0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% 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 10:32:08 EDT 2019
0.13/0.35	% CPUTime    : 
0.20/0.58	% SZS status Unsatisfiable
0.20/0.58	
0.20/0.59	% SZS output start Proof
0.20/0.59	Take the following subset of the input axioms:
0.45/0.61	  fof(prove_these_axioms_3, negated_conjecture, multiply(a3, multiply(b3, c3))!=multiply(multiply(a3, b3), c3)).
0.45/0.61	  fof(single_axiom, axiom, ![A, B, C, D]: multiply(A, inverse(multiply(B, multiply(multiply(multiply(C, inverse(C)), inverse(multiply(D, B))), A))))=D).
0.45/0.61	
0.45/0.61	Now clausify the problem and encode Horn clauses using encoding 3 of
0.45/0.61	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.45/0.61	We repeatedly replace C & s=t => u=v by the two clauses:
0.45/0.61	  fresh(y, y, x1...xn) = u
0.45/0.61	  C => fresh(s, t, x1...xn) = v
0.45/0.61	where fresh is a fresh function symbol and x1..xn are the free
0.45/0.61	variables of u and v.
0.45/0.61	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.45/0.61	input problem has no model of domain size 1).
0.45/0.61	
0.45/0.61	The encoding turns the above axioms into the following unit equations and goals:
0.45/0.61	
0.55/0.71	Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, Y))), X)))) = W.
0.55/0.71	
0.55/0.71	Lemma 2: multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(W, Y)))) = X.
0.55/0.71	Proof:
0.55/0.71	  multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(W, Y))))
0.55/0.71	= { by axiom 1 (single_axiom) }
0.55/0.71	  multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(multiply(multiply(V, inverse(V)), inverse(multiply(X, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V)))))), Y))))
0.55/0.71	= { by axiom 1 (single_axiom) }
0.55/0.71	  X
0.55/0.71	
0.55/0.71	Lemma 3: multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W))) = multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?)))).
0.55/0.71	Proof:
0.55/0.71	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
0.55/0.71	= { by lemma 2 }
0.55/0.71	  multiply(?, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))))), multiply(?, inverse(?))), multiply(Z, ?))))
0.55/0.71	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?))))
0.55/0.72	
0.55/0.72	Lemma 4: multiply(Y, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(X, ?)))), multiply(Z, Y)))) = X.
0.55/0.72	Proof:
0.55/0.72	  multiply(Y, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(X, ?)))), multiply(Z, Y))))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(Y, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(Z, X))), multiply(?, inverse(?))), multiply(Z, Y))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 5: multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?)))))) = multiply(?, inverse(multiply(Y, multiply(Z, ?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?))))))
0.55/0.72	= { by lemma 4 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?)))))), ?)))), multiply(Z, ?))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(?, inverse(multiply(Y, multiply(Z, ?))))
0.55/0.72	
0.55/0.72	Lemma 6: multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V)))) = multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(V, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))))), multiply(U, inverse(U))), multiply(Z, V))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(multiply(W, inverse(W)), inverse(multiply(Z, multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))))), multiply(?, inverse(?))), multiply(Z, ?))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?))))
0.55/0.72	
0.55/0.72	Lemma 7: multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(Z, inverse(Z))) = multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(?, inverse(?))).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(Z, inverse(Z)))
0.55/0.72	= { by lemma 5 }
0.55/0.72	  multiply(multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(Y, multiply(?, inverse(?)))))), multiply(Z, inverse(Z)))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(multiply(Y, multiply(?, inverse(?))), ?))))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(Y, multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 5 }
0.55/0.72	  multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(?, inverse(?)))
0.55/0.72	
0.55/0.72	Lemma 8: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.55/0.72	Proof:
0.55/0.72	  multiply(X, inverse(X))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(?, inverse(multiply(W, multiply(V, ?)))), multiply(X, inverse(X))))), multiply(U, inverse(U))), multiply(multiply(?, inverse(multiply(W, multiply(V, ?)))), Y))))
0.55/0.72	= { by lemma 7 }
0.55/0.72	  multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(multiply(?, inverse(multiply(W, multiply(V, ?)))), multiply(?, inverse(?))))), multiply(U, inverse(U))), multiply(multiply(?, inverse(multiply(W, multiply(V, ?)))), Y))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  multiply(?, inverse(?))
0.55/0.72	
0.55/0.72	Lemma 9: multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?)))) = inverse(X).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?))))
0.55/0.72	= { by lemma 8 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), multiply(?, inverse(?))), multiply(X, ?))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  inverse(X)
0.55/0.72	
0.55/0.72	Lemma 10: inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))) = X.
0.55/0.72	Proof:
0.55/0.72	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.55/0.72	= { by lemma 5 }
0.55/0.72	  inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))))), ?))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 11: multiply(W, inverse(multiply(Y, multiply(Z, W)))) = multiply(?, inverse(multiply(Y, multiply(Z, ?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(W, inverse(multiply(Y, multiply(Z, W))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(W, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?)))))), ?)))), multiply(Z, W))))
0.55/0.72	= { by lemma 4 }
0.55/0.72	  multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?))))))
0.55/0.72	= { by lemma 4 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?)))))), ?)))), multiply(Z, ?))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  multiply(?, inverse(multiply(Y, multiply(Z, ?))))
0.55/0.72	
0.55/0.72	Lemma 12: multiply(multiply(?, inverse(?)), multiply(?, inverse(?))) = inverse(inverse(multiply(?, inverse(?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 10 }
0.55/0.72	  inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?)))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  inverse(inverse(multiply(?, inverse(?))))
0.55/0.72	
0.55/0.72	Lemma 13: multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?)))) = inverse(inverse(multiply(?, inverse(?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?))))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 8 }
0.55/0.72	  multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 12 }
0.55/0.72	  inverse(inverse(multiply(?, inverse(?))))
0.55/0.72	
0.55/0.72	Lemma 14: multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?)))) = inverse(X).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?))))
0.55/0.72	= { by lemma 13 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?)))), multiply(X, ?))))
0.55/0.72	= { by lemma 4 }
0.55/0.72	  inverse(X)
0.55/0.72	
0.55/0.72	Lemma 15: inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))) = X.
