0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n019.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 14:07:37 EDT 2019
0.12/0.34	% CPUTime    : 
17.99/18.24	% SZS status Unsatisfiable
17.99/18.24	
18.08/18.25	% SZS output start Proof
18.08/18.25	Take the following subset of the input axioms:
18.08/18.25	  fof(goals, negated_conjecture, f(x1, f(f(x0, x2), f(x0, x2)))!=f(x0, f(f(x1, x2), f(x1, x2)))).
18.08/18.25	  fof(sos, axiom, ![B, A, C, D]: B=f(f(f(f(A, B), f(B, C)), D), f(B, f(f(B, f(f(A, A), A)), C)))).
18.08/18.25	
18.08/18.25	Now clausify the problem and encode Horn clauses using encoding 3 of
18.08/18.25	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
18.08/18.25	We repeatedly replace C & s=t => u=v by the two clauses:
18.08/18.25	  fresh(y, y, x1...xn) = u
18.08/18.25	  C => fresh(s, t, x1...xn) = v
18.08/18.25	where fresh is a fresh function symbol and x1..xn are the free
18.08/18.25	variables of u and v.
18.08/18.25	A predicate p(X) is encoded as p(X)=true (this is sound, because the
18.08/18.25	input problem has no model of domain size 1).
18.08/18.25	
18.08/18.25	The encoding turns the above axioms into the following unit equations and goals:
18.08/18.25	
28.27/28.46	Axiom 1 (sos): X = f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(f(Y, Y), Y)), Z))).
28.27/28.46	
28.27/28.46	Lemma 2: f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W))) = f(X, Y).
28.27/28.46	Proof:
28.27/28.46	  f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(f(f(Z, X), f(X, Y)), f(f(X, Y), W)), f(X, f(f(X, f(f(Z, Z), Z)), Y))), f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), W)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(X, Y)
28.27/28.46	
28.27/28.46	Lemma 3: f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y)) = f(f(X, Y), f(Y, Z)).
28.27/28.46	Proof:
28.27/28.46	  f(f(X, Y), f(f(f(X, Y), f(Y, Z)), Y))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(X, Y), f(f(f(X, Y), f(Y, Z)), f(f(f(f(X, Y), f(Y, Z)), f(f(f(?, f(X, Y)), f(?, f(X, Y))), f(?, f(X, Y)))), f(Y, f(f(Y, f(f(X, X), X)), Z)))))
28.27/28.46	= { by lemma 2 }
28.27/28.46	  f(f(X, Y), f(Y, Z))
28.27/28.46	
28.27/28.46	Lemma 4: f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, Y)) = Y.
28.27/28.46	Proof:
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, Y))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), Y), f(f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, f(f(Y, f(f(X, X), X)), Z))), Y))
28.27/28.46	= { by lemma 3 }
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), Y), f(Y, f(f(Y, f(f(X, X), X)), Z)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  Y
28.27/28.46	
28.27/28.46	Lemma 5: f(f(X, X), f(X, X)) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(X, X), f(X, X))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(f(f(f(?, X), f(X, ?)), X), f(X, f(f(X, f(f(?, ?), ?)), ?))), X), f(X, X))
28.27/28.46	= { by lemma 4 }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 6: f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))
28.27/28.46	= { by lemma 5 }
28.27/28.46	  f(f(f(f(X, X), f(X, X)), Y), f(X, f(f(X, f(f(X, X), X)), X)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 7: f(X, f(f(X, Y), f(X, Y))) = f(X, Y).
28.27/28.46	Proof:
28.27/28.46	  f(X, f(f(X, Y), f(X, Y)))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(?, X), f(?, X)), f(?, X))), f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y))))))
28.27/28.46	= { by lemma 2 }
28.27/28.46	  f(X, Y)
28.27/28.46	
28.27/28.46	Lemma 8: f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y)) = Y.
28.27/28.46	Proof:
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), W), f(Y, Y))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z))), Y))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), W), f(f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z))), f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z)))))
28.27/28.46	= { by lemma 7 }
28.27/28.46	  f(f(f(f(X, Y), f(Y, Z)), W), f(Y, f(f(Y, f(f(X, X), X)), Z)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  Y
28.27/28.46	
28.27/28.46	Lemma 9: f(f(Y, X), f(X, X)) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(Y, X), f(X, X))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(f(f(Y, X), f(X, ?)), f(f(Y, X), f(f(f(Y, X), f(f(f(Y, X), f(Y, X)), f(Y, X))), f(Y, X)))), f(X, X))
28.27/28.46	= { by lemma 8 }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 10: f(f(X, Y), f(X, X)) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(X, Y), f(X, X))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(X, Y), f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), X))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(X, Y), f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))))
28.27/28.46	= { by lemma 7 }
28.27/28.46	  f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 11: f(Y, f(f(Y, f(f(Y, Y), W)), f(Y, Y))) = f(Y, f(f(Y, Y), W)).
28.27/28.46	Proof:
28.27/28.46	  f(Y, f(f(Y, f(f(Y, Y), W)), f(Y, Y)))
28.27/28.46	= { by lemma 4 }
28.27/28.46	  f(f(f(f(f(?, Y), f(Y, ?)), Y), f(Y, Y)), f(f(Y, f(f(Y, Y), W)), f(Y, Y)))
28.27/28.46	= { by lemma 4 }
28.27/28.46	  f(f(f(f(f(?, Y), f(Y, ?)), Y), f(Y, Y)), f(f(f(f(f(f(?, Y), f(Y, ?)), Y), f(Y, Y)), f(f(Y, Y), W)), f(Y, Y)))
28.27/28.46	= { by lemma 3 }
28.27/28.46	  f(f(f(f(f(?, Y), f(Y, ?)), Y), f(Y, Y)), f(f(Y, Y), W))
28.27/28.46	= { by lemma 4 }
28.27/28.46	  f(Y, f(f(Y, Y), W))
28.27/28.46	
28.27/28.46	Lemma 12: f(f(X, X), f(X, Y)) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(X, X), f(X, Y))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  f(f(X, X), f(f(f(X, X), f(X, X)), Y))
28.27/28.46	= { by lemma 11 }
28.27/28.46	  f(f(X, X), f(f(f(X, X), f(f(f(X, X), f(X, X)), Y)), f(f(X, X), f(X, X))))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  f(f(X, X), f(f(f(X, X), f(X, Y)), f(f(X, X), f(X, X))))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  f(f(X, X), f(X, X))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 13: f(f(f(X, Y), f(X, Y)), X) = f(X, Y).
28.27/28.46	Proof:
28.27/28.46	  f(f(f(X, Y), f(X, Y)), X)
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(f(X, Y), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))
28.27/28.46	= { by lemma 12 }
28.27/28.46	  f(X, Y)
28.27/28.46	
28.27/28.46	Lemma 14: f(f(X, X), f(Y, X)) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(X, X), f(Y, X))
28.27/28.46	= { by lemma 9 }
28.27/28.46	  f(f(f(f(Y, X), f(X, X)), X), f(Y, X))
28.27/28.46	= { by lemma 9 }
28.27/28.46	  f(f(f(f(Y, X), f(X, X)), f(f(Y, X), f(X, X))), f(Y, X))
28.27/28.46	= { by lemma 13 }
28.27/28.46	  f(f(Y, X), f(X, X))
28.27/28.46	= { by lemma 9 }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 15: f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Y), f(Y, Z))) = f(f(X, f(Y, Z)), Y).
