0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n011.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 11:35:27 EDT 2019
0.13/0.34	% CPUTime    : 
0.19/0.52	% SZS status Unsatisfiable
0.19/0.52	
0.19/0.52	% SZS output start Proof
0.19/0.52	Take the following subset of the input axioms:
0.71/0.91	  fof(multiply, axiom, ![A, B]: multiply(A, B)=inverse(double_divide(B, A))).
0.71/0.91	  fof(prove_these_axioms_2, negated_conjecture, multiply(multiply(inverse(b2), b2), a2)!=a2).
0.71/0.91	  fof(single_axiom, axiom, ![C, A, B, D]: C=double_divide(double_divide(A, inverse(double_divide(B, C))), double_divide(inverse(B), inverse(double_divide(D, double_divide(A, D)))))).
0.71/0.91	
0.71/0.91	Now clausify the problem and encode Horn clauses using encoding 3 of
0.71/0.91	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.71/0.91	We repeatedly replace C & s=t => u=v by the two clauses:
0.71/0.91	  fresh(y, y, x1...xn) = u
0.71/0.91	  C => fresh(s, t, x1...xn) = v
0.71/0.91	where fresh is a fresh function symbol and x1..xn are the free
0.71/0.91	variables of u and v.
0.71/0.91	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.71/0.91	input problem has no model of domain size 1).
0.71/0.91	
0.71/0.91	The encoding turns the above axioms into the following unit equations and goals:
0.71/0.91	
0.71/0.91	Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
0.71/0.91	Axiom 2 (single_axiom): X = double_divide(double_divide(Y, inverse(double_divide(Z, X))), double_divide(inverse(Z), inverse(double_divide(W, double_divide(Y, W))))).
0.71/0.91	
0.71/0.91	Lemma 3: double_divide(double_divide(Y, multiply(X, Z)), double_divide(inverse(Z), multiply(double_divide(Y, W), W))) = X.
0.71/0.91	Proof:
0.71/0.91	  double_divide(double_divide(Y, multiply(X, Z)), double_divide(inverse(Z), multiply(double_divide(Y, W), W)))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  double_divide(double_divide(Y, inverse(double_divide(Z, X))), double_divide(inverse(Z), multiply(double_divide(Y, W), W)))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  double_divide(double_divide(Y, inverse(double_divide(Z, X))), double_divide(inverse(Z), inverse(double_divide(W, double_divide(Y, W)))))
0.71/0.91	= { by axiom 2 (single_axiom) }
0.71/0.91	  X
0.71/0.91	
0.71/0.91	Lemma 4: multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X))) = inverse(W).
0.71/0.91	Proof:
0.71/0.91	  multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(W, X)))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  inverse(double_divide(double_divide(Y, multiply(W, X)), double_divide(inverse(X), multiply(double_divide(Y, Z), Z))))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  inverse(W)
0.71/0.91	
0.71/0.91	Lemma 5: double_divide(inverse(X), multiply(double_divide(Y, Z), Z)) = double_divide(inverse(X), multiply(double_divide(Y, ?), ?)).
0.71/0.91	Proof:
0.71/0.91	  double_divide(inverse(X), multiply(double_divide(Y, Z), Z))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  double_divide(double_divide(W, multiply(double_divide(inverse(X), multiply(double_divide(Y, Z), Z)), double_divide(Y, multiply(V, X)))), double_divide(inverse(double_divide(Y, multiply(V, X))), multiply(double_divide(W, U), U)))
0.71/0.91	= { by lemma 4 }
0.71/0.91	  double_divide(double_divide(W, inverse(V)), double_divide(inverse(double_divide(Y, multiply(V, X))), multiply(double_divide(W, U), U)))
0.71/0.91	= { by lemma 4 }
0.71/0.91	  double_divide(double_divide(W, multiply(double_divide(inverse(X), multiply(double_divide(Y, ?), ?)), double_divide(Y, multiply(V, X)))), double_divide(inverse(double_divide(Y, multiply(V, X))), multiply(double_divide(W, U), U)))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  double_divide(inverse(X), multiply(double_divide(Y, ?), ?))
0.71/0.91	
0.71/0.91	Lemma 6: multiply(multiply(double_divide(X, Y), Y), inverse(Z)) = multiply(multiply(double_divide(X, ?), ?), inverse(Z)).
0.71/0.91	Proof:
0.71/0.91	  multiply(multiply(double_divide(X, Y), Y), inverse(Z))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  inverse(double_divide(inverse(Z), multiply(double_divide(X, Y), Y)))
0.71/0.91	= { by lemma 5 }
0.71/0.91	  inverse(double_divide(inverse(Z), multiply(double_divide(X, ?), ?)))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  multiply(multiply(double_divide(X, ?), ?), inverse(Z))
0.71/0.91	
0.71/0.91	Lemma 7: multiply(double_divide(X, Y), Y) = multiply(double_divide(X, ?), ?).
0.71/0.91	Proof:
0.71/0.91	  multiply(double_divide(X, Y), Y)
0.71/0.91	= { by lemma 3 }
0.71/0.91	  double_divide(double_divide(Z, multiply(multiply(double_divide(X, Y), Y), inverse(W))), double_divide(inverse(inverse(W)), multiply(double_divide(Z, V), V)))
0.71/0.91	= { by lemma 6 }
0.71/0.91	  double_divide(double_divide(Z, multiply(multiply(double_divide(X, ?), ?), inverse(W))), double_divide(inverse(inverse(W)), multiply(double_divide(Z, V), V)))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  multiply(double_divide(X, ?), ?)
0.71/0.91	
0.71/0.91	Lemma 8: double_divide(double_divide(Y, multiply(X, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(Y, V), V))) = X.
0.71/0.91	Proof:
0.71/0.91	  double_divide(double_divide(Y, multiply(X, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(Y, V), V)))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  double_divide(double_divide(Y, multiply(X, double_divide(Z, W))), double_divide(inverse(double_divide(Z, W)), multiply(double_divide(Y, V), V)))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  X
0.71/0.91	
0.71/0.91	Lemma 9: double_divide(double_divide(inverse(W), multiply(double_divide(X, ?), ?)), double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?))) = double_divide(X, double_divide(Y, Z)).
0.71/0.91	Proof:
0.71/0.91	  double_divide(double_divide(inverse(W), multiply(double_divide(X, ?), ?)), double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?)))
0.71/0.91	= { by lemma 5 }
0.71/0.91	  double_divide(double_divide(inverse(W), multiply(double_divide(X, double_divide(Y, Z)), double_divide(Y, Z))), double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?)))