0.55/0.72	Proof:
0.55/0.72	  inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))))
0.55/0.72	= { by lemma 14 }
0.55/0.72	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?))))
0.55/0.72	= { by axiom 1 (single_axiom) }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 16: multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?))) = inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 15 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))), ?))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	
0.55/0.72	Lemma 17: multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), X) = multiply(?, inverse(?)).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), X)
0.55/0.72	= { by lemma 10 }
0.55/0.72	  multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))
0.55/0.72	= { by lemma 8 }
0.55/0.72	  multiply(?, inverse(?))
0.55/0.72	
0.55/0.72	Lemma 18: multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))) = inverse(inverse(multiply(?, inverse(?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?))))
0.55/0.72	= { by lemma 17 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.72	= { by lemma 10 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?))))), ?))))
0.55/0.72	= { by lemma 13 }
0.55/0.72	  inverse(inverse(multiply(?, inverse(?))))
0.55/0.72	
0.55/0.72	Lemma 19: inverse(inverse(inverse(multiply(?, inverse(?))))) = multiply(?, inverse(?)).
0.55/0.72	Proof:
0.55/0.72	  inverse(inverse(inverse(multiply(?, inverse(?)))))
0.55/0.72	= { by lemma 18 }
0.55/0.72	  inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))
0.55/0.72	= { by lemma 10 }
0.55/0.72	  multiply(?, inverse(?))
0.55/0.72	
0.55/0.72	Lemma 20: inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))) = inverse(multiply(?, inverse(?))).
0.55/0.72	Proof:
0.55/0.72	  inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 16 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 19 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), inverse(inverse(inverse(multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 12 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  inverse(multiply(?, inverse(?)))
0.55/0.72	
0.55/0.72	Lemma 21: multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.55/0.72	Proof:
0.55/0.72	  multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 18 }
0.55/0.72	  multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 17 }
0.55/0.72	  multiply(?, inverse(?))
0.55/0.72	
0.55/0.72	Lemma 22: multiply(inverse(Y), inverse(multiply(X, multiply(?, inverse(?))))) = multiply(?, inverse(multiply(X, multiply(Y, ?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(inverse(Y), inverse(multiply(X, multiply(?, inverse(?)))))
0.55/0.72	= { by lemma 8 }
0.55/0.72	  multiply(inverse(Y), inverse(multiply(X, multiply(Y, inverse(Y)))))
0.55/0.72	= { by lemma 11 }
0.55/0.72	  multiply(?, inverse(multiply(X, multiply(Y, ?))))
0.55/0.72	
0.55/0.72	Lemma 23: multiply(inverse(X), inverse(multiply(?, inverse(?)))) = inverse(X).
0.55/0.72	Proof:
0.55/0.72	  multiply(inverse(X), inverse(multiply(?, inverse(?))))
0.55/0.72	= { by lemma 21 }
0.55/0.72	  multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))))
0.55/0.72	= { by lemma 22 }
0.55/0.72	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?))))
0.55/0.72	= { by lemma 14 }
0.55/0.72	  inverse(X)
0.55/0.72	
0.55/0.72	Lemma 24: inverse(multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.55/0.72	Proof:
0.55/0.72	  inverse(multiply(?, inverse(?)))
0.55/0.72	= { by lemma 20 }
0.55/0.72	  inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 16 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 8 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))), inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 20 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))), inverse(multiply(?, inverse(?))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 23 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(inverse(inverse(multiply(?, inverse(?)))), ?))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  inverse(inverse(inverse(multiply(?, inverse(?)))))
0.55/0.72	= { by lemma 19 }
0.55/0.72	  multiply(?, inverse(?))
0.55/0.72	
0.55/0.72	Lemma 25: multiply(X, inverse(multiply(?, inverse(?)))) = X.
0.55/0.72	Proof:
0.55/0.72	  multiply(X, inverse(multiply(?, inverse(?))))
0.55/0.72	= { by lemma 10 }
0.55/0.72	  multiply(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), inverse(multiply(?, inverse(?))))
0.55/0.72	= { by lemma 23 }
0.55/0.72	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.55/0.72	= { by lemma 10 }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 26: multiply(X, multiply(?, inverse(?))) = X.
0.55/0.72	Proof:
0.55/0.72	  multiply(X, multiply(?, inverse(?)))
0.55/0.72	= { by lemma 24 }
0.55/0.72	  multiply(X, inverse(multiply(?, inverse(?))))
0.55/0.72	= { by lemma 25 }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 27: multiply(multiply(?, inverse(?)), X) = inverse(inverse(X)).
0.55/0.72	Proof:
0.55/0.72	  multiply(multiply(?, inverse(?)), X)
0.55/0.72	= { by lemma 26 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 16 }
0.55/0.72	  inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 24 }
0.55/0.72	  inverse(inverse(multiply(X, inverse(multiply(?, inverse(?))))))
0.55/0.72	= { by lemma 25 }
0.55/0.72	  inverse(inverse(X))
0.55/0.72	
0.55/0.72	Lemma 28: inverse(inverse(inverse(inverse(X)))) = X.
0.55/0.72	Proof:
0.55/0.72	  inverse(inverse(inverse(inverse(X))))
0.55/0.72	= { by lemma 23 }
0.55/0.72	  inverse(inverse(inverse(multiply(inverse(X), inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 24 }
0.55/0.72	  inverse(inverse(inverse(multiply(inverse(X), inverse(inverse(multiply(?, inverse(?))))))))
0.55/0.72	= { by lemma 27 }
0.55/0.72	  multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?)))), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), X))), multiply(?, inverse(?))), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.72	= { by lemma 12 }
0.55/0.72	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), X))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  X
0.55/0.72	
0.55/0.72	Lemma 29: multiply(?, inverse(inverse(inverse(multiply(X, ?))))) = inverse(X).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(inverse(inverse(multiply(X, ?)))))
0.55/0.72	= { by lemma 27 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(X, ?))))
0.55/0.72	= { by lemma 26 }
0.55/0.72	  multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(X, ?)))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 5 }
0.55/0.72	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), multiply(X, multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(X, multiply(?, inverse(?))), ?))))