28.27/28.46	Proof:
28.27/28.46	  f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Y), f(Y, Z)))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), f(f(Y, Z), f(Y, f(f(Y, f(f(Y, Y), Y)), Y)))), f(Y, Z)))
28.27/28.46	= { by lemma 3 }
28.27/28.46	  f(f(X, f(Y, Z)), f(f(Y, Z), f(Y, f(f(Y, f(f(Y, Y), Y)), Y))))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(X, f(Y, Z)), Y)
28.27/28.46	
28.27/28.46	Lemma 16: f(X, f(f(X, Y), f(Y, X))) = f(X, Y).
28.27/28.46	Proof:
28.27/28.46	  f(X, f(f(X, Y), f(Y, X)))
28.27/28.46	= { by lemma 14 }
28.27/28.46	  f(f(f(X, X), f(Y, X)), f(f(X, Y), f(Y, X)))
28.27/28.46	= { by lemma 14 }
28.27/28.46	  f(f(f(X, X), f(Y, X)), f(f(f(f(X, X), f(Y, X)), Y), f(Y, X)))
28.27/28.46	= { by lemma 15 }
28.27/28.46	  f(f(f(X, X), f(Y, X)), Y)
28.27/28.46	= { by lemma 14 }
28.27/28.46	  f(X, Y)
28.27/28.46	
28.27/28.46	Lemma 17: f(X, f(f(X, X), Y)) = f(X, X).
28.27/28.46	Proof:
28.27/28.46	  f(X, f(f(X, X), Y))
28.27/28.46	= { by lemma 11 }
28.27/28.46	  f(X, f(f(X, f(f(X, X), Y)), f(X, X)))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  f(X, X)
28.27/28.46	
28.27/28.46	Lemma 18: f(Y, f(f(X, Y), f(X, Y))) = f(X, Y).
28.27/28.46	Proof:
28.27/28.46	  f(Y, f(f(X, Y), f(X, Y)))
28.27/28.46	= { by lemma 9 }
28.27/28.46	  f(f(f(X, Y), f(Y, Y)), f(f(X, Y), f(X, Y)))
28.27/28.46	= { by lemma 17 }
28.27/28.46	  f(f(f(X, Y), f(Y, Y)), f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))))
28.27/28.46	= { by lemma 17 }
28.27/28.46	  f(f(f(X, Y), f(Y, Y)), f(f(X, Y), f(f(f(X, Y), f(f(f(X, Y), f(X, Y)), f(X, Y))), f(X, Y))))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(X, Y)
28.27/28.46	
28.27/28.46	Lemma 19: f(f(f(X, X), Y), X) = f(X, X).
28.27/28.46	Proof:
28.27/28.46	  f(f(f(X, X), Y), X)
28.27/28.46	= { by lemma 5 }
28.27/28.46	  f(f(f(X, X), Y), f(f(X, X), f(X, X)))
28.27/28.46	= { by lemma 10 }
28.27/28.46	  f(X, X)
28.27/28.46	
28.27/28.46	Lemma 20: f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))) = f(Y, f(f(X, Y), f(Y, Z))).
28.27/28.46	Proof:
28.27/28.46	  f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z)))
28.27/28.46	= { by lemma 19 }
28.27/28.46	  f(f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))), f(Y, f(f(Y, f(f(X, X), X)), Z))), f(f(X, Y), f(Y, Z)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(Y, f(f(X, Y), f(Y, Z)))
28.27/28.46	
28.27/28.46	Lemma 21: f(f(f(X, Y), f(Y, Z)), Y) = f(Y, f(f(X, Y), f(Y, Z))).
28.27/28.46	Proof:
28.27/28.46	  f(f(f(X, Y), f(Y, Z)), Y)
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  f(f(f(X, Y), f(Y, Z)), f(f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z))), f(Y, f(f(Y, f(f(X, X), X)), Z))))
28.27/28.46	= { by lemma 17 }
28.27/28.46	  f(f(f(X, Y), f(Y, Z)), f(f(X, Y), f(Y, Z)))
28.27/28.46	= { by lemma 20 }
28.27/28.46	  f(Y, f(f(X, Y), f(Y, Z)))
28.27/28.46	
28.27/28.46	Lemma 22: f(f(f(Y, X), f(Z, X)), X) = f(X, f(f(Y, X), f(Z, X))).
28.27/28.46	Proof:
28.27/28.46	  f(f(f(Y, X), f(Z, X)), X)
28.27/28.46	= { by lemma 18 }
28.27/28.46	  f(f(f(Y, X), f(X, f(f(Z, X), f(Z, X)))), X)
28.27/28.46	= { by lemma 21 }
28.27/28.46	  f(X, f(f(Y, X), f(X, f(f(Z, X), f(Z, X)))))
28.27/28.46	= { by lemma 18 }
28.27/28.46	  f(X, f(f(Y, X), f(Z, X)))
28.27/28.46	
28.27/28.46	Lemma 23: f(f(Y, X), f(X, f(f(X, f(f(Y, Y), Y)), Z))) = X.
28.27/28.46	Proof:
28.27/28.46	  f(f(Y, X), f(X, f(f(X, f(f(Y, Y), Y)), Z)))
28.27/28.46	= { by lemma 6 }
28.27/28.46	  f(f(f(f(Y, X), f(X, Z)), f(f(Y, X), f(f(f(Y, X), f(f(f(Y, X), f(Y, X)), f(Y, X))), f(Y, X)))), f(X, f(f(X, f(f(Y, Y), Y)), Z)))
28.27/28.46	= { by axiom 1 (sos) }
28.27/28.46	  X
28.27/28.46	
28.27/28.46	Lemma 24: f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Z), f(Y, Z))) = f(f(X, f(Y, Z)), Z).
28.27/28.46	Proof:
28.27/28.46	  f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Z), f(Y, Z)))
28.27/28.46	= { by lemma 23 }
28.27/28.46	  f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(Y, Z)))
28.27/28.46	= { by lemma 3 }
28.27/28.46	  f(f(X, f(Y, Z)), f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?))))
28.27/28.46	= { by lemma 23 }
28.27/28.47	  f(f(X, f(Y, Z)), Z)
28.27/28.47	
28.27/28.47	Lemma 25: f(f(X, Z), f(Z, f(f(X, Z), f(Y, Z)))) = f(f(X, Z), f(Y, Z)).
28.27/28.47	Proof:
28.27/28.47	  f(f(X, Z), f(Z, f(f(X, Z), f(Y, Z))))
28.27/28.47	= { by lemma 23 }
28.27/28.47	  f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(Z, f(f(X, Z), f(Y, Z))))
28.27/28.47	= { by lemma 22 }
28.27/28.47	  f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(f(f(X, Z), f(Y, Z)), Z))
28.27/28.47	= { by lemma 23 }
28.27/28.47	  f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(Y, Z)), Z))
28.27/28.47	= { by lemma 23 }
28.27/28.47	  f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(Y, Z)), f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(X, f(f(Y, Z), f(Z, f(f(Z, f(f(Y, Y), Y)), ?)))), f(Y, Z))
28.27/28.47	= { by lemma 23 }
28.27/28.47	  f(f(X, Z), f(Y, Z))
28.27/28.47	
28.27/28.47	Lemma 26: f(f(X, f(Y, Z)), f(f(Y, Z), f(f(X, f(Y, Z)), Z))) = f(f(X, f(Y, Z)), Z).
