0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n004.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 11:47:23 EDT 2019
0.13/0.34	% CPUTime    : 
0.54/0.70	% SZS status Unsatisfiable
0.54/0.70	
0.54/0.71	% SZS output start Proof
0.54/0.71	Take the following subset of the input axioms:
0.70/0.88	  fof(prove_these_axioms_3, negated_conjecture, multiply(multiply(a3, b3), c3)!=multiply(a3, multiply(b3, c3))).
0.70/0.88	  fof(single_axiom, axiom, ![D, A, B, C]: D=multiply(A, inverse(multiply(B, multiply(C, multiply(multiply(inverse(C), inverse(multiply(D, B))), A)))))).
0.70/0.88	
0.70/0.88	Now clausify the problem and encode Horn clauses using encoding 3 of
0.70/0.88	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.70/0.88	We repeatedly replace C & s=t => u=v by the two clauses:
0.70/0.88	  fresh(y, y, x1...xn) = u
0.70/0.88	  C => fresh(s, t, x1...xn) = v
0.70/0.88	where fresh is a fresh function symbol and x1..xn are the free
0.70/0.88	variables of u and v.
0.70/0.88	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.70/0.88	input problem has no model of domain size 1).
0.70/0.88	
0.70/0.88	The encoding turns the above axioms into the following unit equations and goals:
0.70/0.88	
0.70/0.89	Axiom 1 (single_axiom): X = multiply(Y, inverse(multiply(Z, multiply(W, multiply(multiply(inverse(W), inverse(multiply(X, Z))), Y))))).
0.70/0.89	
0.70/0.89	Lemma 2: multiply(Y, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, X))), inverse(V))), multiply(V, multiply(W, Y))))) = X.
0.70/0.89	Proof:
0.70/0.89	  multiply(Y, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, X))), inverse(V))), multiply(V, multiply(W, Y)))))
0.70/0.89	= { by axiom 1 (single_axiom) }
0.70/0.89	  multiply(Y, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, X))), inverse(V))), multiply(V, multiply(multiply(inverse(V), inverse(multiply(X, multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(W, X))), inverse(V)))))), Y)))))
0.70/0.89	= { by axiom 1 (single_axiom) }
0.70/0.89	  X
0.70/0.89	
0.70/0.89	Lemma 3: multiply(V, inverse(multiply(multiply(W, multiply(Y, inverse(U))), multiply(U, multiply(Z, V))))) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W))).
0.70/0.89	Proof:
0.70/0.89	  multiply(V, inverse(multiply(multiply(W, multiply(Y, inverse(U))), multiply(U, multiply(Z, V)))))
0.70/0.89	= { by axiom 1 (single_axiom) }
0.70/0.89	  multiply(V, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W)))))), inverse(U))), multiply(U, multiply(Z, V)))))
0.70/0.89	= { by lemma 2 }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W)))
0.70/0.89	
0.70/0.89	Lemma 4: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X))) = Z.
0.70/0.89	Proof:
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X)))
0.70/0.89	= { by lemma 3 }
0.70/0.89	  multiply(?, inverse(multiply(multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(?))), multiply(?, multiply(Y, ?)))))
0.70/0.89	= { by lemma 2 }
0.70/0.89	  Z
0.70/0.89	
0.70/0.89	Lemma 5: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(Z)), W))), inverse(V))) = inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W)))).
0.70/0.89	Proof:
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(Z)), W))), inverse(V)))
0.70/0.89	= { by axiom 1 (single_axiom) }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(multiply(W, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W))))))), W))), inverse(V)))
0.70/0.89	= { by lemma 4 }
0.70/0.89	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W))))
0.70/0.89	
0.70/0.89	Lemma 6: inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X)))) = Y.
0.70/0.89	Proof:
0.70/0.89	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X))))
0.70/0.89	= { by lemma 5 }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(X, Y))), X))), inverse(?)))
0.70/0.89	= { by lemma 4 }
0.70/0.89	  Y
0.70/0.89	
0.70/0.89	Lemma 7: inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), Y)))) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?)).
0.70/0.89	Proof:
0.70/0.89	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), Y))))
0.70/0.89	= { by lemma 5 }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))), inverse(X)), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?))))))
0.70/0.89	= { by lemma 6 }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?))))))
0.70/0.89	= { by lemma 6 }
0.70/0.89	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?))
0.70/0.89	
0.70/0.89	Lemma 8: multiply(Y, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?))) = X.
0.70/0.89	Proof:
0.70/0.89	  multiply(Y, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?)))
0.70/0.89	= { by lemma 7 }
0.70/0.89	  multiply(Y, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), Y)))))
0.70/0.89	= { by axiom 1 (single_axiom) }
0.70/0.90	  X
0.70/0.90	
0.70/0.90	Lemma 9: multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W))) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W))).
0.70/0.90	Proof:
0.70/0.90	  multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W)))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(V, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, Z))), inverse(W)))))), inverse(U))), multiply(U, multiply(Z, V)))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(V, inverse(multiply(multiply(W, multiply(Y, inverse(U))), multiply(U, multiply(Z, V)))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(V, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W)))))), inverse(U))), multiply(U, multiply(Z, V)))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, Z))), inverse(W)))
0.70/0.90	
0.70/0.90	Lemma 10: multiply(X, multiply(multiply(inverse(X), inverse(Z)), inverse(Y))) = multiply(?, multiply(multiply(inverse(?), inverse(Z)), inverse(Y))).
0.70/0.90	Proof:
0.70/0.90	  multiply(X, multiply(multiply(inverse(X), inverse(Z)), inverse(Y)))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(X, multiply(multiply(inverse(X), inverse(multiply(U, inverse(multiply(V, multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, V))), U))))))), inverse(Y)))
0.70/0.90	= { by lemma 9 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(U, inverse(multiply(V, multiply(W, multiply(multiply(inverse(W), inverse(multiply(Z, V))), U))))))), inverse(Y)))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(Z)), inverse(Y)))
0.70/0.90	
0.70/0.90	Lemma 11: multiply(W, multiply(multiply(inverse(W), inverse(X)), Z)) = multiply(?, multiply(multiply(inverse(?), inverse(X)), Z)).
0.70/0.90	Proof:
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), inverse(X)), Z))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), inverse(X)), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Y, Z), ?))), Y))))))
0.70/0.90	= { by lemma 10 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Y, Z), ?))), Y))))))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(X)), Z))
0.70/0.90	
0.70/0.90	Lemma 12: inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W)))) = inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W)))).
0.70/0.90	Proof:
0.70/0.90	  inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W))))
0.70/0.90	= { by lemma 4 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(multiply(W, inverse(multiply(X, multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, X))), W))))))), W))), inverse(V)))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(Z)), W))), inverse(V)))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(V), inverse(multiply(W, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W))))))), W))), inverse(V)))
0.70/0.90	= { by lemma 4 }
0.70/0.90	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), W))))
0.70/0.90	
0.70/0.90	Lemma 13: multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(X, inverse(Y))))))))), inverse(W))) = Z.
0.70/0.90	Proof:
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(X, inverse(Y))))))))), inverse(W)))
0.70/0.90	= { by lemma 3 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(W, multiply(X, inverse(Y))), multiply(Y, multiply(multiply(inverse(Y), inverse(multiply(Z, multiply(W, multiply(X, inverse(Y)))))), ?)))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  Z
0.70/0.90	
0.70/0.90	Lemma 14: multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))) = multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?))))).
0.70/0.90	Proof:
0.70/0.90	  multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(W, multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))))), inverse(Z))), multiply(Z, multiply(W, ?)))))
0.70/0.90	= { by lemma 13 }
0.70/0.90	  multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?)))))
0.70/0.90	
0.70/0.90	Lemma 15: multiply(inverse(Y), inverse(multiply(multiply(?, inverse(multiply(W, multiply(Y, multiply(X, ?))))), W))) = X.
0.70/0.90	Proof:
0.70/0.90	  multiply(inverse(Y), inverse(multiply(multiply(?, inverse(multiply(W, multiply(Y, multiply(X, ?))))), W)))
0.70/0.90	= { by lemma 14 }
0.70/0.90	  multiply(inverse(Y), inverse(multiply(multiply(inverse(?), inverse(multiply(W, multiply(Y, multiply(X, inverse(?)))))), W)))
0.70/0.90	= { by lemma 13 }
0.70/0.90	  multiply(inverse(Y), inverse(multiply(multiply(inverse(?), inverse(multiply(W, multiply(Y, multiply(X, inverse(?)))))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(inverse(?), inverse(multiply(W, multiply(Y, multiply(X, inverse(?))))))))), inverse(Y))))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  X
0.70/0.90	
0.70/0.90	Lemma 16: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, inverse(multiply(V, X))), V))), W)) = X.