0.55/0.72	= { by lemma 9 }
0.55/0.72	  inverse(multiply(X, multiply(?, inverse(?))))
0.55/0.72	= { by lemma 26 }
0.55/0.72	  inverse(X)
0.55/0.72	
0.55/0.72	Lemma 30: multiply(?, inverse(multiply(X, multiply(?, ?)))) = inverse(inverse(inverse(multiply(X, ?)))).
0.55/0.72	Proof:
0.55/0.72	  multiply(?, inverse(multiply(X, multiply(?, ?))))
0.55/0.72	= { by lemma 28 }
0.55/0.72	  multiply(?, inverse(multiply(inverse(inverse(inverse(inverse(X)))), multiply(?, ?))))
0.55/0.72	= { by lemma 27 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(X))), multiply(?, ?))))
0.55/0.72	= { by lemma 26 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(X))), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.72	= { by lemma 29 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(inverse(inverse(multiply(X, ?))))))), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  inverse(inverse(inverse(multiply(X, ?))))
0.55/0.72	
0.55/0.72	Lemma 31: inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, ?)))), ?)))) = Y.
0.55/0.72	Proof:
0.55/0.72	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, ?)))), ?))))
0.55/0.72	= { by lemma 26 }
0.55/0.72	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(multiply(?, multiply(?, inverse(?))), multiply(Y, ?)))), ?))))
0.55/0.72	= { by lemma 3 }
0.55/0.72	  inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, Y))), multiply(?, inverse(?))), ?))))
0.55/0.72	= { by lemma 30 }
0.55/0.72	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, Y))), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.72	= { by lemma 2 }
0.55/0.72	  Y
0.55/0.72	
0.55/0.72	Lemma 32: inverse(multiply(?, inverse(multiply(?, multiply(X, ?))))) = multiply(?, X).
0.55/0.72	Proof:
0.55/0.72	  inverse(multiply(?, inverse(multiply(?, multiply(X, ?)))))
0.55/0.72	= { by lemma 29 }
0.55/0.72	  multiply(?, inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(X, ?)))), ?)))))
0.55/0.72	= { by lemma 31 }
0.55/0.73	  multiply(?, X)
0.55/0.73	
0.55/0.73	Lemma 33: inverse(inverse(?)) = ?.
0.55/0.73	Proof:
0.55/0.73	  inverse(inverse(?))
0.55/0.73	= { by lemma 28 }
0.55/0.73	  inverse(inverse(inverse(inverse(inverse(inverse(?))))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(?)), ?)))))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(?))))), ?)))))
0.55/0.73	= { by lemma 17 }
0.55/0.73	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(?)), ?)))), ?)))), ?)))))
0.55/0.73	= { by lemma 31 }
0.55/0.73	  inverse(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(?)), ?)))))
0.55/0.73	= { by lemma 32 }
0.55/0.73	  multiply(?, multiply(?, inverse(?)))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  ?
0.55/0.73	
0.55/0.73	Lemma 34: multiply(?, inverse(multiply(inverse(X), multiply(multiply(?, inverse(?)), ?)))) = X.
0.55/0.73	Proof:
0.55/0.73	  multiply(?, inverse(multiply(inverse(X), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 8 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(X), multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), ?))))
0.55/0.73	= { by axiom 1 (single_axiom) }
0.55/0.73	  X
0.55/0.73	
0.55/0.73	Lemma 35: multiply(?, multiply(inverse(multiply(X, ?)), ?)) = inverse(inverse(multiply(inverse(X), ?))).
0.55/0.73	Proof:
0.55/0.73	  multiply(?, multiply(inverse(multiply(X, ?)), ?))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  multiply(?, multiply(inverse(multiply(X, inverse(inverse(?)))), ?))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(?, multiply(inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))), ?))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))), ?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 2 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(multiply(?, multiply(inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))), ?)))))), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 32 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 30 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), multiply(?, inverse(?))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?)))
0.55/0.73	= { by lemma 10 }
0.55/0.73	  inverse(inverse(multiply(inverse(X), ?)))
0.55/0.73	
0.55/0.73	Lemma 36: multiply(?, inverse(multiply(X, ?))) = inverse(inverse(inverse(X))).
0.55/0.73	Proof:
0.55/0.73	  multiply(?, inverse(multiply(X, ?)))
0.55/0.73	= { by lemma 32 }
0.55/0.73	  inverse(multiply(?, inverse(multiply(?, multiply(inverse(multiply(X, ?)), ?)))))
0.55/0.73	= { by lemma 35 }
0.55/0.73	  inverse(multiply(?, inverse(inverse(inverse(multiply(inverse(X), ?))))))
0.55/0.73	= { by lemma 29 }
0.55/0.73	  inverse(inverse(inverse(X)))
0.55/0.73	
0.55/0.73	Lemma 37: inverse(inverse(inverse(multiply(inverse(inverse(X)), ?)))) = inverse(multiply(X, ?)).
0.55/0.73	Proof:
0.55/0.73	  inverse(inverse(inverse(multiply(inverse(inverse(X)), ?))))
0.55/0.73	= { by lemma 29 }
0.55/0.73	  inverse(inverse(inverse(multiply(multiply(?, inverse(inverse(inverse(multiply(inverse(X), ?))))), ?))))
0.55/0.73	= { by lemma 35 }
0.55/0.73	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(X, ?)), ?)))), ?))))
0.55/0.73	= { by lemma 31 }
0.55/0.73	  inverse(multiply(X, ?))
0.55/0.73	
0.55/0.73	Lemma 38: inverse(inverse(multiply(X, ?))) = multiply(inverse(inverse(X)), ?).
0.55/0.73	Proof:
0.55/0.73	  inverse(inverse(multiply(X, ?)))
0.55/0.73	= { by lemma 37 }
0.55/0.73	  inverse(inverse(inverse(inverse(multiply(inverse(inverse(X)), ?)))))
0.55/0.73	= { by lemma 28 }
0.55/0.73	  multiply(inverse(inverse(X)), ?)
0.55/0.73	
0.55/0.73	Lemma 39: multiply(inverse(multiply(inverse(inverse(Y)), ?)), inverse(multiply(X, inverse(Y)))) = inverse(multiply(inverse(inverse(X)), ?)).