0.71/0.91	= { by lemma 8 }
0.71/0.91	  double_divide(X, double_divide(Y, Z))
0.71/0.91	
0.71/0.91	Lemma 10: double_divide(X, double_divide(Y, double_divide(Z, Y))) = double_divide(X, double_divide(?, double_divide(Z, ?))).
0.71/0.91	Proof:
0.71/0.91	  double_divide(X, double_divide(Y, double_divide(Z, Y)))
0.71/0.91	= { by lemma 9 }
0.71/0.91	  double_divide(double_divide(inverse(W), multiply(double_divide(X, ?), ?)), double_divide(multiply(double_divide(Z, Y), Y), multiply(double_divide(inverse(W), ?), ?)))
0.71/0.91	= { by lemma 7 }
0.71/0.91	  double_divide(double_divide(inverse(W), multiply(double_divide(X, ?), ?)), double_divide(multiply(double_divide(Z, ?), ?), multiply(double_divide(inverse(W), ?), ?)))
0.71/0.91	= { by lemma 9 }
0.71/0.91	  double_divide(X, double_divide(?, double_divide(Z, ?)))
0.71/0.91	
0.71/0.91	Lemma 11: multiply(double_divide(X, double_divide(Y, X)), Z) = multiply(double_divide(?, double_divide(Y, ?)), Z).
0.71/0.91	Proof:
0.71/0.91	  multiply(double_divide(X, double_divide(Y, X)), Z)
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  inverse(double_divide(Z, double_divide(X, double_divide(Y, X))))
0.71/0.91	= { by lemma 10 }
0.71/0.91	  inverse(double_divide(Z, double_divide(?, double_divide(Y, ?))))
0.71/0.91	= { by axiom 1 (multiply) }
0.71/0.91	  multiply(double_divide(?, double_divide(Y, ?)), Z)
0.71/0.91	
0.71/0.91	Lemma 12: multiply(double_divide(?, double_divide(X, ?)), double_divide(X, Y)) = multiply(double_divide(Y, ?), ?).
0.71/0.91	Proof:
0.71/0.91	  multiply(double_divide(?, double_divide(X, ?)), double_divide(X, Y))
0.71/0.91	= { by lemma 11 }
0.71/0.91	  multiply(double_divide(Y, double_divide(X, Y)), double_divide(X, Y))
0.71/0.91	= { by lemma 7 }
0.71/0.91	  multiply(double_divide(Y, ?), ?)
0.71/0.91	
0.71/0.91	Lemma 13: double_divide(X, double_divide(Y, X)) = double_divide(?, double_divide(Y, ?)).
0.71/0.91	Proof:
0.71/0.91	  double_divide(X, double_divide(Y, X))
0.71/0.91	= { by lemma 3 }
0.71/0.91	  double_divide(double_divide(Z, multiply(double_divide(X, double_divide(Y, X)), W)), double_divide(inverse(W), multiply(double_divide(Z, V), V)))
0.71/0.91	= { by lemma 11 }
0.71/0.91	  double_divide(double_divide(Z, multiply(double_divide(?, double_divide(Y, ?)), W)), double_divide(inverse(W), multiply(double_divide(Z, V), V)))
0.71/0.91	= { by lemma 3 }
0.71/0.92	  double_divide(?, double_divide(Y, ?))
0.71/0.92	
0.71/0.92	Lemma 14: double_divide(W, double_divide(Y, multiply(double_divide(?, double_divide(W, ?)), X))) = double_divide(inverse(X), multiply(double_divide(Y, ?), ?)).
0.71/0.92	Proof:
0.71/0.92	  double_divide(W, double_divide(Y, multiply(double_divide(?, double_divide(W, ?)), X)))
0.71/0.92	= { by lemma 9 }
0.71/0.92	  double_divide(double_divide(inverse(?), multiply(double_divide(W, ?), ?)), double_divide(multiply(multiply(double_divide(?, double_divide(W, ?)), X), Y), multiply(double_divide(inverse(?), ?), ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  double_divide(double_divide(inverse(?), inverse(double_divide(?, double_divide(W, ?)))), double_divide(multiply(multiply(double_divide(?, double_divide(W, ?)), X), Y), multiply(double_divide(inverse(?), ?), ?)))
0.71/0.92	= { by lemma 4 }
0.71/0.92	  double_divide(double_divide(inverse(?), multiply(double_divide(inverse(X), multiply(double_divide(Y, ?), ?)), double_divide(Y, multiply(double_divide(?, double_divide(W, ?)), X)))), double_divide(multiply(multiply(double_divide(?, double_divide(W, ?)), X), Y), multiply(double_divide(inverse(?), ?), ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  double_divide(double_divide(inverse(?), multiply(double_divide(inverse(X), multiply(double_divide(Y, ?), ?)), double_divide(Y, multiply(double_divide(?, double_divide(W, ?)), X)))), double_divide(inverse(double_divide(Y, multiply(double_divide(?, double_divide(W, ?)), X))), multiply(double_divide(inverse(?), ?), ?)))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  double_divide(inverse(X), multiply(double_divide(Y, ?), ?))
0.71/0.92	
0.71/0.92	Lemma 15: double_divide(multiply(?, X), multiply(double_divide(Y, ?), ?)) = double_divide(X, double_divide(Y, multiply(double_divide(?, ?), ?))).
0.71/0.92	Proof:
0.71/0.92	  double_divide(multiply(?, X), multiply(double_divide(Y, ?), ?))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  double_divide(inverse(double_divide(X, ?)), multiply(double_divide(Y, ?), ?))
0.71/0.92	= { by lemma 14 }
0.71/0.92	  double_divide(X, double_divide(Y, multiply(double_divide(?, double_divide(X, ?)), double_divide(X, ?))))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  double_divide(X, double_divide(Y, multiply(double_divide(?, ?), ?)))
0.71/0.92	
0.71/0.92	Lemma 16: double_divide(multiply(?, X), multiply(double_divide(inverse(Y), ?), ?)) = double_divide(X, double_divide(inverse(Y), multiply(double_divide(?, ?), ?))).
0.71/0.92	Proof:
0.71/0.92	  double_divide(multiply(?, X), multiply(double_divide(inverse(Y), ?), ?))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  double_divide(inverse(double_divide(X, ?)), multiply(double_divide(inverse(Y), ?), ?))
0.71/0.92	= { by lemma 14 }
0.71/0.92	  double_divide(X, double_divide(inverse(Y), multiply(double_divide(?, double_divide(X, ?)), double_divide(X, ?))))
