%--------------------------------------------------------------------------
% File     : CSR001+2 : TPTP v9.0.0. Bugfixed v3.1.0.
% Domain   : Commonsense Reasoning
% Problem  : Water level is 3 at time 4
% Version  : [Mue04] axioms : Augmented > Especial.
% English  :

% Refs     : [MS05]  Mueller & Sutcliffe (2005), Reasoning in the Event Cal
%          : [Mue04] Mueller (2004), A Tool for Satisfiability-based Common
%          : [MS02]  Miller & Shanahan (2002), Some Alternative Formulation
% Source   : [MS05]
% Names    :

% Status   : Theorem
% Rating   : 0.52 v9.0.0, 0.53 v8.2.0, 0.50 v8.1.0, 0.53 v7.5.0, 0.66 v7.4.0, 0.50 v7.3.0, 0.59 v7.1.0, 0.61 v7.0.0, 0.40 v6.4.0, 0.46 v6.3.0, 0.50 v6.2.0, 0.56 v6.1.0, 0.63 v6.0.0, 0.57 v5.5.0, 0.70 v5.4.0, 0.64 v5.3.0, 0.74 v5.2.0, 0.60 v5.1.0, 0.57 v5.0.0, 0.62 v4.1.0, 0.65 v4.0.1, 0.70 v4.0.0, 0.71 v3.7.0, 0.70 v3.5.0, 0.68 v3.4.0, 0.74 v3.3.0, 0.64 v3.1.0
% Syntax   : Number of formulae    :   56 (  26 unt;   0 def)
%            Number of atoms       :  137 (  40 equ)
%            Maximal formula atoms :   11 (   2 avg)
%            Number of connectives :  109 (  28   ~;   8   |;  43   &)
%                                         (  18 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   0 prp; 2-4 aty)
%            Number of functors    :   17 (  17 usr;  15 con; 0-2 aty)
%            Number of variables   :   86 (  74   !;  12   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%--------------------------------------------------------------------------
%----Include standard discrete event calculus axioms
include('Axioms/CSR001+0.ax').
%----Include kitchen sink scenario axioms
include('Axioms/CSR001+1.ax').
%--------------------------------------------------------------------------
fof(plus0_0,axiom,
    plus(n0,n0) = n0 ).

fof(plus0_1,axiom,
    plus(n0,n1) = n1 ).

fof(plus0_2,axiom,
    plus(n0,n2) = n2 ).

fof(plus0_3,axiom,
    plus(n0,n3) = n3 ).

fof(plus1_1,axiom,
    plus(n1,n1) = n2 ).

fof(plus1_2,axiom,
    plus(n1,n2) = n3 ).

fof(plus1_3,axiom,
    plus(n1,n3) = n4 ).

fof(plus2_2,axiom,
    plus(n2,n2) = n4 ).

fof(plus2_3,axiom,
    plus(n2,n3) = n5 ).

fof(plus3_3,axiom,
    plus(n3,n3) = n6 ).

fof(symmetry_of_plus,axiom,
    ! [X,Y] : plus(X,Y) = plus(Y,X) ).

fof(less_or_equal,axiom,
    ! [X,Y] :
      ( less_or_equal(X,Y)
    <=> ( less(X,Y)
        | X = Y ) ) ).

fof(less0,axiom,
    ~ ? [X] : less(X,n0) ).

fof(less1,axiom,
    ! [X] :
      ( less(X,n1)
    <=> less_or_equal(X,n0) ) ).

fof(less2,axiom,
    ! [X] :
      ( less(X,n2)
    <=> less_or_equal(X,n1) ) ).

fof(less3,axiom,
    ! [X] :
      ( less(X,n3)
    <=> less_or_equal(X,n2) ) ).

fof(less4,axiom,
    ! [X] :
      ( less(X,n4)
    <=> less_or_equal(X,n3) ) ).

fof(less5,axiom,
    ! [X] :
      ( less(X,n5)
    <=> less_or_equal(X,n4) ) ).

fof(less6,axiom,
    ! [X] :
      ( less(X,n6)
    <=> less_or_equal(X,n5) ) ).

fof(less7,axiom,
    ! [X] :
      ( less(X,n7)
    <=> less_or_equal(X,n6) ) ).

fof(less8,axiom,
    ! [X] :
      ( less(X,n8)
    <=> less_or_equal(X,n7) ) ).

fof(less9,axiom,
    ! [X] :
      ( less(X,n9)
    <=> less_or_equal(X,n8) ) ).

fof(less_property,axiom,
    ! [X,Y] :
      ( less(X,Y)
    <=> ( ~ less(Y,X)
        & Y != X ) ) ).

%----Initial conditions
fof(waterLevel_0,hypothesis,
    holdsAt(waterLevel(n0),n0) ).

fof(not_filling_0,hypothesis,
    ~ holdsAt(filling,n0) ).

fof(not_spilling_0,hypothesis,
    ~ holdsAt(spilling,n0) ).

fof(not_released_waterLevel_0,hypothesis,
    ! [Height] : ~ releasedAt(waterLevel(Height),n0) ).

fof(not_released_filling_0,hypothesis,
    ~ releasedAt(filling,n0) ).

fof(not_released_spilling_0,hypothesis,
    ~ releasedAt(spilling,n0) ).

%----Useful lemma
fof(waterLevel_3,lemma,
    holdsAt(waterLevel(n3),n3) ).

fof(waterLevel_4,conjecture,
    holdsAt(waterLevel(n3),n4) ).

%--------------------------------------------------------------------------