0.55/0.73	Proof:
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(Y)), ?)), inverse(multiply(X, inverse(Y))))
0.55/0.73	= { by lemma 38 }
0.55/0.73	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(X, inverse(Y))))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(multiply(X, multiply(?, inverse(?))), inverse(Y))))
0.55/0.73	= { by lemma 29 }
0.55/0.73	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(?, inverse(inverse(inverse(multiply(Y, ?))))))))
0.55/0.73	= { by lemma 6 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.73	= { by lemma 30 }
0.55/0.73	  inverse(inverse(inverse(multiply(multiply(X, multiply(?, inverse(?))), ?))))
0.55/0.73	= { by lemma 38 }
0.55/0.73	  inverse(multiply(inverse(inverse(multiply(X, multiply(?, inverse(?))))), ?))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  inverse(multiply(inverse(inverse(X)), ?))
0.55/0.73	
0.55/0.73	Lemma 40: multiply(inverse(multiply(inverse(inverse(X)), ?)), X) = inverse(?).
0.55/0.73	Proof:
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(X)), ?)), X)
0.55/0.73	= { by lemma 25 }
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(multiply(?, inverse(?)))))), ?)), X)
0.55/0.73	= { by lemma 24 }
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?)), X)
0.55/0.73	= { by lemma 15 }
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?)), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))))
0.55/0.73	= { by lemma 39 }
0.55/0.73	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?))
0.55/0.73	= { by lemma 24 }
0.55/0.73	  inverse(multiply(inverse(multiply(?, inverse(?))), ?))
0.55/0.73	= { by lemma 24 }
0.55/0.73	  inverse(multiply(multiply(?, inverse(?)), ?))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  inverse(inverse(inverse(?)))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  inverse(?)
0.55/0.73	
0.55/0.73	Lemma 41: inverse(inverse(inverse(multiply(X, inverse(?))))) = multiply(?, inverse(X)).
0.55/0.73	Proof:
0.55/0.73	  inverse(inverse(inverse(multiply(X, inverse(?)))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))
0.55/0.73	= { by lemma 40 }
0.55/0.73	  multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(?, inverse(?))))))
0.55/0.73	= { by lemma 5 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), ?))))
0.55/0.73	= { by lemma 24 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(inverse(multiply(?, inverse(?))), ?)), ?))))
0.55/0.73	= { by lemma 24 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(multiply(?, inverse(?)), ?)), ?))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(inverse(inverse(inverse(?))), ?))))
0.55/0.73	= { by lemma 28 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(inverse(inverse(inverse(?))), inverse(inverse(inverse(inverse(?))))))))
0.55/0.73	= { by lemma 8 }
0.55/0.73	  multiply(?, inverse(multiply(X, multiply(?, inverse(?)))))
0.55/0.73	= { by lemma 26 }
0.55/0.73	  multiply(?, inverse(X))
0.55/0.73	
0.55/0.73	Lemma 42: inverse(inverse(multiply(?, inverse(X)))) = inverse(multiply(X, inverse(?))).
0.55/0.73	Proof:
0.55/0.73	  inverse(inverse(multiply(?, inverse(X))))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(X))))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 36 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(X)), ?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 41 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), ?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), inverse(inverse(?))))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), multiply(multiply(?, inverse(?)), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(multiply(X, inverse(?)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  inverse(multiply(X, inverse(?)))
0.55/0.73	
0.55/0.73	Lemma 43: inverse(multiply(?, inverse(X))) = multiply(X, inverse(?)).
0.55/0.73	Proof:
0.55/0.73	  inverse(multiply(?, inverse(X)))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(X)))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 42 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(multiply(X, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.55/0.73	= { by lemma 34 }
0.55/0.73	  multiply(X, inverse(?))
0.55/0.73	
0.55/0.73	Lemma 44: multiply(multiply(X, ?), inverse(?)) = X.
0.55/0.73	Proof:
0.55/0.73	  multiply(multiply(X, ?), inverse(?))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  multiply(multiply(X, inverse(inverse(?))), inverse(?))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(multiply(X, multiply(multiply(?, inverse(?)), ?)), inverse(?))
0.55/0.73	= { by lemma 43 }
0.55/0.73	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.55/0.73	= { by lemma 10 }
0.55/0.73	  X
0.55/0.73	
0.55/0.73	Lemma 45: inverse(multiply(inverse(inverse(X)), ?)) = multiply(inverse(?), inverse(X)).
0.55/0.73	Proof:
0.55/0.73	  inverse(multiply(inverse(inverse(X)), ?))
0.55/0.73	= { by lemma 39 }
0.55/0.73	  multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(?))))), ?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.73	= { by lemma 19 }
0.55/0.73	  multiply(inverse(multiply(multiply(?, inverse(?)), ?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(inverse(inverse(inverse(?))), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  multiply(inverse(?), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.73	= { by lemma 24 }
0.55/0.73	  multiply(inverse(?), inverse(multiply(X, inverse(multiply(?, inverse(?))))))
0.55/0.73	= { by lemma 25 }
0.55/0.73	  multiply(inverse(?), inverse(X))
0.55/0.73	
0.55/0.73	Lemma 46: multiply(?, inverse(multiply(inverse(?), multiply(X, ?)))) = multiply(inverse(X), ?).
0.55/0.73	Proof:
0.55/0.73	  multiply(?, inverse(multiply(inverse(?), multiply(X, ?))))
0.55/0.73	= { by lemma 14 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, ?)))), multiply(X, ?))))
0.55/0.73	= { by lemma 11 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))))), multiply(X, ?))))
0.55/0.73	= { by lemma 21 }
0.55/0.73	  multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(X, ?))))
0.55/0.73	= { by lemma 45 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(X, ?))))
0.55/0.73	= { by lemma 22 }
0.55/0.73	  multiply(inverse(X), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(?, inverse(?)))))
0.55/0.73	= { by lemma 40 }
0.55/0.73	  multiply(inverse(X), inverse(inverse(?)))
0.55/0.73	= { by lemma 33 }
0.55/0.73	  multiply(inverse(X), ?)