28.27/28.47	Proof:
28.27/28.47	  f(f(X, f(Y, Z)), f(f(Y, Z), f(f(X, f(Y, Z)), Z)))
28.27/28.47	= { by lemma 24 }
28.27/28.47	  f(f(X, f(Y, Z)), f(f(Y, Z), f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Z), f(Y, Z)))))
28.27/28.47	= { by lemma 25 }
28.27/28.47	  f(f(X, f(Y, Z)), f(f(f(X, f(Y, Z)), Z), f(Y, Z)))
28.27/28.47	= { by lemma 24 }
28.27/28.47	  f(f(X, f(Y, Z)), Z)
28.27/28.47	
28.27/28.47	Lemma 27: f(f(f(Z, f(Y, X)), Y), f(Y, X)) = f(f(Y, X), f(f(Z, f(Y, X)), Y)).
28.27/28.47	Proof:
28.27/28.47	  f(f(f(Z, f(Y, X)), Y), f(Y, X))
28.27/28.47	= { by lemma 16 }
28.27/28.47	  f(f(f(Z, f(Y, X)), Y), f(f(f(f(Z, f(Y, X)), Y), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), Y))))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))), f(f(f(f(Z, f(Y, X)), Y), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), Y))))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))), f(f(f(f(Z, f(Y, X)), Y), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))))))
28.27/28.47	= { by lemma 22 }
28.27/28.47	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))), f(f(f(f(Z, f(Y, X)), Y), f(Y, X)), f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))), f(Y, X))))
28.27/28.47	= { by lemma 26 }
28.27/28.47	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))), f(Y, X))
28.27/28.47	= { by lemma 22 }
28.27/28.47	  f(f(Y, X), f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), Y), f(Y, X))))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(Y, X), f(f(Z, f(Y, X)), Y))
28.27/28.47	
28.27/28.47	Lemma 28: f(X, f(f(Y, X), f(X, Y))) = f(X, Y).
28.27/28.47	Proof:
28.27/28.47	  f(X, f(f(Y, X), f(X, Y)))
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(f(f(X, X), f(Y, X)), f(f(Y, X), f(X, Y)))
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(f(f(X, X), f(Y, X)), f(f(Y, X), f(f(f(X, X), f(Y, X)), Y)))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(f(X, X), f(Y, X)), f(f(Y, X), f(f(f(X, X), f(Y, X)), f(f(f(f(X, X), f(Y, X)), Y), f(Y, X)))))
28.27/28.47	= { by lemma 25 }
28.27/28.47	  f(f(f(X, X), f(Y, X)), f(f(f(f(X, X), f(Y, X)), Y), f(Y, X)))
28.27/28.47	= { by lemma 15 }
28.27/28.47	  f(f(f(X, X), f(Y, X)), Y)
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(X, Y)
28.27/28.47	
28.27/28.47	Lemma 29: f(f(f(X, Y), f(Y, X)), X) = f(X, Y).
28.27/28.47	Proof:
28.27/28.47	  f(f(f(X, Y), f(Y, X)), X)
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(f(f(f(f(X, X), f(Y, X)), Y), f(Y, X)), X)
28.27/28.47	= { by lemma 27 }
28.27/28.47	  f(f(f(Y, X), f(f(f(X, X), f(Y, X)), Y)), X)
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(f(f(Y, X), f(X, Y)), X)
28.27/28.47	= { by lemma 21 }
28.27/28.47	  f(X, f(f(Y, X), f(X, Y)))
28.27/28.47	= { by lemma 28 }
28.27/28.47	  f(X, Y)
28.27/28.47	
28.27/28.47	Lemma 30: f(X, Y) = f(Y, X).
28.27/28.47	Proof:
28.27/28.47	  f(X, Y)
28.27/28.47	= { by lemma 29 }
28.27/28.47	  f(f(f(X, Y), f(Y, X)), X)
28.27/28.47	= { by lemma 24 }
28.27/28.47	  f(f(f(X, Y), f(Y, X)), f(f(f(f(X, Y), f(Y, X)), X), f(Y, X)))
28.27/28.47	= { by lemma 29 }
28.27/28.47	  f(f(f(X, Y), f(Y, X)), f(f(X, Y), f(Y, X)))
28.27/28.47	= { by lemma 20 }
28.27/28.47	  f(Y, f(f(X, Y), f(Y, X)))
28.27/28.47	= { by lemma 28 }
28.27/28.47	  f(Y, X)
28.27/28.47	
28.27/28.47	Lemma 31: f(f(Y, f(X, X)), X) = f(X, X).
28.27/28.47	Proof:
28.27/28.47	  f(f(Y, f(X, X)), X)
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(f(Y, f(X, X)), f(f(X, X), f(X, X)))
28.27/28.47	= { by lemma 9 }
28.27/28.47	  f(X, X)
28.27/28.47	
28.27/28.47	Lemma 32: f(f(X, f(Y, Y)), f(f(f(X, f(Y, Y)), Y), f(Y, Y))) = f(f(X, f(Y, Y)), Y).
28.27/28.47	Proof:
28.27/28.47	  f(f(X, f(Y, Y)), f(f(f(X, f(Y, Y)), Y), f(Y, Y)))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(f(X, f(Y, Y)), f(f(f(X, f(Y, Y)), f(f(Y, Y), f(Y, Y))), f(Y, Y)))
28.27/28.47	= { by lemma 3 }
28.27/28.47	  f(f(X, f(Y, Y)), f(f(Y, Y), f(Y, Y)))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(f(X, f(Y, Y)), Y)
28.27/28.47	
28.27/28.47	Lemma 33: f(X, f(Y, f(X, X))) = f(X, X).
28.27/28.47	Proof:
28.27/28.47	  f(X, f(Y, f(X, X)))
28.27/28.47	= { by lemma 14 }
28.27/28.47	  f(f(f(X, X), f(f(Y, f(X, X)), X)), f(Y, f(X, X)))
28.27/28.47	= { by lemma 31 }
28.27/28.47	  f(f(f(f(Y, f(X, X)), X), f(f(Y, f(X, X)), X)), f(Y, f(X, X)))
28.27/28.47	= { by lemma 13 }
28.27/28.47	  f(f(Y, f(X, X)), X)
28.27/28.47	= { by lemma 31 }
28.27/28.47	  f(X, X)
28.27/28.47	
28.27/28.47	Lemma 34: f(f(f(f(X, Y), f(X, Y)), Z), f(X, X)) = X.
28.27/28.47	Proof:
28.27/28.47	  f(f(f(f(X, Y), f(X, Y)), Z), f(X, X))
28.27/28.47	= { by lemma 19 }
28.27/28.47	  f(f(f(f(f(f(X, Y), f(X, Y)), X), f(X, Y)), Z), f(X, X))
28.27/28.47	= { by lemma 8 }
28.27/28.47	  X
28.27/28.47	
28.27/28.47	Lemma 35: f(X, f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X)))) = f(X, Y).
28.27/28.47	Proof:
28.27/28.47	  f(X, f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))))
28.27/28.47	= { by lemma 2 }
28.27/28.47	  f(X, f(f(X, Y), f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(f(X, Y), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(?, f(X, Y)), f(?, f(X, Y))), f(?, f(X, Y)))), ?))))
28.27/28.47	= { by lemma 2 }
28.27/28.47	  f(X, Y)
28.27/28.47	
28.27/28.47	Lemma 36: f(f(f(X, f(X, X)), f(X, f(X, X))), Y) = f(X, f(X, X)).
28.27/28.47	Proof:
28.27/28.47	  f(f(f(X, f(X, X)), f(X, f(X, X))), Y)
28.27/28.47	= { by lemma 23 }
28.27/28.47	  f(f(f(X, X), f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y))), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)))), ?))))
28.27/28.47	= { by lemma 33 }
28.27/28.47	  f(f(f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(X, X))), f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y))), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)))), ?))))
28.27/28.47	= { by lemma 34 }
28.27/28.47	  f(f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(X, X))), f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y))), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)))), ?))))
