0.12/0.28	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.29	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.17/0.57	% Computer   : n015.cluster.edu
0.17/0.57	% Model      : x86_64 x86_64
0.17/0.57	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.17/0.57	% Memory     : 8042.1875MB
0.17/0.57	% OS         : Linux 3.10.0-693.el7.x86_64
0.17/0.57	% CPULimit   : 180
0.17/0.57	% DateTime   : Thu Aug 29 10:08:22 EDT 2019
0.17/0.57	% CPUTime    : 
0.21/0.66	% SZS status Unsatisfiable
0.21/0.66	
0.21/0.66	% SZS output start Proof
0.21/0.66	Take the following subset of the input axioms:
0.21/0.66	  fof(prove_these_axioms_1, negated_conjecture, multiply(inverse(a1), a1)!=multiply(inverse(b1), b1)).
0.21/0.66	  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).
0.21/0.66	
0.21/0.66	Now clausify the problem and encode Horn clauses using encoding 3 of
0.21/0.66	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.21/0.66	We repeatedly replace C & s=t => u=v by the two clauses:
0.21/0.66	  fresh(y, y, x1...xn) = u
0.21/0.66	  C => fresh(s, t, x1...xn) = v
0.21/0.66	where fresh is a fresh function symbol and x1..xn are the free
0.21/0.66	variables of u and v.
0.21/0.66	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.21/0.66	input problem has no model of domain size 1).
0.21/0.66	
0.21/0.66	The encoding turns the above axioms into the following unit equations and goals:
0.21/0.66	
0.21/0.87	Axiom 1 (single_axiom): multiply(X, inverse(multiply(Y, multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, Y))), X)))) = W.
0.21/0.87	
0.21/0.87	Lemma 2: multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(W, Y)))) = X.
0.21/0.87	Proof:
0.21/0.87	  multiply(Y, inverse(multiply(multiply(multiply(multiply(Z, inverse(Z)), inverse(multiply(W, X))), multiply(V, inverse(V))), multiply(W, Y))))
0.21/0.87	= { by axiom 1 (single_axiom) }
0.21/0.87	  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))))
0.21/0.87	= { by axiom 1 (single_axiom) }
0.21/0.87	  X
0.21/0.87	
0.21/0.87	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, ?)))).
0.21/0.87	Proof:
0.21/0.87	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
0.21/0.87	= { by lemma 2 }
0.21/0.87	  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, ?))))
0.21/0.87	= { by axiom 1 (single_axiom) }
0.21/0.87	  multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?))))
0.21/0.87	
0.21/0.87	Lemma 4: multiply(Y, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(X, ?)))), multiply(Z, Y)))) = X.
0.21/0.87	Proof:
0.21/0.87	  multiply(Y, inverse(multiply(multiply(?, inverse(multiply(multiply(Z, multiply(?, inverse(?))), multiply(X, ?)))), multiply(Z, Y))))
0.21/0.87	= { by lemma 3 }
0.21/0.87	  multiply(Y, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(Z, X))), multiply(?, inverse(?))), multiply(Z, Y))))
0.21/0.87	= { by lemma 2 }
0.21/0.87	  X
0.21/0.87	
0.21/0.87	Lemma 5: multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?)))))) = multiply(?, inverse(multiply(Y, multiply(Z, ?)))).
0.21/0.87	Proof:
0.21/0.87	  multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?))))))
0.21/0.87	= { by lemma 4 }
0.21/0.87	  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, ?))))
0.21/0.87	= { by axiom 1 (single_axiom) }
0.21/0.87	  multiply(?, inverse(multiply(Y, multiply(Z, ?))))
0.21/0.87	
0.21/0.87	Lemma 6: multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(Z, inverse(Z))) = multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(?, inverse(?))).
0.21/0.87	Proof:
0.21/0.87	  multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(Z, inverse(Z)))
0.21/0.87	= { by lemma 5 }
0.21/0.87	  multiply(multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(Y, multiply(?, inverse(?)))))), multiply(Z, inverse(Z)))
0.21/0.87	= { by lemma 3 }
0.21/0.87	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(multiply(Y, multiply(?, inverse(?))), ?))))