0.71/0.92	= { by lemma 5 }
0.71/0.92	  double_divide(X, double_divide(inverse(Y), multiply(double_divide(?, ?), ?)))
0.71/0.92	
0.71/0.92	Lemma 17: multiply(double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), ?), ?) = multiply(Y, double_divide(multiply(W, Z), multiply(double_divide(X, ?), ?))).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), ?), ?)
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(Y, double_divide(Z, W))), double_divide(multiply(W, Z), multiply(double_divide(X, ?), ?))), double_divide(multiply(W, Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by lemma 8 }
0.71/0.92	  multiply(Y, double_divide(multiply(W, Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	
0.71/0.92	Lemma 18: multiply(double_divide(X, multiply(double_divide(?, double_divide(Y, ?)), Z)), Y) = multiply(multiply(double_divide(X, ?), ?), inverse(Z)).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(?, double_divide(Y, ?)), Z)), Y)
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  inverse(double_divide(Y, double_divide(X, multiply(double_divide(?, double_divide(Y, ?)), Z))))
0.71/0.92	= { by lemma 14 }
0.71/0.92	  inverse(double_divide(inverse(Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), inverse(Z))
0.71/0.92	
0.71/0.92	Lemma 19: double_divide(double_divide(inverse(Y), multiply(X, double_divide(double_divide(?, multiply(Z, Y)), ?))), Z) = X.
0.71/0.92	Proof:
0.71/0.92	  double_divide(double_divide(inverse(Y), multiply(X, double_divide(double_divide(?, multiply(Z, Y)), ?))), Z)
0.71/0.92	= { by lemma 3 }
0.71/0.92	  double_divide(double_divide(inverse(Y), multiply(X, double_divide(double_divide(?, multiply(Z, Y)), ?))), double_divide(double_divide(?, multiply(Z, Y)), double_divide(inverse(Y), multiply(double_divide(?, ?), ?))))
0.71/0.92	= { by lemma 16 }
0.71/0.92	  double_divide(double_divide(inverse(Y), multiply(X, double_divide(double_divide(?, multiply(Z, Y)), ?))), double_divide(multiply(?, double_divide(?, multiply(Z, Y))), multiply(double_divide(inverse(Y), ?), ?)))
0.71/0.92	= { by lemma 8 }
0.71/0.92	  X
0.71/0.92	
0.71/0.92	Lemma 20: multiply(multiply(Y, multiply(double_divide(?, double_divide(Z, ?)), W)), inverse(W)) = multiply(Y, Z).
0.71/0.92	Proof:
0.71/0.92	  multiply(multiply(Y, multiply(double_divide(?, double_divide(Z, ?)), W)), inverse(W))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  multiply(multiply(Y, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(Z, ?)), W), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), inverse(W))
0.71/0.92	= { by lemma 16 }
0.71/0.92	  multiply(multiply(Y, double_divide(multiply(?, double_divide(?, multiply(multiply(double_divide(?, double_divide(Z, ?)), W), ?))), multiply(double_divide(inverse(?), ?), ?))), inverse(W))
0.71/0.92	= { by lemma 17 }
0.71/0.92	  multiply(multiply(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(Z, ?)), W), ?)), ?))), ?), ?), inverse(W))
0.71/0.92	= { by lemma 18 }
0.71/0.92	  multiply(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(Z, ?)), W), ?)), ?))), multiply(double_divide(?, double_divide(Z, ?)), W)), Z)
0.71/0.92	= { by lemma 19 }
0.71/0.92	  multiply(Y, Z)
0.71/0.92	
0.71/0.92	Lemma 21: double_divide(Y, double_divide(inverse(Z), multiply(Y, multiply(X, Z)))) = X.
0.71/0.92	Proof:
0.71/0.92	  double_divide(Y, double_divide(inverse(Z), multiply(Y, multiply(X, Z))))
0.71/0.92	= { by lemma 19 }
0.71/0.92	  double_divide(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), ?))), multiply(X, Z)), double_divide(inverse(Z), multiply(Y, multiply(X, Z))))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  double_divide(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), ?))), multiply(X, Z)), double_divide(inverse(Z), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))))
0.71/0.92	= { by lemma 16 }
0.71/0.92	  double_divide(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), ?))), multiply(X, Z)), double_divide(inverse(Z), multiply(Y, double_divide(multiply(?, double_divide(?, multiply(multiply(X, Z), ?))), multiply(double_divide(inverse(?), ?), ?)))))
0.71/0.92	= { by lemma 17 }
0.71/0.92	  double_divide(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), ?))), multiply(X, Z)), double_divide(inverse(Z), multiply(double_divide(double_divide(inverse(?), multiply(Y, double_divide(double_divide(?, multiply(multiply(X, Z), ?)), ?))), ?), ?)))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  X
0.71/0.92	
0.71/0.92	Lemma 22: multiply(X, multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)) = X.
0.71/0.92	Proof:
0.71/0.92	  multiply(X, multiply(double_divide(?, double_divide(inverse(Y), ?)), Y))
0.71/0.92	= { by lemma 21 }
0.71/0.92	  double_divide(double_divide(?, multiply(X, inverse(Y))), double_divide(inverse(inverse(Y)), multiply(double_divide(?, multiply(X, inverse(Y))), multiply(multiply(X, multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), inverse(Y)))))
0.71/0.92	= { by lemma 20 }
0.71/0.92	  double_divide(double_divide(?, multiply(X, inverse(Y))), double_divide(inverse(inverse(Y)), multiply(double_divide(?, multiply(X, inverse(Y))), multiply(X, inverse(Y)))))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  X
0.71/0.92	
0.71/0.92	Lemma 23: multiply(double_divide(X, multiply(double_divide(?, ?), ?)), Y) = multiply(multiply(double_divide(X, ?), ?), multiply(?, Y)).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(?, ?), ?)), Y)
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(?, double_divide(Y, ?)), double_divide(Y, ?))), Y)
0.71/0.92	= { by lemma 18 }
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), inverse(double_divide(Y, ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), multiply(?, Y))
0.71/0.92	
0.71/0.92	Lemma 24: multiply(Y, double_divide(inverse(Z), multiply(double_divide(X, ?), ?))) = multiply(double_divide(double_divide(X, multiply(Y, Z)), ?), ?).
0.71/0.92	Proof:
0.71/0.92	  multiply(Y, double_divide(inverse(Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(Y, Z)), double_divide(inverse(Z), multiply(double_divide(X, ?), ?))), double_divide(inverse(Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(Y, Z)), ?), ?)
