0.06/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.06/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n020.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 11:40:40 EDT 2019
0.12/0.33	% CPUTime    : 
0.54/0.76	% SZS status Unsatisfiable
0.54/0.76	
0.54/0.77	% SZS output start Proof
0.54/0.77	Take the following subset of the input axioms:
0.54/0.77	  fof(prove_these_axioms_3, negated_conjecture, multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3))).
0.54/0.77	  fof(single_axiom, axiom, ![C, A, B]: C=multiply(A, inverse(multiply(inverse(multiply(inverse(multiply(A, B)), C)), multiply(inverse(B), multiply(inverse(B), B)))))).
0.54/0.77	
0.54/0.77	Now clausify the problem and encode Horn clauses using encoding 3 of
0.54/0.77	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.54/0.77	We repeatedly replace C & s=t => u=v by the two clauses:
0.54/0.77	  fresh(y, y, x1...xn) = u
0.54/0.77	  C => fresh(s, t, x1...xn) = v
0.54/0.77	where fresh is a fresh function symbol and x1..xn are the free
0.54/0.77	variables of u and v.
0.54/0.77	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.54/0.77	input problem has no model of domain size 1).
0.54/0.77	
0.54/0.77	The encoding turns the above axioms into the following unit equations and goals:
0.54/0.77	
0.76/0.98	Axiom 1 (single_axiom): X = multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), X)), multiply(inverse(Z), multiply(inverse(Z), Z))))).
0.76/0.98	
0.76/0.98	Lemma 2: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?)))) = Z.
0.76/0.98	Proof:
0.76/0.98	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  Z
0.76/0.98	
0.76/0.98	Lemma 3: multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), multiply(inverse(Z), Z)))))) = X.
0.76/0.98	Proof:
0.76/0.98	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(X), multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  multiply(inverse(multiply(Y, Z)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, Z)), ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.98	= { by axiom 1 (single_axiom) }
0.76/0.98	  X
0.76/0.98	
0.76/0.98	Lemma 4: multiply(inverse(multiply(W, ?)), multiply(W, Z)) = multiply(inverse(multiply(?, ?)), multiply(?, Z)).
0.76/0.98	Proof:
0.76/0.98	  multiply(inverse(multiply(W, ?)), multiply(W, Z))
0.76/0.98	= { by lemma 2 }
0.76/0.98	  multiply(inverse(multiply(W, ?)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.76/0.98	= { by lemma 3 }
0.76/0.98	  multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))
0.76/0.98	= { by lemma 3 }
0.76/0.98	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.76/0.98	= { by lemma 2 }
0.76/0.98	  multiply(inverse(multiply(?, ?)), multiply(?, Z))
0.76/0.98	
0.76/0.98	Lemma 5: multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X)))))) = multiply(inverse(X), ?).
0.76/0.98	Proof:
0.76/0.98	  multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))))
0.76/0.98	= { by lemma 4 }
0.76/0.98	  multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(multiply(inverse(X), ?)), multiply(inverse(X), multiply(inverse(X), X))))))
0.76/0.98	= { by lemma 3 }
0.76/0.98	  multiply(inverse(X), ?)
0.76/0.98	
0.76/0.98	Lemma 6: inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))) = X.
0.76/0.98	Proof:
0.76/0.98	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.98	= { by lemma 2 }
0.76/0.98	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.98	= { by lemma 2 }
0.76/0.98	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.98	= { by lemma 2 }
0.76/0.98	  X
0.76/0.98	
0.76/0.98	Lemma 7: multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X)))))) = multiply(inverse(?), multiply(inverse(?), ?)).
0.76/0.98	Proof:
0.76/0.98	  multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))))
0.76/0.98	= { by lemma 6 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(inverse(?), multiply(inverse(?), ?))
0.76/0.99	
0.76/0.99	Lemma 8: multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(X)))), multiply(inverse(?), multiply(inverse(?), ?))) = X.
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(X)))), multiply(inverse(?), multiply(inverse(?), ?)))
0.76/0.99	= { by lemma 7 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(X)))), multiply(inverse(multiply(?, ?)), inverse(multiply(inverse(X), multiply(inverse(multiply(?, inverse(X))), multiply(inverse(multiply(?, inverse(X))), multiply(?, inverse(X))))))))
0.76/0.99	= { by lemma 3 }
0.76/0.99	  X
0.76/0.99	
0.76/0.99	Lemma 9: inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))) = inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), W)), multiply(inverse(?), multiply(inverse(?), ?)))).
0.76/0.99	Proof:
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), W)), multiply(inverse(Z), multiply(inverse(Z), Z)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(W), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), W)), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), W)), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.99	
0.76/0.99	Lemma 10: inverse(multiply(inverse(multiply(inverse(multiply(Z, X)), Y)), multiply(inverse(X), multiply(inverse(X), X)))) = inverse(multiply(inverse(multiply(inverse(multiply(Z, ?)), Y)), multiply(inverse(?), multiply(inverse(?), ?)))).
0.76/0.99	Proof:
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(Z, X)), Y)), multiply(inverse(X), multiply(inverse(X), X))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, W)), ?)), multiply(inverse(multiply(V, W)), Z))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), Y)), multiply(inverse(X), multiply(inverse(X), X))))
0.76/0.99	= { by lemma 9 }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(V, W)), ?)), multiply(inverse(multiply(V, W)), Z))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), Y)), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(Z, ?)), Y)), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.99	
0.76/0.99	Lemma 11: multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z)) = multiply(inverse(multiply(?, ?)), multiply(?, Z)).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))
0.76/0.99	= { by lemma 3 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, Z))
0.76/0.99	
0.76/0.99	Lemma 12: multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), inverse(multiply(Z, multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), Z)))))) = multiply(inverse(?), multiply(inverse(?), ?)).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), inverse(multiply(Z, multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), Z))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(multiply(X, Y)), Z))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(multiply(X, Y)), Z))))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(inverse(?), multiply(inverse(?), ?))
0.76/0.99	
0.76/0.99	Lemma 13: multiply(inverse(multiply(X, ?)), inverse(multiply(Y, multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(X, Y)), multiply(X, Y)))))) = multiply(inverse(?), multiply(inverse(?), ?)).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(X, ?)), inverse(multiply(Y, multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(X, Y)), multiply(X, Y))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(Y, multiply(inverse(multiply(X, Y)), multiply(inverse(multiply(X, Y)), multiply(X, Y))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y)), multiply(inverse(multiply(X, Y)), multiply(X, Y))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y)), multiply(X, Y))))))
0.76/0.99	= { by lemma 2 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(Y, multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?)))), Y))))))
0.76/0.99	= { by lemma 12 }
0.76/0.99	  multiply(inverse(?), multiply(inverse(?), ?))
0.76/0.99	
0.76/0.99	Lemma 14: inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X))))) = inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(Y, ?)), multiply(Y, ?))))).
0.76/0.99	Proof:
0.76/0.99	  inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, ?)), inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 13 }
0.76/0.99	  multiply(Y, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 13 }
0.76/0.99	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, ?)), inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(Y, ?)), multiply(Y, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(Y, ?)), multiply(Y, ?)))))
0.76/0.99	
0.76/0.99	Lemma 15: multiply(inverse(multiply(X, ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = multiply(inverse(?), multiply(inverse(?), ?)).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(X, ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.76/0.99	= { by lemma 6 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.76/0.99	= { by lemma 6 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.76/0.99	= { by lemma 11 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))))))
0.76/0.99	= { by lemma 12 }
0.76/0.99	  multiply(inverse(?), multiply(inverse(?), ?))
0.76/0.99	
0.76/0.99	Lemma 16: multiply(X, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))) = inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))).
0.76/0.99	Proof:
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 15 }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.76/0.99	
0.76/0.99	Lemma 17: multiply(X, inverse(multiply(inverse(multiply(inverse(Y), multiply(inverse(Y), Y))), multiply(inverse(Y), multiply(inverse(Y), Y))))) = inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))).
0.76/0.99	Proof:
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(Y), multiply(inverse(Y), Y))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(Y), multiply(inverse(Y), Y)))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), multiply(inverse(Y), multiply(inverse(Y), Y)))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.99	= { by lemma 10 }
0.76/0.99	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(X, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 16 }
0.76/0.99	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.76/0.99	
0.76/0.99	Lemma 18: multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y))))))) = multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), Z).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(inverse(Z), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), Z)), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(Y), multiply(inverse(Y), Y)))))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), Z)), multiply(inverse(?), multiply(inverse(?), ?))))))
0.76/0.99	= { by lemma 3 }
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(X, Y)), ?)), Z)
0.76/0.99	
0.76/0.99	Lemma 19: inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))) = inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))).
0.76/0.99	Proof:
0.76/0.99	  inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 7 }
0.76/0.99	  multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by lemma 7 }
0.76/0.99	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.76/0.99	= { by axiom 1 (single_axiom) }
0.76/0.99	  inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.76/0.99	
0.76/0.99	Lemma 20: multiply(inverse(multiply(inverse(multiply(X, multiply(?, inverse(Y)))), ?)), Y) = multiply(inverse(multiply(inverse(multiply(X, multiply(?, inverse(?)))), ?)), ?).
0.76/0.99	Proof:
0.76/0.99	  multiply(inverse(multiply(inverse(multiply(X, multiply(?, inverse(Y)))), ?)), Y)
0.76/0.99	= { by lemma 18 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(inverse(Y), multiply(inverse(multiply(?, inverse(Y))), multiply(inverse(multiply(?, inverse(Y))), multiply(?, inverse(Y)))))))))
0.76/0.99	= { by lemma 19 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))))
0.76/0.99	= { by lemma 19 }
0.76/0.99	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(X, inverse(multiply(inverse(?), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))))
0.76/0.99	= { by lemma 18 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(X, multiply(?, inverse(?)))), ?)), ?)