0.21/0.87	= { by lemma 3 }
0.21/0.87	  multiply(multiply(multiply(W, inverse(W)), inverse(multiply(X, multiply(Y, multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.21/0.87	= { by lemma 5 }
0.21/0.88	  multiply(multiply(?, inverse(multiply(X, multiply(Y, ?)))), multiply(?, inverse(?)))
0.21/0.88	
0.21/0.88	Lemma 7: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.21/0.88	Proof:
0.21/0.88	  multiply(X, inverse(X))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  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))))
0.21/0.88	= { by lemma 6 }
0.21/0.88	  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))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  multiply(?, inverse(?))
0.21/0.88	
0.21/0.88	Lemma 8: multiply(W, inverse(multiply(Y, multiply(Z, W)))) = multiply(?, inverse(multiply(Y, multiply(Z, ?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(W, inverse(multiply(Y, multiply(Z, W))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  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))))
0.21/0.88	= { by lemma 4 }
0.21/0.88	  multiply(multiply(X, inverse(X)), inverse(multiply(Y, multiply(Z, multiply(?, inverse(?))))))
0.21/0.88	= { by lemma 4 }
0.21/0.88	  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, ?))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  multiply(?, inverse(multiply(Y, multiply(Z, ?))))
0.21/0.88	
0.21/0.88	Lemma 9: multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V)))) = multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(V, inverse(multiply(multiply(Y, multiply(U, inverse(U))), multiply(Z, V))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  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))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(Y, Z))), multiply(W, inverse(W)))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  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, ?))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  multiply(?, inverse(multiply(multiply(Y, multiply(?, inverse(?))), multiply(Z, ?))))
0.21/0.88	
0.21/0.88	Lemma 10: multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?)))) = inverse(X).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?))))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), multiply(?, inverse(?))), multiply(X, ?))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  inverse(X)
0.21/0.88	
0.21/0.88	Lemma 11: inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))) = X.
0.21/0.88	Proof:
0.21/0.88	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 5 }
0.21/0.88	  inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))))), ?))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 12: multiply(multiply(?, inverse(?)), multiply(?, inverse(?))) = inverse(inverse(multiply(?, inverse(?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  inverse(inverse(multiply(?, inverse(?))))
0.21/0.88	
0.21/0.88	Lemma 13: multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?)))) = inverse(inverse(multiply(?, inverse(?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?))))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(multiply(?, inverse(?)), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 12 }
0.21/0.88	  inverse(inverse(multiply(?, inverse(?))))
0.21/0.88	
0.21/0.88	Lemma 14: multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?)))) = inverse(X).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?))))
0.21/0.88	= { by lemma 13 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(inverse(X), ?)))), multiply(X, ?))))
0.21/0.88	= { by lemma 4 }
0.21/0.88	  inverse(X)
0.21/0.88	
0.21/0.88	Lemma 15: inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))) = X.
0.21/0.88	Proof:
0.21/0.88	  inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))))
0.21/0.88	= { by lemma 14 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 16: multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?))) = inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))).
0.21/0.88	Proof:
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 15 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))), ?))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	
0.21/0.88	Lemma 17: multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), X) = multiply(?, inverse(?)).
0.21/0.88	Proof:
0.21/0.88	  multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), X)
0.21/0.88	= { by lemma 11 }
0.21/0.88	  multiply(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))), inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(?, inverse(?))
0.21/0.88	
0.21/0.88	Lemma 18: multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))) = inverse(inverse(multiply(?, inverse(?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 17 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?))), multiply(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?))))), ?))))
0.21/0.88	= { by lemma 13 }
0.21/0.88	  inverse(inverse(multiply(?, inverse(?))))
0.21/0.88	
0.21/0.88	Lemma 19: inverse(inverse(inverse(multiply(?, inverse(?))))) = multiply(?, inverse(?)).
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(inverse(multiply(?, inverse(?)))))
0.21/0.88	= { by lemma 18 }
0.21/0.88	  inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  multiply(?, inverse(?))
0.21/0.88	
0.21/0.88	Lemma 20: inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))) = inverse(multiply(?, inverse(?))).
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 16 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 19 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), inverse(inverse(inverse(multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 12 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  inverse(multiply(?, inverse(?)))
0.21/0.88	
0.21/0.88	Lemma 21: multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.21/0.88	Proof:
0.21/0.88	  multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 18 }
0.21/0.88	  multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 17 }
0.21/0.88	  multiply(?, inverse(?))
