0.00/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.23	% Computer   : n016.star.cs.uiowa.edu
0.03/0.23	% Model      : x86_64 x86_64
0.03/0.23	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.23	% Memory     : 32218.625MB
0.03/0.23	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.23	% CPULimit   : 300
0.03/0.23	% DateTime   : Sat Jul 14 05:27:42 CDT 2018
0.03/0.23	% CPUTime    : 
6.79/6.99	% SZS status Theorem
6.79/6.99	
7.79/7.99	% SZS output start Proof
7.79/7.99	Take the following subset of the input axioms:
7.79/7.99	  fof(f01, axiom, ![B, A]: B=mult(A, ld(A, B))).
7.79/7.99	  fof(f02, axiom, ![B, A]: ld(A, mult(A, B))=B).
7.79/7.99	  fof(f03, axiom, ![B, A]: mult(rd(A, B), B)=A).
7.79/7.99	  fof(f04, axiom, ![B, A]: A=rd(mult(A, B), B)).
7.79/7.99	  fof(f05, axiom,
7.79/7.99	      ![B, A, C]:
7.79/7.99	        mult(mult(mult(A, B), A), C)=mult(A, mult(B, mult(A, C)))).
7.79/7.99	  fof(goals, conjecture,
7.79/7.99	      ?[X0]: ![X1]: (X1=mult(X1, X0) & mult(X0, X1)=X1)).
7.79/7.99	
7.79/7.99	Now clausify the problem and encode Horn clauses using encoding 3 of
7.79/7.99	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
7.79/7.99	We repeatedly replace C & s=t => u=v by the two clauses:
7.79/7.99	  $$fresh(y, y, x1...xn) = u
7.79/7.99	  C => $$fresh(s, t, x1...xn) = v
7.79/7.99	where $$fresh is a fresh function symbol and x1..xn are the free
7.79/7.99	variables of u and v.
7.79/7.99	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
7.79/7.99	input problem has no model of domain size 1).
7.79/7.99	
7.79/7.99	The encoding turns the above axioms into the following unit equations and goals:
7.79/7.99	
7.79/7.99	Axiom 1 (f02): ld(X, mult(X, Y)) = Y.
7.79/7.99	Axiom 2 (f05): mult(mult(mult(X, Y), X), Z) = mult(X, mult(Y, mult(X, Z))).
7.79/7.99	Axiom 3 (f03): mult(rd(X, Y), Y) = X.
7.79/7.99	Axiom 4 (f04): X = rd(mult(X, Y), Y).
7.79/7.99	Axiom 5 (f01): X = mult(Y, ld(Y, X)).
7.79/7.99	
7.79/7.99	Lemma 6: ld(rd(Y, X), Y) = X.
7.79/7.99	Proof:
7.79/7.99	  ld(rd(Y, X), Y)
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  ld(rd(Y, X), mult(rd(Y, X), X))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  X
7.79/7.99	
7.79/7.99	Lemma 7: rd(Y, ld(X, Y)) = X.
7.79/7.99	Proof:
7.79/7.99	  rd(Y, ld(X, Y))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  rd(mult(X, ld(X, Y)), ld(X, Y))
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  X
7.79/7.99	
7.79/7.99	Lemma 8: rd(mult(X, mult(Y, mult(X, Z))), Z) = mult(mult(X, Y), X).
7.79/7.99	Proof:
7.79/7.99	  rd(mult(X, mult(Y, mult(X, Z))), Z)
7.79/7.99	= { by axiom 2 (f05) }
7.79/7.99	  rd(mult(mult(mult(X, Y), X), Z), Z)
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  mult(mult(X, Y), X)
7.79/7.99	
7.79/7.99	Lemma 9: mult(X, mult(ld(X, Y), mult(X, Z))) = mult(mult(Y, X), Z).