28.27/28.47	= { by lemma 13 }
28.27/28.47	  f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(X, X)), f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y))), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)))), ?))))
28.27/28.47	= { by lemma 34 }
28.27/28.47	  f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))), f(f(f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y))), f(?, f(f(f(X, f(X, X)), f(X, f(X, X))), Y)))), ?))))
28.27/28.47	= { by lemma 2 }
28.27/28.47	  f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(f(f(X, X), f(X, X)), f(X, X))))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(X, f(f(f(f(X, f(X, X)), f(X, f(X, X))), Y), f(X, f(X, X))))
28.27/28.47	= { by lemma 19 }
28.27/28.47	  f(X, f(f(X, f(X, X)), f(X, f(X, X))))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(X, f(f(X, f(X, X)), f(f(f(X, X), f(X, X)), f(X, X))))
28.27/28.47	= { by lemma 35 }
28.27/28.47	  f(X, f(X, X))
28.27/28.47	
28.27/28.47	Lemma 37: f(X, X) = f(f(?, f(?, ?)), X).
28.27/28.47	Proof:
28.27/28.47	  f(X, X)
28.27/28.47	= { by lemma 31 }
28.27/28.47	  f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X)
28.27/28.47	= { by lemma 32 }
28.27/28.47	  f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X), f(X, X)))
28.27/28.47	= { by lemma 36 }
28.27/28.47	  f(f(?, f(?, ?)), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X), f(X, X)))
28.27/28.47	= { by lemma 9 }
28.27/28.47	  f(f(?, f(?, ?)), X)
28.27/28.47	
28.27/28.47	Lemma 38: f(f(Y, X), f(f(?, f(?, ?)), X)) = X.
28.27/28.47	Proof:
28.27/28.47	  f(f(Y, X), f(f(?, f(?, ?)), X))
28.27/28.47	= { by lemma 37 }
28.27/28.47	  f(f(Y, X), f(X, X))
28.27/28.47	= { by lemma 9 }
28.27/28.47	  X
28.27/28.47	
28.27/28.47	Lemma 39: f(f(f(X, Y), f(X, Z)), X) = f(X, f(f(X, Y), f(X, Z))).
28.27/28.47	Proof:
28.27/28.47	  f(f(f(X, Y), f(X, Z)), X)
28.27/28.47	= { by lemma 13 }
28.27/28.47	  f(f(f(f(f(X, Y), f(X, Y)), X), f(X, Z)), X)
28.27/28.47	= { by lemma 21 }
28.27/28.47	  f(X, f(f(f(f(X, Y), f(X, Y)), X), f(X, Z)))
28.27/28.47	= { by lemma 13 }
28.27/28.47	  f(X, f(f(X, Y), f(X, Z)))
28.27/28.47	
28.27/28.47	Lemma 40: f(f(X, X), f(X, f(f(f(Y, f(X, X)), f(Y, f(X, X))), f(Y, f(X, X))))) = X.
28.27/28.47	Proof:
28.27/28.47	  f(f(X, X), f(X, f(f(f(Y, f(X, X)), f(Y, f(X, X))), f(Y, f(X, X)))))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  f(f(X, X), f(f(f(X, X), f(X, X)), f(f(f(Y, f(X, X)), f(Y, f(X, X))), f(Y, f(X, X)))))
28.27/28.47	= { by lemma 35 }
28.27/28.47	  f(f(X, X), f(X, X))
28.27/28.47	= { by lemma 5 }
28.27/28.47	  X
28.27/28.47	
28.27/28.47	Lemma 41: f(f(Y, f(Y, Y)), X) = f(f(?, f(?, ?)), X).
28.27/28.47	Proof:
28.27/28.47	  f(f(Y, f(Y, Y)), X)
28.27/28.47	= { by lemma 36 }
28.27/28.47	  f(f(f(f(Y, f(Y, Y)), f(Y, f(Y, Y))), f(X, X)), X)
28.27/28.47	= { by lemma 31 }
28.27/28.47	  f(X, X)
28.27/28.47	= { by lemma 31 }
28.27/28.47	  f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X)
28.27/28.47	= { by lemma 32 }
28.27/28.47	  f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X), f(X, X)))
28.27/28.47	= { by lemma 36 }
28.27/28.47	  f(f(?, f(?, ?)), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)), X), f(X, X)))
28.27/28.47	= { by lemma 9 }
28.27/28.47	  f(f(?, f(?, ?)), X)
28.27/28.47	
28.27/28.47	Lemma 42: f(f(X, Y), f(X, f(f(f(Z, f(X, Y)), f(Z, f(X, Y))), f(Z, f(X, Y))))) = X.
28.27/28.47	Proof:
28.27/28.47	  f(f(X, Y), f(X, f(f(f(Z, f(X, Y)), f(Z, f(X, Y))), f(Z, f(X, Y)))))
28.27/28.47	= { by lemma 6 }
28.27/28.47	  f(f(X, Y), f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), f(f(f(Z, f(X, Y)), f(Z, f(X, Y))), f(Z, f(X, Y)))))
28.27/28.47	= { by lemma 35 }
28.27/28.47	  f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X)))
28.27/28.47	= { by lemma 6 }
28.27/28.47	  X
28.27/28.47	
28.27/28.47	Lemma 43: f(X, f(X, X)) = f(?, f(?, ?)).
28.27/28.47	Proof:
28.27/28.47	  f(X, f(X, X))
28.27/28.47	= { by lemma 40 }
28.27/28.47	  f(f(f(X, f(X, X)), f(X, f(X, X))), f(f(X, f(X, X)), f(f(f(Y, f(f(X, f(X, X)), f(X, f(X, X)))), f(Y, f(f(X, f(X, X)), f(X, f(X, X))))), f(Y, f(f(X, f(X, X)), f(X, f(X, X)))))))
28.27/28.47	= { by lemma 41 }
28.27/28.48	  f(f(f(?, f(?, ?)), f(X, f(X, X))), f(f(X, f(X, X)), f(f(f(Y, f(f(X, f(X, X)), f(X, f(X, X)))), f(Y, f(f(X, f(X, X)), f(X, f(X, X))))), f(Y, f(f(X, f(X, X)), f(X, f(X, X)))))))
28.27/28.48	= { by lemma 41 }
28.27/28.48	  f(f(f(?, f(?, ?)), f(X, f(X, X))), f(f(?, f(?, ?)), f(f(f(Y, f(f(X, f(X, X)), f(X, f(X, X)))), f(Y, f(f(X, f(X, X)), f(X, f(X, X))))), f(Y, f(f(X, f(X, X)), f(X, f(X, X)))))))
28.27/28.48	= { by lemma 41 }
28.27/28.48	  f(f(f(?, f(?, ?)), f(X, f(X, X))), f(f(?, f(?, ?)), f(f(f(Y, f(f(?, f(?, ?)), f(X, f(X, X)))), f(Y, f(f(X, f(X, X)), f(X, f(X, X))))), f(Y, f(f(X, f(X, X)), f(X, f(X, X)))))))
28.27/28.48	= { by lemma 41 }
28.27/28.48	  f(f(f(?, f(?, ?)), f(X, f(X, X))), f(f(?, f(?, ?)), f(f(f(Y, f(f(?, f(?, ?)), f(X, f(X, X)))), f(Y, f(f(?, f(?, ?)), f(X, f(X, X))))), f(Y, f(f(X, f(X, X)), f(X, f(X, X)))))))
28.27/28.48	= { by lemma 41 }
28.27/28.48	  f(f(f(?, f(?, ?)), f(X, f(X, X))), f(f(?, f(?, ?)), f(f(f(Y, f(f(?, f(?, ?)), f(X, f(X, X)))), f(Y, f(f(?, f(?, ?)), f(X, f(X, X))))), f(Y, f(f(?, f(?, ?)), f(X, f(X, X)))))))
28.27/28.48	= { by lemma 42 }
28.27/28.48	  f(?, f(?, ?))
