Proof step 1 from proof equivstar-both-leqstar (conclusion) (back to tree)

System applied rule normalize

And obtained the following new goals

• Proof step 2:

  ¬(C_≡*T_A(cioaut, aioaut) ↔ C_≤*T_A(cioaut, aioaut) ∧ C_≤*T_A(aioaut, cioaut)) ⊦

Rule argument

Additional information

Proof step 2 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 3:

  ⊦ (∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el)) ↔ (∀ el. trace*(cioaut)(el) → trace*(aioaut)(el)) ∧ (∀ el. trace*(aioaut)(el) → trace*(cioaut)(el))

Rule argument

Additional information

Used simplifier rules: equivstar-def: ⊦ C_≡*T_A(cioaut, aioaut) ↔ (∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el)); leqstar-def: ⊦ C_≤*T_A(cioaut, aioaut) ↔ (∀ el. trace*(cioaut)(el) → trace*(aioaut)(el));

Proof step 3 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic pl case distinction applied rule case distinction

And obtained the following new goals

• Proof step 4:

  ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦ (∀ el. trace*(cioaut)(el) → trace*(aioaut)(el)) ∧ (∀ el. trace*(aioaut)(el) → trace*(cioaut)(el))

• Proof step 10:

  ∀ el. trace*(cioaut)(el) → trace*(aioaut)(el), ∀ el. trace*(aioaut)(el) → trace*(cioaut)(el) ⊦ ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el)

Rule argument

Additional information

Proof step 4 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 5:

  ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦ (trace*(cioaut)(el) → trace*(aioaut)(el)) ∧ (trace*(aioaut)(el0) → trace*(cioaut)(el0))

Rule argument

Additional information

Proof step 5 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic pl case distinction applied rule case distinction

And obtained the following new goals

• Proof step 6:

  trace*(cioaut)(el), ¬ trace*(aioaut)(el), ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦

• Proof step 8:

  trace*(aioaut)(el0), ¬ trace*(cioaut)(el0), ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦

Rule argument

Additional information

Proof step 6 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 7:

  trace*(cioaut)(el), ¬ trace*(aioaut)(el), ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦

Rule argument

Additional information

Proof step 7 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: el

Proof step 8 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 9:

  trace*(aioaut)(el0), ¬ trace*(cioaut)(el0), ∀ el. trace*(cioaut)(el) ↔ trace*(aioaut)(el) ⊦

Rule argument

Additional information

Proof step 9 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: el0

Proof step 10 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

• Proof step 11:

  ¬(trace*(cioaut)(el) ↔ trace*(aioaut)(el)), ∀ el. trace*(aioaut)(el) → trace*(cioaut)(el), ∀ el. trace*(cioaut)(el) → trace*(aioaut)(el) ⊦

Rule argument

Additional information

Proof step 11 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic pl case distinction applied rule case distinction

And obtained the following new goals

• Proof step 12:

  trace*(cioaut)(el), ¬ trace*(aioaut)(el), ∀ el. trace*(cioaut)(el) → trace*(aioaut)(el), ∀ el. trace*(aioaut)(el) → trace*(cioaut)(el) ⊦

• Proof step 13:

  trace*(aioaut)(el), ¬ trace*(cioaut)(el), ∀ el. trace*(cioaut)(el) → trace*(aioaut)(el), ∀ el. trace*(aioaut)(el) → trace*(cioaut)(el) ⊦

Rule argument

Additional information

Proof step 12 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: el

Proof step 13 from proof equivstar-both-leqstar (previous step) (back to tree)

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

Additional information

Used terms: el