7.79/7.99	Proof:
7.79/7.99	  mult(X, mult(ld(X, Y), mult(X, Z)))
7.79/7.99	= { by axiom 2 (f05) }
7.79/7.99	  mult(mult(mult(X, ld(X, Y)), X), Z)
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  mult(mult(Y, X), Z)
7.79/7.99	
7.79/7.99	Lemma 10: ld(X, mult(mult(Y, X), Z)) = mult(ld(X, Y), mult(X, Z)).
7.79/7.99	Proof:
7.79/7.99	  ld(X, mult(mult(Y, X), Z))
7.79/7.99	= { by lemma 9 }
7.79/7.99	  ld(X, mult(X, mult(ld(X, Y), mult(X, Z))))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  mult(ld(X, Y), mult(X, Z))
7.79/7.99	
7.79/7.99	Lemma 11: mult(mult(X, Y), ld(Y, Z)) = mult(Y, mult(ld(Y, X), Z)).
7.79/7.99	Proof:
7.79/7.99	  mult(mult(X, Y), ld(Y, Z))
7.79/7.99	= { by lemma 9 }
7.79/7.99	  mult(Y, mult(ld(Y, X), mult(Y, ld(Y, Z))))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  mult(Y, mult(ld(Y, X), Z))
7.79/7.99	
7.79/7.99	Lemma 12: mult(mult(X, rd(Y, mult(X, Z))), X) = rd(mult(X, Y), Z).
7.79/7.99	Proof:
7.79/7.99	  mult(mult(X, rd(Y, mult(X, Z))), X)
7.79/7.99	= { by lemma 8 }
7.79/7.99	  rd(mult(X, mult(rd(Y, mult(X, Z)), mult(X, Z))), Z)
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  rd(mult(X, Y), Z)
7.79/7.99	
7.79/7.99	Lemma 13: rd(rd(mult(X, Y), Z), X) = mult(X, rd(Y, mult(X, Z))).
7.79/7.99	Proof:
7.79/7.99	  rd(rd(mult(X, Y), Z), X)
7.79/7.99	= { by lemma 12 }
7.79/7.99	  rd(mult(mult(X, rd(Y, mult(X, Z))), X), X)
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  mult(X, rd(Y, mult(X, Z)))
7.79/7.99	
7.79/7.99	Lemma 14: mult(X, rd(Y, mult(X, Y))) = rd(X, X).
7.79/7.99	Proof:
7.79/7.99	  mult(X, rd(Y, mult(X, Y)))
7.79/7.99	= { by lemma 13 }
7.79/7.99	  rd(rd(mult(X, Y), Y), X)
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  rd(X, X)
7.79/7.99	
7.79/7.99	Lemma 16: ld(Y, rd(Y, Y)) = rd(?, mult(Y, ?)).
7.79/7.99	Proof:
7.79/7.99	  ld(Y, rd(Y, Y))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  ld(Y, mult(Y, rd(?, mult(Y, ?))))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  rd(?, mult(Y, ?))
7.79/7.99	
7.79/7.99	Lemma 16: rd(?, mult(Y, ?)) = ld(Y, rd(Y, Y)).
7.79/7.99	Proof:
7.79/7.99	  rd(?, mult(Y, ?))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(Y, mult(Y, rd(?, mult(Y, ?))))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  ld(Y, rd(Y, Y))
7.79/7.99	
7.79/7.99	Lemma 17: rd(X, mult(Y, X)) = rd(?, mult(Y, ?)).
7.79/7.99	Proof:
7.79/7.99	  rd(X, mult(Y, X))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(Y, mult(Y, rd(X, mult(Y, X))))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  ld(Y, rd(Y, Y))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  ld(Y, mult(Y, rd(?, mult(Y, ?))))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  rd(?, mult(Y, ?))
7.79/7.99	
7.79/7.99	Lemma 18: rd(mult(X, Y), ld(X, Z)) = mult(mult(X, rd(Y, Z)), X).