0.71/0.92	
0.71/0.92	Lemma 25: multiply(double_divide(double_divide(X, multiply(double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?)), W)), ?), ?) = multiply(double_divide(Y, Z), X).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?)), W)), ?), ?)
0.71/0.92	= { by lemma 24 }
0.71/0.92	  multiply(double_divide(multiply(Z, Y), multiply(double_divide(inverse(W), ?), ?)), double_divide(inverse(W), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(double_divide(inverse(double_divide(Y, Z)), multiply(double_divide(inverse(W), ?), ?)), double_divide(inverse(W), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by lemma 5 }
0.71/0.92	  multiply(double_divide(inverse(double_divide(Y, Z)), multiply(double_divide(inverse(W), ?), ?)), double_divide(inverse(W), multiply(double_divide(X, double_divide(Y, Z)), double_divide(Y, Z))))
0.71/0.92	= { by lemma 4 }
0.71/0.92	  inverse(double_divide(X, double_divide(Y, Z)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(double_divide(Y, Z), X)
0.71/0.92	
0.71/0.92	Lemma 26: multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), ?), ?)), Z)), ?), ?) = multiply(Y, X).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), ?), ?)), Z)), ?), ?)
0.71/0.92	= { by lemma 24 }
0.71/0.92	  multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), ?), ?)), double_divide(inverse(Z), multiply(double_divide(X, ?), ?)))
0.71/0.92	= { by lemma 5 }
0.71/0.92	  multiply(double_divide(inverse(Y), multiply(double_divide(inverse(Z), ?), ?)), double_divide(inverse(Z), multiply(double_divide(X, Y), Y)))
0.71/0.92	= { by lemma 4 }
0.71/0.92	  inverse(double_divide(X, Y))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(Y, X)
0.71/0.92	
0.71/0.92	Lemma 27: multiply(multiply(double_divide(X, ?), ?), multiply(?, multiply(double_divide(?, ?), ?))) = multiply(double_divide(X, ?), ?).
0.71/0.92	Proof:
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), multiply(?, multiply(double_divide(?, ?), ?)))
0.71/0.92	= { by lemma 23 }
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(?, ?), ?)), multiply(double_divide(?, ?), ?))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(X, ?), ?)
0.71/0.92	
0.71/0.92	Lemma 28: multiply(multiply(Y, X), multiply(?, multiply(double_divide(?, ?), ?))) = multiply(Y, X).
0.71/0.92	Proof:
0.71/0.92	  multiply(multiply(Y, X), multiply(?, multiply(double_divide(?, ?), ?)))
0.71/0.92	= { by lemma 26 }
0.71/0.92	  multiply(multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?), multiply(?, multiply(double_divide(?, ?), ?)))
0.71/0.92	= { by lemma 27 }
0.71/0.92	  multiply(double_divide(double_divide(X, multiply(double_divide(inverse(Y), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.92	= { by lemma 26 }
0.71/0.92	  multiply(Y, X)
0.71/0.92	
0.71/0.92	Lemma 29: multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X)), Y) = multiply(X, Y).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X)), Y)
0.71/0.92	= { by lemma 25 }
0.71/0.92	  multiply(double_divide(double_divide(Y, multiply(double_divide(multiply(inverse(X), multiply(?, multiply(double_divide(?, ?), ?))), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.92	= { by lemma 4 }
0.71/0.92	  multiply(double_divide(double_divide(Y, multiply(double_divide(multiply(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(X, ?))), multiply(?, multiply(double_divide(?, ?), ?))), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.92	= { by lemma 28 }
0.71/0.92	  multiply(double_divide(double_divide(Y, multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(X, ?))), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.92	= { by lemma 4 }
0.71/0.92	  multiply(double_divide(double_divide(Y, multiply(double_divide(inverse(X), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.92	= { by lemma 26 }
0.71/0.92	  multiply(X, Y)
0.71/0.92	
0.71/0.92	Lemma 30: multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?) = multiply(?, inverse(?)).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?)
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(?)), inverse(?))
0.71/0.92	= { by lemma 29 }
0.71/0.92	  multiply(?, inverse(?))
0.71/0.92	
0.71/0.92	Lemma 31: multiply(Y, double_divide(inverse(Z), multiply(X, multiply(Y, Z)))) = multiply(double_divide(X, ?), ?).
0.71/0.92	Proof:
0.71/0.92	  multiply(Y, double_divide(inverse(Z), multiply(X, multiply(Y, Z))))
0.71/0.92	= { by lemma 21 }
0.71/0.92	  multiply(double_divide(X, double_divide(inverse(Z), multiply(X, multiply(Y, Z)))), double_divide(inverse(Z), multiply(X, multiply(Y, Z))))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(X, ?), ?)
0.71/0.92	
0.71/0.92	Lemma 32: multiply(multiply(X, multiply(double_divide(Z, ?), ?)), Z) = X.
0.71/0.92	Proof:
0.71/0.92	  multiply(multiply(X, multiply(double_divide(Z, ?), ?)), Z)
0.71/0.92	= { by lemma 31 }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), double_divide(inverse(?), multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?))))), Z)
0.71/0.92	= { by lemma 22 }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), double_divide(inverse(?), multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?))))), multiply(Z, multiply(double_divide(?, double_divide(inverse(?), ?)), ?)))
0.71/0.92	= { by lemma 20 }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), double_divide(inverse(?), multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?))))), multiply(multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?)), inverse(?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), double_divide(inverse(?), multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?))))), inverse(double_divide(inverse(?), multiply(Z, multiply(double_divide(?, double_divide(multiply(double_divide(?, double_divide(inverse(?), ?)), ?), ?)), ?)))))
0.71/0.92	= { by lemma 20 }
0.71/0.92	  multiply(X, multiply(double_divide(?, double_divide(inverse(?), ?)), ?))
0.71/0.92	= { by lemma 22 }
0.71/0.92	  X
0.71/0.92	
0.71/0.92	Lemma 33: multiply(X, multiply(?, inverse(?))) = X.
0.71/0.92	Proof:
0.71/0.92	  multiply(X, multiply(?, inverse(?)))
0.71/0.92	= { by lemma 30 }
0.71/0.92	  multiply(X, multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?))
0.71/0.92	= { by lemma 28 }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?)), multiply(?, multiply(double_divide(?, ?), ?)))
0.71/0.92	= { by lemma 32 }
0.71/0.92	  X
0.71/0.92	
0.71/0.92	Lemma 34: multiply(X, multiply(double_divide(?, ?), ?)) = multiply(X, inverse(?)).
