%------------------------------------------------------------------------------
% File     : CSR024+1.009 : TPTP v9.0.0. Bugfixed v3.1.0.
% Domain   : Commonsense Reasoning
% Problem  : Multiple trolleys, size 9
% Version  : [Mue05] axioms : Especial.
% English  : Each agent pushes and pulls, so all trolleys spin together.

% Refs     : [Mue05] Mueller (2005), Email to Geoff Sutcliffe
% Source   : [Mue05]
% Names    :

% Status   : Theorem
% Rating   : 0.42 v9.0.0, 0.47 v8.1.0, 0.44 v7.5.0, 0.47 v7.4.0, 0.30 v7.3.0, 0.41 v7.1.0, 0.35 v7.0.0, 0.40 v6.4.0, 0.46 v6.3.0, 0.42 v6.2.0, 0.56 v6.1.0, 0.60 v6.0.0, 0.57 v5.5.0, 0.56 v5.4.0, 0.57 v5.3.0, 0.63 v5.2.0, 0.50 v5.1.0, 0.52 v5.0.0, 0.54 v4.1.0, 0.57 v4.0.1, 0.61 v4.0.0, 0.62 v3.7.0, 0.65 v3.5.0, 0.68 v3.3.0, 0.79 v3.2.0, 0.55 v3.1.0
% Syntax   : Number of formulae    :   58 (  23 unt;   0 def)
%            Number of atoms       :  316 ( 177 equ)
%            Maximal formula atoms :   72 (   5 avg)
%            Number of connectives :  409 ( 151   ~;  34   |; 192   &)
%                                         (  18 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   73 (   7 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   0 prp; 2-4 aty)
%            Number of functors    :   34 (  34 usr;  28 con; 0-2 aty)
%            Number of variables   :  116 (  99   !;  17   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments :
%------------------------------------------------------------------------------
%----Include standard discrete event calculus axioms
include('Axioms/CSR001+0.ax').
%----Include axioms for supermarket trolley scenario for multiple trolleys
include('Axioms/CSR001+3.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 ) ) ).

fof(initiates_all_defn,axiom,
    ! [Event,Fluent,Time] :
      ( initiates(Event,Fluent,Time)
    <=> ? [Agent,Trolley] :
          ( ( Event = push(Agent,Trolley)
            & Fluent = forwards(Trolley)
            & ~ happens(pull(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = backwards(Trolley)
            & ~ happens(push(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = spinning(Trolley)
            & happens(push(Agent,Trolley),Time) ) ) ) ).

fof(terminates_all_defn,axiom,
    ! [Event,Fluent,Time] :
      ( terminates(Event,Fluent,Time)
    <=> ? [Agent,Trolley] :
          ( ( Event = push(Agent,Trolley)
            & Fluent = backwards(Trolley)
            & ~ happens(pull(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = forwards(Trolley)
            & ~ happens(push(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = forwards(Trolley)
            & happens(push(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = backwards(Trolley)
            & happens(push(Agent,Trolley),Time) )
          | ( Event = push(Agent,Trolley)
            & Fluent = spinning(Trolley)
            & ~ happens(pull(Agent,Trolley),Time) )
          | ( Event = pull(Agent,Trolley)
            & Fluent = spinning(Trolley)
            & ~ happens(push(Agent,Trolley),Time) ) ) ) ).

fof(releases_all_defn,axiom,
    ! [Event,Fluent,Time] : ~ releases(Event,Fluent,Time) ).

fof(happens_all_defn,axiom,
    ! [Event,Time] :
      ( happens(Event,Time)
    <=> ( ( Event = pull(agent1,trolley1)
          & Time = n0 )
        | ( Event = push(agent1,trolley1)
          & Time = n0 )
        | ( Event = pull(agent2,trolley2)
          & Time = n0 )
        | ( Event = push(agent2,trolley2)
          & Time = n0 )
        | ( Event = pull(agent3,trolley3)
          & Time = n0 )
        | ( Event = push(agent3,trolley3)
          & Time = n0 )
        | ( Event = pull(agent4,trolley4)
          & Time = n0 )
        | ( Event = push(agent4,trolley4)
          & Time = n0 )
        | ( Event = pull(agent5,trolley5)
          & Time = n0 )
        | ( Event = push(agent5,trolley5)
          & Time = n0 )
        | ( Event = pull(agent6,trolley6)
          & Time = n0 )
        | ( Event = push(agent6,trolley6)
          & Time = n0 )
        | ( Event = pull(agent7,trolley7)
          & Time = n0 )
        | ( Event = push(agent7,trolley7)
          & Time = n0 )
        | ( Event = pull(agent8,trolley8)
          & Time = n0 )
        | ( Event = push(agent8,trolley8)
          & Time = n0 )
        | ( Event = pull(agent9,trolley9)
          & Time = n0 )
        | ( Event = push(agent9,trolley9)
          & Time = n0 ) ) ) ).

%----Distinct events
fof(push_not_pull,axiom,
    ! [Agent,Trolley] : push(Agent,Trolley) != pull(Agent,Trolley) ).

fof(push_unique,axiom,
    ! [Agent1,Agent2,Trolley1,Trolley2] :
      ( ( Agent1 != Agent2
        & Trolley1 != Trolley2 )
     => push(Agent1,Trolley1) != push(Agent2,Trolley2) ) ).

fof(pull_unique,axiom,
    ! [Agent1,Agent2,Trolley1,Trolley2] :
      ( ( Agent1 != Agent2
        & Trolley1 != Trolley2 )
     => pull(Agent1,Trolley1) != pull(Agent2,Trolley2) ) ).