0.70/0.90	Proof:
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, inverse(multiply(V, X))), V))), W))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, inverse(multiply(V, X))), V))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, W), ?))), ?))))))
0.70/0.90	= { by lemma 3 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, W), ?))), ?))), multiply(multiply(W, inverse(multiply(V, X))), inverse(?))), multiply(?, multiply(V, ?)))))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, W), ?))), ?))), multiply(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, W), ?))), ?)))), inverse(multiply(V, X))), inverse(?))), multiply(?, multiply(V, ?)))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  X
0.70/0.90	
0.70/0.90	Lemma 17: multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(X, Y))), X))) = multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?))).
0.70/0.90	Proof:
0.70/0.90	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(X, Y))), X)))
0.70/0.90	= { by lemma 15 }
0.70/0.90	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(X, Y))), X))), ?))))), Z)))
0.70/0.90	= { by lemma 16 }
0.70/0.90	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(Z, Y))), Z)))
0.70/0.90	= { by lemma 16 }
0.70/0.90	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?))), ?))))), Z)))
0.70/0.90	= { by lemma 15 }
0.70/0.90	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?)))
0.70/0.90	
0.70/0.90	Lemma 18: inverse(multiply(multiply(?, inverse(multiply(X, Y))), X)) = inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?)).
0.70/0.90	Proof:
0.70/0.90	  inverse(multiply(multiply(?, inverse(multiply(X, Y))), X))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(X, Y))), X))))), inverse(V))), multiply(V, multiply(inverse(?), Z)))))
0.70/0.90	= { by lemma 17 }
0.70/0.90	  multiply(Z, inverse(multiply(multiply(W, multiply(multiply(inverse(W), inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?))))), inverse(V))), multiply(V, multiply(inverse(?), Z)))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?))
0.70/0.90	
0.70/0.90	Lemma 19: multiply(multiply(?, inverse(multiply(X, Y))), X) = multiply(multiply(?, inverse(multiply(?, Y))), ?).
0.70/0.90	Proof:
0.70/0.90	  multiply(multiply(?, inverse(multiply(X, Y))), X)
0.70/0.90	= { by lemma 8 }
0.70/0.90	  multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(multiply(X, Y))), X))), Z))), ?)))
0.70/0.90	= { by lemma 18 }
0.70/0.90	  multiply(Z, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, Y))), ?))), Z))), ?)))
0.70/0.90	= { by lemma 8 }
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, Y))), ?)
0.70/0.90	
0.70/0.90	Lemma 20: multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), inverse(Y)))) = multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), ?).
0.70/0.90	Proof:
0.70/0.90	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), inverse(Y))))
0.70/0.90	= { by lemma 8 }
0.70/0.90	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), inverse(Y)))))), ?))), ?)))
0.70/0.90	= { by lemma 12 }
0.70/0.90	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?)))))))), inverse(Y)))))), ?))), ?)))
0.70/0.90	= { by lemma 8 }
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?)))))))), inverse(Y))))
0.70/0.90	= { by lemma 3 }
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), multiply(?, inverse(multiply(multiply(Y, multiply(X, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), ?))))))
0.70/0.90	= { by lemma 14 }
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), multiply(?, inverse(multiply(multiply(Y, multiply(X, inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(Y, multiply(X, inverse(?)))))), ?))))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(X, ?))))), ?)
0.70/0.90	
0.70/0.90	Lemma 21: multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(X)), ?))))), ?) = X.
0.70/0.90	Proof:
0.70/0.90	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(X)), ?))))), ?)
0.70/0.90	= { by lemma 20 }
0.70/0.90	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(X)), ?))), inverse(?))))
0.70/0.90	= { by lemma 5 }
0.70/0.90	  multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), ?)))))
0.70/0.90	= { by axiom 1 (single_axiom) }
0.70/0.90	  X
0.70/0.90	
0.70/0.90	Lemma 22: multiply(W, multiply(multiply(inverse(W), Y), inverse(Z))) = multiply(?, multiply(multiply(inverse(?), Y), inverse(Z))).
0.70/0.90	Proof:
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), Y), inverse(Z)))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X))))), inverse(Z)))
0.70/0.90	= { by lemma 9 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X))))), inverse(Z)))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), Y), inverse(Z)))
0.70/0.90	
0.70/0.90	Lemma 23: multiply(W, multiply(multiply(inverse(W), X), Z)) = multiply(?, multiply(multiply(inverse(?), X), Z)).
0.70/0.90	Proof:
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), X), Z))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(W, multiply(multiply(inverse(W), X), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Y, Z), ?))), Y))))))
0.70/0.90	= { by lemma 22 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), X), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Y, Z), ?))), Y))))))
0.70/0.90	= { by lemma 6 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), X), Z))
0.70/0.90	
0.70/0.90	Lemma 24: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Z)), inverse(Y)))), ?)) = inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(Z, ?))))), ?)).
0.70/0.90	Proof:
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Z)), inverse(Y)))), ?))
0.70/0.90	= { by lemma 7 }
0.70/0.90	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), inverse(Y)))))
0.70/0.90	= { by lemma 5 }
0.70/0.90	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(Z)), inverse(Y)))), inverse(?)))
0.70/0.90	= { by lemma 3 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(Z)), inverse(?))), multiply(?, multiply(inverse(Y), ?)))))
0.70/0.90	= { by lemma 15 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(Y), inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(Z, ?))))), ?))))), inverse(?))), multiply(?, multiply(inverse(Y), ?)))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, multiply(Z, ?))))), ?))
0.70/0.90	
0.70/0.90	Lemma 25: multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V))))) = multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?))))).
0.70/0.90	Proof:
0.70/0.90	  multiply(V, inverse(multiply(Y, multiply(Z, multiply(W, V)))))
0.70/0.90	= { by lemma 13 }
0.70/0.90	  multiply(V, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(W, multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))))), inverse(Z))), multiply(Z, multiply(W, V)))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))
0.70/0.90	= { by lemma 2 }
0.70/0.90	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(W, multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X))))))))), inverse(Z))), multiply(Z, multiply(W, ?)))))
0.70/0.90	= { by lemma 13 }
0.70/0.91	  multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?)))))
0.70/0.91	
0.70/0.91	Lemma 26: inverse(multiply(multiply(?, multiply(X, ?)), multiply(?, multiply(multiply(inverse(?), inverse(Y)), ?)))) = multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?)).
0.70/0.91	Proof:
0.70/0.91	  inverse(multiply(multiply(?, multiply(X, ?)), multiply(?, multiply(multiply(inverse(?), inverse(Y)), ?))))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(multiply(?, multiply(X, ?)), multiply(?, multiply(multiply(inverse(?), inverse(Y)), ?))))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by axiom 1 (single_axiom) }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Y)), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?)))))), ?)), multiply(?, multiply(multiply(inverse(?), inverse(Y)), ?))))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by lemma 7 }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, ?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?))))))), multiply(?, multiply(multiply(inverse(?), inverse(Y)), ?))))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by axiom 1 (single_axiom) }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, ?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?))))))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, ?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?)))))))))), ?))))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by axiom 1 (single_axiom) }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(X, multiply(?, inverse(Y))))), inverse(?))
0.70/0.91	
0.70/0.91	Lemma 27: multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X)) = inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), ?)))).
0.70/0.91	Proof:
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(multiply(Y, Z))), Y))), inverse(X))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by lemma 4 }
0.70/0.91	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(Z)), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.91	= { by lemma 3 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(Z)), ?))), inverse(?)))
0.70/0.91	= { by lemma 5 }
0.70/0.91	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Z, ?))), ?))))
0.70/0.91	
0.70/0.91	Lemma 28: inverse(multiply(multiply(?, X), multiply(?, multiply(inverse(?), ?)))) = multiply(multiply(inverse(?), inverse(X)), inverse(?)).
0.70/0.91	Proof:
0.70/0.91	  inverse(multiply(multiply(?, X), multiply(?, multiply(inverse(?), ?))))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))))), multiply(?, multiply(inverse(?), ?))))