7.79/7.99	Proof:
7.79/7.99	  rd(mult(X, Y), ld(X, Z))
7.79/7.99	= { by lemma 12 }
7.79/7.99	  mult(mult(X, rd(Y, mult(X, ld(X, Z)))), X)
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  mult(mult(X, rd(Y, Z)), X)
7.79/7.99	
7.79/7.99	Lemma 19: mult(X, rd(ld(X, Y), Y)) = rd(X, X).
7.79/7.99	Proof:
7.79/7.99	  mult(X, rd(ld(X, Y), Y))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  mult(X, rd(ld(X, Y), mult(X, ld(X, Y))))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  rd(X, X)
7.79/7.99	
7.79/7.99	Lemma 20: rd(ld(X, Y), Y) = rd(ld(X, ?), ?).
7.79/7.99	Proof:
7.79/7.99	  rd(ld(X, Y), Y)
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(X, mult(X, rd(ld(X, Y), Y)))
7.79/7.99	= { by lemma 19 }
7.79/7.99	  ld(X, rd(X, X))
7.79/7.99	= { by lemma 19 }
7.79/7.99	  ld(X, mult(X, rd(ld(X, ?), ?)))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  rd(ld(X, ?), ?)
7.79/7.99	
7.79/7.99	Lemma 21: rd(rd(X, Y), rd(X, Y)) = mult(rd(X, Y), rd(Y, X)).
7.79/7.99	Proof:
7.79/7.99	  rd(rd(X, Y), rd(X, Y))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  mult(rd(X, Y), rd(Y, mult(rd(X, Y), Y)))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  mult(rd(X, Y), rd(Y, X))
7.79/7.99	
7.79/7.99	Lemma 22: rd(ld(X, ?), ?) = rd(?, mult(X, ?)).
7.79/7.99	Proof:
7.79/7.99	  rd(ld(X, ?), ?)
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(X, mult(X, rd(ld(X, ?), ?)))
7.79/7.99	= { by lemma 19 }
7.79/7.99	  ld(X, rd(X, X))
7.79/7.99	= { by lemma 16 }
7.79/7.99	  rd(?, mult(X, ?))
7.79/7.99	
7.79/7.99	Lemma 23: rd(mult(rd(X, Y), mult(Z, X)), Y) = mult(mult(rd(X, Y), Z), rd(X, Y)).
7.79/7.99	Proof:
7.79/7.99	  rd(mult(rd(X, Y), mult(Z, X)), Y)
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  rd(mult(rd(X, Y), mult(Z, mult(rd(X, Y), Y))), Y)
7.79/7.99	= { by lemma 8 }
7.79/7.99	  mult(mult(rd(X, Y), Z), rd(X, Y))
7.79/7.99	
7.79/7.99	Lemma 24: mult(ld(X, rd(Y, X)), mult(X, Z)) = ld(X, mult(Y, Z)).
7.79/7.99	Proof:
7.79/7.99	  mult(ld(X, rd(Y, X)), mult(X, Z))
7.79/7.99	= { by lemma 10 }
7.79/7.99	  ld(X, mult(mult(rd(Y, X), X), Z))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  ld(X, mult(Y, Z))
7.79/7.99	
7.79/7.99	Lemma 25: ld(X, mult(Y, ld(X, Z))) = mult(ld(X, rd(Y, X)), Z).
7.79/7.99	Proof:
7.79/7.99	  ld(X, mult(Y, ld(X, Z)))
7.79/7.99	= { by lemma 24 }
7.79/7.99	  mult(ld(X, rd(Y, X)), mult(X, ld(X, Z)))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  mult(ld(X, rd(Y, X)), Z)
7.79/7.99	
7.79/7.99	Lemma 26: mult(ld(X, rd(X, X)), Y) = ld(X, Y).
7.79/7.99	Proof:
7.79/7.99	  mult(ld(X, rd(X, X)), Y)
7.79/7.99	= { by lemma 25 }
7.79/7.99	  ld(X, mult(X, ld(X, Y)))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(X, Y)
7.79/7.99	
7.79/7.99	Lemma 27: ld(rd(X, Y), Z) = mult(rd(Y, X), Z).