0.55/0.73	
0.55/0.73	Lemma 47: multiply(multiply(X, inverse(?)), ?) = X.
0.55/0.73	Proof:
0.55/0.73	  multiply(multiply(X, inverse(?)), ?)
0.55/0.73	= { by lemma 28 }
0.55/0.73	  multiply(inverse(inverse(inverse(inverse(multiply(X, inverse(?)))))), ?)
0.55/0.73	= { by lemma 27 }
0.55/0.73	  multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))), ?)
0.55/0.73	= { by lemma 46 }
0.55/0.73	  multiply(?, inverse(multiply(inverse(?), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.55/0.73	= { by axiom 1 (single_axiom) }
0.55/0.73	  X
0.55/0.73	
0.55/0.73	Lemma 48: inverse(multiply(inverse(X), ?)) = multiply(inverse(?), X).
0.55/0.73	Proof:
0.55/0.73	  inverse(multiply(inverse(X), ?))
0.55/0.73	= { by lemma 10 }
0.55/0.73	  inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?))
0.55/0.73	= { by lemma 45 }
0.55/0.73	  multiply(inverse(?), inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))
0.55/0.73	= { by lemma 10 }
0.55/0.74	  multiply(inverse(?), X)
0.55/0.74	
0.55/0.74	Lemma 49: multiply(?, inverse(inverse(inverse(X)))) = inverse(multiply(X, inverse(?))).
0.55/0.74	Proof:
0.55/0.74	  multiply(?, inverse(inverse(inverse(X))))
0.55/0.74	= { by lemma 27 }
0.55/0.74	  multiply(?, inverse(multiply(multiply(?, inverse(?)), X)))
0.55/0.74	= { by lemma 24 }
0.55/0.74	  multiply(?, inverse(multiply(inverse(multiply(?, inverse(?))), X)))
0.55/0.74	= { by lemma 42 }
0.55/0.74	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), X)))
0.55/0.74	= { by lemma 12 }
0.55/0.74	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), X)))
0.55/0.74	= { by lemma 47 }
0.55/0.74	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(X, inverse(?)), ?))))
0.55/0.74	= { by lemma 9 }
0.55/0.74	  inverse(multiply(X, inverse(?)))
0.55/0.74	
0.55/0.74	Lemma 50: multiply(inverse(?), multiply(?, X)) = X.
0.55/0.74	Proof:
0.55/0.74	  multiply(inverse(?), multiply(?, X))
0.55/0.74	= { by lemma 48 }
0.55/0.74	  inverse(multiply(inverse(multiply(?, X)), ?))
0.55/0.74	= { by lemma 10 }
0.55/0.74	  inverse(multiply(inverse(multiply(?, inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))), ?))
0.55/0.74	= { by lemma 41 }
0.55/0.74	  inverse(multiply(inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), inverse(?)))))), ?))
0.55/0.74	= { by lemma 49 }
0.55/0.74	  inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))))))), ?))
0.55/0.74	= { by lemma 42 }
0.55/0.74	  inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), inverse(?)))), ?))
0.55/0.74	= { by lemma 10 }
0.55/0.74	  inverse(multiply(inverse(inverse(multiply(inverse(X), inverse(?)))), ?))
0.55/0.74	= { by lemma 38 }
0.55/0.74	  inverse(inverse(inverse(multiply(multiply(inverse(X), inverse(?)), ?))))
0.55/0.74	= { by lemma 30 }
0.55/0.74	  multiply(?, inverse(multiply(multiply(inverse(X), inverse(?)), multiply(?, ?))))
0.55/0.74	= { by lemma 22 }
0.55/0.74	  multiply(inverse(?), inverse(multiply(multiply(inverse(X), inverse(?)), multiply(?, inverse(?)))))
0.55/0.74	= { by lemma 45 }
0.55/0.74	  inverse(multiply(inverse(inverse(multiply(multiply(inverse(X), inverse(?)), multiply(?, inverse(?))))), ?))
0.55/0.74	= { by lemma 38 }
0.55/0.74	  inverse(inverse(inverse(multiply(multiply(multiply(inverse(X), inverse(?)), multiply(?, inverse(?))), ?))))
0.55/0.74	= { by lemma 30 }
0.55/0.74	  multiply(?, inverse(multiply(multiply(multiply(inverse(X), inverse(?)), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.74	= { by lemma 3 }
0.55/0.74	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(inverse(X), inverse(?)), ?))), multiply(?, inverse(?)))
0.55/0.74	= { by lemma 47 }
0.55/0.74	  multiply(multiply(multiply(?, inverse(?)), inverse(inverse(X))), multiply(?, inverse(?)))
0.55/0.74	= { by lemma 16 }
0.55/0.74	  inverse(inverse(multiply(inverse(inverse(X)), inverse(inverse(multiply(?, inverse(?)))))))
0.55/0.74	= { by lemma 42 }
0.55/0.74	  inverse(inverse(multiply(inverse(inverse(X)), inverse(multiply(?, inverse(?))))))
0.55/0.74	= { by lemma 23 }
0.55/0.74	  inverse(inverse(inverse(inverse(X))))
0.55/0.74	= { by lemma 28 }
0.55/0.76	  X
0.55/0.76	
0.55/0.76	Lemma 51: multiply(multiply(X, multiply(Y, ?)), inverse(?)) = multiply(X, Y).
0.55/0.76	Proof:
0.55/0.76	  multiply(multiply(X, multiply(Y, ?)), inverse(?))
0.55/0.76	= { by lemma 2 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(multiply(X, multiply(Y, ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 50 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(inverse(?), multiply(?, inverse(?))), multiply(multiply(X, multiply(Y, ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 48 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), ?)), multiply(multiply(X, multiply(Y, ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 10 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(multiply(X, multiply(Y, ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 26 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(multiply(multiply(X, multiply(?, inverse(?))), multiply(Y, ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 43 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), inverse(multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(Y, ?)))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 3 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, Y))), multiply(?, inverse(?))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 10 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, Y))), inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 39 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, Y))))), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 45 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, Y))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 27 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), inverse(inverse(inverse(inverse(multiply(X, Y)))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 36 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, Y)), ?)))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 33 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, Y)), inverse(inverse(?)))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 27 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, Y)), multiply(multiply(?, inverse(?)), ?))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 48 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(X, Y)), multiply(multiply(?, inverse(?)), ?))))), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 10 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(multiply(X, Y)), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 48 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(X, Y)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.55/0.76	= { by lemma 2 }
0.55/0.76	  multiply(X, Y)
0.55/0.76	
0.55/0.76	Lemma 52: multiply(multiply(X, Y), inverse(?)) = multiply(X, multiply(Y, inverse(?))).