0.70/0.91	= { by lemma 16 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))))), multiply(?, multiply(inverse(?), ?))))))), inverse(?)))), ?))
0.70/0.91	= { by lemma 24 }
0.70/0.91	  inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))))), multiply(?, multiply(inverse(?), ?))))), ?))))), ?))
0.70/0.91	= { by lemma 7 }
0.70/0.91	  inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))), ?))), multiply(?, multiply(inverse(?), ?))))))))), ?))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))), ?))), multiply(?, multiply(inverse(?), ?))))))))), ?))), ?))), ?))))
0.70/0.91	= { by lemma 27 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(?), multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))), ?))), multiply(?, multiply(inverse(?), ?))))))))), ?)))))), inverse(?)))), inverse(?))
0.70/0.91	= { by lemma 26 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(inverse(multiply(multiply(?, multiply(inverse(?), ?)), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))), ?))), multiply(?, multiply(inverse(?), ?))))))))), ?))), ?)))))), inverse(?))
0.70/0.91	= { by lemma 16 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(inverse(multiply(multiply(?, multiply(inverse(?), ?)), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))), ?))), multiply(?, multiply(inverse(?), ?)))))))))), inverse(?))
0.70/0.91	= { by axiom 1 (single_axiom) }
0.70/0.91	  multiply(multiply(inverse(?), inverse(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))), inverse(?))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(X)), inverse(?))
0.70/0.91	
0.70/0.91	Lemma 29: multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(?))), multiply(?, X)))) = inverse(?).
0.70/0.91	Proof:
0.70/0.91	  multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(?))), multiply(?, X))))
0.70/0.91	= { by lemma 28 }
0.70/0.91	  multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(?, X), multiply(?, multiply(inverse(?), ?))))), multiply(?, X))))
0.70/0.91	= { by lemma 15 }
0.70/0.91	  inverse(?)
0.70/0.91	
0.70/0.91	Lemma 30: multiply(multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(?))), multiply(?, X)) = multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?).
0.70/0.91	Proof:
0.70/0.91	  multiply(multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(?))), multiply(?, X))
0.70/0.91	= { by lemma 21 }
0.70/0.91	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(X)), inverse(?))), multiply(?, X)))), ?))))), ?)
0.70/0.91	= { by lemma 29 }
0.70/0.91	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)
0.70/0.91	
0.70/0.91	Lemma 31: multiply(X, inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))) = X.
0.70/0.91	Proof:
0.70/0.91	  multiply(X, inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))
0.70/0.91	= { by lemma 30 }
0.70/0.91	  multiply(X, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, X))), inverse(?))), multiply(?, multiply(?, X)))))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  X
0.70/0.91	
0.70/0.91	Lemma 32: multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))), U)) = multiply(X, multiply(multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?))))), U)).
0.70/0.91	Proof:
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))), U))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, U), ?))), ?))))))
0.70/0.91	= { by lemma 9 }
0.70/0.91	  multiply(X, multiply(multiply(inverse(X), inverse(multiply(Y, multiply(Z, multiply(W, inverse(X)))))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, U), ?))), ?))))))
0.70/0.91	= { by lemma 14 }
0.70/0.91	  multiply(X, multiply(multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?))))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, U), ?))), ?))))))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(X, multiply(multiply(?, inverse(multiply(Y, multiply(Z, multiply(W, ?))))), U))
0.70/0.91	
0.70/0.91	Lemma 33: multiply(X, multiply(inverse(X), Z)) = multiply(?, multiply(inverse(?), Z)).
0.70/0.91	Proof:
0.70/0.91	  multiply(X, multiply(inverse(X), Z))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(X, multiply(multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, inverse(X)))), inverse(?))), multiply(?, multiply(Y, ?))))), Z))
0.70/0.91	= { by lemma 32 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, inverse(X)))), inverse(?))), multiply(?, multiply(Y, inverse(X)))))), Z))
0.70/0.91	= { by lemma 29 }
0.70/0.91	  multiply(?, multiply(inverse(?), Z))
0.70/0.91	
0.70/0.91	Lemma 34: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.70/0.91	Proof:
0.70/0.91	  multiply(X, inverse(X))
0.70/0.91	= { by lemma 31 }
0.70/0.91	  multiply(X, multiply(inverse(X), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))
0.70/0.91	= { by lemma 33 }
0.70/0.91	  multiply(?, multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))
0.70/0.91	= { by lemma 15 }
0.70/0.91	  multiply(?, inverse(?))
0.70/0.91	
0.70/0.91	Lemma 35: multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?) = multiply(?, inverse(?)).
0.70/0.91	Proof:
0.70/0.91	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)
0.70/0.91	= { by lemma 31 }
0.70/0.91	  multiply(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))
0.70/0.91	= { by lemma 34 }
0.70/0.91	  multiply(?, inverse(?))
0.70/0.91	
0.70/0.91	Lemma 36: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X)) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?)).
0.70/0.91	Proof:
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X))
0.70/0.91	= { by lemma 16 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Z, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, Y), ?))), X))))), ?))), Z))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Z, Y), ?))), Z))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Z, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))))), ?))), Z))
0.70/0.91	= { by lemma 16 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))
0.70/0.91	
0.70/0.91	Lemma 37: multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))) = inverse(?).
0.70/0.91	Proof:
0.70/0.91	  multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?)))
0.70/0.91	= { by lemma 7 }
0.70/0.91	  multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, ?))), ?)))))
0.70/0.91	= { by lemma 27 }
0.70/0.91	  multiply(inverse(?), multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), multiply(?, ?)))), inverse(?)))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(inverse(?), multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))))))), inverse(?)))
0.70/0.91	= { by lemma 26 }
0.70/0.91	  multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)), multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?))))), ?)))))
0.70/0.91	= { by lemma 36 }
0.70/0.91	  multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), ?), ?))), inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?))))), ?)))))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), ?), ?))), inverse(?))), multiply(?, multiply(multiply(inverse(?), ?), ?)))))
0.70/0.91	= { by lemma 29 }
0.70/0.91	  inverse(?)
0.70/0.91	
0.70/0.91	Lemma 38: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Z, inverse(X)), Y))), Z)) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?)).
0.70/0.91	Proof:
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(Z, inverse(X)), Y))), Z))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, Z), ?))), W)))), inverse(X)), Y))), Z))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, Z), ?))), W)))), inverse(X)), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, Z), ?))), W))))))
0.70/0.91	= { by lemma 5 }
0.70/0.91	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), Y))))
0.70/0.91	= { by lemma 5 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, ?), ?))), W)))), inverse(X)), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, ?), ?))), W))))))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(W, ?), ?))), W))))))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), Y))), ?))
0.70/0.91	
0.70/0.91	Lemma 39: multiply(multiply(inverse(?), inverse(multiply(multiply(X, inverse(Y)), Z))), X) = multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Y)), Z))), ?).
0.70/0.91	Proof:
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(X, inverse(Y)), Z))), X)
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(X, inverse(Y)), Z))), X)))), inverse(U))), multiply(U, multiply(?, W)))))
0.70/0.91	= { by lemma 38 }
0.70/0.91	  multiply(W, inverse(multiply(multiply(V, multiply(multiply(inverse(V), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Y)), Z))), ?)))), inverse(U))), multiply(U, multiply(?, W)))))
0.70/0.91	= { by lemma 2 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(Y)), Z))), ?)
0.70/0.91	
0.70/0.91	Lemma 40: multiply(multiply(inverse(?), inverse(multiply(inverse(?), X))), inverse(?)) = multiply(multiply(inverse(?), inverse(multiply(?, X))), ?).
0.70/0.91	Proof:
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(inverse(?), X))), inverse(?))
0.70/0.91	= { by lemma 37 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))), X))), inverse(?))
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))), ?))), ?))))), X))), inverse(?))
0.70/0.91	= { by lemma 39 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))), ?))), ?))))), X))), ?)
0.70/0.91	= { by lemma 6 }
0.70/0.91	  multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))), X))), ?)
0.70/0.91	= { by lemma 8 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, X))), ?)
0.70/0.92	
0.70/0.92	Lemma 41: multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(X), Y))), inverse(X))) = multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?)).
0.70/0.92	Proof:
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(X), Y))), inverse(X)))
0.70/0.92	= { by lemma 3 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(X, multiply(inverse(X), inverse(?))), multiply(?, multiply(Y, ?)))))