28.27/28.48	
28.27/28.48	Lemma 44: f(X, X) = f(X, f(?, f(?, ?))).
28.27/28.48	Proof:
28.27/28.48	  f(X, X)
28.27/28.48	= { by lemma 33 }
28.27/28.48	  f(X, f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)))
28.27/28.48	= { by lemma 36 }
28.27/28.48	  f(X, f(?, f(?, ?)))
28.27/28.48	
28.27/28.48	Lemma 45: f(X, f(?, f(?, ?))) = f(f(?, f(?, ?)), X).
28.27/28.48	Proof:
28.27/28.48	  f(X, f(?, f(?, ?)))
28.27/28.48	= { by lemma 44 }
28.27/28.48	  f(X, X)
28.27/28.48	= { by lemma 37 }
28.27/28.48	  f(f(?, f(?, ?)), X)
28.27/28.48	
28.27/28.48	Lemma 46: f(f(X, X), X) = f(?, f(?, ?)).
28.27/28.48	Proof:
28.27/28.48	  f(f(X, X), X)
28.27/28.48	= { by lemma 5 }
28.27/28.48	  f(f(X, X), f(f(X, X), f(X, X)))
28.27/28.48	= { by lemma 43 }
28.27/28.48	  f(?, f(?, ?))
28.27/28.48	
28.27/28.48	Lemma 47: f(f(X, X), f(?, f(?, ?))) = X.
28.27/28.48	Proof:
28.27/28.48	  f(f(X, X), f(?, f(?, ?)))
28.27/28.48	= { by lemma 36 }
28.27/28.48	  f(f(X, X), f(f(f(?, f(?, ?)), f(?, f(?, ?))), X))
28.27/28.48	= { by lemma 14 }
28.31/28.49	  X
28.31/28.49	
28.31/28.49	Lemma 48: f(f(X, X), f(Y, f(f(X, Z), f(X, W)))) = X.
28.31/28.49	Proof:
28.31/28.49	  f(f(X, X), f(Y, f(f(X, Z), f(X, W))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(X, X), f(Y, f(f(Z, X), f(X, W))))
28.31/28.49	= { by lemma 5 }
28.31/28.49	  f(f(X, X), f(Y, f(f(Z, f(f(X, X), f(X, X))), f(X, W))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(X, X), f(Y, f(f(Z, f(f(X, X), f(X, X))), f(W, X))))
28.31/28.49	= { by lemma 14 }
28.31/28.49	  f(f(X, X), f(Y, f(f(Z, f(f(X, X), f(X, X))), f(W, f(f(X, X), f(X, X))))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(X, X), f(f(f(Z, f(f(X, X), f(X, X))), f(W, f(f(X, X), f(X, X)))), Y))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(W, f(f(X, X), f(X, X)))), Y), f(X, X))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), W)), Y), f(X, X))
28.31/28.49	= { by lemma 2 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), W), f(f(f(f(f(X, X), f(X, X)), W), f(f(f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), W), f(f(f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 4 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), W), f(f(f(X, X), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X)))), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 33 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), W), f(f(f(X, X), f(X, X)), f(f(f(f(?, f(X, X)), f(f(X, X), ?)), f(X, X)), f(f(X, X), f(X, X))))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 8 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), W), f(f(f(X, X), f(X, X)), f(X, X))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 46 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(f(f(X, X), f(X, X)), W), f(?, f(?, ?))), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 45 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(f(f(?, f(?, ?)), f(f(f(X, X), f(X, X)), W)), ?)))), Y), f(X, X))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(f(f(X, X), f(X, X)), W)))))), Y), f(X, X))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))), Y), f(X, X))
28.31/28.49	= { by lemma 12 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))), Y), f(f(f(X, X), f(X, X)), f(f(X, X), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))))
28.31/28.49	= { by lemma 47 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))), Y), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(?, f(?, ?))), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))))
28.31/28.49	= { by lemma 46 }
28.31/28.49	  f(f(f(f(Z, f(f(X, X), f(X, X))), f(f(f(X, X), f(X, X)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))), Y), f(f(f(X, X), f(X, X)), f(f(f(f(X, X), f(X, X)), f(f(Z, Z), Z)), f(f(W, f(f(X, X), f(X, X))), f(?, f(f(?, f(?, ?)), f(W, f(f(X, X), f(X, X)))))))))
28.31/28.49	= { by axiom 1 (sos) }
28.31/28.49	  f(f(X, X), f(X, X))
28.31/28.49	= { by lemma 14 }
28.31/28.49	  X
28.31/28.49	
28.31/28.49	Lemma 49: f(f(f(X, Y), f(X, Y)), f(Z, f(X, f(W, f(X, Y))))) = f(X, Y).
28.31/28.49	Proof:
28.31/28.49	  f(f(f(X, Y), f(X, Y)), f(Z, f(X, f(W, f(X, Y)))))
28.31/28.49	= { by lemma 6 }
28.31/28.49	  f(f(f(X, Y), f(X, Y)), f(Z, f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), f(W, f(X, Y)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(X, Y), f(X, Y)), f(Z, f(f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))), f(f(X, Y), W))))
28.31/28.49	= { by lemma 48 }
28.31/28.49	  f(X, Y)
28.31/28.49	
28.31/28.49	Lemma 50: f(f(X, Z), f(f(?, f(?, ?)), f(Y, f(X, X)))) = f(Y, f(X, X)).
28.31/28.49	Proof:
28.31/28.49	  f(f(X, Z), f(f(?, f(?, ?)), f(Y, f(X, X))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(Z, X), f(f(?, f(?, ?)), f(Y, f(X, X))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(Z, X), f(f(?, f(?, ?)), f(f(X, X), Y)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(?, f(?, ?)), f(f(X, X), Y)), f(Z, X))
28.31/28.49	= { by lemma 45 }
28.31/28.49	  f(f(f(f(X, X), Y), f(?, f(?, ?))), f(Z, X))
28.31/28.49	= { by lemma 44 }
28.31/28.49	  f(f(f(f(X, X), Y), f(f(X, X), Y)), f(Z, X))
28.31/28.49	= { by lemma 12 }
28.31/28.49	  f(f(f(f(X, X), Y), f(f(X, X), Y)), f(Z, f(f(X, X), f(X, f(f(X, X), Y)))))
28.31/28.49	= { by lemma 49 }
28.31/28.49	  f(f(X, X), Y)
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(Y, f(X, X))
28.31/28.49	
28.31/28.49	Lemma 51: f(f(Y, f(f(X, Y), f(Y, Z))), f(W, f(f(X, Y), f(Y, Z)))) = f(f(X, Y), f(Y, Z)).
28.31/28.49	Proof:
28.31/28.49	  f(f(Y, f(f(X, Y), f(Y, Z))), f(W, f(f(X, Y), f(Y, Z))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(W, f(f(X, Y), f(Y, Z))), f(Y, f(f(X, Y), f(Y, Z))))
28.31/28.49	= { by lemma 21 }
28.31/28.49	  f(f(W, f(f(X, Y), f(Y, Z))), f(f(f(X, Y), f(Y, Z)), Y))
28.31/28.49	= { by axiom 1 (sos) }
28.31/28.49	  f(f(W, f(f(X, Y), f(Y, Z))), f(f(f(X, Y), f(Y, Z)), f(f(f(f(X, Y), f(Y, Z)), f(f(W, W), W)), f(Y, f(f(Y, f(f(X, X), X)), Z)))))
28.31/28.49	= { by lemma 23 }
28.31/28.49	  f(f(X, Y), f(Y, Z))
28.31/28.49	
28.31/28.49	Lemma 52: f(X, f(f(X, Y), f(Y, Z))) = f(X, Y).