0.55/0.76	Proof:
0.55/0.76	  multiply(multiply(X, Y), inverse(?))
0.55/0.76	= { by lemma 47 }
0.55/0.76	  multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))
0.55/0.76	= { by lemma 51 }
0.55/0.76	  multiply(X, multiply(Y, inverse(?)))
0.55/0.76	
0.55/0.76	Lemma 53: multiply(multiply(X, Y), inverse(Y)) = X.
0.55/0.76	Proof:
0.55/0.76	  multiply(multiply(X, Y), inverse(Y))
0.55/0.76	= { by lemma 44 }
0.55/0.76	  multiply(multiply(X, multiply(multiply(Y, ?), inverse(?))), inverse(Y))
0.55/0.76	= { by lemma 52 }
0.55/0.76	  multiply(multiply(multiply(X, multiply(Y, ?)), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 43 }
0.55/0.76	  multiply(inverse(multiply(?, inverse(multiply(X, multiply(Y, ?))))), inverse(Y))
0.55/0.76	= { by lemma 15 }
0.55/0.76	  multiply(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?)))))))))), inverse(Y))
0.55/0.76	= { by lemma 43 }
0.55/0.76	  multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?))))))), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 27 }
0.55/0.76	  multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?)))))))), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 42 }
0.55/0.76	  multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(multiply(?, inverse(?))))))), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 25 }
0.55/0.76	  multiply(multiply(inverse(inverse(inverse(inverse(multiply(X, multiply(Y, ?)))))), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 27 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(Y))
0.55/0.76	= { by lemma 44 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), inverse(?))))
0.55/0.76	= { by lemma 33 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), inverse(inverse(inverse(?))))))
0.55/0.76	= { by lemma 27 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), multiply(multiply(?, inverse(?)), inverse(?)))))
0.55/0.76	= { by lemma 8 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?)))), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?)))))), inverse(?)))))
0.55/0.76	= { by lemma 52 }
0.55/0.76	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?)))), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?))))))
0.55/0.76	= { by axiom 1 (single_axiom) }
0.55/0.76	  X
0.55/0.76	
0.55/0.76	Lemma 54: multiply(X, inverse(inverse(Y))) = multiply(X, Y).
0.55/0.76	Proof:
0.55/0.76	  multiply(X, inverse(inverse(Y)))
0.55/0.76	= { by lemma 53 }
0.55/0.76	  multiply(multiply(multiply(X, Y), inverse(Y)), inverse(inverse(Y)))
0.55/0.76	= { by lemma 53 }
0.55/0.76	  multiply(X, Y)
0.55/0.76	
0.55/0.76	Lemma 55: inverse(inverse(X)) = X.
0.55/0.76	Proof:
0.55/0.76	  inverse(inverse(X))
0.55/0.76	= { by lemma 2 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(inverse(X))))), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.76	= { by lemma 54 }
0.55/0.76	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, X))), multiply(?, inverse(?))), multiply(?, ?))))
0.55/0.76	= { by lemma 2 }
0.55/0.76	  X
0.55/0.76	
0.55/0.76	Lemma 56: multiply(?, inverse(multiply(X, multiply(Y, ?)))) = inverse(inverse(inverse(multiply(X, Y)))).
0.55/0.76	Proof:
0.55/0.76	  multiply(?, inverse(multiply(X, multiply(Y, ?))))
0.55/0.76	= { by lemma 41 }
0.55/0.76	  inverse(inverse(inverse(multiply(multiply(X, multiply(Y, ?)), inverse(?)))))
0.55/0.76	= { by lemma 51 }
0.55/0.76	  inverse(inverse(inverse(multiply(X, Y))))
0.55/0.76	
0.55/0.76	Lemma 57: inverse(multiply(X, inverse(Y))) = multiply(Y, inverse(X)).
0.55/0.76	Proof:
0.55/0.76	  inverse(multiply(X, inverse(Y)))
0.55/0.76	= { by lemma 55 }
0.55/0.76	  inverse(inverse(inverse(multiply(X, inverse(Y)))))
0.55/0.76	= { by lemma 56 }
0.55/0.76	  multiply(?, inverse(multiply(X, multiply(inverse(Y), ?))))
0.55/0.76	= { by lemma 22 }
0.55/0.76	  multiply(inverse(inverse(Y)), inverse(multiply(X, multiply(?, inverse(?)))))
0.55/0.76	= { by lemma 55 }
0.55/0.76	  multiply(Y, inverse(multiply(X, multiply(?, inverse(?)))))
0.55/0.76	= { by lemma 26 }
0.55/0.76	  multiply(Y, inverse(X))
0.55/0.76	
0.55/0.76	Lemma 58: multiply(?, multiply(inverse(?), X)) = X.
0.55/0.76	Proof:
0.55/0.76	  multiply(?, multiply(inverse(?), X))
0.55/0.76	= { by lemma 48 }
0.55/0.76	  multiply(?, inverse(multiply(inverse(X), ?)))
0.55/0.76	= { by lemma 36 }
0.55/0.76	  inverse(inverse(inverse(inverse(X))))
0.55/0.76	= { by lemma 28 }
0.62/0.77	  X
0.62/0.77	
0.62/0.77	Lemma 59: inverse(multiply(inverse(?), inverse(X))) = multiply(X, ?).