0.76/1.00	
0.76/1.00	Lemma 21: multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.76/1.00	Proof:
0.76/1.00	  multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 8 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 17 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 17 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)))), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)))))))), multiply(inverse(?), multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 8 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)))), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?))))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?))))
0.76/1.00	= { by lemma 20 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?))))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.76/1.00	= { by lemma 20 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), ?)), ?))
0.76/1.00	= { by lemma 11 }
0.76/1.00	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.76/1.00	
0.76/1.00	Lemma 22: inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))) = multiply(inverse(?), ?).
0.76/1.00	Proof:
0.76/1.00	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.76/1.00	= { by lemma 21 }
0.76/1.00	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))
0.76/1.00	= { by lemma 10 }
0.76/1.00	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?))))
0.76/1.00	= { by lemma 6 }
0.76/1.00	  multiply(inverse(?), ?)
0.76/1.00	
0.76/1.00	Lemma 23: multiply(inverse(multiply(Y, multiply(Z, ?))), multiply(Y, inverse(multiply(inverse(X), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))) = X.
0.76/1.00	Proof:
0.76/1.00	  multiply(inverse(multiply(Y, multiply(Z, ?))), multiply(Y, inverse(multiply(inverse(X), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  multiply(inverse(multiply(Y, multiply(Z, ?))), multiply(Y, inverse(multiply(inverse(X), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(Z, ?)), multiply(Z, ?)))))))
0.76/1.00	= { by lemma 3 }
0.76/1.00	  X
0.76/1.00	
0.76/1.00	Lemma 24: multiply(inverse(multiply(X, multiply(inverse(?), ?))), multiply(X, multiply(inverse(?), ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.76/1.00	Proof:
0.76/1.00	  multiply(inverse(multiply(X, multiply(inverse(?), ?))), multiply(X, multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 22 }
0.76/1.00	  multiply(inverse(multiply(X, multiply(inverse(?), ?))), multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.76/1.00	= { by lemma 23 }
0.76/1.00	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.76/1.00	
0.76/1.00	Lemma 25: multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.76/1.00	Proof:
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.76/1.00	= { by lemma 4 }
0.76/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))
0.76/1.00	= { by lemma 24 }
0.83/1.00	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.00	
0.83/1.00	Lemma 26: multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(X), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = X.
0.83/1.00	Proof:
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(X), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(X), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))))
0.83/1.00	= { by lemma 3 }
0.83/1.00	  X
0.83/1.00	
0.83/1.00	Lemma 27: multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X)))) = multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))).
0.83/1.00	Proof:
0.83/1.00	  multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X))))
0.83/1.00	= { by lemma 3 }
0.83/1.00	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(X, multiply(inverse(multiply(Y, X)), multiply(inverse(multiply(Y, X)), multiply(Y, X))))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.00	= { by lemma 14 }
0.83/1.00	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(Y, ?)), multiply(Y, ?))))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.00	= { by lemma 3 }
0.83/1.00	  multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(Y, ?)), multiply(Y, ?))))
0.83/1.00	= { by lemma 4 }
0.83/1.00	  multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.00	
0.83/1.00	Lemma 28: inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))) = multiply(X, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))).
0.83/1.00	Proof:
0.83/1.00	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 27 }
0.83/1.00	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?)))))
0.83/1.00	= { by axiom 1 (single_axiom) }
0.83/1.00	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.00	= { by lemma 13 }
0.83/1.00	  multiply(X, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.00	= { by lemma 21 }
0.83/1.00	  multiply(X, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.00	
0.83/1.00	Lemma 29: inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.00	Proof:
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.00	= { by lemma 14 }
0.83/1.00	  inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)))))
0.83/1.00	= { by lemma 27 }
0.83/1.00	  inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 28 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.00	= { by lemma 25 }
0.83/1.00	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.00	= { by lemma 25 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.01	= { by axiom 1 (single_axiom) }
0.83/1.01	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.01	
0.83/1.01	Lemma 30: multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.01	Proof:
0.83/1.01	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.01	= { by lemma 26 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.01	= { by lemma 29 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.01	= { by lemma 29 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 25 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.01	= { by lemma 25 }
0.83/1.01	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.01	
0.83/1.01	Lemma 31: inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.01	Proof:
0.83/1.01	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.01	= { by lemma 30 }
0.83/1.01	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 29 }
0.83/1.01	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.01	
0.83/1.01	Lemma 32: inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))) = multiply(?, ?).
0.83/1.01	Proof:
0.83/1.01	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 25 }
0.83/1.01	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 9 }
0.83/1.01	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.01	= { by lemma 2 }
0.83/1.01	  multiply(?, ?)
0.83/1.01	
0.83/1.01	Lemma 33: inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.01	Proof:
0.83/1.01	  inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 32 }
0.83/1.01	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 9 }
0.83/1.01	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.01	= { by lemma 2 }
0.83/1.01	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.01	
0.83/1.01	Lemma 34: multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))) = multiply(inverse(?), multiply(inverse(?), ?)).
0.83/1.01	Proof:
0.83/1.01	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 4 }
0.83/1.01	  multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 31 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 30 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 31 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 30 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 31 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 29 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 33 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 26 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 33 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	= { by lemma 31 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 28 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.01	= { by lemma 27 }
0.83/1.01	  multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))))))
0.83/1.01	= { by lemma 12 }
0.83/1.01	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.01	
0.83/1.01	Lemma 35: multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))) = inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))).
0.83/1.01	Proof:
0.83/1.01	  multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.01	= { by lemma 7 }
0.83/1.01	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.01	= { by axiom 1 (single_axiom) }
0.83/1.01	  inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	
0.83/1.01	Lemma 36: inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))) = multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))).
0.83/1.01	Proof:
0.83/1.01	  inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.01	= { by lemma 35 }
0.83/1.01	  multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.01	= { by lemma 21 }
0.83/1.01	  multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.01	
0.83/1.01	Lemma 37: multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = multiply(inverse(X), multiply(inverse(X), X)).
0.83/1.01	Proof:
0.83/1.01	  multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.01	= { by lemma 17 }
0.83/1.01	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))))))
0.83/1.01	= { by lemma 3 }
0.83/1.02	  multiply(inverse(X), multiply(inverse(X), X))
0.83/1.02	
0.83/1.02	Lemma 38: multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.02	Proof:
0.83/1.02	  multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 36 }
0.83/1.02	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 35 }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 36 }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.02	= { by lemma 19 }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), inverse(multiply(inverse(?), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))
0.83/1.02	= { by axiom 1 (single_axiom) }
0.83/1.02	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(?, inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(?, inverse(?)))), ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))
0.83/1.02	= { by axiom 1 (single_axiom) }
0.83/1.02	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(?, inverse(?)))), ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 18 }
0.83/1.02	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), inverse(multiply(inverse(?), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 19 }
0.83/1.02	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 37 }
0.83/1.02	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 6 }
0.83/1.02	  multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.02	= { by lemma 21 }
0.83/1.02	  multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.02	= { by lemma 16 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.02	= { by lemma 28 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 21 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 25 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.02	= { by lemma 30 }
0.83/1.02	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.02	
0.83/1.02	Lemma 39: inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.02	Proof:
0.83/1.02	  inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 12 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))))))))
0.83/1.02	= { by lemma 38 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))))))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))))))))
0.83/1.02	= { by lemma 27 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))))
0.83/1.02	= { by lemma 28 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.02	= { by lemma 38 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.02	= { by lemma 25 }
0.83/1.02	  inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 28 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.02	= { by lemma 31 }
0.83/1.02	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.02	= { by lemma 30 }
0.83/1.02	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.02	
0.83/1.02	Lemma 40: inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(X, multiply(inverse(?), multiply(inverse(?), ?))))))) = X.
0.83/1.02	Proof:
0.83/1.02	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(X, multiply(inverse(?), multiply(inverse(?), ?)))))))
0.83/1.02	= { by lemma 6 }
0.83/1.02	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?)))))))
0.83/1.02	= { by lemma 3 }
0.83/1.02	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.02	= { by lemma 6 }
0.83/1.02	  X
0.83/1.02	
0.83/1.02	Lemma 41: inverse(multiply(inverse(?), multiply(inverse(?), ?))) = ?.
0.83/1.02	Proof:
0.83/1.02	  inverse(multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.02	= { by lemma 34 }
0.83/1.02	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.02	= { by lemma 39 }
0.83/1.02	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))))))
0.83/1.02	= { by lemma 40 }
0.83/1.02	  ?
0.83/1.02	
0.83/1.02	Lemma 42: multiply(inverse(multiply(inverse(?), ?)), ?) = multiply(?, multiply(inverse(?), ?)).
0.83/1.02	Proof:
0.83/1.02	  multiply(inverse(multiply(inverse(?), ?)), ?)
0.83/1.02	= { by lemma 5 }
0.83/1.02	  multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.02	= { by lemma 41 }
0.83/1.02	  multiply(?, multiply(inverse(?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.02	= { by lemma 4 }
0.83/1.02	  multiply(?, multiply(inverse(?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.02	= { by lemma 34 }
0.83/1.02	  multiply(?, multiply(inverse(?), inverse(multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.02	= { by lemma 41 }
0.83/1.03	  multiply(?, multiply(inverse(?), ?))
0.83/1.03	
0.83/1.03	Lemma 43: multiply(?, multiply(inverse(?), multiply(inverse(?), ?))) = multiply(inverse(multiply(?, ?)), multiply(?, ?)).