0.70/0.92	= { by lemma 33 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(inverse(?), inverse(?))), multiply(?, multiply(Y, ?)))))
0.70/0.92	= { by lemma 3 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), Y))), inverse(?)))
0.70/0.92	= { by lemma 40 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?))
0.70/0.92	
0.70/0.92	Lemma 42: multiply(multiply(inverse(?), inverse(multiply(inverse(X), Y))), inverse(X)) = multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(inverse(X), Y))), inverse(X))
0.70/0.92	= { by lemma 2 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(X), Y))), inverse(X))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 41 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?)))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 2 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?)
0.70/0.92	
0.70/0.92	Lemma 43: multiply(multiply(inverse(?), inverse(?)), ?) = multiply(multiply(?, inverse(?)), inverse(?)).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(inverse(?), inverse(?)), ?)
0.70/0.92	= { by lemma 6 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))))), ?)
0.70/0.92	= { by lemma 40 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))))), inverse(?))
0.70/0.92	= { by lemma 37 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(inverse(?))), inverse(?))
0.70/0.92	= { by lemma 34 }
0.70/0.92	  multiply(multiply(?, inverse(?)), inverse(?))
0.70/0.92	
0.70/0.92	Lemma 44: multiply(multiply(inverse(?), inverse(X)), X) = multiply(multiply(?, inverse(?)), inverse(?)).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(inverse(?), inverse(X)), X)
0.70/0.92	= { by lemma 6 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))), X)
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), X)
0.70/0.92	= { by lemma 6 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))
0.70/0.92	= { by lemma 42 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), ?)
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(?)), ?)
0.70/0.92	= { by lemma 43 }
0.70/0.92	  multiply(multiply(?, inverse(?)), inverse(?))
0.70/0.92	
0.70/0.92	Lemma 45: multiply(X, inverse(multiply(?, inverse(?)))) = X.
0.70/0.92	Proof:
0.70/0.92	  multiply(X, inverse(multiply(?, inverse(?))))
0.70/0.92	= { by lemma 35 }
0.70/0.92	  multiply(X, inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))
0.70/0.92	= { by lemma 31 }
0.70/0.92	  X
0.70/0.92	
0.70/0.92	Lemma 46: multiply(multiply(?, inverse(?)), inverse(?)) = multiply(inverse(?), multiply(?, inverse(?))).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(?)), inverse(?))
0.70/0.92	= { by lemma 44 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(inverse(?), multiply(?, inverse(?)))
0.70/0.92	
0.70/0.92	Lemma 47: multiply(multiply(inverse(?), inverse(multiply(?, inverse(X)))), ?) = multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), X).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(X)))), ?)
0.70/0.92	= { by lemma 6 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))))), ?)
0.70/0.92	= { by lemma 42 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))), inverse(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))
0.70/0.92	= { by lemma 34 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))
0.70/0.92	= { by lemma 6 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), X)
0.70/0.92	
0.70/0.92	Lemma 48: multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), X))), ?))) = inverse(?).
0.70/0.92	Proof:
0.70/0.92	  multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), X))), ?)))
0.70/0.92	= { by lemma 7 }
0.70/0.92	  multiply(inverse(?), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), X)))))
0.70/0.92	= { by lemma 4 }
0.70/0.92	  multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(X, ?))), X))), inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(X, ?))), X)))))
0.70/0.92	= { by lemma 29 }
0.70/0.92	  inverse(?)
0.70/0.92	
0.70/0.92	Lemma 49: multiply(multiply(?, inverse(inverse(?))), inverse(?)) = multiply(multiply(?, inverse(?)), ?).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(inverse(?))), inverse(?))
0.70/0.92	= { by lemma 37 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))))), inverse(?))
0.70/0.92	= { by lemma 19 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))))), ?)
0.70/0.92	= { by lemma 21 }
0.70/0.92	  multiply(multiply(?, inverse(?)), ?)
0.70/0.92	
0.70/0.92	Lemma 50: multiply(multiply(?, inverse(X)), X) = multiply(multiply(?, inverse(?)), ?).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(X)), X)
0.70/0.92	= { by lemma 21 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), X))), ?))))), ?)
0.70/0.92	= { by lemma 19 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(inverse(?), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(X)), X))), ?))))), inverse(?))
0.70/0.92	= { by lemma 48 }
0.70/0.92	  multiply(multiply(?, inverse(inverse(?))), inverse(?))
0.70/0.92	= { by lemma 49 }
0.70/0.92	  multiply(multiply(?, inverse(?)), ?)
0.70/0.92	
0.70/0.92	Lemma 51: multiply(multiply(?, inverse(?)), ?) = multiply(?, multiply(?, inverse(?))).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(?)), ?)
0.70/0.92	= { by lemma 50 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(?, multiply(?, inverse(?)))
0.70/0.92	
0.70/0.92	Lemma 52: inverse(inverse(multiply(?, inverse(?)))) = multiply(?, inverse(?)).
0.70/0.92	Proof:
0.70/0.92	  inverse(inverse(multiply(?, inverse(?))))
0.70/0.92	= { by lemma 2 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(inverse(multiply(?, inverse(?))))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(inverse(multiply(?, inverse(?))))), inverse(multiply(?, inverse(?)))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 50 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 51 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, inverse(?))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.92	= { by lemma 2 }
0.70/0.92	  multiply(?, inverse(?))
0.70/0.92	
0.70/0.92	Lemma 53: multiply(inverse(?), multiply(?, inverse(?))) = inverse(?).
0.70/0.92	Proof:
0.70/0.92	  multiply(inverse(?), multiply(?, inverse(?)))
0.70/0.92	= { by lemma 46 }
0.70/0.92	  multiply(multiply(?, inverse(?)), inverse(?))
0.70/0.92	= { by lemma 44 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))
0.70/0.92	= { by lemma 47 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(?, inverse(?)))))), ?)
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, inverse(?)))), inverse(multiply(?, inverse(?)))))), ?)
0.70/0.92	= { by lemma 39 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), inverse(multiply(?, inverse(?)))))), inverse(?))
0.70/0.92	= { by lemma 34 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, inverse(?))), inverse(inverse(multiply(?, inverse(?))))))), inverse(multiply(?, inverse(?)))))), inverse(?))
0.70/0.92	= { by lemma 52 }
0.70/0.92	  multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(?))))), inverse(multiply(?, inverse(?)))))), inverse(?))
0.70/0.92	= { by lemma 27 }
0.70/0.92	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), ?))))
0.70/0.92	= { by lemma 6 }
0.70/0.92	  inverse(?)
0.70/0.92	
0.70/0.92	Lemma 54: inverse(multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.70/0.92	Proof:
0.70/0.92	  inverse(multiply(?, inverse(?)))
0.70/0.92	= { by lemma 35 }
0.70/0.92	  inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))
0.70/0.92	= { by lemma 24 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(inverse(?))), inverse(?)))), ?))
0.70/0.92	= { by lemma 7 }
0.70/0.92	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), ?))), inverse(?)))))
0.70/0.92	= { by lemma 5 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(inverse(?))), inverse(?)))), inverse(?)))
0.70/0.92	= { by lemma 3 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(inverse(?))), inverse(?))), multiply(?, multiply(inverse(?), ?)))))
0.70/0.92	= { by lemma 53 }
0.70/0.92	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), multiply(?, inverse(?))))), inverse(?))), multiply(?, multiply(inverse(?), ?)))))
0.70/0.92	= { by lemma 2 }
0.70/0.92	  multiply(?, inverse(?))
0.70/0.92	
0.70/0.92	Lemma 55: multiply(X, multiply(?, inverse(?))) = X.
0.70/0.92	Proof:
0.70/0.92	  multiply(X, multiply(?, inverse(?)))
0.70/0.92	= { by lemma 54 }
0.70/0.92	  multiply(X, inverse(multiply(?, inverse(?))))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  X
0.70/0.92	
0.70/0.92	Lemma 56: multiply(multiply(?, inverse(multiply(?, multiply(inverse(X), Y)))), ?) = multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), Y)))), X).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(inverse(X), Y)))), ?)
0.70/0.92	= { by lemma 19 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(X, multiply(inverse(X), Y)))), X)
0.70/0.92	= { by lemma 33 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), Y)))), X)
0.70/0.92	
0.70/0.92	Lemma 57: multiply(multiply(?, inverse(multiply(?, inverse(X)))), ?) = multiply(multiply(?, inverse(multiply(?, inverse(?)))), X).