%----Distinct fluents
fof(forwards_not_backwards,axiom,
    ! [Trolley] : forwards(Trolley) != backwards(Trolley) ).

fof(forwards_not_spinning,axiom,
    ! [Trolley] : forwards(Trolley) != spinning(Trolley) ).

fof(spinning_not_backwards,axiom,
    ! [Trolley] : spinning(Trolley) != backwards(Trolley) ).

%----Initial conditions
fof(initial_cond,hypothesis,
    ( ~ holdsAt(forwards(trolley1),n0)
    & ~ holdsAt(backwards(trolley1),n0)
    & ~ holdsAt(spinning(trolley1),n0)
    & ~ holdsAt(forwards(trolley2),n0)
    & ~ holdsAt(backwards(trolley2),n0)
    & ~ holdsAt(spinning(trolley2),n0)
    & ~ holdsAt(forwards(trolley3),n0)
    & ~ holdsAt(backwards(trolley3),n0)
    & ~ holdsAt(spinning(trolley3),n0)
    & ~ holdsAt(forwards(trolley4),n0)
    & ~ holdsAt(backwards(trolley4),n0)
    & ~ holdsAt(spinning(trolley4),n0)
    & ~ holdsAt(forwards(trolley5),n0)
    & ~ holdsAt(backwards(trolley5),n0)
    & ~ holdsAt(spinning(trolley5),n0)
    & ~ holdsAt(forwards(trolley6),n0)
    & ~ holdsAt(backwards(trolley6),n0)
    & ~ holdsAt(spinning(trolley6),n0)
    & ~ holdsAt(forwards(trolley7),n0)
    & ~ holdsAt(backwards(trolley7),n0)
    & ~ holdsAt(spinning(trolley7),n0)
    & ~ holdsAt(forwards(trolley8),n0)
    & ~ holdsAt(backwards(trolley8),n0)
    & ~ holdsAt(spinning(trolley8),n0)
    & ~ holdsAt(forwards(trolley9),n0)
    & ~ holdsAt(backwards(trolley9),n0)
    & ~ holdsAt(spinning(trolley9),n0) ) ).

fof(not_releasedAt,hypothesis,
    ! [Fluent,Time] : ~ releasedAt(Fluent,Time) ).

%----Distinct agents and trolleys:
fof(distinct_agents_and_trolleys,hypothesis,
    ( trolley1 != trolley2
    & agent1 != agent2
    & trolley1 != trolley3
    & agent1 != agent3
    & trolley1 != trolley4
    & agent1 != agent4
    & trolley1 != trolley5
    & agent1 != agent5
    & trolley1 != trolley6
    & agent1 != agent6
    & trolley1 != trolley7
    & agent1 != agent7
    & trolley1 != trolley8
    & agent1 != agent8
    & trolley1 != trolley9
    & agent1 != agent9
    & trolley2 != trolley3
    & agent2 != agent3
    & trolley2 != trolley4
    & agent2 != agent4
    & trolley2 != trolley5
    & agent2 != agent5
    & trolley2 != trolley6
    & agent2 != agent6
    & trolley2 != trolley7
    & agent2 != agent7
    & trolley2 != trolley8
    & agent2 != agent8
    & trolley2 != trolley9
    & agent2 != agent9
    & trolley3 != trolley4
    & agent3 != agent4
    & trolley3 != trolley5
    & agent3 != agent5
    & trolley3 != trolley6
    & agent3 != agent6
    & trolley3 != trolley7
    & agent3 != agent7
    & trolley3 != trolley8
    & agent3 != agent8
    & trolley3 != trolley9
    & agent3 != agent9
    & trolley4 != trolley5
    & agent4 != agent5
    & trolley4 != trolley6
    & agent4 != agent6
    & trolley4 != trolley7
    & agent4 != agent7
    & trolley4 != trolley8
    & agent4 != agent8
    & trolley4 != trolley9
    & agent4 != agent9
    & trolley5 != trolley6
    & agent5 != agent6
    & trolley5 != trolley7
    & agent5 != agent7
    & trolley5 != trolley8
    & agent5 != agent8
    & trolley5 != trolley9
    & agent5 != agent9
    & trolley6 != trolley7
    & agent6 != agent7
    & trolley6 != trolley8
    & agent6 != agent8
    & trolley6 != trolley9
    & agent6 != agent9
    & trolley7 != trolley8
    & agent7 != agent8
    & trolley7 != trolley9
    & agent7 != agent9
    & trolley8 != trolley9
    & agent8 != agent9 ) ).

fof(spinning_3,conjecture,
    ( holdsAt(spinning(trolley1),n1)
    & holdsAt(spinning(trolley2),n1)
    & holdsAt(spinning(trolley3),n1)
    & holdsAt(spinning(trolley4),n1)
    & holdsAt(spinning(trolley5),n1)
    & holdsAt(spinning(trolley6),n1)
    & holdsAt(spinning(trolley7),n1)
    & holdsAt(spinning(trolley8),n1)
    & holdsAt(spinning(trolley9),n1) ) ).

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