0.83/1.03	Proof:
0.83/1.03	  multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 26 }
0.83/1.03	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 39 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 29 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	= { by lemma 30 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.03	= { by lemma 30 }
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.03	
0.83/1.03	Lemma 44: multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?)) = multiply(?, ?).
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(?, ?))
0.83/1.03	= { by lemma 43 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, ?))
0.83/1.03	= { by lemma 41 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, inverse(multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 34 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.03	= { by lemma 21 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))))))
0.83/1.03	= { by lemma 5 }
0.83/1.03	  multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), ?)
0.83/1.03	= { by lemma 41 }
0.83/1.03	  multiply(?, ?)
0.83/1.03	
0.83/1.03	Lemma 45: multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?) = ?.
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)
0.83/1.03	= { by axiom 1 (single_axiom) }
0.83/1.03	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 44 }
0.83/1.03	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 41 }
0.83/1.03	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 34 }
0.83/1.03	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 5 }
0.83/1.03	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by axiom 1 (single_axiom) }
0.83/1.03	  ?
0.83/1.03	
0.83/1.03	Lemma 46: multiply(inverse(multiply(?, ?)), multiply(?, ?)) = multiply(inverse(?), ?).
0.83/1.03	Proof:
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.03	= { by lemma 4 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))
0.83/1.03	= { by lemma 45 }
0.83/1.03	  multiply(inverse(?), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))
0.83/1.03	= { by lemma 45 }
0.83/1.03	  multiply(inverse(?), ?)
0.83/1.03	
0.83/1.03	Lemma 47: multiply(multiply(inverse(?), ?), multiply(inverse(?), ?)) = multiply(inverse(?), ?).
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(?), ?))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.03	= { by lemma 30 }
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(inverse(?), ?)
0.83/1.03	
0.83/1.03	Lemma 48: inverse(multiply(inverse(?), ?)) = multiply(inverse(?), ?).
0.83/1.03	Proof:
0.83/1.03	  inverse(multiply(inverse(?), ?))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(inverse(?), ?)
0.83/1.03	
0.83/1.03	Lemma 49: multiply(multiply(inverse(?), ?), ?) = ?.
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), ?)
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)
0.83/1.03	= { by lemma 45 }
0.83/1.03	  ?
0.83/1.03	
0.83/1.03	Lemma 50: multiply(?, multiply(inverse(?), ?)) = ?.
0.83/1.03	Proof:
0.83/1.03	  multiply(?, multiply(inverse(?), ?))
0.83/1.03	= { by lemma 42 }
0.83/1.03	  multiply(inverse(multiply(inverse(?), ?)), ?)
0.83/1.03	= { by lemma 5 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.03	= { by lemma 47 }
0.83/1.03	  multiply(inverse(multiply(inverse(?), ?)), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.03	= { by lemma 48 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.03	= { by lemma 4 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.03	= { by lemma 34 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 41 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(multiply(inverse(?), ?), ?))
0.83/1.03	= { by lemma 49 }
0.83/1.03	  multiply(multiply(inverse(?), ?), ?)
0.83/1.03	= { by lemma 49 }
0.83/1.03	  ?
0.83/1.03	
0.83/1.03	Lemma 51: multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X)))) = multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))).
0.83/1.03	Proof:
0.83/1.03	  multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))
0.83/1.03	= { by lemma 3 }
0.83/1.03	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(X, multiply(inverse(multiply(?, X)), multiply(inverse(multiply(?, X)), multiply(?, X))))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.83/1.03	= { by lemma 19 }
0.83/1.03	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.83/1.03	= { by lemma 3 }
0.83/1.03	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	
0.83/1.03	Lemma 52: multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?))) = multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?))).
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	= { by lemma 38 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 51 }
0.83/1.03	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))
0.83/1.03	
0.83/1.03	Lemma 53: multiply(inverse(multiply(Y, X)), inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))).
0.83/1.03	Proof:
0.83/1.03	  multiply(inverse(multiply(Y, X)), inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 17 }
0.83/1.03	  multiply(inverse(multiply(Y, X)), multiply(Y, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))))))
0.83/1.03	= { by lemma 3 }
0.83/1.03	  multiply(inverse(X), multiply(inverse(X), X))
0.83/1.03	= { by lemma 3 }
0.83/1.03	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))))))
0.83/1.03	= { by lemma 17 }
0.83/1.03	  multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	
0.83/1.03	Lemma 54: multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?)) = ?.
0.83/1.03	Proof:
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))
0.83/1.03	= { by lemma 52 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), ?))
0.83/1.03	= { by lemma 47 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.03	= { by lemma 28 }
0.83/1.03	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 53 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 39 }
0.83/1.03	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 36 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(?, multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(multiply(inverse(?), ?), ?)
0.83/1.03	= { by lemma 49 }
0.83/1.03	  ?
0.83/1.03	
0.83/1.03	Lemma 55: multiply(multiply(inverse(?), ?), multiply(inverse(?), X)) = multiply(inverse(multiply(?, ?)), multiply(?, X)).
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), multiply(inverse(?), X))
0.83/1.03	= { by lemma 48 }
0.83/1.03	  multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), X))
0.83/1.03	= { by lemma 54 }
0.83/1.03	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), ?)), multiply(inverse(?), X))
0.83/1.03	= { by lemma 54 }
0.83/1.03	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), X))
0.83/1.03	= { by lemma 11 }
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, X))
0.83/1.03	
0.83/1.03	Lemma 56: multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(Z, ?))), X)), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = X.
0.83/1.03	Proof:
0.83/1.03	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(Z, ?))), X)), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 4 }
0.83/1.03	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(Z, ?))), X)), multiply(inverse(multiply(Z, ?)), multiply(inverse(multiply(Z, ?)), multiply(Z, ?))))))
0.83/1.03	= { by axiom 1 (single_axiom) }
0.83/1.03	  X
0.83/1.03	
0.83/1.03	Lemma 57: multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), X)), multiply(inverse(?), ?)))) = X.
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), X)), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), X)), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), X)), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 55 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), X)), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 47 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), X)), multiply(multiply(inverse(?), ?), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 48 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), X)), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), X)), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.03	= { by lemma 56 }
0.83/1.03	  X
0.83/1.03	
0.83/1.03	Lemma 58: multiply(multiply(inverse(?), ?), inverse(?)) = multiply(inverse(?), multiply(inverse(?), ?)).
0.83/1.03	Proof:
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(?))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(?, multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, multiply(inverse(?), ?)), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 31 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 36 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 19 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?)))))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 57 }
0.83/1.03	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(inverse(?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 24 }
0.83/1.03	  multiply(inverse(?), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.03	
0.83/1.03	Lemma 59: multiply(inverse(?), multiply(inverse(?), ?)) = inverse(?).
0.83/1.03	Proof:
0.83/1.03	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.03	= { by lemma 58 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(?))
0.83/1.03	= { by lemma 50 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(?, multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 41 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 58 }
0.83/1.03	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), inverse(?))), multiply(inverse(?), ?))))
0.83/1.03	= { by lemma 57 }
0.83/1.03	  inverse(?)
0.83/1.03	
0.83/1.03	Lemma 60: inverse(inverse(?)) = ?.
0.83/1.03	Proof:
0.83/1.03	  inverse(inverse(?))
0.83/1.03	= { by lemma 59 }
0.83/1.03	  inverse(multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 41 }
0.83/1.03	  ?
0.83/1.03	
0.83/1.03	Lemma 61: multiply(inverse(?), ?) = multiply(?, inverse(?)).
0.83/1.03	Proof:
0.83/1.03	  multiply(inverse(?), ?)
0.83/1.03	= { by lemma 46 }
0.83/1.03	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.03	= { by lemma 43 }
0.83/1.03	  multiply(?, multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.03	= { by lemma 59 }
0.83/1.04	  multiply(?, inverse(?))
0.83/1.04	
0.83/1.04	Lemma 62: multiply(multiply(?, inverse(?)), inverse(?)) = inverse(?).
0.83/1.04	Proof:
0.83/1.04	  multiply(multiply(?, inverse(?)), inverse(?))
0.83/1.04	= { by lemma 61 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(?))
0.83/1.04	= { by lemma 54 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 52 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 57 }
0.83/1.04	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(?)
0.83/1.04	
0.83/1.04	Lemma 63: multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?))))) = inverse(?).
0.83/1.04	Proof:
0.83/1.04	  multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 61 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(?, multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 50 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, multiply(inverse(?), ?)), multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 46 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 31 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 36 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 51 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?)))))), multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 61 }
0.83/1.04	  multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?)))))), multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 57 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 50 }
0.83/1.04	  multiply(inverse(?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 24 }
0.83/1.04	  multiply(inverse(?), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.04	= { by lemma 46 }
0.83/1.04	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(?)
0.83/1.04	
0.83/1.04	Lemma 64: multiply(inverse(multiply(?, ?)), ?) = inverse(?).
0.83/1.04	Proof:
0.83/1.04	  multiply(inverse(multiply(?, ?)), ?)
0.83/1.04	= { by lemma 60 }
0.83/1.04	  multiply(inverse(multiply(inverse(inverse(?)), ?)), ?)
0.83/1.04	= { by lemma 63 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), ?)
0.83/1.04	= { by lemma 50 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(?, multiply(inverse(?), ?)))
0.83/1.04	= { by lemma 60 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(inverse(?)), multiply(inverse(?), ?)))
0.83/1.04	= { by lemma 63 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), multiply(inverse(?), ?)))