0.70/0.92	Proof:
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, inverse(X)))), ?)
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(inverse(X), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))))), ?)
0.70/0.92	= { by lemma 56 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))))), X)
0.70/0.92	= { by lemma 15 }
0.70/0.92	  multiply(multiply(?, inverse(multiply(?, inverse(?)))), X)
0.70/0.92	
0.70/0.92	Lemma 58: multiply(?, multiply(inverse(?), inverse(inverse(X)))) = multiply(X, multiply(?, inverse(?))).
0.70/0.92	Proof:
0.70/0.92	  multiply(?, multiply(inverse(?), inverse(inverse(X))))
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(?, multiply(inverse(?), multiply(inverse(inverse(X)), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))))
0.70/0.92	= { by lemma 33 }
0.70/0.92	  multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))))
0.70/0.92	= { by lemma 33 }
0.70/0.92	  multiply(X, multiply(?, multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))))
0.70/0.92	= { by lemma 15 }
0.70/0.92	  multiply(X, multiply(?, inverse(?)))
0.70/0.92	
0.70/0.92	Lemma 59: multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), X))) = X.
0.70/0.92	Proof:
0.70/0.92	  multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), X)))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(multiply(?, inverse(?)), X)))
0.70/0.92	= { by lemma 54 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(inverse(multiply(?, inverse(?))), X)))
0.70/0.92	= { by lemma 47 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(inverse(multiply(?, inverse(?))), X))))), ?))
0.70/0.92	= { by lemma 41 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), inverse(multiply(inverse(multiply(?, inverse(?))), X))))), inverse(?)))
0.70/0.92	= { by lemma 45 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, inverse(?))), X))), inverse(multiply(?, inverse(?)))))), inverse(?)))
0.70/0.92	= { by lemma 4 }
0.70/0.92	  X
0.70/0.92	
0.70/0.92	Lemma 60: multiply(?, multiply(multiply(inverse(?), inverse(inverse(X))), Y)) = multiply(X, multiply(multiply(?, inverse(?)), Y)).
0.70/0.92	Proof:
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), inverse(inverse(X))), Y))
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(?, multiply(multiply(inverse(?), multiply(inverse(inverse(X)), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))), Y))
0.70/0.92	= { by lemma 23 }
0.70/0.92	  multiply(X, multiply(multiply(inverse(X), multiply(inverse(inverse(X)), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))), Y))
0.70/0.92	= { by lemma 33 }
0.70/0.92	  multiply(X, multiply(multiply(?, multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)))), Y))
0.70/0.92	= { by lemma 15 }
0.70/0.92	  multiply(X, multiply(multiply(?, inverse(?)), Y))
0.70/0.92	
0.70/0.92	Lemma 61: inverse(inverse(?)) = ?.
0.70/0.92	Proof:
0.70/0.92	  inverse(inverse(?))
0.70/0.92	= { by lemma 59 }
0.70/0.92	  multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), inverse(inverse(?)))))
0.70/0.92	= { by lemma 60 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(inverse(inverse(?)))), inverse(inverse(?)))))
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(inverse(?)), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), inverse(inverse(?)))))
0.70/0.92	= { by lemma 41 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), ?)))
0.70/0.92	= { by lemma 41 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?))))), inverse(?))))
0.70/0.92	= { by lemma 31 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(inverse(?))), inverse(?))))
0.70/0.92	= { by lemma 60 }
0.70/0.92	  multiply(?, multiply(?, multiply(multiply(?, inverse(?)), inverse(?))))
0.70/0.92	= { by lemma 46 }
0.70/0.92	  multiply(?, multiply(?, multiply(inverse(?), multiply(?, inverse(?)))))
0.70/0.92	= { by lemma 53 }
0.70/0.92	  multiply(?, multiply(?, inverse(?)))
0.70/0.92	= { by lemma 55 }
0.70/0.92	  ?
0.70/0.92	
0.70/0.92	Lemma 62: multiply(inverse(?), ?) = multiply(?, inverse(?)).
0.70/0.92	Proof:
0.70/0.92	  multiply(inverse(?), ?)
0.70/0.92	= { by lemma 61 }
0.70/0.92	  multiply(inverse(?), inverse(inverse(?)))
0.70/0.92	= { by lemma 34 }
0.70/0.92	  multiply(?, inverse(?))
0.70/0.92	
0.70/0.92	Lemma 63: multiply(inverse(?), inverse(multiply(X, inverse(?)))) = multiply(?, inverse(multiply(X, ?))).
0.70/0.92	Proof:
0.70/0.92	  multiply(inverse(?), inverse(multiply(X, inverse(?))))
0.70/0.92	= { by lemma 59 }
0.70/0.92	  multiply(inverse(?), inverse(multiply(X, multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), inverse(?)))))))
0.70/0.92	= { by lemma 46 }
0.70/0.92	  multiply(inverse(?), inverse(multiply(X, multiply(?, multiply(inverse(?), multiply(inverse(?), multiply(?, inverse(?))))))))
0.70/0.92	= { by lemma 53 }
0.70/0.92	  multiply(inverse(?), inverse(multiply(X, multiply(?, multiply(inverse(?), inverse(?))))))
0.70/0.92	= { by lemma 14 }
0.70/0.92	  multiply(?, inverse(multiply(X, multiply(?, multiply(inverse(?), ?)))))
0.70/0.92	= { by lemma 62 }
0.70/0.92	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, inverse(?))))))
0.70/0.92	= { by lemma 55 }
0.70/0.93	  multiply(?, inverse(multiply(X, ?)))
0.70/0.93	
0.70/0.93	Lemma 64: multiply(multiply(?, inverse(?)), X) = inverse(inverse(X)).
0.70/0.93	Proof:
0.70/0.93	  multiply(multiply(?, inverse(?)), X)
0.70/0.93	= { by lemma 54 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), X)
0.70/0.93	= { by lemma 55 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(X, multiply(?, inverse(?))))
0.70/0.93	= { by lemma 58 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(inverse(?), inverse(inverse(X)))))
0.70/0.93	= { by axiom 1 (single_axiom) }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(?), ?))), ?))))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 62 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), ?))))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 45 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 62 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(?, inverse(?)))))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 55 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(?, inverse(multiply(?, ?))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 63 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), inverse(inverse(X)))))
0.70/0.93	= { by lemma 47 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(inverse(inverse(X)))))), ?)))
0.70/0.93	= { by lemma 45 }
0.70/0.93	  multiply(inverse(multiply(?, inverse(?))), multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(inverse(inverse(X)))), inverse(multiply(?, inverse(?)))))), ?)))
0.70/0.93	= { by lemma 8 }
0.70/0.93	  inverse(inverse(X))
0.70/0.93	
0.70/0.93	Lemma 65: multiply(multiply(?, inverse(multiply(?, multiply(X, inverse(Y))))), ?) = multiply(?, multiply(Y, multiply(multiply(?, inverse(?)), inverse(X)))).
0.70/0.93	Proof:
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, multiply(X, inverse(Y))))), ?)
0.70/0.93	= { by lemma 21 }
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, multiply(X, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(inverse(Y))), ?))))), ?))))), ?)
0.70/0.93	= { by lemma 20 }
0.70/0.93	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(inverse(Y))), ?))))), ?))), inverse(X))))
0.70/0.93	= { by lemma 21 }
0.70/0.93	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(inverse(Y))), inverse(X))))
0.70/0.93	= { by lemma 60 }
0.70/0.93	  multiply(?, multiply(Y, multiply(multiply(?, inverse(?)), inverse(X))))
0.70/0.93	
0.70/0.93	Lemma 66: multiply(?, inverse(inverse(X))) = multiply(?, X).
0.70/0.93	Proof:
0.70/0.93	  multiply(?, inverse(inverse(X)))
0.70/0.93	= { by lemma 45 }
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, inverse(?)))), inverse(inverse(X)))
0.70/0.93	= { by lemma 57 }
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, inverse(inverse(inverse(X)))))), ?)
0.70/0.93	= { by lemma 64 }
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(?)), inverse(X))))), ?)
0.70/0.93	= { by lemma 65 }
0.70/0.93	  multiply(?, multiply(X, multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(?))))))