0.21/0.88	
0.21/0.88	Lemma 22: multiply(inverse(Y), inverse(multiply(X, multiply(?, inverse(?))))) = multiply(?, inverse(multiply(X, multiply(Y, ?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(inverse(Y), inverse(multiply(X, multiply(?, inverse(?)))))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(inverse(Y), inverse(multiply(X, multiply(Y, inverse(Y)))))
0.21/0.88	= { by lemma 8 }
0.21/0.88	  multiply(?, inverse(multiply(X, multiply(Y, ?))))
0.21/0.88	
0.21/0.88	Lemma 23: multiply(inverse(X), inverse(multiply(?, inverse(?)))) = inverse(X).
0.21/0.88	Proof:
0.21/0.88	  multiply(inverse(X), inverse(multiply(?, inverse(?))))
0.21/0.88	= { by lemma 21 }
0.21/0.88	  multiply(inverse(X), inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?)))))
0.21/0.88	= { by lemma 22 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(X, ?))))
0.21/0.88	= { by lemma 14 }
0.21/0.88	  inverse(X)
0.21/0.88	
0.21/0.88	Lemma 24: inverse(multiply(?, inverse(?))) = multiply(?, inverse(?)).
0.21/0.88	Proof:
0.21/0.88	  inverse(multiply(?, inverse(?)))
0.21/0.88	= { by lemma 20 }
0.21/0.88	  inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 16 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))), inverse(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 20 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), multiply(inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?)))))), inverse(multiply(?, inverse(?))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 23 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(?, inverse(?))))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(inverse(inverse(multiply(?, inverse(?)))), ?))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  inverse(inverse(inverse(multiply(?, inverse(?)))))
0.21/0.88	= { by lemma 19 }
0.21/0.88	  multiply(?, inverse(?))
0.21/0.88	
0.21/0.88	Lemma 25: multiply(X, inverse(multiply(?, inverse(?)))) = X.
0.21/0.88	Proof:
0.21/0.88	  multiply(X, inverse(multiply(?, inverse(?))))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  multiply(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), inverse(multiply(?, inverse(?))))
0.21/0.88	= { by lemma 23 }
0.21/0.88	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 26: multiply(X, multiply(?, inverse(?))) = X.
0.21/0.88	Proof:
0.21/0.88	  multiply(X, multiply(?, inverse(?)))
0.21/0.88	= { by lemma 24 }
0.21/0.88	  multiply(X, inverse(multiply(?, inverse(?))))
0.21/0.88	= { by lemma 25 }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 27: multiply(multiply(?, inverse(?)), X) = inverse(inverse(X)).
0.21/0.88	Proof:
0.21/0.88	  multiply(multiply(?, inverse(?)), X)
0.21/0.88	= { by lemma 26 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), X), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 16 }
0.21/0.88	  inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 24 }
0.21/0.88	  inverse(inverse(multiply(X, inverse(multiply(?, inverse(?))))))
0.21/0.88	= { by lemma 25 }
0.21/0.88	  inverse(inverse(X))
0.21/0.88	
0.21/0.88	Lemma 28: inverse(inverse(inverse(inverse(X)))) = X.
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(inverse(inverse(X))))
0.21/0.88	= { by lemma 23 }
0.21/0.88	  inverse(inverse(inverse(multiply(inverse(X), inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 24 }
0.21/0.88	  inverse(inverse(inverse(multiply(inverse(X), inverse(inverse(multiply(?, inverse(?))))))))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  multiply(multiply(?, inverse(?)), inverse(multiply(inverse(X), inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(X, ?)))), inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), X))), multiply(?, inverse(?))), inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.88	= { by lemma 12 }
0.21/0.88	  multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), X))), multiply(?, inverse(?))), multiply(multiply(?, inverse(?)), multiply(?, inverse(?))))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 29: multiply(?, inverse(inverse(inverse(multiply(X, ?))))) = inverse(X).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(inverse(inverse(multiply(X, ?)))))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(X, ?))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  multiply(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(X, ?)))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 5 }
0.21/0.88	  multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(?)), multiply(X, multiply(?, inverse(?)))))), multiply(?, inverse(?)))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(X, multiply(?, inverse(?))), ?))))