0.83/1.04	= { by lemma 46 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.04	= { by lemma 31 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.04	= { by lemma 28 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.04	= { by lemma 27 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?)))))), ?))))))
0.83/1.04	= { by lemma 12 }
0.83/1.04	  multiply(inverse(?), multiply(inverse(?), ?))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(?)
0.83/1.04	
0.83/1.04	Lemma 65: multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))) = ?.
0.83/1.04	Proof:
0.83/1.04	  multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?)))
0.83/1.04	= { by lemma 4 }
0.83/1.04	  multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(multiply(inverse(?), ?), multiply(?, ?)))
0.83/1.04	= { by lemma 49 }
0.83/1.04	  multiply(inverse(?), multiply(multiply(inverse(?), ?), multiply(?, ?)))
0.83/1.04	= { by lemma 50 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), multiply(?, ?)))
0.83/1.04	= { by lemma 46 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(?, ?)))
0.83/1.04	= { by lemma 44 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, ?))
0.83/1.04	= { by lemma 41 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, inverse(multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.04	= { by lemma 34 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.04	= { by lemma 4 }
0.83/1.04	  multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?)))))))
0.83/1.04	= { by lemma 5 }
0.83/1.04	  multiply(inverse(multiply(inverse(?), ?)), ?)
0.83/1.04	= { by lemma 42 }
0.83/1.04	  multiply(?, multiply(inverse(?), ?))
0.83/1.04	= { by lemma 50 }
0.83/1.04	  ?
0.83/1.04	
0.83/1.04	Lemma 66: inverse(multiply(inverse(multiply(?, X)), inverse(?))) = multiply(?, inverse(multiply(inverse(X), inverse(?)))).
0.83/1.04	Proof:
0.83/1.04	  inverse(multiply(inverse(multiply(?, X)), inverse(?)))
0.83/1.04	= { by lemma 60 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(inverse(?)), X)), inverse(?)))
0.83/1.04	= { by lemma 64 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), X)), inverse(?)))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), X)), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.04	= { by axiom 1 (single_axiom) }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.04	= { by axiom 1 (single_axiom) }
0.83/1.04	  multiply(?, inverse(multiply(inverse(X), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(X), inverse(?))))
0.83/1.04	
0.83/1.04	Lemma 67: multiply(inverse(multiply(?, ?)), multiply(?, X)) = multiply(?, multiply(inverse(multiply(?, ?)), X)).
0.83/1.04	Proof:
0.83/1.04	  multiply(inverse(multiply(?, ?)), multiply(?, X))
0.83/1.04	= { by lemma 11 }
0.83/1.04	  multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))
0.83/1.04	= { by lemma 64 }
0.83/1.04	  multiply(inverse(inverse(?)), multiply(inverse(multiply(?, ?)), X))
0.83/1.04	= { by lemma 60 }
0.83/1.04	  multiply(?, multiply(inverse(multiply(?, ?)), X))
0.83/1.04	
0.83/1.04	Lemma 68: multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), inverse(?)))) = X.
0.83/1.04	Proof:
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), inverse(?))))
0.83/1.04	= { by lemma 66 }
0.83/1.04	  inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), X))), inverse(?)))
0.83/1.04	= { by lemma 67 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), inverse(?)))
0.83/1.04	= { by lemma 55 }
0.83/1.04	  inverse(multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), X))), inverse(?)))
0.83/1.04	= { by lemma 48 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), X))), inverse(?)))
0.83/1.04	= { by lemma 54 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), ?)), multiply(inverse(?), X))), inverse(?)))
0.83/1.04	= { by lemma 54 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), X))), inverse(?)))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), ?)), multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))), multiply(inverse(?), ?))), X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 2 }
0.83/1.04	  X
0.83/1.04	
0.83/1.04	Lemma 69: inverse(multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.83/1.04	Proof:
0.83/1.04	  inverse(multiply(?, inverse(?)))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  inverse(multiply(?, multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.04	= { by lemma 39 }
0.83/1.04	  multiply(inverse(multiply(?, ?)), multiply(?, ?))
0.83/1.04	= { by lemma 46 }
0.83/1.04	  multiply(inverse(?), ?)
0.83/1.04	= { by lemma 61 }
0.83/1.04	  multiply(?, inverse(?))
0.83/1.04	
0.83/1.04	Lemma 70: multiply(?, multiply(?, inverse(?))) = ?.
0.83/1.04	Proof:
0.83/1.04	  multiply(?, multiply(?, inverse(?)))
0.83/1.04	= { by lemma 69 }
0.83/1.04	  multiply(?, inverse(multiply(?, inverse(?))))
0.83/1.04	= { by lemma 60 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(inverse(?)), inverse(?))))
0.83/1.04	= { by lemma 64 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))
0.83/1.04	= { by lemma 59 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(?), multiply(inverse(?), ?)))))
0.83/1.04	= { by axiom 1 (single_axiom) }
0.83/1.04	  ?
0.83/1.04	
0.83/1.04	Lemma 71: multiply(inverse(X), multiply(inverse(X), X)) = multiply(inverse(multiply(?, X)), ?).
0.83/1.04	Proof:
0.83/1.04	  multiply(inverse(X), multiply(inverse(X), X))
0.83/1.04	= { by lemma 37 }
0.83/1.04	  multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.04	= { by lemma 36 }
0.83/1.04	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.04	= { by lemma 67 }
0.83/1.04	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(?, multiply(inverse(multiply(?, ?)), ?)))))
0.83/1.04	= { by lemma 64 }
0.83/1.04	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(?, inverse(?)))))
0.83/1.04	= { by lemma 69 }
0.83/1.04	  multiply(inverse(multiply(?, X)), multiply(?, multiply(?, inverse(?))))
0.83/1.04	= { by lemma 70 }
0.83/1.04	  multiply(inverse(multiply(?, X)), ?)
0.83/1.04	
0.83/1.04	Lemma 72: multiply(?, inverse(multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), ?)))) = X.
0.83/1.04	Proof:
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), ?))))
0.83/1.04	= { by lemma 68 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(Y), ?))))
0.83/1.04	= { by lemma 68 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), ?))))
0.83/1.04	= { by lemma 71 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))))))
0.83/1.04	= { by axiom 1 (single_axiom) }
0.83/1.04	  X
0.83/1.04	
0.83/1.04	Lemma 73: multiply(?, inverse(multiply(inverse(multiply(multiply(?, inverse(?)), X)), ?))) = X.
0.83/1.04	Proof:
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(multiply(?, inverse(?)), X)), ?)))
0.83/1.04	= { by lemma 61 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(multiply(inverse(?), ?), X)), ?)))
0.83/1.04	= { by lemma 22 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), ?)))
0.83/1.04	= { by lemma 49 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), multiply(multiply(inverse(?), ?), ?))))
0.83/1.04	= { by lemma 22 }
0.83/1.04	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))))
0.83/1.04	= { by lemma 72 }
0.83/1.04	  X
0.83/1.05	
0.83/1.05	Lemma 74: multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(inverse(multiply(?, ?)), ?))), X)), multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?)))))) = X.
0.83/1.05	Proof:
0.83/1.05	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(inverse(multiply(?, ?)), ?))), X)), multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))
0.83/1.05	= { by lemma 11 }
0.83/1.05	  multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(Y, multiply(inverse(multiply(?, ?)), ?))), X)), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.05	= { by lemma 56 }
0.83/1.05	  X
0.83/1.05	
0.83/1.05	Lemma 75: inverse(multiply(inverse(multiply(?, X)), ?)) = multiply(?, inverse(multiply(inverse(X), ?))).
0.83/1.05	Proof:
0.83/1.05	  inverse(multiply(inverse(multiply(?, X)), ?))
0.83/1.05	= { by lemma 60 }
0.83/1.05	  inverse(multiply(inverse(multiply(inverse(inverse(?)), X)), ?))
0.83/1.05	= { by lemma 62 }
0.83/1.05	  inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(?))), X)), ?))
0.83/1.05	= { by lemma 64 }
0.83/1.05	  inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, ?)), ?))), X)), ?))
0.83/1.05	= { by lemma 65 }
0.83/1.05	  inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, ?)), ?))), X)), multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?)))))
0.83/1.05	= { by lemma 73 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, ?)), ?))), X)), multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), ?)))
0.83/1.05	= { by lemma 74 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(X), ?)))
0.83/1.05	
0.83/1.05	Lemma 76: multiply(?, inverse(multiply(inverse(multiply(Y, X)), multiply(Y, ?)))) = X.
0.83/1.05	Proof:
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(Y, X)), multiply(Y, ?))))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), multiply(Y, ?))))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))))
0.83/1.05	= { by lemma 72 }
0.83/1.05	  X
0.83/1.05	
0.83/1.05	Lemma 77: multiply(inverse(multiply(X, ?)), multiply(?, inverse(?))) = multiply(inverse(multiply(?, multiply(X, ?))), ?).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(multiply(X, ?)), multiply(?, inverse(?)))
0.83/1.05	= { by lemma 61 }
0.83/1.05	  multiply(inverse(multiply(X, ?)), multiply(inverse(?), ?))
0.83/1.05	= { by lemma 46 }
0.83/1.05	  multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, ?))))
0.83/1.05	= { by lemma 16 }
0.83/1.05	  multiply(?, inverse(multiply(multiply(X, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(?), multiply(inverse(?), ?))))), multiply(?, ?))))
0.83/1.05	= { by lemma 13 }
0.83/1.05	  multiply(?, inverse(multiply(multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?))))))), multiply(inverse(?), multiply(inverse(?), ?))))), multiply(?, ?))))
0.83/1.05	= { by axiom 1 (single_axiom) }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?))))), multiply(?, ?))))