28.31/28.49	Proof:
28.31/28.49	  f(X, f(f(X, Y), f(Y, Z)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(X, f(f(Y, X), f(Y, Z)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(X, f(f(Y, Z), f(Y, X)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(X, f(f(Y, Z), f(X, Y)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Z), f(X, Y)), X)
28.31/28.49	= { by lemma 6 }
28.31/28.49	  f(f(f(Y, Z), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))
28.31/28.49	= { by lemma 51 }
28.31/28.49	  f(f(f(X, Y), f(f(f(Y, Z), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))), f(f(Y, Y), f(f(f(Y, Z), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))))
28.31/28.49	= { by lemma 6 }
28.31/28.49	  f(f(f(X, Y), f(f(f(Y, Z), f(X, Y)), X)), f(f(Y, Y), f(f(f(Y, Z), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(X, Y), f(X, f(f(Y, Z), f(X, Y)))), f(f(Y, Y), f(f(f(Y, Z), f(X, Y)), f(f(X, Y), f(X, f(f(X, f(f(X, X), X)), X))))))
28.31/28.49	= { by lemma 6 }
28.31/28.49	  f(f(f(X, Y), f(X, f(f(Y, Z), f(X, Y)))), f(f(Y, Y), f(f(f(Y, Z), f(X, Y)), X)))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(X, Y), f(X, f(f(Y, Z), f(X, Y)))), f(f(Y, Y), f(X, f(f(Y, Z), f(X, Y)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(X, Y)))), f(f(X, Y), f(X, f(f(Y, Z), f(X, Y)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(X, Y), f(X, f(f(Y, Z), f(X, Y)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(Y, X), f(X, f(f(Y, Z), f(X, Y)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(Y, X), f(X, f(f(Y, Z), f(Y, X)))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(X, f(f(Y, Z), f(Y, X))), f(Y, X)))
28.31/28.49	= { by lemma 48 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(X, f(f(Y, Z), f(Y, X))), f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), X)))
28.31/28.49	= { by lemma 27 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), f(f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), X), f(X, f(f(Y, Z), f(Y, X)))))
28.31/28.49	= { by lemma 15 }
28.31/28.49	  f(f(f(Y, Y), f(X, f(f(Y, Z), f(Y, X)))), X)
28.31/28.49	= { by lemma 48 }
28.31/28.49	  f(Y, X)
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(X, Y)
28.31/28.49	
28.31/28.49	Lemma 53: f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(?, f(?, ?))), Z))) = X.
28.31/28.49	Proof:
28.31/28.49	  f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(?, f(?, ?))), Z)))
28.31/28.49	= { by lemma 46 }
28.31/28.49	  f(f(f(f(Y, X), f(X, Z)), W), f(X, f(f(X, f(f(Y, Y), Y)), Z)))
28.31/28.49	= { by axiom 1 (sos) }
28.31/28.49	  X
28.31/28.49	
28.31/28.49	Lemma 54: f(f(X, Y), f(X, f(f(X, X), f(Z, f(X, X))))) = X.
28.31/28.49	Proof:
28.31/28.49	  f(f(X, Y), f(X, f(f(X, X), f(Z, f(X, X)))))
28.31/28.49	= { by lemma 53 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, X), f(Z, f(X, X)))))
28.31/28.49	= { by lemma 33 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X))), f(Z, f(X, X)))))
28.31/28.49	= { by lemma 36 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, f(?, f(?, ?))), f(Z, f(X, X)))))
28.31/28.49	= { by lemma 33 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, f(?, f(?, ?))), f(Z, f(X, f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(X, X)))))))
28.31/28.49	= { by lemma 36 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, f(?, f(?, ?))), f(Z, f(X, f(?, f(?, ?)))))))
28.31/28.49	= { by lemma 30 }
28.31/28.49	  f(f(f(f(f(f(?, X), f(X, Z)), X), f(X, f(f(X, f(?, f(?, ?))), Z))), Y), f(X, f(f(X, f(?, f(?, ?))), f(f(X, f(?, f(?, ?))), Z))))
28.31/28.50	= { by lemma 53 }
28.31/28.50	  X
28.31/28.50	
28.31/28.50	Lemma 55: f(f(X, X), f(W, f(f(Y, X), f(?, f(?, ?))))) = X.
28.31/28.50	Proof:
28.31/28.50	  f(f(X, X), f(W, f(f(Y, X), f(?, f(?, ?)))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(X, X), f(f(f(Y, X), f(?, f(?, ?))), W))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(f(f(Y, X), f(?, f(?, ?))), W), f(X, X))
28.31/28.50	= { by lemma 43 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(X, X))), W), f(X, X))
28.31/28.50	= { by lemma 33 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(X, f(?, f(X, X))))), W), f(X, X))
28.31/28.50	= { by lemma 54 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(f(f(X, f(f(X, X), f(?, f(X, X)))), f(X, f(f(X, X), f(?, f(X, X))))), f(?, f(X, X))))), W), f(X, X))
28.31/28.50	= { by lemma 54 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(f(f(X, f(f(X, X), f(?, f(X, X)))), f(X, f(f(X, X), f(?, f(X, X))))), f(?, f(X, f(f(X, ?), f(X, f(f(X, X), f(?, f(X, X)))))))))), W), f(X, X))
28.31/28.50	= { by lemma 49 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(X, f(f(X, X), f(?, f(X, X)))))), W), f(X, X))
28.31/28.50	= { by lemma 54 }
28.31/28.50	  f(f(f(f(Y, X), f(X, f(X, f(f(X, X), f(?, f(X, X)))))), W), f(X, f(f(X, f(?, f(?, ?))), f(X, f(f(X, X), f(?, f(X, X)))))))
28.31/28.50	= { by lemma 53 }
28.31/28.50	  X
28.31/28.50	
28.31/28.50	Lemma 56: f(X, f(f(X, Y), f(?, f(?, ?)))) = f(X, Y).
28.31/28.50	Proof:
28.31/28.50	  f(X, f(f(X, Y), f(?, f(?, ?))))
28.31/28.50	= { by lemma 36 }
28.31/28.50	  f(X, f(f(X, Y), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(?, f(?, ?)))))
28.31/28.50	= { by lemma 36 }
28.31/28.50	  f(X, f(f(X, Y), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), X), f(?, f(?, ?))), f(?, f(?, ?)))))
28.31/28.50	= { by lemma 36 }
28.31/28.50	  f(X, f(f(X, Y), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), X), f(f(f(?, f(?, ?)), f(?, f(?, ?))), X)), f(?, f(?, ?)))))
28.31/28.50	= { by lemma 36 }
28.31/28.50	  f(X, f(f(X, Y), f(f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), X), f(f(f(?, f(?, ?)), f(?, f(?, ?))), X)), f(f(f(?, f(?, ?)), f(?, f(?, ?))), X))))
28.31/28.50	= { by lemma 35 }
28.31/28.50	  f(X, Y)
28.31/28.50	
28.31/28.50	Lemma 57: f(f(X, Z), f(f(?, f(?, ?)), f(W, f(Z, f(Y, f(X, Z)))))) = f(W, f(Z, f(Y, f(X, Z)))).