0.21/0.88	= { by lemma 10 }
0.21/0.88	  inverse(multiply(X, multiply(?, inverse(?))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  inverse(X)
0.21/0.88	
0.21/0.88	Lemma 30: multiply(?, inverse(multiply(X, multiply(?, ?)))) = inverse(inverse(inverse(multiply(X, ?)))).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(X, multiply(?, ?))))
0.21/0.88	= { by lemma 28 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(inverse(inverse(X)))), multiply(?, ?))))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(X))), multiply(?, ?))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(X))), multiply(?, inverse(?))), multiply(?, ?))))
0.21/0.88	= { by lemma 29 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, inverse(inverse(inverse(multiply(X, ?))))))), multiply(?, inverse(?))), multiply(?, ?))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  inverse(inverse(inverse(multiply(X, ?))))
0.21/0.88	
0.21/0.88	Lemma 31: inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, ?)))), ?)))) = Y.
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(Y, ?)))), ?))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(multiply(?, multiply(?, inverse(?))), multiply(Y, ?)))), ?))))
0.21/0.88	= { by lemma 3 }
0.21/0.88	  inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, Y))), multiply(?, inverse(?))), ?))))
0.21/0.88	= { by lemma 30 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(?, Y))), multiply(?, inverse(?))), multiply(?, ?))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  Y
0.21/0.88	
0.21/0.88	Lemma 32: inverse(multiply(?, inverse(multiply(?, multiply(X, ?))))) = multiply(?, X).
0.21/0.88	Proof:
0.21/0.88	  inverse(multiply(?, inverse(multiply(?, multiply(X, ?)))))
0.21/0.88	= { by lemma 29 }
0.21/0.88	  multiply(?, inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(X, ?)))), ?)))))
0.21/0.88	= { by lemma 31 }
0.21/0.88	  multiply(?, X)
0.21/0.88	
0.21/0.88	Lemma 33: inverse(inverse(?)) = ?.
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(?))
0.21/0.88	= { by lemma 28 }
0.21/0.88	  inverse(inverse(inverse(inverse(inverse(inverse(?))))))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(?, inverse(?))))), ?)))))
0.21/0.88	= { by lemma 17 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(?)), ?)))), ?)))), ?)))))
0.21/0.88	= { by lemma 31 }
0.21/0.88	  inverse(multiply(?, inverse(multiply(?, multiply(multiply(?, inverse(?)), ?)))))
0.21/0.88	= { by lemma 32 }
0.21/0.88	  multiply(?, multiply(?, inverse(?)))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  ?
0.21/0.88	
0.21/0.88	Lemma 34: multiply(?, inverse(multiply(inverse(X), multiply(multiply(?, inverse(?)), ?)))) = X.
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(inverse(X), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 7 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(X), multiply(multiply(multiply(X, inverse(X)), inverse(multiply(X, inverse(X)))), ?))))
0.21/0.88	= { by axiom 1 (single_axiom) }
0.21/0.88	  X
0.21/0.88	
0.21/0.88	Lemma 35: multiply(?, multiply(inverse(multiply(X, ?)), ?)) = inverse(inverse(multiply(inverse(X), ?))).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, multiply(inverse(multiply(X, ?)), ?))
0.21/0.88	= { by lemma 33 }
0.21/0.88	  multiply(?, multiply(inverse(multiply(X, inverse(inverse(?)))), ?))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  multiply(?, multiply(inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))), ?))
0.21/0.88	= { by lemma 34 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(multiply(?, multiply(inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))), ?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 2 }
0.21/0.88	  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(?)), ?))))
0.21/0.88	= { by lemma 32 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 30 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), multiply(?, inverse(?))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 27 }
0.21/0.88	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.88	= { by lemma 34 }
0.21/0.88	  inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?)))
0.21/0.88	= { by lemma 11 }
0.21/0.88	  inverse(inverse(multiply(inverse(X), ?)))
0.21/0.88	
0.21/0.88	Lemma 36: multiply(?, inverse(multiply(X, ?))) = inverse(inverse(inverse(X))).
0.21/0.88	Proof:
0.21/0.88	  multiply(?, inverse(multiply(X, ?)))
0.21/0.88	= { by lemma 32 }
0.21/0.88	  inverse(multiply(?, inverse(multiply(?, multiply(inverse(multiply(X, ?)), ?)))))