0.62/0.77	Proof:
0.62/0.77	  inverse(multiply(inverse(?), inverse(X)))
0.62/0.77	= { by lemma 34 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(inverse(multiply(inverse(?), inverse(X)))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 25 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(inverse(multiply(multiply(inverse(?), inverse(X)), inverse(multiply(?, inverse(?)))))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 42 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(inverse(multiply(multiply(inverse(?), inverse(X)), inverse(inverse(multiply(?, inverse(?))))))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 16 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), inverse(X))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 45 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(X)), ?))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 3 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(inverse(inverse(X)), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 30 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(inverse(inverse(X)), multiply(?, inverse(?))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 38 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(X)), multiply(?, inverse(?))))), ?)), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 45 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(inverse(X)), multiply(?, inverse(?))))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 22 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(X)), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 30 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(X)), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 37 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(multiply(X, ?)), multiply(multiply(?, inverse(?)), ?))))
0.62/0.77	= { by lemma 34 }
0.62/0.77	  multiply(X, ?)
0.62/0.77	
0.62/0.77	Lemma 60: inverse(inverse(multiply(inverse(?), X))) = multiply(inverse(?), inverse(inverse(X))).
0.62/0.77	Proof:
0.62/0.77	  inverse(inverse(multiply(inverse(?), X)))
0.62/0.77	= { by lemma 25 }
0.62/0.77	  inverse(inverse(multiply(multiply(inverse(?), X), inverse(multiply(?, inverse(?))))))
0.62/0.77	= { by lemma 42 }
0.62/0.77	  inverse(inverse(multiply(multiply(inverse(?), X), inverse(inverse(multiply(?, inverse(?)))))))
0.62/0.77	= { by lemma 16 }
0.62/0.77	  multiply(multiply(multiply(?, inverse(?)), multiply(inverse(?), X)), multiply(?, inverse(?)))
0.62/0.77	= { by lemma 48 }
0.62/0.77	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, inverse(?)))
0.62/0.77	= { by lemma 3 }
0.62/0.77	  multiply(?, inverse(multiply(multiply(inverse(X), multiply(?, inverse(?))), multiply(?, ?))))
0.62/0.77	= { by lemma 30 }
0.62/0.77	  inverse(inverse(inverse(multiply(multiply(inverse(X), multiply(?, inverse(?))), ?))))
0.62/0.77	= { by lemma 38 }
0.62/0.77	  inverse(multiply(inverse(inverse(multiply(inverse(X), multiply(?, inverse(?))))), ?))
0.62/0.77	= { by lemma 45 }
0.62/0.77	  multiply(inverse(?), inverse(multiply(inverse(X), multiply(?, inverse(?)))))
0.62/0.77	= { by lemma 22 }
0.62/0.77	  multiply(?, inverse(multiply(inverse(X), multiply(?, ?))))
0.62/0.77	= { by lemma 30 }
0.62/0.77	  inverse(inverse(inverse(multiply(inverse(X), ?))))
0.62/0.77	= { by lemma 38 }
0.62/0.77	  inverse(multiply(inverse(inverse(inverse(X))), ?))
0.62/0.77	= { by lemma 45 }
0.62/0.84	  multiply(inverse(?), inverse(inverse(X)))
0.62/0.84	
0.62/0.84	Lemma 61: multiply(multiply(X, ?), inverse(Y)) = multiply(X, multiply(?, inverse(Y))).
0.62/0.84	Proof:
0.62/0.84	  multiply(multiply(X, ?), inverse(Y))
0.62/0.84	= { by lemma 58 }
0.62/0.84	  multiply(multiply(?, multiply(inverse(?), multiply(X, ?))), inverse(Y))
0.62/0.84	= { by lemma 34 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(inverse(multiply(inverse(?), multiply(X, ?))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 2 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(multiply(inverse(?), multiply(X, ?)))))), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 46 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 30 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, inverse(?))), ?)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 38 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(inverse(multiply(inverse(inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, inverse(?))))), ?)), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 45 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, inverse(?))))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 22 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 30 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))), ?)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 38 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(inverse(multiply(inverse(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))))), ?)), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 45 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), ?))))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 48 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), multiply(inverse(?), X)))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 27 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), inverse(inverse(inverse(multiply(inverse(?), X))))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 60 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(?), inverse(inverse(X))))), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 59 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), multiply(inverse(X), ?)), multiply(multiply(?, inverse(?)), ?))))), inverse(Y))
0.62/0.84	= { by lemma 27 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), multiply(inverse(X), ?)), inverse(inverse(?)))))), inverse(Y))
0.62/0.84	= { by lemma 33 }
0.62/0.84	  multiply(multiply(?, multiply(?, inverse(multiply(multiply(inverse(?), multiply(inverse(X), ?)), ?)))), inverse(Y))
0.62/0.84	= { by lemma 36 }
0.62/0.84	  multiply(multiply(?, inverse(inverse(inverse(multiply(inverse(?), multiply(inverse(X), ?)))))), inverse(Y))
0.62/0.84	= { by lemma 60 }
0.62/0.84	  multiply(multiply(?, inverse(multiply(inverse(?), inverse(inverse(multiply(inverse(X), ?)))))), inverse(Y))
0.62/0.84	= { by lemma 59 }
0.62/0.84	  multiply(multiply(?, multiply(inverse(multiply(inverse(X), ?)), ?)), inverse(Y))
0.62/0.84	= { by lemma 48 }
0.62/0.84	  multiply(multiply(?, multiply(multiply(inverse(?), X), ?)), inverse(Y))
0.62/0.84	= { by lemma 26 }
0.62/0.84	  multiply(multiply(?, multiply(multiply(inverse(?), X), ?)), inverse(multiply(Y, multiply(?, inverse(?)))))
0.62/0.84	= { by lemma 57 }
0.62/0.84	  inverse(multiply(multiply(Y, multiply(?, inverse(?))), inverse(multiply(?, multiply(multiply(inverse(?), X), ?)))))
0.62/0.84	= { by lemma 55 }
0.62/0.84	  inverse(inverse(inverse(multiply(multiply(Y, multiply(?, inverse(?))), inverse(multiply(?, multiply(multiply(inverse(?), X), ?)))))))
0.62/0.84	= { by lemma 56 }
0.62/0.84	  multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(multiply(inverse(?), X), ?))), ?))))