0.71/0.92	Proof:
0.71/0.92	  multiply(X, multiply(double_divide(?, ?), ?))
0.71/0.92	= { by lemma 33 }
0.71/0.92	  multiply(multiply(X, multiply(double_divide(?, ?), ?)), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 3 }
0.71/0.92	  multiply(multiply(X, double_divide(double_divide(?, multiply(multiply(double_divide(?, ?), ?), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 16 }
0.71/0.92	  multiply(multiply(X, double_divide(multiply(?, double_divide(?, multiply(multiply(double_divide(?, ?), ?), ?))), multiply(double_divide(inverse(?), ?), ?))), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 17 }
0.71/0.92	  multiply(multiply(double_divide(double_divide(inverse(?), multiply(X, double_divide(double_divide(?, multiply(multiply(double_divide(?, ?), ?), ?)), ?))), ?), ?), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 23 }
0.71/0.92	  multiply(double_divide(double_divide(inverse(?), multiply(X, double_divide(double_divide(?, multiply(multiply(double_divide(?, ?), ?), ?)), ?))), multiply(double_divide(?, ?), ?)), inverse(?))
0.71/0.92	= { by lemma 19 }
0.71/0.92	  multiply(X, inverse(?))
0.71/0.92	
0.71/0.92	Lemma 35: double_divide(?, double_divide(?, ?)) = ?.
0.71/0.92	Proof:
0.71/0.92	  double_divide(?, double_divide(?, ?))
0.71/0.92	= { by lemma 13 }
0.71/0.92	  double_divide(multiply(double_divide(?, ?), ?), double_divide(?, multiply(double_divide(?, ?), ?)))
0.71/0.92	= { by lemma 15 }
0.71/0.92	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), multiply(double_divide(?, ?), ?))
0.71/0.92	= { by lemma 22 }
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), multiply(double_divide(?, ?), ?)), multiply(double_divide(?, double_divide(inverse(?), ?)), ?))
0.71/0.92	= { by lemma 23 }
0.71/0.92	  multiply(multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?), multiply(?, multiply(double_divide(?, double_divide(inverse(?), ?)), ?)))
0.71/0.92	= { by lemma 30 }
0.71/0.92	  multiply(multiply(?, inverse(?)), multiply(?, multiply(double_divide(?, double_divide(inverse(?), ?)), ?)))
0.71/0.92	= { by lemma 34 }
0.71/0.92	  multiply(multiply(?, multiply(double_divide(?, ?), ?)), multiply(?, multiply(double_divide(?, double_divide(inverse(?), ?)), ?)))
0.71/0.92	= { by lemma 22 }
0.71/0.92	  multiply(multiply(?, multiply(double_divide(?, ?), ?)), ?)
0.71/0.92	= { by lemma 32 }
0.71/0.92	  ?
0.71/0.92	
0.71/0.92	Lemma 36: multiply(double_divide(X, ?), ?) = multiply(?, double_divide(?, X)).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(X, ?), ?)
0.71/0.92	= { by lemma 12 }
0.71/0.92	  multiply(double_divide(?, double_divide(?, ?)), double_divide(?, X))
0.71/0.92	= { by lemma 35 }
0.71/0.92	  multiply(?, double_divide(?, X))
0.71/0.92	
0.71/0.92	Lemma 37: multiply(multiply(double_divide(X, ?), ?), Y) = double_divide(X, multiply(double_divide(Y, ?), ?)).
0.71/0.92	Proof:
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), Y)
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(multiply(double_divide(X, multiply(double_divide(Y, ?), ?)), multiply(double_divide(Y, ?), ?)), Y)
0.71/0.92	= { by lemma 32 }
0.71/0.92	  double_divide(X, multiply(double_divide(Y, ?), ?))
0.71/0.92	
0.71/0.92	Lemma 38: multiply(double_divide(X, multiply(double_divide(Z, ?), ?)), Y) = multiply(multiply(double_divide(X, ?), ?), multiply(Z, Y)).
0.71/0.92	Proof:
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(Z, ?), ?)), Y)
0.71/0.92	= { by lemma 12 }
0.71/0.92	  multiply(double_divide(X, multiply(double_divide(?, double_divide(Y, ?)), double_divide(Y, Z))), Y)
0.71/0.92	= { by lemma 18 }
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), inverse(double_divide(Y, Z)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(multiply(double_divide(X, ?), ?), multiply(Z, Y))
0.71/0.92	
0.71/0.92	Lemma 39: double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), multiply(?, double_divide(?, multiply(Z, double_divide(Z, X))))) = inverse(X).
0.71/0.92	Proof:
0.71/0.92	  double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), multiply(?, double_divide(?, multiply(Z, double_divide(Z, X)))))
0.71/0.92	= { by lemma 36 }
0.71/0.92	  double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), multiply(double_divide(multiply(Z, double_divide(Z, X)), ?), ?))
0.71/0.92	= { by lemma 37 }
0.71/0.92	  multiply(multiply(double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), ?), ?), multiply(Z, double_divide(Z, X)))
0.71/0.92	= { by lemma 38 }
0.71/0.92	  multiply(double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), multiply(double_divide(Z, ?), ?)), double_divide(Z, X))
0.71/0.92	= { by lemma 22 }
0.71/0.92	  multiply(double_divide(inverse(multiply(double_divide(?, double_divide(inverse(Y), ?)), Y)), multiply(double_divide(Z, ?), ?)), double_divide(Z, multiply(X, multiply(double_divide(?, double_divide(inverse(Y), ?)), Y))))
0.71/0.92	= { by lemma 4 }
0.71/0.92	  inverse(X)
0.71/0.92	
0.71/0.92	Lemma 40: inverse(multiply(X, multiply(inverse(Y), Y))) = inverse(X).
0.71/0.92	Proof:
0.71/0.92	  inverse(multiply(X, multiply(inverse(Y), Y)))
0.71/0.92	= { by lemma 39 }
0.71/0.92	  double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(inverse(Y), double_divide(inverse(Y), multiply(X, multiply(inverse(Y), Y)))))))
0.71/0.92	= { by lemma 31 }
0.71/0.92	  double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(double_divide(X, ?), ?))))
0.71/0.92	= { by lemma 36 }
0.71/0.92	  double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, X)))))
0.71/0.92	= { by lemma 39 }
0.71/0.92	  inverse(X)
0.71/0.92	
0.71/0.92	Lemma 41: double_divide(X, multiply(?, inverse(?))) = multiply(double_divide(X, ?), ?).
0.71/0.92	Proof:
0.71/0.92	  double_divide(X, multiply(?, inverse(?)))