0.21/0.88	= { by lemma 35 }
0.21/0.88	  inverse(multiply(?, inverse(inverse(inverse(multiply(inverse(X), ?))))))
0.21/0.88	= { by lemma 29 }
0.21/0.88	  inverse(inverse(inverse(X)))
0.21/0.88	
0.21/0.88	Lemma 37: inverse(inverse(multiply(X, ?))) = multiply(inverse(inverse(X)), ?).
0.21/0.88	Proof:
0.21/0.88	  inverse(inverse(multiply(X, ?)))
0.21/0.88	= { by lemma 31 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(?, multiply(inverse(multiply(X, ?)), ?)))), ?)))))
0.21/0.88	= { by lemma 35 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(inverse(inverse(multiply(inverse(X), ?))))), ?)))))
0.21/0.88	= { by lemma 29 }
0.21/0.88	  inverse(inverse(inverse(inverse(multiply(inverse(inverse(X)), ?)))))
0.21/0.88	= { by lemma 28 }
0.21/0.88	  multiply(inverse(inverse(X)), ?)
0.21/0.88	
0.21/0.88	Lemma 38: multiply(inverse(multiply(inverse(inverse(Y)), ?)), inverse(multiply(X, inverse(Y)))) = inverse(multiply(inverse(inverse(X)), ?)).
0.21/0.88	Proof:
0.21/0.88	  multiply(inverse(multiply(inverse(inverse(Y)), ?)), inverse(multiply(X, inverse(Y))))
0.21/0.88	= { by lemma 37 }
0.21/0.88	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(X, inverse(Y))))
0.21/0.88	= { by lemma 26 }
0.21/0.88	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(multiply(X, multiply(?, inverse(?))), inverse(Y))))
0.21/0.88	= { by lemma 29 }
0.21/0.88	  multiply(inverse(inverse(inverse(multiply(Y, ?)))), inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(?, inverse(inverse(inverse(multiply(Y, ?))))))))
0.21/0.88	= { by lemma 9 }
0.21/0.88	  multiply(?, inverse(multiply(multiply(X, multiply(?, inverse(?))), multiply(?, ?))))
0.21/0.89	= { by lemma 30 }
0.21/0.89	  inverse(inverse(inverse(multiply(multiply(X, multiply(?, inverse(?))), ?))))
0.21/0.89	= { by lemma 37 }
0.21/0.89	  inverse(multiply(inverse(inverse(multiply(X, multiply(?, inverse(?))))), ?))
0.21/0.89	= { by lemma 26 }
0.21/0.89	  inverse(multiply(inverse(inverse(X)), ?))
0.21/0.89	
0.21/0.89	Lemma 39: multiply(inverse(multiply(inverse(inverse(X)), ?)), X) = inverse(?).
0.21/0.89	Proof:
0.21/0.89	  multiply(inverse(multiply(inverse(inverse(X)), ?)), X)
0.21/0.89	= { by lemma 25 }
0.21/0.89	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(multiply(?, inverse(?)))))), ?)), X)
0.21/0.89	= { by lemma 24 }
0.21/0.89	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?)), X)
0.21/0.89	= { by lemma 15 }
0.21/0.89	  multiply(inverse(multiply(inverse(inverse(multiply(X, inverse(inverse(multiply(?, inverse(?))))))), ?)), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))))
0.21/0.89	= { by lemma 38 }
0.21/0.89	  inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?))
0.21/0.89	= { by lemma 24 }
0.21/0.89	  inverse(multiply(inverse(multiply(?, inverse(?))), ?))
0.21/0.89	= { by lemma 24 }
0.21/0.89	  inverse(multiply(multiply(?, inverse(?)), ?))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  inverse(inverse(inverse(?)))
0.21/0.89	= { by lemma 33 }
0.21/0.89	  inverse(?)
0.21/0.89	
0.21/0.89	Lemma 40: inverse(inverse(inverse(multiply(X, inverse(?))))) = multiply(?, inverse(X)).
0.21/0.89	Proof:
0.21/0.89	  inverse(inverse(inverse(multiply(X, inverse(?)))))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))
0.21/0.89	= { by lemma 39 }
0.21/0.89	  multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(?, inverse(?))))))
0.21/0.89	= { by lemma 5 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), ?))))