0.62/0.84	= { by lemma 6 }
0.62/0.84	  multiply(multiply(?, multiply(inverse(?), X)), inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(multiply(inverse(?), X), ?))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 58 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(multiply(inverse(?), X), ?))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 54 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(multiply(inverse(?), X), inverse(inverse(?))))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 27 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 54 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 43 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(multiply(inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?))), inverse(?)), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 50 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(multiply(inverse(?), multiply(?, multiply(inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?))), inverse(?)))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 32 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(?, multiply(multiply(inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?))), inverse(?)), ?)))))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 47 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(multiply(inverse(?), inverse(multiply(?, inverse(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))))))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 43 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(multiply(inverse(?), multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?))), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 48 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?))), ?)), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 10 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(?, multiply(inverse(?), X))))))
0.62/0.84	= { by lemma 10 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(?, inverse(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?))))))))))
0.62/0.84	= { by lemma 41 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)))))))))
0.62/0.84	= { by lemma 36 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), ?)))))))
0.62/0.84	= { by lemma 33 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), inverse(inverse(?)))))))))
0.62/0.84	= { by lemma 27 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?)))))), ?)), multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(inverse(?), X), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), multiply(multiply(?, inverse(?)), ?))))))))
0.62/0.84	= { by lemma 40 }
0.62/0.84	  multiply(X, inverse(multiply(multiply(Y, multiply(?, inverse(?))), inverse(?))))
0.62/0.84	= { by lemma 49 }
0.62/0.84	  multiply(X, multiply(?, inverse(inverse(inverse(multiply(Y, multiply(?, inverse(?))))))))
0.62/0.84	= { by lemma 54 }
0.62/0.84	  multiply(X, multiply(?, inverse(multiply(Y, multiply(?, inverse(?))))))
0.62/0.84	= { by lemma 26 }
0.62/0.84	  multiply(X, multiply(?, inverse(Y)))
0.62/0.84	
0.62/0.84	Lemma 62: multiply(inverse(Y), inverse(X)) = inverse(multiply(X, Y)).
0.62/0.84	Proof:
0.62/0.84	  multiply(inverse(Y), inverse(X))
0.62/0.84	= { by lemma 53 }
0.62/0.84	  multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(?, inverse(?)))), inverse(inverse(multiply(?, inverse(?)))))))
0.62/0.84	= { by lemma 54 }
0.62/0.84	  multiply(inverse(Y), inverse(multiply(multiply(X, inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))))
0.62/0.84	= { by lemma 22 }
0.62/0.84	  multiply(?, inverse(multiply(multiply(X, inverse(multiply(?, inverse(?)))), multiply(Y, ?))))
0.62/0.84	= { by lemma 56 }
0.62/0.84	  inverse(inverse(inverse(multiply(multiply(X, inverse(multiply(?, inverse(?)))), Y))))
0.62/0.84	= { by lemma 55 }
0.62/0.84	  inverse(multiply(multiply(X, inverse(multiply(?, inverse(?)))), Y))
0.62/0.84	= { by lemma 25 }
0.71/0.87	  inverse(multiply(X, Y))
0.71/0.87	
0.71/0.87	Goal 1 (prove_these_axioms_3): multiply(a3, multiply(b3, c3)) = multiply(multiply(a3, b3), c3).
0.71/0.87	Proof:
0.71/0.87	  multiply(a3, multiply(b3, c3))
0.71/0.87	= { by lemma 10 }
0.71/0.87	  multiply(a3, multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))
0.71/0.87	= { by lemma 34 }
0.71/0.87	  multiply(?, inverse(multiply(inverse(multiply(a3, multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 26 }
0.71/0.87	  multiply(?, inverse(multiply(inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 56 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 6 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))), multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 34 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(multiply(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))), multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 62 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(multiply(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?)), inverse(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 57 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(multiply(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))), inverse(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?))))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 62 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?)))), inverse(multiply(b3, inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))))))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 29 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(multiply(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?)))), inverse(multiply(b3, multiply(?, inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?)))))))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 11 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(multiply(?, inverse(multiply(b3, multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 30 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(b3, ?)))), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(multiply(b3, ?)), multiply(multiply(?, inverse(?)), ?))))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 34 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), ?), inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(b3, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 61 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(multiply(multiply(a3, multiply(?, inverse(?))), multiply(b3, ?))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 56 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(inverse(inverse(multiply(multiply(a3, multiply(?, inverse(?))), b3))))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 54 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(multiply(a3, multiply(?, inverse(?))), b3))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 26 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 56 }
0.71/0.87	  inverse(inverse(inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))))
0.71/0.87	= { by lemma 26 }
0.71/0.87	  inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))), multiply(?, inverse(?))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))), multiply(?, inverse(?))))))
0.71/0.87	= { by lemma 56 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.71/0.87	= { by lemma 3 }
0.71/0.87	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(?))))), multiply(?, inverse(?)))
0.71/0.87	= { by lemma 61 }
0.71/0.87	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), inverse(?)))), multiply(?, inverse(?)))
0.71/0.87	= { by lemma 3 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/0.87	= { by lemma 56 }
0.71/0.87	  inverse(inverse(inverse(multiply(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), multiply(?, inverse(?))), inverse(?)))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  inverse(multiply(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), multiply(?, inverse(?))), inverse(?)))
0.71/0.87	= { by lemma 57 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), multiply(?, inverse(?)))))
0.71/0.87	= { by lemma 10 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?), inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?))))))))
0.71/0.87	= { by lemma 61 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))))))
0.71/0.87	= { by lemma 10 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), multiply(?, multiply(?, inverse(?))))))
0.71/0.87	= { by lemma 26 }
0.71/0.87	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))), ?)))
0.71/0.87	= { by lemma 36 }
0.71/0.87	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))))))
0.71/0.87	= { by lemma 55 }
0.71/0.87	  inverse(multiply(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(a3, b3))))
0.71/0.87	= { by lemma 57 }
0.71/0.87	  multiply(multiply(a3, b3), inverse(multiply(?, inverse(multiply(c3, multiply(multiply(?, inverse(?)), ?))))))
0.71/0.87	= { by lemma 10 }
0.71/0.87	  multiply(multiply(a3, b3), c3)
0.71/0.87	% SZS output end Proof
0.71/0.87	
0.71/0.87	RESULT: Unsatisfiable (the axioms are contradictory).
0.71/0.87	EOF