0.71/0.92	= { by lemma 33 }
0.71/0.92	  multiply(double_divide(X, multiply(?, inverse(?))), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(X, ?), ?)
0.71/0.92	
0.71/0.92	Lemma 42: multiply(X, inverse(X)) = multiply(?, inverse(?)).
0.71/0.92	Proof:
0.71/0.92	  multiply(X, inverse(X))
0.71/0.92	= { by lemma 29 }
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X)), inverse(X))
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?)
0.71/0.92	= { by lemma 7 }
0.71/0.92	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(?)), inverse(?))
0.71/0.92	= { by lemma 29 }
0.71/0.92	  multiply(?, inverse(?))
0.71/0.92	
0.71/0.92	Lemma 43: multiply(?, inverse(?)) = double_divide(inverse(?), ?).
0.71/0.92	Proof:
0.71/0.92	  multiply(?, inverse(?))
0.71/0.92	= { by lemma 42 }
0.71/0.92	  multiply(double_divide(inverse(?), ?), inverse(double_divide(inverse(?), ?)))
0.71/0.92	= { by axiom 1 (multiply) }
0.71/0.92	  multiply(double_divide(inverse(?), ?), multiply(?, inverse(?)))
0.71/0.92	= { by lemma 33 }
0.71/0.93	  double_divide(inverse(?), ?)
0.71/0.93	
0.71/0.93	Lemma 44: multiply(double_divide(inverse(X), ?), ?) = multiply(double_divide(inverse(?), ?), X).
0.71/0.93	Proof:
0.71/0.93	  multiply(double_divide(inverse(X), ?), ?)
0.71/0.93	= { by lemma 7 }
0.71/0.93	  multiply(double_divide(inverse(X), X), X)
0.71/0.93	= { by lemma 25 }
0.71/0.93	  multiply(double_divide(double_divide(X, multiply(double_divide(multiply(X, inverse(X)), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.93	= { by lemma 42 }
0.71/0.93	  multiply(double_divide(double_divide(X, multiply(double_divide(multiply(?, inverse(?)), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)
0.71/0.93	= { by lemma 25 }
0.71/0.93	  multiply(double_divide(inverse(?), ?), X)
0.71/0.93	
0.71/0.93	Lemma 45: multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y) = inverse(Z).
0.71/0.93	Proof:
0.71/0.93	  multiply(double_divide(inverse(X), multiply(Y, multiply(Z, X))), Y)
0.71/0.93	= { by axiom 1 (multiply) }
0.71/0.93	  inverse(double_divide(Y, double_divide(inverse(X), multiply(Y, multiply(Z, X)))))
0.71/0.93	= { by lemma 21 }
0.71/0.93	  inverse(Z)
0.71/0.93	
0.71/0.93	Lemma 46: double_divide(X, double_divide(inverse(Y), Y)) = double_divide(X, double_divide(inverse(?), ?)).
0.71/0.93	Proof:
0.71/0.93	  double_divide(X, double_divide(inverse(Y), Y))
0.71/0.93	= { by lemma 9 }
0.71/0.93	  double_divide(double_divide(inverse(Z), multiply(double_divide(X, ?), ?)), double_divide(multiply(Y, inverse(Y)), multiply(double_divide(inverse(Z), ?), ?)))
0.71/0.93	= { by lemma 42 }
0.71/0.93	  double_divide(double_divide(inverse(Z), multiply(double_divide(X, ?), ?)), double_divide(multiply(?, inverse(?)), multiply(double_divide(inverse(Z), ?), ?)))
0.71/0.93	= { by lemma 9 }
0.71/0.93	  double_divide(X, double_divide(inverse(?), ?))
0.71/0.93	
0.71/0.93	Lemma 47: multiply(double_divide(inverse(?), ?), X) = multiply(inverse(?), multiply(?, X)).
0.71/0.93	Proof:
0.71/0.93	  multiply(double_divide(inverse(?), ?), X)
0.71/0.93	= { by lemma 44 }
0.71/0.93	  multiply(double_divide(inverse(X), ?), ?)
0.71/0.93	= { by axiom 1 (multiply) }
0.71/0.93	  inverse(double_divide(?, double_divide(inverse(X), ?)))
0.71/0.93	= { by lemma 13 }
0.71/0.93	  inverse(double_divide(X, double_divide(inverse(X), X)))
0.71/0.93	= { by lemma 46 }
0.71/0.93	  inverse(double_divide(X, double_divide(inverse(?), ?)))
0.71/0.93	= { by lemma 46 }
0.77/0.93	  inverse(double_divide(X, double_divide(inverse(multiply(double_divide(?, ?), ?)), multiply(double_divide(?, ?), ?))))
0.77/0.93	= { by lemma 16 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(multiply(double_divide(?, ?), ?)), ?), ?)))
0.77/0.93	= { by lemma 19 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(multiply(double_divide(?, ?), ?)), double_divide(double_divide(inverse(?), multiply(?, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?), ?)), ?))), multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?))), ?)))
0.77/0.93	= { by lemma 14 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(double_divide(double_divide(inverse(?), multiply(?, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?), ?)), ?))), ?), ?)), ?)))
0.77/0.93	= { by lemma 17 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, double_divide(multiply(?, double_divide(?, multiply(multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?), ?))), multiply(double_divide(inverse(?), ?), ?)))), ?)))
0.77/0.93	= { by lemma 16 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, double_divide(double_divide(?, multiply(multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))), ?)))
0.77/0.93	= { by lemma 3 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, multiply(double_divide(?, double_divide(inverse(multiply(double_divide(?, ?), ?)), ?)), ?))), ?)))
0.77/0.93	= { by lemma 13 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, multiply(double_divide(multiply(double_divide(?, ?), ?), double_divide(inverse(multiply(double_divide(?, ?), ?)), multiply(double_divide(?, ?), ?))), ?))), ?)))
0.77/0.93	= { by lemma 27 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, multiply(double_divide(multiply(double_divide(?, ?), ?), double_divide(inverse(multiply(double_divide(?, ?), ?)), multiply(multiply(double_divide(?, ?), ?), multiply(?, multiply(double_divide(?, ?), ?))))), ?))), ?)))
0.77/0.93	= { by lemma 21 }
0.77/0.93	  inverse(double_divide(multiply(?, X), multiply(double_divide(inverse(?), multiply(?, multiply(?, ?))), ?)))
0.77/0.93	= { by lemma 45 }
0.77/0.93	  inverse(double_divide(multiply(?, X), inverse(?)))