0.21/0.89	= { by lemma 24 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(inverse(multiply(?, inverse(?))), ?)), ?))))
0.21/0.89	= { by lemma 24 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(inverse(multiply(multiply(?, inverse(?)), ?)), ?))))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(inverse(inverse(inverse(?))), ?))))
0.21/0.89	= { by lemma 28 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(inverse(inverse(inverse(?))), inverse(inverse(inverse(inverse(?))))))))
0.21/0.89	= { by lemma 7 }
0.21/0.89	  multiply(?, inverse(multiply(X, multiply(?, inverse(?)))))
0.21/0.89	= { by lemma 26 }
0.21/0.89	  multiply(?, inverse(X))
0.21/0.89	
0.21/0.89	Lemma 41: inverse(inverse(multiply(?, inverse(X)))) = inverse(multiply(X, inverse(?))).
0.21/0.89	Proof:
0.21/0.89	  inverse(inverse(multiply(?, inverse(X))))
0.21/0.89	= { by lemma 34 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(X))))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 36 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(multiply(?, inverse(X)), ?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 40 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), ?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 33 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), inverse(inverse(?))))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(inverse(multiply(X, inverse(?))))), multiply(multiply(?, inverse(?)), ?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 34 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(inverse(multiply(X, inverse(?)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 34 }
0.21/0.89	  inverse(multiply(X, inverse(?)))
0.21/0.89	
0.21/0.89	Lemma 42: inverse(multiply(?, inverse(X))) = multiply(X, inverse(?)).
0.21/0.89	Proof:
0.21/0.89	  inverse(multiply(?, inverse(X)))
0.21/0.89	= { by lemma 34 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(X)))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 41 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(multiply(X, inverse(?))), multiply(multiply(?, inverse(?)), ?))))
0.21/0.89	= { by lemma 34 }
0.21/0.89	  multiply(X, inverse(?))
0.21/0.89	
0.21/0.89	Lemma 43: multiply(multiply(X, ?), inverse(?)) = X.
0.21/0.89	Proof:
0.21/0.89	  multiply(multiply(X, ?), inverse(?))
0.21/0.89	= { by lemma 33 }
0.21/0.89	  multiply(multiply(X, inverse(inverse(?))), inverse(?))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(multiply(X, multiply(multiply(?, inverse(?)), ?)), inverse(?))
0.21/0.89	= { by lemma 42 }
0.21/0.89	  inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))
0.21/0.89	= { by lemma 11 }
0.21/0.89	  X
0.21/0.89	
0.21/0.89	Lemma 44: inverse(multiply(inverse(inverse(X)), ?)) = multiply(inverse(?), inverse(X)).
0.21/0.89	Proof:
0.21/0.89	  inverse(multiply(inverse(inverse(X)), ?))
0.21/0.89	= { by lemma 38 }
0.21/0.89	  multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(?))))), ?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.89	= { by lemma 19 }
0.21/0.89	  multiply(inverse(multiply(multiply(?, inverse(?)), ?)), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(inverse(inverse(inverse(?))), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.89	= { by lemma 33 }
0.21/0.89	  multiply(inverse(?), inverse(multiply(X, inverse(inverse(multiply(?, inverse(?)))))))
0.21/0.89	= { by lemma 24 }
0.21/0.89	  multiply(inverse(?), inverse(multiply(X, inverse(multiply(?, inverse(?))))))
0.21/0.89	= { by lemma 25 }
0.21/0.89	  multiply(inverse(?), inverse(X))
0.21/0.89	
0.21/0.89	Lemma 45: multiply(multiply(X, inverse(?)), ?) = X.
0.21/0.89	Proof:
0.21/0.89	  multiply(multiply(X, inverse(?)), ?)
0.21/0.89	= { by lemma 28 }
0.21/0.89	  multiply(inverse(inverse(inverse(inverse(multiply(X, inverse(?)))))), ?)
0.21/0.89	= { by lemma 27 }
0.21/0.89	  multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))), ?)
0.21/0.89	= { by lemma 33 }
0.21/0.89	  multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))), inverse(inverse(?)))
0.21/0.89	= { by lemma 39 }
0.21/0.89	  multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?))))), inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(?, inverse(?)))))