0.70/0.93	= { by lemma 64 }
0.70/0.93	  multiply(?, multiply(X, inverse(inverse(inverse(multiply(?, inverse(?)))))))
0.70/0.93	= { by lemma 52 }
0.70/0.93	  multiply(?, multiply(X, inverse(multiply(?, inverse(?)))))
0.70/0.93	= { by lemma 45 }
0.70/0.93	  multiply(?, X)
0.70/0.93	
0.70/0.93	Lemma 67: inverse(inverse(X)) = X.
0.70/0.93	Proof:
0.70/0.93	  inverse(inverse(X))
0.70/0.93	= { by lemma 2 }
0.70/0.93	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(inverse(X))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.93	= { by lemma 66 }
0.70/0.93	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, X))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.93	= { by lemma 2 }
0.70/0.93	  X
0.70/0.93	
0.70/0.93	Lemma 68: multiply(inverse(?), multiply(?, X)) = multiply(?, multiply(inverse(?), X)).
0.70/0.93	Proof:
0.70/0.93	  multiply(inverse(?), multiply(?, X))
0.70/0.93	= { by lemma 61 }
0.70/0.93	  multiply(inverse(?), multiply(inverse(inverse(?)), X))
0.70/0.93	= { by lemma 33 }
0.70/0.93	  multiply(?, multiply(inverse(?), X))
0.70/0.93	
0.70/0.93	Lemma 69: multiply(?, multiply(inverse(?), X)) = X.
0.70/0.93	Proof:
0.70/0.93	  multiply(?, multiply(inverse(?), X))
0.70/0.93	= { by lemma 68 }
0.70/0.93	  multiply(inverse(?), multiply(?, X))
0.70/0.93	= { by lemma 66 }
0.70/0.93	  multiply(inverse(?), multiply(?, inverse(inverse(X))))
0.70/0.93	= { by lemma 68 }
0.70/0.93	  multiply(?, multiply(inverse(?), inverse(inverse(X))))
0.70/0.93	= { by lemma 58 }
0.70/0.93	  multiply(X, multiply(?, inverse(?)))
0.70/0.93	= { by lemma 55 }
0.70/0.93	  X
0.70/0.93	
0.70/0.93	Lemma 70: multiply(multiply(X, Y), inverse(Y)) = X.
0.70/0.93	Proof:
0.70/0.93	  multiply(multiply(X, Y), inverse(Y))
0.70/0.93	= { by lemma 55 }
0.70/0.93	  multiply(multiply(X, multiply(Y, multiply(?, inverse(?)))), inverse(Y))
0.70/0.93	= { by lemma 67 }
0.70/0.93	  multiply(multiply(X, multiply(Y, multiply(?, inverse(?)))), inverse(inverse(inverse(Y))))
0.70/0.93	= { by lemma 64 }
0.70/0.93	  multiply(multiply(X, multiply(Y, multiply(?, inverse(?)))), multiply(multiply(?, inverse(?)), inverse(Y)))
0.70/0.93	= { by lemma 60 }
0.70/0.93	  multiply(?, multiply(multiply(inverse(?), inverse(inverse(multiply(X, multiply(Y, multiply(?, inverse(?))))))), inverse(Y)))
0.70/0.93	= { by lemma 69 }
0.70/0.93	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(inverse(?), inverse(multiply(X, multiply(Y, multiply(?, inverse(?))))))))), inverse(Y)))
0.70/0.93	= { by lemma 13 }
0.70/0.93	  X
0.70/0.93	
0.70/0.93	Lemma 71: multiply(multiply(inverse(?), inverse(X)), inverse(?)) = inverse(multiply(multiply(?, X), ?)).
0.70/0.93	Proof:
0.70/0.93	  multiply(multiply(inverse(?), inverse(X)), inverse(?))
0.70/0.93	= { by lemma 28 }
0.70/0.93	  inverse(multiply(multiply(?, X), multiply(?, multiply(inverse(?), ?))))
0.70/0.93	= { by lemma 62 }
0.70/0.93	  inverse(multiply(multiply(?, X), multiply(?, multiply(?, inverse(?)))))
0.70/0.93	= { by lemma 55 }
0.70/0.93	  inverse(multiply(multiply(?, X), ?))
0.70/0.93	
0.70/0.93	Lemma 72: multiply(multiply(?, X), ?) = multiply(?, multiply(X, ?)).
0.70/0.93	Proof:
0.70/0.93	  multiply(multiply(?, X), ?)
0.70/0.93	= { by lemma 66 }
0.70/0.93	  multiply(multiply(?, inverse(inverse(X))), ?)
0.70/0.93	= { by lemma 69 }
0.70/0.93	  multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), inverse(X))))), ?)
0.70/0.93	= { by lemma 65 }
0.70/0.93	  multiply(?, multiply(X, multiply(multiply(?, inverse(?)), inverse(inverse(?)))))
0.70/0.93	= { by lemma 64 }
0.70/0.93	  multiply(?, multiply(X, inverse(inverse(inverse(inverse(?))))))
0.70/0.93	= { by lemma 67 }
0.70/0.93	  multiply(?, multiply(X, inverse(inverse(?))))
0.70/0.93	= { by lemma 61 }
0.70/0.93	  multiply(?, multiply(X, ?))
0.70/0.93	
0.70/0.93	Lemma 73: multiply(inverse(X), X) = multiply(?, inverse(?)).
0.70/0.93	Proof:
0.70/0.93	  multiply(inverse(X), X)
0.70/0.93	= { by lemma 67 }
0.70/0.93	  multiply(inverse(X), inverse(inverse(X)))
0.70/0.93	= { by lemma 34 }
0.70/0.94	  multiply(?, inverse(?))
0.70/0.94	
0.70/0.94	Lemma 74: multiply(Y, inverse(multiply(X, Y))) = inverse(X).
0.70/0.94	Proof:
0.70/0.94	  multiply(Y, inverse(multiply(X, Y)))
0.70/0.94	= { by lemma 69 }
0.70/0.94	  multiply(Y, inverse(multiply(?, multiply(inverse(?), multiply(X, Y)))))
0.70/0.94	= { by lemma 25 }
0.70/0.94	  multiply(?, inverse(multiply(?, multiply(inverse(?), multiply(X, ?)))))
0.70/0.94	= { by lemma 69 }
0.70/0.94	  multiply(?, inverse(multiply(X, ?)))
0.70/0.94	= { by lemma 55 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, inverse(?))))))
0.70/0.94	= { by lemma 53 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(inverse(?), multiply(?, inverse(?))))))))
0.70/0.94	= { by lemma 46 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(multiply(?, inverse(?)), inverse(?)))))))
0.70/0.94	= { by lemma 43 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(?)), ?))))))
0.70/0.94	= { by lemma 29 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(?)), inverse(?))), multiply(?, ?)))), inverse(?)), ?))))))
0.70/0.94	= { by lemma 71 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(inverse(multiply(multiply(?, multiply(multiply(?, multiply(multiply(inverse(?), inverse(?)), inverse(?))), multiply(?, ?))), ?)), ?))))))
0.70/0.94	= { by lemma 30 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(inverse(multiply(multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), ?))))), ?)), ?)), ?))))))
0.70/0.94	= { by lemma 35 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(inverse(multiply(multiply(?, multiply(?, inverse(?))), ?)), ?))))))
0.70/0.94	= { by lemma 55 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(?, multiply(inverse(multiply(?, ?)), ?))))))
0.70/0.94	= { by lemma 72 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(multiply(?, inverse(multiply(?, ?))), ?)))))
0.70/0.94	= { by lemma 63 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), ?)))))
0.70/0.94	= { by lemma 73 }
0.70/0.94	  multiply(?, inverse(multiply(X, multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(X), X))), ?)))))
0.70/0.94	= { by axiom 1 (single_axiom) }
0.70/0.94	  inverse(X)
0.70/0.94	
0.70/0.94	Lemma 75: multiply(inverse(Y), inverse(X)) = inverse(multiply(X, Y)).
0.70/0.94	Proof:
0.70/0.94	  multiply(inverse(Y), inverse(X))
0.70/0.94	= { by lemma 70 }
0.70/0.94	  multiply(inverse(Y), inverse(multiply(multiply(X, Y), inverse(Y))))
0.70/0.94	= { by lemma 74 }
0.70/0.94	  inverse(multiply(X, Y))
0.70/0.94	
0.70/0.94	Lemma 76: multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(X, multiply(Y, ?))))), ?))), inverse(Z))) = multiply(X, multiply(Y, inverse(Z))).