0.77/0.93	= { by axiom 1 (multiply) }
0.77/0.93	  multiply(inverse(?), multiply(?, X))
0.77/0.93	
0.77/0.93	Lemma 48: multiply(inverse(?), multiply(?, X)) = double_divide(?, double_divide(X, ?)).
0.77/0.93	Proof:
0.77/0.93	  multiply(inverse(?), multiply(?, X))
0.77/0.93	= { by lemma 47 }
0.77/0.93	  multiply(double_divide(inverse(?), ?), X)
0.77/0.93	= { by lemma 43 }
0.77/0.93	  multiply(multiply(?, inverse(?)), X)
0.77/0.93	= { by lemma 30 }
0.77/0.93	  multiply(multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?), ?), X)
0.77/0.93	= { by lemma 37 }
0.77/0.93	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), multiply(double_divide(X, ?), ?))
0.77/0.93	= { by lemma 15 }
0.77/0.93	  double_divide(multiply(double_divide(?, ?), ?), double_divide(X, multiply(double_divide(?, ?), ?)))
0.77/0.93	= { by lemma 13 }
0.77/0.93	  double_divide(?, double_divide(X, ?))
0.77/0.93	
0.77/0.93	Lemma 49: multiply(multiply(inverse(X), X), Y) = double_divide(?, double_divide(Y, ?)).
0.77/0.93	Proof:
0.77/0.93	  multiply(multiply(inverse(X), X), Y)
0.77/0.93	= { by axiom 1 (multiply) }
0.77/0.93	  inverse(double_divide(Y, multiply(inverse(X), X)))
0.77/0.93	= { by lemma 40 }
0.77/0.93	  inverse(multiply(double_divide(Y, multiply(inverse(X), X)), multiply(inverse(X), X)))
0.77/0.93	= { by lemma 7 }
0.77/0.93	  inverse(multiply(double_divide(Y, ?), ?))
0.77/0.93	= { by lemma 41 }
0.77/0.93	  inverse(double_divide(Y, multiply(?, inverse(?))))
0.77/0.93	= { by axiom 1 (multiply) }
0.77/0.93	  multiply(multiply(?, inverse(?)), Y)
0.77/0.93	= { by lemma 43 }
0.77/0.93	  multiply(double_divide(inverse(?), ?), Y)
0.77/0.93	= { by lemma 47 }
0.77/0.93	  multiply(inverse(?), multiply(?, Y))
0.77/0.93	= { by lemma 48 }
0.77/0.93	  double_divide(?, double_divide(Y, ?))
0.77/0.93	
0.77/0.93	Lemma 50: double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X)) = X.
0.77/0.93	Proof:
0.77/0.93	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X))
0.77/0.93	= { by lemma 3 }
0.77/0.93	  double_divide(double_divide(?, multiply(double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(X)), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))
0.77/0.93	= { by lemma 29 }
0.77/0.93	  double_divide(double_divide(?, multiply(X, ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))
0.77/0.93	= { by lemma 3 }
0.77/0.93	  X
0.77/0.93	
0.77/0.93	Lemma 51: double_divide(?, double_divide(X, ?)) = inverse(inverse(X)).
0.77/0.93	Proof:
0.77/0.93	  double_divide(?, double_divide(X, ?))
0.77/0.93	= { by lemma 48 }
0.77/0.93	  multiply(inverse(?), multiply(?, X))
0.77/0.93	= { by lemma 47 }
0.77/0.93	  multiply(double_divide(inverse(?), ?), X)
0.77/0.93	= { by lemma 44 }
0.77/0.93	  multiply(double_divide(inverse(X), ?), ?)
0.77/0.93	= { by lemma 50 }
0.77/0.93	  multiply(double_divide(inverse(X), double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(?))), ?)
0.77/0.93	= { by lemma 40 }
0.77/0.93	  multiply(double_divide(inverse(X), double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(multiply(?, multiply(inverse(X), X))))), ?)
0.77/0.93	= { by lemma 50 }
0.77/0.93	  multiply(double_divide(inverse(X), multiply(?, multiply(inverse(X), X))), ?)
0.77/0.93	= { by lemma 45 }
0.77/0.93	  inverse(inverse(X))
0.77/0.93	
0.77/0.93	Lemma 52: double_divide(inverse(?), ?) = double_divide(?, inverse(?)).
0.77/0.93	Proof:
0.77/0.93	  double_divide(inverse(?), ?)
0.77/0.93	= { by lemma 43 }
0.77/0.93	  multiply(?, inverse(?))
0.77/0.93	= { by lemma 42 }
0.77/0.93	  multiply(inverse(?), inverse(inverse(?)))
0.77/0.93	= { by lemma 19 }
0.77/0.93	  multiply(inverse(?), inverse(double_divide(double_divide(inverse(?), multiply(inverse(?), double_divide(double_divide(?, multiply(?, ?)), ?))), ?)))
0.77/0.93	= { by axiom 1 (multiply) }
0.77/0.93	  multiply(inverse(?), multiply(?, double_divide(inverse(?), multiply(inverse(?), double_divide(double_divide(?, multiply(?, ?)), ?)))))
0.77/0.93	= { by lemma 48 }
0.77/0.93	  double_divide(?, double_divide(double_divide(inverse(?), multiply(inverse(?), double_divide(double_divide(?, multiply(?, ?)), ?))), ?))
0.77/0.93	= { by lemma 19 }
0.77/0.93	  double_divide(?, inverse(?))
0.77/0.93	
0.77/0.93	Lemma 53: double_divide(?, double_divide(?, inverse(?))) = inverse(?).
0.77/0.93	Proof:
0.77/0.93	  double_divide(?, double_divide(?, inverse(?)))
0.77/0.93	= { by lemma 52 }
0.77/0.93	  double_divide(?, double_divide(inverse(?), ?))
0.77/0.93	= { by lemma 48 }
0.77/0.93	  multiply(inverse(?), multiply(?, inverse(?)))
0.77/0.93	= { by lemma 33 }
1.07/1.24	  inverse(?)
1.07/1.24	
1.07/1.24	Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
1.07/1.24	Proof:
1.07/1.24	  multiply(multiply(inverse(b2), b2), a2)
1.07/1.24	= { by lemma 49 }
1.07/1.24	  double_divide(?, double_divide(a2, ?))
1.07/1.24	= { by lemma 51 }
1.07/1.24	  inverse(inverse(a2))
1.07/1.24	= { by lemma 50 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(inverse(inverse(a2))))
1.07/1.24	= { by lemma 39 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, inverse(inverse(a2))))))))
1.07/1.24	= { by lemma 51 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(?, double_divide(a2, ?))))))))