0.21/0.89	= { by lemma 22 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), ?)), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.21/0.89	= { by lemma 44 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(?, inverse(?)))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.21/0.89	= { by lemma 21 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(inverse(?), inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(?))))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.21/0.89	= { by lemma 8 }
0.21/0.89	  multiply(?, inverse(multiply(multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, ?)))), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.21/0.89	= { by lemma 14 }
0.21/0.89	  multiply(?, inverse(multiply(inverse(?), multiply(multiply(multiply(?, inverse(?)), inverse(multiply(X, inverse(?)))), ?))))
0.21/0.89	= { by axiom 1 (single_axiom) }
0.21/0.89	  X
0.21/0.89	
0.21/0.89	Lemma 46: inverse(multiply(inverse(X), ?)) = multiply(inverse(?), X).
0.21/0.89	Proof:
0.21/0.89	  inverse(multiply(inverse(X), ?))
0.21/0.89	= { by lemma 11 }
0.21/0.89	  inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?)))))), ?))
0.21/0.89	= { by lemma 44 }
0.21/0.89	  multiply(inverse(?), inverse(multiply(?, inverse(multiply(X, multiply(multiply(?, inverse(?)), ?))))))
0.21/0.89	= { by lemma 11 }
0.71/1.09	  multiply(inverse(?), X)
0.71/1.09	
0.71/1.09	Lemma 47: multiply(multiply(X, Y), inverse(?)) = multiply(X, multiply(Y, inverse(?))).
0.71/1.09	Proof:
0.71/1.09	  multiply(multiply(X, Y), inverse(?))
0.71/1.09	= { by lemma 45 }
0.71/1.09	  multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))
0.71/1.09	= { by lemma 2 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 28 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(inverse(inverse(inverse(?))))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 23 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(multiply(inverse(inverse(inverse(?))), inverse(multiply(?, inverse(?)))))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 41 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(multiply(inverse(inverse(inverse(?))), inverse(inverse(multiply(?, inverse(?))))))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 16 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(inverse(?)))), multiply(?, inverse(?))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 45 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(inverse(inverse(?)), inverse(?)), ?))), multiply(?, inverse(?))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 3 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(multiply(multiply(multiply(inverse(inverse(?)), inverse(?)), multiply(?, inverse(?))), multiply(?, ?)))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 30 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(inverse(multiply(multiply(multiply(inverse(inverse(?)), inverse(?)), multiply(?, inverse(?))), ?)))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 37 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(multiply(inverse(inverse(?)), inverse(?)), multiply(?, inverse(?))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 44 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(inverse(?), inverse(multiply(multiply(inverse(inverse(?)), inverse(?)), multiply(?, inverse(?))))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 22 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(multiply(?, inverse(multiply(multiply(inverse(inverse(?)), inverse(?)), multiply(?, ?)))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 30 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(inverse(inverse(multiply(multiply(inverse(inverse(?)), inverse(?)), ?)))), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 37 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(?)), inverse(?)))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 11 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(multiply(inverse(inverse(multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))))), inverse(?)))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 41 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(inverse(inverse(multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?))))))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 27 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 24 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(multiply(inverse(multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 41 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(multiply(inverse(inverse(multiply(?, inverse(?)))), multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 12 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 45 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(multiply(?, inverse(multiply(multiply(multiply(?, inverse(?)), multiply(?, inverse(?))), multiply(multiply(multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))), inverse(?)), ?))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 10 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(inverse(inverse(inverse(multiply(multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?)))), inverse(?)))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 40 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(multiply(?, inverse(multiply(inverse(?), multiply(multiply(?, inverse(?)), ?))))))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 11 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(inverse(multiply(?, inverse(?))), ?)), multiply(multiply(X, multiply(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 11 }
0.71/1.09	  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(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 26 }
0.71/1.09	  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(multiply(Y, inverse(?)), ?)), inverse(?))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 42 }
0.71/1.09	  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(multiply(Y, inverse(?)), ?)))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 3 }
0.71/1.09	  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, multiply(Y, inverse(?))))), multiply(?, inverse(?))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 11 }
0.71/1.09	  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, multiply(Y, inverse(?))))), inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), multiply(multiply(?, inverse(?)), ?)))))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 38 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, inverse(?))))))), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 44 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, inverse(?))))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 27 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), inverse(inverse(inverse(inverse(multiply(X, multiply(Y, inverse(?)))))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 36 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, multiply(Y, inverse(?)))), ?)))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 33 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, multiply(Y, inverse(?)))), inverse(inverse(?)))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 27 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(?, inverse(multiply(inverse(multiply(X, multiply(Y, inverse(?)))), multiply(multiply(?, inverse(?)), ?))))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 46 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(multiply(?, inverse(multiply(inverse(multiply(X, multiply(Y, inverse(?)))), multiply(multiply(?, inverse(?)), ?))))), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 11 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(inverse(multiply(inverse(multiply(X, multiply(Y, inverse(?)))), ?)))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 46 }
0.71/1.09	  multiply(?, inverse(multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(?), multiply(X, multiply(Y, inverse(?)))))), multiply(?, inverse(?))), multiply(inverse(?), ?))))