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?)))
0.83/1.05	= { by lemma 71 }
0.83/1.05	  multiply(inverse(multiply(?, multiply(X, ?))), ?)
0.83/1.05	
0.83/1.05	Lemma 78: multiply(inverse(Y), multiply(?, inverse(multiply(inverse(X), multiply(inverse(Y), ?))))) = X.
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(Y), multiply(?, inverse(multiply(inverse(X), multiply(inverse(Y), ?)))))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), multiply(?, inverse(multiply(inverse(X), multiply(inverse(Y), ?)))))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), multiply(?, inverse(multiply(inverse(X), multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), ?)))))
0.83/1.05	= { by lemma 71 }
0.83/1.05	  multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), multiply(?, inverse(multiply(inverse(X), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))))))))
0.83/1.05	= { by lemma 3 }
0.83/1.05	  X
0.83/1.05	
0.83/1.05	Lemma 79: multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(inverse(X), ?)))) = X.
0.83/1.05	Proof:
0.83/1.05	  multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(inverse(X), ?))))
0.83/1.05	= { by lemma 61 }
0.83/1.05	  multiply(multiply(inverse(?), ?), multiply(?, inverse(multiply(inverse(X), ?))))
0.83/1.05	= { by lemma 22 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(multiply(inverse(X), ?))))
0.83/1.05	= { by lemma 49 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(multiply(inverse(X), multiply(multiply(inverse(?), ?), ?)))))
0.83/1.05	= { by lemma 22 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?)))))
0.83/1.05	= { by lemma 78 }
0.83/1.05	  X
0.83/1.05	
0.83/1.05	Lemma 80: multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y))) = multiply(inverse(multiply(inverse(multiply(X, ?)), Z)), multiply(inverse(?), multiply(inverse(?), ?))).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y)))
0.83/1.05	= { by lemma 3 }
0.83/1.05	  multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, Y)), Z)), multiply(inverse(Y), multiply(inverse(Y), Y)))), multiply(inverse(V), multiply(inverse(V), V))))))
0.83/1.05	= { by lemma 10 }
0.83/1.05	  multiply(inverse(multiply(W, V)), multiply(W, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(X, ?)), Z)), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(V), multiply(inverse(V), V))))))
0.83/1.05	= { by lemma 3 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(X, ?)), Z)), multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.05	
0.83/1.05	Lemma 81: multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), ?)) = multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?)).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(multiply(inverse(Y), X)), multiply(inverse(Y), ?))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(Y), ?))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), ?))
0.83/1.05	= { by lemma 71 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), Y)), inverse(?))))))
0.83/1.05	= { by lemma 80 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.05	= { by lemma 80 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))))
0.83/1.05	= { by lemma 71 }
0.83/1.05	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))), ?))
0.83/1.05	= { by lemma 68 }
0.83/1.05	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?))
0.83/1.05	
0.83/1.05	Lemma 82: multiply(inverse(multiply(Y, X)), multiply(Y, ?)) = multiply(inverse(multiply(?, X)), multiply(?, ?)).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(multiply(Y, X)), multiply(Y, ?))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), multiply(Y, ?))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))
0.83/1.05	= { by lemma 81 }
0.83/1.05	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?))
0.83/1.05	= { by lemma 81 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(inverse(multiply(?, X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Z, W)), ?)), multiply(inverse(multiply(Z, W)), ?))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))
0.83/1.05	= { by lemma 2 }
0.83/1.05	  multiply(inverse(multiply(?, X)), multiply(?, ?))
0.83/1.05	
0.83/1.05	Lemma 83: inverse(multiply(inverse(multiply(?, X)), multiply(?, ?))) = multiply(?, inverse(multiply(inverse(X), multiply(?, ?)))).
0.83/1.05	Proof:
0.83/1.05	  inverse(multiply(inverse(multiply(?, X)), multiply(?, ?)))
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(?, X)), multiply(?, ?))))), multiply(?, ?))))
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(?, inverse(multiply(inverse(X), multiply(?, ?))))
0.83/1.05	
0.83/1.05	Lemma 84: multiply(inverse(multiply(multiply(?, inverse(?)), X)), ?) = multiply(inverse(multiply(?, X)), multiply(?, ?)).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(multiply(multiply(?, inverse(?)), X)), ?)
0.83/1.05	= { by lemma 61 }
0.83/1.05	  multiply(inverse(multiply(multiply(inverse(?), ?), X)), ?)
0.83/1.05	= { by lemma 22 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), ?)
0.83/1.05	= { by lemma 49 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), multiply(multiply(inverse(?), ?), ?))
0.83/1.05	= { by lemma 22 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), X)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), ?))
0.83/1.05	= { by lemma 81 }
0.83/1.05	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?))
0.83/1.05	= { by lemma 82 }
0.83/1.05	  multiply(inverse(multiply(?, X)), multiply(?, ?))
0.83/1.05	
0.83/1.05	Lemma 85: multiply(inverse(X), X) = multiply(?, inverse(?)).
0.83/1.05	Proof:
0.83/1.05	  multiply(inverse(X), X)
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(multiply(?, inverse(multiply(inverse(multiply(?, inverse(X))), multiply(?, ?)))), X)
0.83/1.05	= { by lemma 83 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(X)))), multiply(?, ?))), X)
0.83/1.05	= { by lemma 84 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(X)))), ?)), X)
0.83/1.05	= { by lemma 20 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))), ?)), ?)
0.83/1.05	= { by lemma 84 }
0.83/1.05	  multiply(inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), multiply(?, ?))), ?)
0.83/1.05	= { by lemma 83 }
0.83/1.05	  multiply(multiply(?, inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, ?)))), ?)
0.83/1.05	= { by lemma 76 }
0.83/1.05	  multiply(inverse(?), ?)
0.83/1.05	= { by lemma 61 }
0.83/1.06	  multiply(?, inverse(?))
0.83/1.06	
0.83/1.06	Lemma 86: multiply(?, inverse(multiply(inverse(X), ?))) = X.
0.83/1.06	Proof:
0.83/1.06	  multiply(?, inverse(multiply(inverse(X), ?)))
0.83/1.06	= { by lemma 75 }
0.83/1.06	  inverse(multiply(inverse(multiply(?, X)), ?))
0.83/1.06	= { by lemma 79 }
0.83/1.06	  inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), ?)))))
0.83/1.06	= { by lemma 69 }
0.83/1.06	  inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), ?)))))
0.83/1.06	= { by lemma 85 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), ?)))))
0.83/1.06	= { by lemma 26 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), ?)))))
0.83/1.06	= { by lemma 45 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))))))
0.83/1.06	= { by lemma 31 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?))))))
0.83/1.06	= { by lemma 72 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.06	= { by lemma 31 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.06	= { by lemma 46 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.06	= { by lemma 61 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.06	= { by lemma 46 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(inverse(?), ?))))))
0.83/1.06	= { by lemma 61 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), multiply(?, inverse(?)))))))
0.83/1.06	= { by lemma 77 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, X)), ?))), ?)))))
0.83/1.06	= { by lemma 75 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), ?))))))
0.83/1.06	= { by lemma 79 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(multiply(?, X)), ?)))
0.83/1.06	= { by lemma 71 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(X), multiply(inverse(X), X))))
0.83/1.06	= { by lemma 9 }
0.83/1.06	  inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), X))), multiply(inverse(?), multiply(inverse(?), ?))))
0.83/1.06	= { by lemma 2 }
0.83/1.06	  X
0.83/1.06	
0.83/1.06	Lemma 87: multiply(inverse(multiply(?, X)), ?) = multiply(?, inverse(multiply(X, ?))).
0.83/1.06	Proof:
0.83/1.06	  multiply(inverse(multiply(?, X)), ?)
0.83/1.06	= { by lemma 86 }
0.83/1.06	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, X)), ?)), ?)))
0.83/1.06	= { by lemma 75 }
0.83/1.06	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(X), ?))), ?)))
0.83/1.06	= { by lemma 86 }
0.83/1.06	  multiply(?, inverse(multiply(X, ?)))
0.83/1.06	
0.83/1.06	Lemma 88: inverse(multiply(?, inverse(multiply(X, ?)))) = X.
0.83/1.06	Proof:
0.83/1.06	  inverse(multiply(?, inverse(multiply(X, ?))))
0.83/1.06	= { by lemma 87 }
0.83/1.06	  inverse(multiply(inverse(multiply(?, X)), ?))
0.83/1.06	= { by lemma 75 }
0.83/1.06	  multiply(?, inverse(multiply(inverse(X), ?)))
0.83/1.06	= { by lemma 86 }
0.83/1.06	  X
0.83/1.06	
0.83/1.06	Lemma 89: multiply(inverse(X), multiply(?, inverse(?))) = multiply(?, inverse(multiply(X, ?))).
0.83/1.06	Proof:
0.83/1.06	  multiply(inverse(X), multiply(?, inverse(?)))
0.83/1.06	= { by lemma 85 }
0.83/1.06	  multiply(inverse(X), multiply(inverse(X), X))
0.83/1.06	= { by lemma 3 }
0.83/1.06	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(inverse(multiply(inverse(X), multiply(inverse(X), X))), multiply(inverse(X), multiply(inverse(X), X))))))
0.83/1.06	= { by lemma 17 }
0.83/1.06	  multiply(inverse(multiply(?, X)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.06	= { by lemma 36 }
0.83/1.06	  multiply(inverse(multiply(?, X)), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.06	= { by lemma 76 }
0.83/1.06	  multiply(inverse(multiply(?, X)), ?)
0.83/1.06	= { by lemma 87 }
0.83/1.06	  multiply(?, inverse(multiply(X, ?)))