0.70/0.94	Proof:
0.70/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(X, multiply(Y, ?))))), ?))), inverse(Z)))
0.70/0.94	= { by lemma 3 }
0.70/0.94	  multiply(?, inverse(multiply(multiply(Z, multiply(multiply(?, inverse(multiply(?, multiply(X, multiply(Y, ?))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.94	= { by lemma 14 }
0.70/0.94	  multiply(?, inverse(multiply(multiply(Z, multiply(multiply(inverse(Z), inverse(multiply(?, multiply(X, multiply(Y, inverse(Z)))))), inverse(?))), multiply(?, multiply(?, ?)))))
0.70/0.94	= { by lemma 2 }
0.70/0.94	  multiply(X, multiply(Y, inverse(Z)))
0.70/0.94	
0.70/0.94	Lemma 77: inverse(multiply(inverse(X), Y)) = multiply(inverse(Y), X).
0.70/0.94	Proof:
0.70/0.94	  inverse(multiply(inverse(X), Y))
0.70/0.94	= { by lemma 2 }
0.70/0.94	  multiply(?, inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Y)))), multiply(multiply(inverse(inverse(multiply(Y, inverse(multiply(inverse(X), Y))))), inverse(multiply(Y, inverse(multiply(inverse(X), Y))))), inverse(?))), multiply(?, multiply(Y, ?)))))
0.70/0.94	= { by lemma 73 }
0.70/0.94	  multiply(?, inverse(multiply(multiply(inverse(multiply(Y, inverse(multiply(inverse(X), Y)))), multiply(multiply(?, inverse(?)), inverse(?))), multiply(?, multiply(Y, ?)))))
0.70/0.94	= { by lemma 3 }
0.70/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), Y))), inverse(inverse(multiply(Y, inverse(multiply(inverse(X), Y)))))))
0.70/0.94	= { by lemma 64 }
0.70/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(inverse(inverse(Y)))), inverse(inverse(multiply(Y, inverse(multiply(inverse(X), Y)))))))
0.70/0.94	= { by lemma 67 }
0.70/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(inverse(inverse(Y)))), multiply(Y, inverse(multiply(inverse(X), Y)))))
0.70/0.94	= { by lemma 60 }
0.70/0.94	  multiply(inverse(Y), multiply(multiply(?, inverse(?)), multiply(Y, inverse(multiply(inverse(X), Y)))))
0.70/0.94	= { by lemma 64 }
0.70/0.94	  multiply(inverse(Y), inverse(inverse(multiply(Y, inverse(multiply(inverse(X), Y))))))
0.70/0.94	= { by lemma 67 }
0.70/0.94	  multiply(inverse(Y), multiply(Y, inverse(multiply(inverse(X), Y))))
0.70/0.94	= { by lemma 69 }
0.70/0.94	  multiply(inverse(Y), multiply(multiply(?, multiply(inverse(?), Y)), inverse(multiply(inverse(X), Y))))
0.70/0.94	= { by lemma 33 }
0.70/0.94	  multiply(inverse(Y), multiply(multiply(X, multiply(inverse(X), Y)), inverse(multiply(inverse(X), Y))))
0.70/0.94	= { by lemma 70 }
0.79/0.94	  multiply(inverse(Y), X)
0.79/0.94	
0.79/0.94	Lemma 78: multiply(inverse(multiply(?, X)), ?) = inverse(X).
0.79/0.94	Proof:
0.79/0.94	  multiply(inverse(multiply(?, X)), ?)
0.79/0.94	= { by lemma 55 }
0.79/0.94	  multiply(inverse(multiply(?, X)), multiply(?, multiply(?, inverse(?))))
0.79/0.94	= { by lemma 51 }
0.79/0.94	  multiply(inverse(multiply(?, X)), multiply(multiply(?, inverse(?)), ?))
0.79/0.94	= { by lemma 60 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(inverse(inverse(multiply(?, X))))), ?))
0.79/0.94	= { by lemma 64 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), multiply(?, X)))), ?))
0.79/0.94	= { by lemma 7 }
0.79/0.94	  inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, ?))), multiply(?, X)))))
0.79/0.94	= { by lemma 5 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(?)), multiply(?, X)))), inverse(?)))
0.79/0.94	= { by lemma 3 }
0.79/0.94	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(?)), inverse(?))), multiply(?, multiply(multiply(?, X), ?)))))
0.79/0.94	= { by lemma 55 }
0.79/0.94	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, multiply(?, inverse(?))))), inverse(?))), multiply(?, multiply(multiply(?, X), ?)))))
0.79/0.94	= { by lemma 51 }
0.79/0.94	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), inverse(?))), multiply(?, multiply(multiply(?, X), ?)))))
0.79/0.94	= { by lemma 50 }
0.79/0.94	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(inverse(X))), inverse(X)))), inverse(?))), multiply(?, multiply(multiply(?, X), ?)))))
0.79/0.94	= { by lemma 66 }
0.79/0.94	  multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), inverse(X)))), inverse(?))), multiply(?, multiply(multiply(?, X), ?)))))
0.79/0.94	= { by lemma 2 }
0.79/0.94	  inverse(X)
0.79/0.94	
0.79/0.94	Lemma 79: multiply(multiply(?, X), Y) = multiply(?, multiply(X, Y)).
0.79/0.94	Proof:
0.79/0.94	  multiply(multiply(?, X), Y)
0.79/0.94	= { by lemma 66 }
0.79/0.94	  multiply(multiply(?, inverse(inverse(X))), Y)
0.79/0.94	= { by lemma 74 }
0.79/0.94	  multiply(multiply(?, inverse(multiply(Y, inverse(multiply(X, Y))))), Y)
0.79/0.94	= { by lemma 19 }
0.79/0.94	  multiply(multiply(?, inverse(multiply(?, inverse(multiply(X, Y))))), ?)
0.79/0.94	= { by lemma 57 }
0.79/0.94	  multiply(multiply(?, inverse(multiply(?, inverse(?)))), multiply(X, Y))
0.79/0.94	= { by lemma 45 }
0.79/0.94	  multiply(?, multiply(X, Y))
0.79/0.94	
0.79/0.94	Lemma 80: inverse(multiply(inverse(?), X)) = multiply(inverse(X), ?).
0.79/0.94	Proof:
0.79/0.94	  inverse(multiply(inverse(?), X))
0.79/0.94	= { by lemma 67 }
0.79/0.94	  inverse(multiply(inverse(?), inverse(inverse(X))))
0.79/0.94	= { by lemma 78 }
0.79/0.94	  multiply(inverse(multiply(?, multiply(inverse(?), inverse(inverse(X))))), ?)
0.79/0.94	= { by lemma 58 }
0.79/0.94	  multiply(inverse(multiply(X, multiply(?, inverse(?)))), ?)
0.79/0.94	= { by lemma 55 }
0.79/0.94	  multiply(inverse(X), ?)
0.79/0.94	
0.79/0.94	Lemma 81: multiply(inverse(?), inverse(X)) = inverse(multiply(X, ?)).
0.79/0.94	Proof:
0.79/0.94	  multiply(inverse(?), inverse(X))
0.79/0.94	= { by lemma 70 }
0.79/0.94	  multiply(multiply(multiply(inverse(?), inverse(X)), inverse(?)), inverse(inverse(?)))
0.79/0.94	= { by lemma 71 }
0.79/0.94	  multiply(inverse(multiply(multiply(?, X), ?)), inverse(inverse(?)))
0.79/0.94	= { by lemma 72 }
0.79/0.94	  multiply(inverse(multiply(?, multiply(X, ?))), inverse(inverse(?)))
0.79/0.94	= { by lemma 67 }
0.79/0.94	  multiply(inverse(multiply(?, multiply(X, ?))), ?)
0.79/0.94	= { by lemma 78 }
0.79/0.94	  inverse(multiply(X, ?))
0.79/0.94	
0.79/0.94	Lemma 82: multiply(multiply(X, Y), ?) = multiply(X, multiply(Y, ?)).
0.79/0.94	Proof:
0.79/0.94	  multiply(multiply(X, Y), ?)
0.79/0.94	= { by lemma 67 }
0.79/0.94	  multiply(inverse(inverse(multiply(X, Y))), ?)