0.71/1.09	= { by lemma 2 }
0.71/1.10	  multiply(X, multiply(Y, inverse(?)))
0.71/1.10	
0.71/1.10	Lemma 48: multiply(multiply(X, Y), inverse(Y)) = X.
0.71/1.10	Proof:
0.71/1.10	  multiply(multiply(X, Y), inverse(Y))
0.71/1.10	= { by lemma 43 }
0.71/1.10	  multiply(multiply(X, multiply(multiply(Y, ?), inverse(?))), inverse(Y))
0.71/1.10	= { by lemma 47 }
0.71/1.10	  multiply(multiply(multiply(X, multiply(Y, ?)), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 42 }
0.71/1.10	  multiply(inverse(multiply(?, inverse(multiply(X, multiply(Y, ?))))), inverse(Y))
0.71/1.10	= { by lemma 15 }
0.71/1.10	  multiply(inverse(multiply(?, inverse(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?)))))))))), inverse(Y))
0.71/1.10	= { by lemma 42 }
0.71/1.10	  multiply(multiply(multiply(multiply(?, inverse(?)), inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?))))))), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 27 }
0.71/1.10	  multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(inverse(multiply(?, inverse(?)))))))), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 41 }
0.71/1.10	  multiply(multiply(inverse(inverse(inverse(multiply(inverse(multiply(X, multiply(Y, ?))), inverse(multiply(?, inverse(?))))))), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 25 }
0.71/1.10	  multiply(multiply(inverse(inverse(inverse(inverse(multiply(X, multiply(Y, ?)))))), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 27 }
0.71/1.10	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(Y))
0.71/1.10	= { by lemma 43 }
0.71/1.10	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), inverse(?))))
0.71/1.10	= { by lemma 33 }
0.71/1.10	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), inverse(inverse(inverse(?))))))
0.71/1.10	= { by lemma 27 }
0.71/1.10	  multiply(multiply(inverse(multiply(multiply(?, inverse(?)), inverse(multiply(X, multiply(Y, ?))))), inverse(?)), inverse(multiply(multiply(Y, ?), multiply(multiply(?, inverse(?)), inverse(?)))))
0.71/1.10	= { by lemma 7 }
0.71/1.10	  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(?)))))
0.71/1.10	= { by lemma 47 }
0.71/1.10	  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(?))))))
0.71/1.10	= { by axiom 1 (single_axiom) }
0.71/1.10	  X
0.71/1.10	
0.71/1.10	Lemma 49: multiply(inverse(X), X) = multiply(?, inverse(?)).
0.71/1.10	Proof:
0.71/1.10	  multiply(inverse(X), X)
0.71/1.10	= { by lemma 48 }
0.71/1.10	  multiply(multiply(multiply(inverse(X), X), inverse(X)), inverse(inverse(X)))
0.71/1.10	= { by lemma 48 }
0.71/1.10	  multiply(inverse(X), inverse(inverse(X)))
0.71/1.10	= { by lemma 7 }
0.71/1.10	  multiply(?, inverse(?))
0.71/1.10	
0.71/1.10	Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
0.71/1.10	Proof:
0.71/1.10	  multiply(inverse(a1), a1)
0.71/1.10	= { by lemma 49 }
0.71/1.10	  multiply(?, inverse(?))
0.71/1.10	= { by lemma 49 }
0.71/1.10	  multiply(inverse(b1), b1)
0.71/1.10	% SZS output end Proof
0.71/1.10	
0.71/1.10	RESULT: Unsatisfiable (the axioms are contradictory).
0.71/1.10	EOF