1.07/1.24	= { by lemma 48 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, multiply(inverse(?), multiply(?, a2))))))))
1.07/1.24	= { by lemma 47 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, multiply(double_divide(inverse(?), ?), a2)))))))
1.07/1.24	= { by lemma 44 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, multiply(double_divide(inverse(a2), ?), ?)))))))
1.07/1.24	= { by lemma 41 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, inverse(?)))))))))
1.07/1.24	= { by lemma 53 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, inverse(?)))))))))))
1.07/1.24	= { by lemma 53 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(?, double_divide(?, inverse(?)))))))))))))
1.07/1.24	= { by lemma 52 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(?, double_divide(inverse(?), ?))))))))))))
1.07/1.24	= { by lemma 13 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(double_divide(?, inverse(?)), double_divide(inverse(?), double_divide(?, inverse(?))))))))))))))
1.07/1.24	= { by lemma 10 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(double_divide(?, inverse(?)), double_divide(?, double_divide(?, ?)))))))))))))
1.07/1.24	= { by lemma 52 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(double_divide(inverse(?), ?), double_divide(?, double_divide(?, ?)))))))))))))
1.07/1.24	= { by lemma 43 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(multiply(?, inverse(?)), double_divide(?, double_divide(?, ?)))))))))))))
1.07/1.24	= { by lemma 34 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(?, double_divide(?, ?)))))))))))))
1.07/1.24	= { by lemma 35 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, double_divide(?, double_divide(multiply(?, multiply(double_divide(?, ?), ?)), ?)))))))))))
1.07/1.24	= { by lemma 49 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, multiply(multiply(inverse(?), ?), multiply(?, multiply(double_divide(?, ?), ?))))))))))))
1.07/1.24	= { by lemma 28 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(?, double_divide(?, multiply(inverse(?), ?))))))))))
1.07/1.24	= { by lemma 36 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(double_divide(multiply(inverse(?), ?), ?), ?))))))))
1.07/1.24	= { by lemma 12 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(inverse(a2), multiply(double_divide(?, double_divide(?, ?)), double_divide(?, multiply(inverse(?), ?))))))))))
1.07/1.24	= { by lemma 14 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(inverse(double_divide(?, multiply(inverse(?), ?))), multiply(double_divide(inverse(a2), ?), ?)))))))
1.07/1.24	= { by axiom 1 (multiply) }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(multiply(multiply(inverse(?), ?), ?), multiply(double_divide(inverse(a2), ?), ?)))))))
1.07/1.24	= { by lemma 37 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, multiply(multiply(double_divide(multiply(multiply(inverse(?), ?), ?), ?), ?), inverse(a2)))))))
1.07/1.24	= { by axiom 1 (multiply) }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(double_divide(inverse(a2), multiply(double_divide(multiply(multiply(inverse(?), ?), ?), ?), ?))))))))
1.07/1.24	= { by lemma 37 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(multiply(multiply(double_divide(inverse(a2), ?), ?), multiply(multiply(inverse(?), ?), ?))))))))
1.07/1.24	= { by lemma 38 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(multiply(double_divide(inverse(a2), multiply(double_divide(multiply(inverse(?), ?), ?), ?)), ?)))))))
1.07/1.24	= { by lemma 37 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(multiply(multiply(multiply(double_divide(inverse(a2), ?), ?), multiply(inverse(?), ?)), ?)))))))
1.07/1.24	= { by lemma 38 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(multiply(multiply(double_divide(inverse(a2), multiply(double_divide(inverse(?), ?), ?)), ?), ?)))))))
1.07/1.24	= { by axiom 1 (multiply) }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, inverse(inverse(double_divide(?, multiply(double_divide(inverse(a2), multiply(double_divide(inverse(?), ?), ?)), ?)))))))))
1.07/1.24	= { by lemma 51 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(double_divide(?, multiply(double_divide(inverse(a2), multiply(double_divide(inverse(?), ?), ?)), ?)), ?)))))))
1.07/1.24	= { by lemma 4 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, double_divide(double_divide(?, multiply(double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?)), ?)), ?)))))))
1.07/1.24	= { by lemma 3 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(?, multiply(double_divide(?, double_divide(double_divide(?, multiply(double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?)), ?)), ?)), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))))))
1.07/1.24	= { by lemma 25 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(?, multiply(double_divide(double_divide(?, multiply(double_divide(multiply(double_divide(double_divide(?, multiply(double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?)), ?)), ?), ?), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))))))
1.07/1.24	= { by lemma 24 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(?, multiply(double_divide(double_divide(?, multiply(double_divide(multiply(double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))), multiply(double_divide(inverse(?), ?), ?)), ?)), ?), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))))))
1.07/1.24	= { by lemma 25 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(?, multiply(double_divide(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?))), ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?))))))))
1.07/1.24	= { by lemma 3 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?))))))))
1.07/1.24	= { by lemma 4 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), multiply(double_divide(?, ?), ?)), double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?))))))))
1.07/1.24	= { by axiom 1 (multiply) }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(inverse(double_divide(double_divide(?, multiply(?, ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), multiply(double_divide(?, ?), ?)), double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?))))))))
1.07/1.24	= { by lemma 5 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(inverse(double_divide(double_divide(?, multiply(?, ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), multiply(double_divide(?, a2), a2)), double_divide(inverse(a2), multiply(double_divide(multiply(double_divide(inverse(?), multiply(double_divide(?, ?), ?)), double_divide(?, multiply(?, ?))), ?), ?))))))))
1.07/1.24	= { by axiom 1 (multiply) }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(double_divide(inverse(double_divide(double_divide(?, multiply(?, ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), multiply(double_divide(?, a2), a2)), double_divide(inverse(a2), multiply(double_divide(inverse(double_divide(double_divide(?, multiply(?, ?)), double_divide(inverse(?), multiply(double_divide(?, ?), ?)))), ?), ?))))))))
1.07/1.24	= { by lemma 3 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), double_divide(inverse(multiply(double_divide(?, double_divide(inverse(?), ?)), ?)), multiply(?, double_divide(?, multiply(?, double_divide(?, a2))))))
1.07/1.24	= { by lemma 39 }
1.07/1.24	  double_divide(multiply(?, multiply(double_divide(?, ?), ?)), inverse(a2))
1.07/1.24	= { by lemma 50 }
1.07/1.24	  a2
1.07/1.24	% SZS output end Proof
1.07/1.24	
1.07/1.24	RESULT: Unsatisfiable (the axioms are contradictory).
1.08/1.24	EOF