0.83/1.06	
0.83/1.06	Lemma 90: multiply(inverse(Y), multiply(Y, X)) = X.
0.83/1.06	Proof:
0.83/1.06	  multiply(inverse(Y), multiply(Y, X))
0.83/1.06	= { by lemma 88 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(?, inverse(multiply(multiply(Y, X), ?)))))
0.83/1.06	= { by lemma 89 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(Y, X)), multiply(?, inverse(?)))))
0.83/1.06	= { by lemma 88 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(Y, ?)))), X)), multiply(?, inverse(?)))))
0.83/1.06	= { by lemma 89 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(?, inverse(?)))))
0.83/1.06	= { by lemma 50 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(?, inverse(multiply(?, multiply(inverse(?), ?)))))))
0.83/1.06	= { by lemma 76 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(inverse(?), ?)))))))
0.83/1.06	= { by lemma 36 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), ?)))))))
0.83/1.06	= { by lemma 19 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))), multiply(inverse(?), ?)))))))
0.83/1.06	= { by lemma 76 }
0.83/1.06	  multiply(inverse(Y), inverse(multiply(inverse(multiply(inverse(multiply(inverse(Y), multiply(?, inverse(?)))), X)), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))
0.83/1.06	= { by axiom 1 (single_axiom) }
0.83/1.06	  X
0.83/1.06	
0.83/1.06	Lemma 91: multiply(inverse(inverse(X)), Y) = multiply(X, Y).
0.83/1.06	Proof:
0.83/1.06	  multiply(inverse(inverse(X)), Y)
0.83/1.06	= { by lemma 90 }
0.83/1.06	  multiply(inverse(inverse(X)), multiply(inverse(X), multiply(X, Y)))
0.83/1.06	= { by lemma 90 }
0.83/1.06	  multiply(X, Y)
0.83/1.06	
0.83/1.06	Lemma 92: multiply(?, inverse(multiply(X, ?))) = inverse(X).
0.83/1.06	Proof:
0.83/1.06	  multiply(?, inverse(multiply(X, ?)))
0.83/1.06	= { by lemma 89 }
0.83/1.06	  multiply(inverse(X), multiply(?, inverse(?)))
0.83/1.06	= { by lemma 90 }
0.83/1.06	  multiply(inverse(X), multiply(?, inverse(multiply(inverse(inverse(X)), multiply(inverse(X), ?)))))
0.83/1.06	= { by lemma 78 }
0.83/1.07	  inverse(X)
0.83/1.07	
0.83/1.07	Lemma 93: multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?)))))) = X.
0.83/1.07	Proof:
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 61 }
0.83/1.07	  multiply(multiply(inverse(?), ?), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 46 }
0.83/1.07	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 31 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 55 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 61 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(X), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 61 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(X), multiply(inverse(?), ?)))))
0.83/1.07	= { by lemma 47 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(X), multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))))))
0.83/1.07	= { by lemma 48 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?))))))
0.83/1.07	= { by lemma 46 }
0.83/1.07	  multiply(inverse(multiply(multiply(inverse(?), ?), multiply(inverse(?), ?))), multiply(multiply(inverse(?), ?), inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
0.83/1.07	= { by lemma 23 }
0.83/1.07	  X
0.83/1.07	
0.83/1.07	Lemma 94: multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))) = inverse(?).
0.83/1.07	Proof:
0.83/1.07	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))
0.83/1.07	= { by lemma 61 }
0.83/1.07	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(?), ?)))
0.83/1.07	= { by lemma 46 }
0.83/1.07	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.07	= { by lemma 93 }
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 36 }
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 31 }
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 46 }
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, multiply(inverse(?), ?)), multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 50 }
0.83/1.07	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, inverse(?))))))
0.83/1.07	= { by lemma 63 }
0.83/1.07	  multiply(multiply(?, inverse(?)), inverse(?))
0.83/1.07	= { by lemma 62 }
0.83/1.07	  inverse(?)
0.83/1.07	
0.83/1.07	Lemma 95: inverse(multiply(inverse(?), X)) = multiply(inverse(X), ?).
0.83/1.07	Proof:
0.83/1.07	  inverse(multiply(inverse(?), X))
0.83/1.07	= { by lemma 94 }
0.83/1.07	  inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))), X))
0.83/1.07	= { by lemma 85 }
0.83/1.07	  inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(X), X))), X))
0.83/1.07	= { by lemma 67 }
0.83/1.07	  inverse(multiply(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))), X))
0.83/1.07	= { by lemma 91 }
0.83/1.07	  inverse(multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))), X))
0.83/1.07	= { by lemma 92 }
0.83/1.07	  multiply(?, inverse(multiply(multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))), X), ?)))
0.83/1.07	= { by lemma 89 }
0.83/1.07	  multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))), X)), multiply(?, inverse(?)))
0.83/1.07	= { by lemma 85 }
0.83/1.07	  multiply(inverse(multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))), X)), multiply(inverse(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(X), X))))))
0.83/1.07	= { by lemma 5 }
0.83/1.07	  multiply(inverse(X), ?)
0.83/1.07	
0.83/1.07	Lemma 96: multiply(Y, multiply(?, inverse(multiply(inverse(X), multiply(Y, ?))))) = X.
0.83/1.07	Proof:
0.83/1.07	  multiply(Y, multiply(?, inverse(multiply(inverse(X), multiply(Y, ?)))))
0.83/1.07	= { by lemma 2 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, inverse(multiply(inverse(X), multiply(Y, ?)))))
0.83/1.07	= { by lemma 2 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(?, inverse(multiply(inverse(X), multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), ?)))))
0.83/1.07	= { by lemma 78 }
0.83/1.07	  X
0.83/1.07	
0.83/1.07	Lemma 97: multiply(X, multiply(?, inverse(?))) = X.
0.83/1.07	Proof:
0.83/1.07	  multiply(X, multiply(?, inverse(?)))
0.83/1.07	= { by lemma 90 }
0.83/1.07	  multiply(X, multiply(?, inverse(multiply(inverse(X), multiply(X, ?)))))
0.83/1.07	= { by lemma 96 }
0.83/1.07	  X
0.83/1.07	
0.83/1.07	Lemma 98: multiply(multiply(X, inverse(?)), ?) = X.
0.83/1.07	Proof:
0.83/1.07	  multiply(multiply(X, inverse(?)), ?)
0.83/1.07	= { by lemma 86 }
0.83/1.07	  multiply(multiply(?, inverse(multiply(inverse(multiply(X, inverse(?))), ?))), ?)
0.83/1.07	= { by lemma 75 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(?, multiply(X, inverse(?)))), ?)), ?)
0.83/1.07	= { by lemma 71 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(X, inverse(?))), multiply(inverse(multiply(X, inverse(?))), multiply(X, inverse(?))))), ?)
0.83/1.07	= { by lemma 95 }
0.83/1.07	  inverse(multiply(inverse(?), multiply(inverse(multiply(X, inverse(?))), multiply(inverse(multiply(X, inverse(?))), multiply(X, inverse(?))))))
0.83/1.07	= { by lemma 14 }
0.83/1.07	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(X, ?)), multiply(X, ?)))))
0.83/1.07	= { by lemma 27 }
0.83/1.07	  inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.83/1.07	= { by lemma 28 }
0.83/1.07	  multiply(X, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.83/1.07	= { by lemma 31 }
0.83/1.07	  multiply(X, multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.83/1.07	= { by lemma 46 }
0.83/1.07	  multiply(X, multiply(inverse(?), ?))
0.83/1.07	= { by lemma 61 }
0.83/1.07	  multiply(X, multiply(?, inverse(?)))
0.83/1.07	= { by lemma 97 }
0.83/1.07	  X
0.83/1.07	
0.83/1.07	Lemma 99: multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z)))))) = multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(X, multiply(inverse(?), multiply(inverse(?), ?)))))).
0.83/1.07	Proof:
0.83/1.07	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(X, multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.83/1.07	= { by lemma 6 }
0.83/1.07	  multiply(inverse(multiply(Y, Z)), multiply(Y, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(Z), multiply(inverse(Z), Z))))))
0.83/1.07	= { by lemma 3 }
0.83/1.07	  multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))
0.83/1.07	= { by lemma 3 }
0.83/1.07	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.07	= { by lemma 6 }
0.83/1.07	  multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(X, multiply(inverse(?), multiply(inverse(?), ?))))))
0.83/1.07	
0.83/1.07	Lemma 100: multiply(inverse(multiply(Y, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), X)), multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = X.
0.83/1.07	Proof:
0.83/1.07	  multiply(inverse(multiply(Y, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), X)), multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.07	= { by lemma 4 }
0.83/1.07	  multiply(inverse(multiply(Y, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(Y, ?)), multiply(Y, ?))), X)), multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.83/1.07	= { by lemma 56 }
0.90/1.07	  X
0.90/1.07	
0.90/1.07	Lemma 101: multiply(inverse(multiply(Y, ?)), inverse(multiply(X, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))) = multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))).
0.90/1.07	Proof:
0.90/1.07	  multiply(inverse(multiply(Y, ?)), inverse(multiply(X, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.90/1.07	= { by lemma 40 }
0.90/1.07	  multiply(inverse(multiply(Y, ?)), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, inverse(multiply(X, multiply(inverse(?), multiply(inverse(?), ?))))))), multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.90/1.07	= { by lemma 99 }
0.90/1.07	  multiply(inverse(multiply(Y, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))), multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.90/1.07	= { by lemma 100 }
0.90/1.07	  multiply(inverse(multiply(?, ?)), inverse(multiply(X, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
0.90/1.07	
0.90/1.07	Lemma 102: multiply(multiply(?, inverse(?)), multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.90/1.07	Proof:
0.90/1.07	  multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))
0.90/1.07	= { by lemma 61 }
0.90/1.07	  multiply(multiply(?, inverse(?)), multiply(inverse(?), ?))