28.31/28.50	Proof:
28.31/28.50	  f(f(X, Z), f(f(?, f(?, ?)), f(W, f(Z, f(Y, f(X, Z))))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(Z, X), f(f(?, f(?, ?)), f(W, f(Z, f(Y, f(X, Z))))))
28.31/28.50	= { by lemma 49 }
28.31/28.50	  f(f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))), f(f(?, f(?, ?)), f(W, f(Z, f(Y, f(X, Z))))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))), f(f(?, f(?, ?)), f(W, f(Z, f(Y, f(Z, X))))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))), f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))
28.31/28.50	= { by lemma 44 }
28.31/28.50	  f(f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))), f(f(W, f(Z, f(Y, f(Z, X)))), f(W, f(Z, f(Y, f(Z, X))))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(f(W, f(Z, f(Y, f(Z, X)))), f(W, f(Z, f(Y, f(Z, X))))), f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))))
28.31/28.50	= { by lemma 56 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(Z, f(Y, f(Z, X))))), f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))))
28.31/28.50	= { by lemma 56 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))), f(f(f(Z, X), f(Z, X)), f(W, f(Z, f(Y, f(Z, X))))))
28.31/28.50	= { by lemma 2 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))), f(f(f(Z, X), f(Z, X)), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(f(f(W, f(Z, f(Y, f(Z, X)))), f(f(f(W, W), f(W, W)), f(W, W))), W)))))
28.31/28.50	= { by lemma 5 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))), f(f(f(Z, X), f(Z, X)), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(f(f(W, f(Z, f(Y, f(Z, X)))), f(W, f(W, W))), W)))))
28.31/28.50	= { by lemma 43 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))), f(f(f(Z, X), f(Z, X)), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))), W)))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(f(f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))), f(f(f(Z, X), f(Z, X)), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))))))
28.31/28.50	= { by lemma 49 }
28.31/28.50	  f(W, f(f(W, f(Z, f(Y, f(Z, X)))), f(?, f(?, ?))))
28.31/28.50	= { by lemma 56 }
28.31/28.50	  f(W, f(Z, f(Y, f(Z, X))))
28.31/28.50	= { by lemma 30 }
28.31/28.50	  f(W, f(Z, f(Y, f(X, Z))))
28.31/28.50	
28.31/28.50	Lemma 58: f(f(f(Z, f(Y, X)), X), f(Y, X)) = f(f(Y, X), f(f(Z, f(Y, X)), X)).
28.31/28.50	Proof:
28.31/28.50	  f(f(f(Z, f(Y, X)), X), f(Y, X))
28.31/28.50	= { by lemma 16 }
28.31/28.50	  f(f(f(Z, f(Y, X)), X), f(f(f(f(Z, f(Y, X)), X), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), X))))
28.31/28.50	= { by lemma 24 }
28.31/28.50	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))), f(f(f(f(Z, f(Y, X)), X), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), X))))
28.31/28.50	= { by lemma 24 }
28.31/28.50	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))), f(f(f(f(Z, f(Y, X)), X), f(Y, X)), f(f(Y, X), f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))))))
28.31/28.50	= { by lemma 22 }
28.31/28.50	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))), f(f(f(f(Z, f(Y, X)), X), f(Y, X)), f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))), f(Y, X))))
28.31/28.50	= { by lemma 26 }
28.31/28.50	  f(f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))), f(Y, X))
28.31/28.50	= { by lemma 22 }
28.31/28.50	  f(f(Y, X), f(f(Z, f(Y, X)), f(f(f(Z, f(Y, X)), X), f(Y, X))))
28.31/28.50	= { by lemma 24 }
28.31/28.50	  f(f(Y, X), f(f(Z, f(Y, X)), X))
28.31/28.50	
28.31/28.50	Lemma 59: f(f(?, f(?, ?)), f(X, f(Z, f(X, Y)))) = f(f(X, Y), f(X, f(Z, f(X, Y)))).
28.31/28.50	Proof:
28.31/28.50	  f(f(?, f(?, ?)), f(X, f(Z, f(X, Y))))
28.31/28.50	= { by lemma 45 }
28.31/28.50	  f(f(X, f(Z, f(X, Y))), f(?, f(?, ?)))
28.31/28.50	= { by lemma 44 }
28.31/28.50	  f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))
28.31/28.50	= { by lemma 31 }
28.31/28.50	  f(f(f(f(X, Y), f(X, Y)), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))), f(X, f(Z, f(X, Y))))
28.31/28.50	= { by lemma 32 }
28.31/28.50	  f(f(f(f(X, Y), f(X, Y)), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))), f(f(f(f(f(X, Y), f(X, Y)), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))), f(X, f(Z, f(X, Y)))), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))))
28.31/28.50	= { by lemma 49 }
28.31/28.50	  f(f(X, Y), f(f(f(f(f(X, Y), f(X, Y)), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))), f(X, f(Z, f(X, Y)))), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))))
28.31/28.50	= { by lemma 58 }
28.31/28.50	  f(f(X, Y), f(f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y)))), f(f(f(f(X, Y), f(X, Y)), f(f(X, f(Z, f(X, Y))), f(X, f(Z, f(X, Y))))), f(X, f(Z, f(X, Y))))))
28.31/28.50	= { by lemma 14 }
38.67/38.87	  f(f(X, Y), f(X, f(Z, f(X, Y))))
38.67/38.87	
38.67/38.87	Lemma 60: f(f(f(X, Z), f(X, Z)), f(f(Y, Z), f(Y, Z))) = f(X, f(f(Y, Z), f(Y, Z))).
38.67/38.87	Proof:
38.67/38.87	  f(f(f(X, Z), f(X, Z)), f(f(Y, Z), f(Y, Z)))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, Z)))
38.67/38.87	= { by lemma 33 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(f(X, Z), f(X, Z)))))
38.67/38.87	= { by lemma 36 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(?, f(?, ?))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(?, f(?, ?)), f(X, Z)))
38.67/38.87	= { by lemma 38 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(?, f(?, ?)), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(?, f(?, ?))))
38.67/38.87	= { by lemma 44 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))))
38.67/38.87	= { by lemma 13 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))))
38.67/38.87	= { by lemma 52 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(f(f(Y, Z), f(f(?, f(?, ?)), Z)), f(f(?, f(?, ?)), f(X, f(f(Y, Z), f(Y, Z)))))))))
38.67/38.87	= { by lemma 7 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(X, f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))))), f(f(f(Y, Z), f(f(?, f(?, ?)), Z)), f(f(?, f(?, ?)), f(X, f(f(Y, Z), f(Y, Z)))))))))
38.67/38.87	= { by lemma 39 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(f(f(Y, Z), f(f(?, f(?, ?)), Z)), f(f(?, f(?, ?)), f(X, f(f(Y, Z), f(Y, Z)))))))))
38.67/38.87	= { by lemma 50 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(Y, Z), f(Y, Z)))))))
38.67/38.87	= { by lemma 21 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(Y, Z), f(Y, Z)))), X)))
38.67/38.87	= { by lemma 3 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))), X), f(X, f(f(Y, Z), f(Y, Z)))))
38.67/38.87	= { by lemma 39 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))))), f(X, f(f(Y, Z), f(Y, Z)))))
38.67/38.87	= { by lemma 7 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z))), f(X, f(f(Y, Z), f(Y, Z)))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, f(f(Y, Z), f(f(?, f(?, ?)), Z)))))
38.67/38.87	= { by lemma 38 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, f(f(Y, Z), f(Y, Z))), f(X, Z)))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(Y, Z), f(Y, Z)))))
38.67/38.87	= { by lemma 12 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(Y, Z), f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(?, f(?, ?))))))))
