Step 1 [1]
 
?- proof? * ((some y a (all x b (f x y))) ->
                              (all x
                                   b
                                   (some y a (f x y))))
 
TT0>> answer-sequent 
==================================================
Step 2 [2]
 
?- proof? * ((some y a (all x b (f x y))) ->
                              (all x
                                   b
                                   (some y a (f x y))))
 
TT0>> ->-right 
==================================================
Step 3 [2] 
 
?- 3166? * (all x b (some y a (f x y)))
 
1. t949 * (some y a (all x b (f x y)))

TT0>> all-right 
==================================================
Step 4 [2] 
 
?- ((/. 3224? b 3226?) t950) * (some y a (f t950 y))
 
1. t950 * b
2. t949 * (some y a (all x b (f x y)))

TT0>> ->-left 
==================================================
Step 5 [3] 
 
?- (/. 3224? b 3226?) * (3345? -> (some y a (f t950 y)))
 
1. t950 * b
2. t949 * (some y a (all x b (f x y)))

TT0>> ->-right 
==================================================
Step 6 [3] 
 
?- 3226? * (some y a (f t950 y))
 
1. t951 * b
2. t950 * b
3. t949 * (some y a (all x b (f x y)))

TT0>> some-right 
==================================================
Step 7 [4] 
 
?- 3458? * (f t950 3461?)
 
1. t951 * b
2. t950 * b
3. t949 * (some y a (all x b (f x y)))

TT0>> some-left2 
==================================================
Step 8 [4] 
 
?- 3458? * (f t950 3461?)
 
1. t949 * (some y a (all x b (f x y)))
2. (snd t949) * (all x b (f x (fst t949)))
3. t951 * b
4. t950 * b

TT0>> all-left 
==================================================
Step 9 [5] 
 
?- 3595? * b
 
1. (snd t949) * (all x b (f x (fst t949)))
2. t949 * (some y a (all x b (f x y)))
3. t951 * b
4. t950 * b

TT0>> rotate 1 2 
==================================================
Step 10 [5] 
 
?- 3458? * (f t950 3461?)
 
1. (snd t949) * (all x b (f x (fst t949)))
2. ((snd t949) 3595?) * (f 3595? (fst t949))
3. t949 * (some y a (all x b (f x y)))
4. t951 * b
5. t950 * b

TT0>> xtt 
==================================================
Step 11 [4] 
 
?- t950 * b
 
1. (snd t949) * (all x b (f x (fst t949)))
2. t949 * (some y a (all x b (f x y)))
3. t951 * b
4. t950 * b

TT0>> xtt 
==================================================
Step 12 [3] 
 
?- (fst t949) * a
 
1. t951 * b
2. t950 * b
3. t949 * (some y a (all x b (f x y)))

TT0>> some-left1 
==================================================
Step 13 [3] 
 
?- t949 * (some 3995? a 3997?)
 
1. t951 * b
2. t950 * b
3. t949 * (some y a (all x b (f x y)))

TT0>> xtt 
==================================================
Step 14 [2] 
 
?- t950 * b
 
1. t950 * b
2. t949 * (some y a (all x b (f x y)))

TT0>> xtt 
==================================================
Step 15 [1] 
 
?- (/. t949
    (some y a (all x b (f x y)))
    (/. t951
        b
        (subst t951
               t950
               (tuple (fst t949)
                      ((snd t949) t950))))) * ((some y a (all x b (f x y))) ->
                              (all x
                                   b
                                   (some y a (f x y))))
 
1. (/. t949
    (some y a (all x b (f x y)))
    (/. t951
        b
        (subst t951
               t950
               (tuple (fst t949)
                      ((snd t949) t950))))) * ((some y a (all x b (f x y))) ->
                              (all x
                                   b
                                   (some y a (f x y))))

TT0>> xtt 

i.e.

(/. t949
    (some y a (all x b (f x y)))
    (/. t951
        b (tuple (fst t949)
                      ((snd t949) t951))))) * ((some y a (all x b (f x y))) ->
                              (all x
                                   b
                                   (some y a (f x y))))