0.90/1.07	= { by lemma 46 }
0.90/1.07	  multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
0.90/1.07	= { by lemma 31 }
0.90/1.07	  multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))
0.90/1.07	= { by lemma 28 }
0.90/1.07	  inverse(multiply(?, multiply(inverse(multiply(multiply(?, inverse(?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
0.90/1.07	= { by lemma 27 }
0.90/1.07	  inverse(multiply(?, multiply(inverse(multiply(multiply(?, inverse(?)), ?)), multiply(inverse(multiply(multiply(?, inverse(?)), ?)), multiply(multiply(?, inverse(?)), ?)))))
0.90/1.07	= { by lemma 14 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(?))), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(?))), multiply(multiply(?, inverse(?)), inverse(?))))))
0.90/1.07	= { by lemma 62 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(inverse(inverse(?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(?))), multiply(multiply(?, inverse(?)), inverse(?))))))
0.90/1.07	= { by lemma 60 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(?, multiply(inverse(multiply(multiply(?, inverse(?)), inverse(?))), multiply(multiply(?, inverse(?)), inverse(?))))))
0.90/1.07	= { by lemma 62 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(?, multiply(inverse(inverse(?)), multiply(multiply(?, inverse(?)), inverse(?))))))
0.90/1.07	= { by lemma 60 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(?, multiply(?, multiply(multiply(?, inverse(?)), inverse(?))))))
0.90/1.07	= { by lemma 62 }
0.90/1.07	  inverse(multiply(inverse(?), multiply(?, multiply(?, inverse(?)))))
0.90/1.07	= { by lemma 70 }
0.90/1.07	  inverse(multiply(inverse(?), ?))
0.90/1.07	= { by lemma 48 }
0.90/1.07	  multiply(inverse(?), ?)
0.90/1.07	= { by lemma 61 }
1.07/1.25	  multiply(?, inverse(?))
1.07/1.25	
1.07/1.25	Lemma 103: multiply(inverse(multiply(?, multiply(?, ?))), ?) = inverse(multiply(?, ?)).
1.07/1.25	Proof:
1.07/1.25	  multiply(inverse(multiply(?, multiply(?, ?))), ?)
1.07/1.25	= { by lemma 71 }
1.07/1.25	  multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))
1.07/1.25	= { by lemma 72 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?))))
1.07/1.25	= { by lemma 32 }
1.07/1.25	  multiply(?, inverse(multiply(multiply(?, ?), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?))))
1.07/1.25	= { by lemma 31 }
1.07/1.25	  multiply(?, inverse(multiply(multiply(?, ?), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?))))
1.07/1.25	= { by lemma 45 }
1.07/1.25	  multiply(?, inverse(multiply(multiply(?, ?), ?)))
1.07/1.25	= { by axiom 1 (single_axiom) }
1.07/1.25	  multiply(?, inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 41 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 15 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 11 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 65 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 11 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 27 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 25 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 25 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 67 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, multiply(inverse(multiply(?, ?)), ?)))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 64 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), ?))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 60 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), inverse(inverse(?))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 94 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 102 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 69 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?))))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 67 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(?, ?), multiply(?, inverse(?)))), multiply(multiply(?, ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?))))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 5 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), ?)), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 50 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 46 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 31 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 36 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 53 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(multiply(inverse(?), ?), inverse(?))), inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 58 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), multiply(inverse(?), ?))), inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 41 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, inverse(multiply(?, multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 28 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(multiply(inverse(?), ?), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 61 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 31 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 46 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(multiply(?, inverse(?)), multiply(inverse(?), ?)))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 61 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 102 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), multiply(inverse(?), multiply(inverse(?), ?)))))))
1.07/1.25	= { by lemma 59 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), inverse(multiply(inverse(multiply(?, multiply(?, inverse(?)))), inverse(?))))))
1.07/1.25	= { by lemma 66 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(?, inverse(multiply(inverse(multiply(?, inverse(?))), inverse(?)))))))
1.07/1.25	= { by lemma 60 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(inverse(?)), inverse(multiply(inverse(multiply(?, inverse(?))), inverse(?)))))))
1.07/1.25	= { by lemma 64 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(inverse(multiply(?, inverse(?))), inverse(?)))))))
1.07/1.25	= { by lemma 66 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(?, inverse(multiply(inverse(inverse(?)), inverse(?))))))))
1.07/1.25	= { by lemma 60 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(?, inverse(multiply(?, inverse(?))))))))
1.07/1.25	= { by lemma 69 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(?, multiply(?, inverse(?)))))))
1.07/1.25	= { by lemma 70 }
1.07/1.25	  multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))), multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), ?))))
1.07/1.25	= { by lemma 72 }
1.07/1.25	  inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?)))))
1.07/1.25	= { by lemma 65 }
1.07/1.26	  inverse(multiply(?, ?))
1.07/1.26	
1.07/1.26	Lemma 104: multiply(inverse(X), inverse(Y)) = inverse(multiply(Y, X)).
1.07/1.26	Proof:
1.07/1.26	  multiply(inverse(X), inverse(Y))
1.07/1.26	= { by lemma 92 }
1.07/1.26	  multiply(multiply(?, inverse(multiply(X, ?))), inverse(Y))
1.07/1.26	= { by lemma 92 }
1.07/1.26	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(X, ?), ?)))), inverse(Y))
1.07/1.26	= { by lemma 87 }
1.07/1.26	  multiply(multiply(?, multiply(inverse(multiply(?, multiply(X, ?))), ?)), inverse(Y))
1.07/1.26	= { by lemma 77 }
1.07/1.26	  multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(?, inverse(?)))), inverse(Y))
1.07/1.26	= { by lemma 61 }
1.07/1.26	  multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(?), ?))), inverse(Y))
1.07/1.26	= { by lemma 46 }
1.07/1.26	  multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), inverse(Y))
1.07/1.26	= { by lemma 91 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), inverse(Y))
1.07/1.26	= { by lemma 92 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(?, inverse(multiply(Y, ?))))
1.07/1.26	= { by lemma 2 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), ?))))
1.07/1.26	= { by lemma 45 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(multiply(inverse(multiply(?, ?)), multiply(?, ?)), ?)))))
1.07/1.26	= { by lemma 31 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)))))
1.07/1.26	= { by lemma 100 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))), ?)))))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 78 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), multiply(inverse(multiply(?, ?)), Y))), multiply(inverse(?), multiply(inverse(?), ?)))), multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 2 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, ?)), inverse(multiply(Y, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 101 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), inverse(?)), ?)), inverse(multiply(Y, multiply(inverse(multiply(multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), inverse(?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 98 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, multiply(inverse(multiply(multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), inverse(?)), ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 98 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 46 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(inverse(?), ?))))))
1.07/1.26	= { by lemma 61 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), multiply(?, inverse(?)))))))
1.07/1.26	= { by lemma 89 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, multiply(?, inverse(multiply(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), ?)))))))
1.07/1.26	= { by lemma 92 }
1.07/1.26	  multiply(inverse(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))), multiply(inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))), inverse(multiply(Y, inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))))
1.07/1.26	= { by lemma 90 }
1.07/1.26	  inverse(multiply(Y, inverse(multiply(?, multiply(inverse(multiply(X, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))))))
1.07/1.26	= { by lemma 28 }
1.07/1.26	  inverse(multiply(Y, multiply(X, inverse(multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
1.07/1.26	= { by lemma 31 }
1.07/1.26	  inverse(multiply(Y, multiply(X, multiply(inverse(multiply(?, ?)), multiply(?, ?)))))
1.07/1.26	= { by lemma 46 }
1.07/1.26	  inverse(multiply(Y, multiply(X, multiply(inverse(?), ?))))
1.07/1.26	= { by lemma 61 }
1.07/1.26	  inverse(multiply(Y, multiply(X, multiply(?, inverse(?)))))
1.07/1.26	= { by lemma 97 }
1.07/1.26	  inverse(multiply(Y, X))
1.07/1.26	
1.07/1.26	Lemma 105: multiply(inverse(multiply(inverse(multiply(?, ?)), X)), inverse(?)) = multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?)).
1.07/1.26	Proof:
1.07/1.26	  multiply(inverse(multiply(inverse(multiply(?, ?)), X)), inverse(?))
1.07/1.26	= { by lemma 59 }
1.07/1.26	  multiply(inverse(multiply(inverse(multiply(?, ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))
1.07/1.26	= { by lemma 80 }
1.07/1.26	  multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))))
1.07/1.26	= { by lemma 68 }
1.07/1.26	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), multiply(inverse(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?)))), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))))
1.07/1.26	= { by lemma 71 }
1.07/1.26	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))))), ?))
1.07/1.26	= { by lemma 68 }
1.07/1.26	  multiply(inverse(multiply(inverse(?), X)), multiply(inverse(?), ?))
1.07/1.26	
1.07/1.26	Lemma 106: multiply(multiply(?, inverse(?)), X) = X.
1.07/1.26	Proof:
1.07/1.26	  multiply(multiply(?, inverse(?)), X)
1.07/1.26	= { by lemma 86 }
1.07/1.26	  multiply(?, inverse(multiply(inverse(multiply(multiply(?, inverse(?)), X)), ?)))
1.07/1.26	= { by lemma 73 }
1.07/1.27	  X
1.07/1.27	
1.07/1.27	Lemma 107: multiply(inverse(?), multiply(?, X)) = X.