0.79/0.94	= { by lemma 80 }
0.79/0.94	  inverse(multiply(inverse(?), inverse(multiply(X, Y))))
0.79/0.94	= { by lemma 74 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(X, Y))), X)))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))), Y))), X)))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?)))))))
0.79/0.94	= { by lemma 42 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(?, Y))), ?)))
0.79/0.94	= { by lemma 42 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))), Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))))))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(X, inverse(multiply(multiply(inverse(?), inverse(multiply(?, Y))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))))))
0.79/0.94	= { by lemma 81 }
0.79/0.94	  multiply(X, inverse(multiply(inverse(multiply(multiply(?, Y), ?)), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, ?), ?))), ?)))))))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(X, inverse(multiply(inverse(multiply(multiply(?, Y), ?)), ?)))
0.79/0.94	= { by lemma 77 }
0.79/0.94	  multiply(X, multiply(inverse(?), multiply(multiply(?, Y), ?)))
0.79/0.94	= { by lemma 72 }
0.79/0.94	  multiply(X, multiply(inverse(?), multiply(?, multiply(Y, ?))))
0.79/0.94	= { by lemma 68 }
0.79/0.94	  multiply(X, multiply(?, multiply(inverse(?), multiply(Y, ?))))
0.79/0.94	= { by lemma 69 }
0.79/0.94	  multiply(X, multiply(Y, ?))
0.79/0.94	
0.79/0.94	Lemma 83: multiply(?, multiply(inverse(multiply(?, ?)), X)) = multiply(inverse(?), X).
0.79/0.94	Proof:
0.79/0.94	  multiply(?, multiply(inverse(multiply(?, ?)), X))
0.79/0.94	= { by lemma 67 }
0.79/0.94	  multiply(?, multiply(inverse(inverse(inverse(multiply(?, ?)))), X))
0.79/0.94	= { by lemma 64 }
0.79/0.94	  multiply(?, multiply(inverse(multiply(multiply(?, inverse(?)), multiply(?, ?))), X))
0.79/0.94	= { by lemma 82 }
0.79/0.94	  multiply(?, multiply(inverse(multiply(multiply(multiply(?, inverse(?)), ?), ?)), X))
0.79/0.94	= { by lemma 81 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), ?))), X))
0.79/0.94	= { by lemma 59 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), ?))))), ?))), X))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), multiply(multiply(?, inverse(?)), ?))))), ?))), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))))))
0.79/0.94	= { by lemma 76 }
0.79/0.94	  multiply(inverse(?), multiply(multiply(?, inverse(?)), inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, X), ?))), ?))))))
0.79/0.94	= { by lemma 6 }
0.79/0.94	  multiply(inverse(?), multiply(multiply(?, inverse(?)), X))
0.79/0.94	= { by lemma 64 }
0.79/0.94	  multiply(inverse(?), inverse(inverse(X)))
0.79/0.94	= { by lemma 81 }
0.79/0.94	  inverse(multiply(inverse(X), ?))
0.79/0.94	= { by lemma 77 }
0.79/0.94	  multiply(inverse(?), X)
0.79/0.94	
0.79/0.94	Lemma 84: multiply(?, inverse(multiply(X, multiply(Y, ?)))) = inverse(multiply(X, Y)).
0.79/0.94	Proof:
0.79/0.94	  multiply(?, inverse(multiply(X, multiply(Y, ?))))
0.79/0.94	= { by lemma 78 }
0.79/0.94	  multiply(?, multiply(inverse(multiply(?, multiply(X, multiply(Y, ?)))), ?))
0.79/0.94	= { by lemma 72 }
0.79/0.94	  multiply(multiply(?, inverse(multiply(?, multiply(X, multiply(Y, ?))))), ?)
0.79/0.94	= { by lemma 20 }
0.79/0.94	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(Y, ?))), inverse(X))))
0.79/0.94	= { by lemma 78 }
0.79/0.94	  multiply(?, multiply(?, multiply(multiply(inverse(?), multiply(inverse(multiply(?, multiply(Y, ?))), ?)), inverse(X))))
0.79/0.94	= { by lemma 72 }
0.79/0.94	  multiply(?, multiply(?, multiply(multiply(inverse(?), multiply(inverse(multiply(multiply(?, Y), ?)), ?)), inverse(X))))
0.79/0.94	= { by lemma 82 }
0.79/0.94	  multiply(?, multiply(?, multiply(multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?), inverse(X))))
0.79/0.94	= { by lemma 79 }
0.79/0.94	  multiply(?, multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?)), inverse(X)))
0.79/0.94	= { by lemma 79 }
0.79/0.94	  multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))), inverse(X))
0.79/0.94	= { by lemma 74 }
0.79/0.94	  multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))), multiply(inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?)))), inverse(multiply(X, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))))))))
0.79/0.94	= { by lemma 33 }
0.79/0.94	  multiply(?, multiply(inverse(?), inverse(multiply(X, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))))))))
0.79/0.94	= { by lemma 69 }
0.79/0.94	  inverse(multiply(X, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, Y), ?))), ?))))))
0.79/0.94	= { by lemma 6 }
0.92/1.09	  inverse(multiply(X, Y))
0.92/1.09	
0.92/1.09	Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
0.92/1.09	Proof:
0.92/1.09	  multiply(multiply(a3, b3), c3)
0.92/1.09	= { by lemma 8 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(multiply(a3, b3), c3))), ?))), ?)))
0.92/1.09	= { by lemma 75 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(inverse(c3), inverse(multiply(a3, b3)))), ?))), ?)))
0.92/1.09	= { by lemma 75 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(inverse(c3), multiply(inverse(b3), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 76 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(c3), multiply(inverse(b3), ?))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 77 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(inverse(multiply(inverse(b3), ?)), c3))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 78 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(?, multiply(inverse(multiply(inverse(b3), ?)), c3))), ?)))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 79 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(multiply(?, inverse(multiply(inverse(b3), ?))), c3)), ?)))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 69 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(inverse(?), multiply(inverse(multiply(multiply(?, inverse(multiply(inverse(b3), ?))), c3)), ?)))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 82 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(inverse(b3), ?))), c3))), ?))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 7 }
0.92/1.09	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(b3), ?), ?))), c3))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.09	= { by lemma 5 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(b3), ?))), c3))), inverse(?)))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 3 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(inverse(b3), ?))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 80 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(inverse(multiply(inverse(?), b3)))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 84 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(inverse(?), multiply(b3, ?)))))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 83 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(b3, ?))))))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 25 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(c3, inverse(multiply(?, multiply(inverse(multiply(?, ?)), multiply(b3, c3))))))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 83 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(c3, inverse(multiply(inverse(?), multiply(b3, c3)))))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 80 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(multiply(multiply(?, multiply(multiply(inverse(?), inverse(multiply(c3, multiply(inverse(multiply(b3, c3)), ?)))), inverse(?))), multiply(?, multiply(c3, ?)))))))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 2 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(b3, c3)), ?)))), ?))), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 81 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, multiply(inverse(multiply(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(b3, c3)), ?)))), ?), ?)), inverse(a3)))), ?))), ?)))
0.92/1.10	= { by lemma 75 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, multiply(?, inverse(multiply(a3, multiply(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(b3, c3)), ?)))), ?), ?))))), ?))), ?)))
0.92/1.10	= { by lemma 84 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(a3, multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(b3, c3)), ?)))), ?)))), ?))), ?)))
0.92/1.10	= { by lemma 56 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(a3, multiply(multiply(?, inverse(multiply(?, multiply(inverse(?), ?)))), multiply(b3, c3))))), ?))), ?)))
0.92/1.10	= { by lemma 79 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(a3, multiply(?, multiply(inverse(multiply(?, multiply(inverse(?), ?))), multiply(b3, c3)))))), ?))), ?)))
0.92/1.10	= { by lemma 69 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(a3, multiply(?, multiply(inverse(?), multiply(b3, c3)))))), ?))), ?)))
0.92/1.10	= { by lemma 69 }
0.92/1.10	  multiply(?, multiply(?, multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(multiply(a3, multiply(b3, c3)))), ?))), ?)))
0.92/1.10	= { by lemma 8 }
0.92/1.10	  multiply(a3, multiply(b3, c3))
0.92/1.10	% SZS output end Proof
0.92/1.10	
0.92/1.10	RESULT: Unsatisfiable (the axioms are contradictory).
0.92/1.10	EOF