[T] There is no woman slicing an onion. 

slice.f1-PRED-pres-progr-t(
  onion-PAT-sg-indef-t,
  *,
  #Neg-RHEM,
  woman-ACT-sg-indef-f)

[H] A woman is slicing an onion. [contradiction]

slice.f1-PRED-pres-progr-f(
 woman-ACT-sg-indef-t,
 *,
 onion-PAT-sg-indef-f)

[T] Every European can travel freely within Europe

travel.f1-PRED-pres-simple-deontmod.poss-f(
  European-ACT-sg-def-t(
    every-RSTR-t,*),
  *,
  free-MANN-f,
  Europe-DIR2-sg-def-f)

[H] Every European can travel freely. [no entailment]

travel.f1-PRED-pres-simple-deontmod.poss-f(
  European-ACT-sg-def-t(
    every-RSTR-t,*),
  *,
  free-MANN-f,
  #Gen-DIR2-t)

[H] Every happy European can travel freely within Europe. [entailment]

travel.f1-PRED-pres-simple-deontmod.poss-f(
  European-ACT-sg-def-t(
    every-RSTR-t,
    happy-RSTR-t,*),
  *,
  free-MANN-f,
  Europe-DIR2-sg-def-f)

[T] A group of scouts are hiking through the grass.

hike.f2-PRED-pres-progr-t(
  group-ACT-sg-indef-t(
    *,scout-RSTR-pl-indef-t)
  *,
  grass-DIR2-sg-def-f)

[H] Some people are walking. [entailment]

walk.f1-PRED-pres-progr-f(
  person-ACT-pl-indef-t(
    *,some-RSTR-t)
  *)

[T] A man, a woman and two girls are walking on the beach.

walk.f1-PRED-pres-progr-f(
  and-COORD(
    man-ACT-sg-t,
    woman-ACT-sg-t,
    *,
    girl-ACT-pl-t(
      *,two-EXT-t)
  ),
  beach-LOC-sg-def-t,
  *)

[H] Four people are walking on the beach. [entailment]

walk.f1-PRED-pres-progr-f(
  person-ACT-pl-t(
    *,four-EXT-t),
  *,
  beach-LOC-sg-def-t)

[T] Romano Prodi will meet the US President George Bush in his capacity as the president of the European commission.

meet.f2-PRED-fut-simple-f(
  Prodi-ACT-sg-def-t-ID[1](
    *,Romano-RSTR-sg-def-t)
  *,
  #Empty-AP(
    president-PAT-sg-def-f(
      USA-RSTR-sg-def-f,*),
    Bush-PAT-sg-def-f(
      George-RSTR-sg-def-f,*)),
  capacity-COMPL-sg-def-f(
    #PersPron-APP-sg-def-f-ref[1],*,
    president-RSTR-sg-def-f(
      EU-RSTR-sg-def-f,*)
  )
)

[H] George Bush is the president of the European commission. [entailment?]

be.f6-PRED-pres-simple-f(
  Bush-ACT-sg-def-t(
    George-RSTR-sg-def-t,*),
  *,
  president-PAT-sg-def-f(
    EU-RSTR-sg-def-f,*))

[H] Romano Prodi is the president of the European commission.[entailment?] 

be.f6-PRED-pres-simple-f(
  Prodi-ACT-sg-def-t(
    Romano-RSTR-sg-def-t,*),
  *,
  president-PAT-sg-def-f(
    EU-RSTR-sg-def-f,*))

[T] Romano Prodi will meet the US President George Bush in their capacities as presidents of big institutions.

meet.f2-PRED-fut-simple-f(
  Prodi-ACT-sg-def-t-ID[1](
    *,Romano-RSTR-sg-def-t)
  *,
  #Empty-AP-ID[2](
    president-PAT-sg-def-f(
      USA-RSTR-sg-def-f,*),
    Bush-PAT-sg-def-f(
      George-RSTR-sg-def-f,*)),
  capacity-COMPL-pl-def-f(
    #PersPron-APP-pl-def-f-ref[1,2],*,
    president-RSTR-pl-def-f(
      institution-RSTR-pl-def-f(
        big-RSTR-def-t,*),
      *)
  )
)

[H] George Bush is the president of a big institution. [entailment?]

be.f6-PRED-pres-simple-f(
  Bush-ACT-sg-def-t(
    George-RSTR-sg-def-t,*),
  *,
  president-PAT-sg-def-f(
    institution-RSTR-pl-indef-f(
      big-RSTR-indef-f,*))
)

[H] Romano Prodi is the president of a big institution. [entailment?]

be.f6-PRED-pres-simple-f(
  Prodi-ACT-sg-def-t(
    Romano-RSTR-sg-def-t,*),
  *,
  president-PAT-sg-def-f(
    institution-RSTR-pl-indef-f(
      big-RSTR-indef-f,*))
)