1.07/1.27	Proof:
1.07/1.27	  multiply(inverse(?), multiply(?, X))
1.07/1.27	= { by lemma 93 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(?), multiply(?, X))), multiply(?, inverse(?))))))
1.07/1.27	= { by lemma 61 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(?), multiply(?, X))), multiply(inverse(?), ?)))))
1.07/1.27	= { by lemma 105 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, X))), inverse(?)))))
1.07/1.27	= { by lemma 11 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), ?)), ?)), multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), ?)), X))), inverse(?)))))
1.07/1.27	= { by lemma 18 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), ?)), X)), multiply(inverse(?), multiply(inverse(?), ?)))))))), inverse(?)))))
1.07/1.27	= { by lemma 10 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), multiply(?, multiply(inverse(multiply(inverse(?), ?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(?, inverse(?)))), X)), multiply(inverse(multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?)))))))))), inverse(?)))))
1.07/1.27	= { by lemma 18 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(?, inverse(?)))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(?, inverse(?)))), X))), inverse(?)))))
1.07/1.27	= { by lemma 61 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(?, inverse(?)))), X))), inverse(?)))))
1.07/1.27	= { by lemma 105 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(?, inverse(?)))), X))), inverse(?)))))
1.07/1.27	= { by lemma 61 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(?), ?)), multiply(inverse(?), ?))), X))), inverse(?)))))
1.07/1.27	= { by lemma 105 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), X))), inverse(?)))))
1.07/1.27	= { by lemma 59 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), ?)), multiply(inverse(multiply(inverse(multiply(inverse(multiply(?, ?)), ?)), inverse(?))), X))), multiply(inverse(?), multiply(inverse(?), ?))))))
1.07/1.27	= { by lemma 2 }
1.07/1.27	  multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), X))
1.07/1.27	= { by lemma 106 }
1.07/1.27	  multiply(multiply(?, inverse(?)), X)
1.07/1.27	= { by lemma 106 }
1.07/1.27	  X
1.07/1.27	
1.07/1.27	Lemma 108: multiply(X, inverse(multiply(inverse(Y), X))) = Y.
1.07/1.27	Proof:
1.07/1.27	  multiply(X, inverse(multiply(inverse(Y), X)))
1.07/1.27	= { by lemma 98 }
1.07/1.27	  multiply(X, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))
1.07/1.27	= { by lemma 107 }
1.07/1.27	  multiply(X, multiply(inverse(?), multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))))
1.07/1.27	= { by lemma 86 }
1.07/1.27	  multiply(X, multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))), ?)))))
1.07/1.27	= { by lemma 107 }
1.07/1.27	  multiply(X, inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))), ?)))
1.07/1.27	= { by lemma 90 }
1.07/1.27	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(inverse(multiply(?, ?)), ?))), multiply(multiply(X, multiply(inverse(multiply(?, ?)), ?)), multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))))), ?)))
1.07/1.27	= { by lemma 65 }
1.07/1.27	  multiply(X, inverse(multiply(inverse(multiply(inverse(multiply(X, multiply(inverse(multiply(?, ?)), ?))), multiply(multiply(X, multiply(inverse(multiply(?, ?)), ?)), multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?))))))), multiply(inverse(multiply(?, ?)), multiply(?, multiply(?, ?))))))
1.07/1.27	= { by lemma 74 }
1.07/1.27	  multiply(multiply(X, multiply(inverse(multiply(?, ?)), ?)), multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?)))))
1.07/1.27	= { by lemma 64 }
1.07/1.27	  multiply(multiply(X, inverse(?)), multiply(?, inverse(multiply(inverse(Y), multiply(multiply(X, inverse(?)), ?)))))
1.07/1.27	= { by lemma 96 }
1.07/1.27	  Y
1.07/1.27	
1.07/1.27	Lemma 109: multiply(?, multiply(inverse(multiply(?, multiply(?, ?))), ?)) = multiply(multiply(inverse(?), inverse(?)), ?).
1.07/1.27	Proof:
1.07/1.27	  multiply(?, multiply(inverse(multiply(?, multiply(?, ?))), ?))
1.07/1.27	= { by lemma 71 }
1.07/1.27	  multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))
1.07/1.27	= { by lemma 51 }
1.07/1.27	  multiply(multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 4 }
1.07/1.27	  multiply(multiply(inverse(multiply(multiply(inverse(?), ?), ?)), multiply(multiply(inverse(?), ?), inverse(?))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 49 }
1.07/1.27	  multiply(multiply(inverse(?), multiply(multiply(inverse(?), ?), inverse(?))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 58 }
1.07/1.27	  multiply(multiply(inverse(?), multiply(inverse(?), multiply(inverse(?), ?))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 59 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 94 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(inverse(inverse(?)), multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 60 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(?, multiply(inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?))))), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 94 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(?, multiply(inverse(inverse(?)), multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 60 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(?, multiply(?, multiply(?, multiply(inverse(multiply(?, ?)), multiply(?, inverse(?)))))))
1.07/1.27	= { by lemma 94 }
1.07/1.27	  multiply(multiply(inverse(?), inverse(?)), multiply(?, multiply(?, inverse(?))))
1.07/1.27	= { by lemma 70 }
1.07/1.28	  multiply(multiply(inverse(?), inverse(?)), ?)
1.07/1.28	
1.07/1.28	Lemma 110: inverse(multiply(inverse(Y), X)) = multiply(inverse(X), Y).
1.07/1.28	Proof:
1.07/1.28	  inverse(multiply(inverse(Y), X))
1.07/1.28	= { by lemma 92 }
1.07/1.28	  inverse(multiply(multiply(?, inverse(multiply(Y, ?))), X))
1.07/1.28	= { by lemma 92 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(?, inverse(multiply(multiply(Y, ?), ?)))), X))
1.07/1.28	= { by lemma 87 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(inverse(multiply(?, multiply(Y, ?))), ?)), X))
1.07/1.28	= { by lemma 77 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(?, inverse(?)))), X))
1.07/1.28	= { by lemma 61 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(?), ?))), X))
1.07/1.28	= { by lemma 46 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), X))
1.07/1.28	= { by lemma 104 }
1.07/1.28	  multiply(inverse(X), inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
1.07/1.28	= { by lemma 108 }
1.07/1.28	  multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Y)))), inverse(multiply(?, multiply(inverse(multiply(Y, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
1.07/1.28	= { by lemma 53 }
1.07/1.28	  multiply(inverse(multiply(?, inverse(multiply(inverse(X), Y)))), inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?))))))
1.07/1.28	= { by lemma 104 }
1.07/1.28	  inverse(multiply(multiply(?, multiply(inverse(multiply(?, ?)), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 51 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(?, multiply(?, inverse(?)))), multiply(inverse(multiply(?, multiply(?, inverse(?)))), multiply(?, multiply(?, inverse(?)))))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 70 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), multiply(inverse(multiply(?, multiply(?, inverse(?)))), multiply(?, multiply(?, inverse(?)))))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 61 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(?, inverse(?)))))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 61 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(?, multiply(inverse(?), ?))))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 24 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), multiply(inverse(multiply(?, ?)), multiply(?, ?)))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 46 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), multiply(inverse(?), ?))), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 59 }
1.07/1.28	  inverse(multiply(multiply(multiply(?, inverse(?)), inverse(?)), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 62 }
1.07/1.28	  inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(X), Y)))))
1.07/1.28	= { by lemma 95 }
1.07/1.28	  multiply(inverse(multiply(?, inverse(multiply(inverse(X), Y)))), ?)
1.07/1.28	= { by lemma 87 }
1.07/1.28	  multiply(?, inverse(multiply(inverse(multiply(inverse(X), Y)), ?)))
1.07/1.28	= { by lemma 86 }
1.07/1.28	  multiply(inverse(X), Y)
1.07/1.28	
1.07/1.28	Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
1.07/1.28	Proof:
1.07/1.28	  multiply(multiply(a3, b3), c3)
1.07/1.28	= { by lemma 91 }
1.07/1.28	  multiply(inverse(inverse(multiply(a3, b3))), c3)
1.07/1.28	= { by lemma 110 }
1.07/1.28	  inverse(multiply(inverse(c3), inverse(multiply(a3, b3))))
1.07/1.28	= { by axiom 1 (single_axiom) }
1.07/1.28	  multiply(a3, inverse(multiply(inverse(multiply(inverse(multiply(a3, b3)), inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))))), multiply(inverse(b3), multiply(inverse(b3), b3)))))
1.07/1.28	= { by lemma 108 }
1.07/1.28	  multiply(a3, inverse(multiply(inverse(c3), multiply(inverse(b3), multiply(inverse(b3), b3)))))
1.07/1.28	= { by lemma 110 }
1.07/1.28	  multiply(a3, multiply(inverse(multiply(inverse(b3), multiply(inverse(b3), b3))), c3))
1.07/1.28	= { by lemma 110 }
1.07/1.28	  multiply(a3, multiply(multiply(inverse(multiply(inverse(b3), b3)), b3), c3))
1.07/1.28	= { by lemma 110 }
1.07/1.28	  multiply(a3, multiply(multiply(multiply(inverse(b3), b3), b3), c3))
1.07/1.28	= { by lemma 85 }
1.07/1.28	  multiply(a3, multiply(multiply(multiply(?, inverse(?)), b3), c3))
1.07/1.28	= { by lemma 106 }
1.07/1.28	  multiply(a3, multiply(b3, c3))
1.07/1.28	% SZS output end Proof
1.07/1.28	
1.07/1.28	RESULT: Unsatisfiable (the axioms are contradictory).
1.07/1.28	EOF