$ki_world'] :
                ( '$ki_accessible'(X3,X5)
               => q(X5) ) ) ) ),
    inference(rectify,[],[f3]) ).

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

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

tff(f25,plain,
    ! [X0: '$ki_world'] : q(X0),
    inference(resolution,[],[f14,f17]) ).

tff(f17,plain,
    ! [X4: '$ki_world'] :
      ( ~ '$ki_accessible'(sK2,X4)
      | q(X4) ),
    inference(cnf_transformation,[],[f13]) ).

tff(f14,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(cnf_transformation,[],[f7]) ).

tff(f7,plain,
    ! [X0: '$ki_world',X1: '$ki_world'] : '$ki_accessible'(X1,X0),
    inference(rectify,[],[f1]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : SYO900_11 : TPTP v8.2.0. Released v8.2.0.
% 0.07/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n021.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 13:12:30 EDT 2023
% 0.13/0.34  % CPUTime    : 
% 0.19/0.48  % (14089)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/467Mi)
% 0.19/0.48  % (14081)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/75Mi)
% 0.19/0.49  % (14081)First to succeed.
% 0.19/0.49  % (14089)Also succeeded, but the first one will report.
% 0.19/0.49  % (14081)Refutation found. Thanks to Tanya!
% 0.19/0.49  % SZS status Theorem for theBenchmark
% 0.19/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49  % (14081)------------------------------
% 0.19/0.49  % (14081)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49  % (14081)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49  % (14081)Termination reason: Refutation
% 0.19/0.49  
% 0.19/0.49  % (14081)Memory used [KB]: 895
% 0.19/0.49  % (14081)Time elapsed: 0.065 s
% 0.19/0.49  % (14081)Instructions burned: 2 (million)
% 0.19/0.49  % (14081)------------------------------
% 0.19/0.49  % (14081)------------------------------
% 0.19/0.49  % (14063)Success in time 0.143 s
%------------------------------------------------------------------------------