38.67/38.87	= { by lemma 44 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(Y, Z), f(f(f(Y, Z), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))
38.67/38.87	= { by lemma 50 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(Y, Z), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))
38.67/38.87	= { by lemma 47 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(Y, Z), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(Y, Z), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))
38.67/38.87	= { by lemma 36 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(Y, Z), f(?, f(?, ?))), f(f(Y, Z), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))))
38.67/38.87	= { by lemma 59 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))))
38.67/38.87	= { by lemma 36 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(Y, Z)), f(f(Y, Z), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(f(Y, Z), f(?, f(?, ?))))))))))))
38.67/38.87	= { by lemma 36 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(Y, Z)), f(f(Y, Z), f(?, f(?, ?))))))))))
38.67/38.87	= { by lemma 44 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(Y, Z)), f(f(Y, Z), f(Y, Z)))))))))
38.67/38.87	= { by lemma 9 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(Y, Z), f(Y, Z)))))))
38.67/38.87	= { by lemma 55 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))
38.67/38.87	= { by lemma 7 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))))
38.67/38.87	= { by lemma 37 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?)))))))
38.67/38.87	= { by lemma 30 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))))))
38.67/38.87	= { by lemma 23 }
38.67/38.87	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))))))))
38.67/38.87	= { by lemma 30 }
38.67/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))))))))
38.67/38.88	= { by lemma 30 }
38.72/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))))))))
38.72/38.88	= { by lemma 30 }
38.72/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))))))))
38.72/38.88	= { by lemma 49 }
38.72/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(f(f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))))))))))
38.72/38.88	= { by axiom 1 (sos) }
38.72/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))), f(?, f(?, ?)))))))
38.72/38.88	= { by lemma 21 }
38.72/38.88	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)))))))))
38.72/38.88	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?)))))))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(?, f(?, ?)))))))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))))))
38.72/38.89	= { by lemma 59 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?)))))), f(f(?, f(?, ?)), f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))))))
38.72/38.89	= { by lemma 57 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(?, f(?, ?)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))
38.72/38.89	= { by lemma 37 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))
38.72/38.89	= { by lemma 31 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))
38.72/38.89	= { by lemma 55 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(?, f(f(?, f(f(Y, Z), f(Y, Z))), f(?, f(?, ?))))))))))
38.72/38.89	= { by lemma 17 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z)))))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(f(Y, Z), f(Y, Z))), f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?)))))))
38.72/38.89	= { by lemma 44 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(f(f(Y, Z), f(?, f(?, ?))), X), f(f(f(Y, Z), f(?, f(?, ?))), X)), f(?, f(?, ?)))))))
38.72/38.89	= { by lemma 47 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(?, f(?, ?))), X)))))
38.72/38.89	= { by lemma 36 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(f(f(?, f(?, ?)), f(?, f(?, ?))), f(f(Y, Z), f(Y, Z)))), X)))))
38.72/38.89	= { by lemma 33 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))
38.72/38.89	= { by lemma 57 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(X, Z), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))), f(X, Z)))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))), f(Z, X)))))
38.72/38.89	= { by lemma 30 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))
38.72/38.89	= { by lemma 14 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 37 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 51 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 21 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 20 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 3 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 51 }
38.72/38.89	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.89	= { by lemma 21 }
38.72/38.90	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.90	= { by lemma 3 }
38.72/38.90	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.90	= { by lemma 45 }
38.72/38.90	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(?, f(?, ?))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.90	= { by lemma 44 }
38.72/38.90	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.90	= { by lemma 31 }
38.72/38.90	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.90	= { by lemma 32 }
38.72/38.91	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.91	= { by lemma 49 }
38.72/38.91	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.91	= { by lemma 30 }
38.72/38.93	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.93	= { by lemma 6 }
38.72/38.93	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.93	= { by lemma 20 }
38.72/38.94	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.94	= { by lemma 58 }
38.72/38.94	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(f(f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.72/38.94	= { by lemma 14 }
38.78/38.95	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.78/38.95	= { by axiom 1 (sos) }
38.78/38.96	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.78/38.96	= { by lemma 30 }
38.78/38.96	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.78/38.96	= { by lemma 30 }
38.80/38.97	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.80/38.97	= { by lemma 30 }
38.80/38.98	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.80/38.98	= { by lemma 6 }
38.80/38.98	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.80/38.99	= { by lemma 20 }
38.80/39.00	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.80/39.00	= { by lemma 4 }
38.80/39.01	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, 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X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.80/39.01	= { by lemma 4 }
38.85/39.03	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), 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f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), ?)), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, 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f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))), f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), ?)), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.85/39.03	= { by lemma 6 }
38.85/39.05	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, 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X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))), f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), ?)), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.85/39.05	= { by lemma 4 }
38.89/39.07	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), 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?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))))), f(f(f(f(?, f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), ?)), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.89/39.08	= { by lemma 35 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))), f(f(f(Z, X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(f(f(Z, X), f(Z, X)), f(Z, X))), f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.89/39.08	= { by axiom 1 (sos) }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))), X), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.89/39.08	= { by lemma 21 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(?, f(?, ?)), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))))
38.89/39.08	= { by lemma 6 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(X, X)), f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))))))))
38.89/39.08	= { by lemma 34 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))))))))
38.89/39.08	= { by lemma 17 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))))))))
38.89/39.08	= { by lemma 17 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))))))
38.89/39.08	= { by lemma 44 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?))), f(?, f(?, ?))))))
38.89/39.08	= { by lemma 45 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(?, f(?, ?)), f(f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))), f(?, f(?, ?)))))))
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(f(f(Y, Z), f(Y, Z)), X), f(X, f(f(?, f(?, ?)), f(f(?, f(?, ?)), f(f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X))))), f(X, f(f(Z, X), f(X, f(f(f(f(Y, Z), f(Y, Z)), f(?, f(?, ?))), f(f(f(Y, Z), f(Y, Z)), X)))))))))))
38.89/39.08	= { by lemma 52 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), X)
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(X, f(f(Y, Z), f(Y, Z)))
38.89/39.08	
38.89/39.08	Lemma 61: f(X, f(f(Y, Z), f(Y, Z))) = f(Y, f(f(X, Z), f(X, Z))).
38.89/39.08	Proof:
38.89/39.08	  f(X, f(f(Y, Z), f(Y, Z)))
38.89/39.08	= { by lemma 60 }
38.89/39.08	  f(f(f(X, Z), f(X, Z)), f(f(Y, Z), f(Y, Z)))
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(f(f(Y, Z), f(Y, Z)), f(f(X, Z), f(X, Z)))
38.89/39.08	= { by lemma 60 }
38.89/39.08	  f(Y, f(f(X, Z), f(X, Z)))
38.89/39.08	
38.89/39.08	Goal 1 (goals): f(x1, f(f(x0, x2), f(x0, x2))) = f(x0, f(f(x1, x2), f(x1, x2))).
38.89/39.08	Proof:
38.89/39.08	  f(x1, f(f(x0, x2), f(x0, x2)))
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(x1, f(f(x0, x2), f(x2, x0)))
38.89/39.08	= { by lemma 30 }
38.89/39.08	  f(x1, f(f(x0, x2), f(x0, x2)))
38.89/39.08	= { by lemma 61 }
38.89/39.08	  f(x0, f(f(x1, x2), f(x1, x2)))
38.89/39.08	% SZS output end Proof
38.89/39.08	
38.89/39.08	RESULT: Unsatisfiable (the axioms are contradictory).
38.89/39.09	EOF