7.79/7.99	Proof:
7.79/7.99	  ld(rd(X, Y), Z)
7.79/7.99	= { by lemma 26 }
7.79/7.99	  mult(ld(rd(X, Y), rd(rd(X, Y), rd(X, Y))), Z)
7.79/7.99	= { by lemma 21 }
7.79/7.99	  mult(ld(rd(X, Y), mult(rd(X, Y), rd(Y, X))), Z)
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  mult(rd(Y, X), Z)
7.79/7.99	
7.79/7.99	Lemma 28: rd(ld(X, rd(X, X)), ld(X, rd(X, X))) = ld(X, X).
7.79/7.99	Proof:
7.79/7.99	  rd(ld(X, rd(X, X)), ld(X, rd(X, X)))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  mult(ld(X, rd(X, X)), rd(?, mult(ld(X, rd(X, X)), ?)))
7.79/7.99	= { by lemma 26 }
7.79/7.99	  ld(X, rd(?, mult(ld(X, rd(X, X)), ?)))
7.79/7.99	= { by lemma 26 }
7.79/7.99	  ld(X, rd(?, ld(X, ?)))
7.79/7.99	= { by lemma 7 }
7.79/7.99	  ld(X, X)
7.79/7.99	
7.79/7.99	Lemma 29: ld(ld(X, X), Y) = mult(ld(X, X), Y).
7.79/7.99	Proof:
7.79/7.99	  ld(ld(X, X), Y)
7.79/7.99	= { by lemma 28 }
7.79/7.99	  ld(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y)
7.79/7.99	= { by lemma 27 }
7.79/7.99	  mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y)
7.79/7.99	= { by lemma 28 }
7.79/7.99	  mult(ld(X, X), Y)
7.79/7.99	
7.79/7.99	Lemma 30: mult(X, mult(ld(X, rd(Y, X)), Z)) = mult(Y, ld(X, Z)).
7.79/7.99	Proof:
7.79/7.99	  mult(X, mult(ld(X, rd(Y, X)), Z))
7.79/7.99	= { by lemma 11 }
7.79/7.99	  mult(mult(rd(Y, X), X), ld(X, Z))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  mult(Y, ld(X, Z))
7.79/7.99	
7.79/7.99	Lemma 31: mult(rd(?, mult(X, ?)), Y) = ld(X, Y).
7.79/7.99	Proof:
7.79/7.99	  mult(rd(?, mult(X, ?)), Y)
7.79/7.99	= { by lemma 16 }
7.79/7.99	  mult(ld(X, rd(X, X)), Y)
7.79/7.99	= { by lemma 26 }
7.79/7.99	  ld(X, Y)
7.79/7.99	
7.79/7.99	Lemma 32: mult(ld(X, X), rd(?, mult(X, ?))) = rd(?, mult(X, ?)).
7.79/7.99	Proof:
7.79/7.99	  mult(ld(X, X), rd(?, mult(X, ?)))
7.79/7.99	= { by lemma 31 }
7.79/7.99	  mult(mult(rd(?, mult(X, ?)), X), rd(?, mult(X, ?)))
7.79/7.99	= { by lemma 23 }
7.79/7.99	  rd(mult(rd(?, mult(X, ?)), mult(X, ?)), mult(X, ?))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  rd(?, mult(X, ?))
7.79/7.99	
7.79/7.99	Lemma 33: mult(mult(rd(X, Y), rd(Z, X)), rd(X, Y)) = rd(mult(rd(X, Y), Z), Y).
7.79/7.99	Proof:
7.79/7.99	  mult(mult(rd(X, Y), rd(Z, X)), rd(X, Y))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  mult(mult(rd(X, Y), rd(Z, mult(rd(X, Y), Y))), rd(X, Y))
7.79/7.99	= { by lemma 12 }
7.79/7.99	  rd(mult(rd(X, Y), Z), Y)
7.79/7.99	
7.79/7.99	Lemma 34: mult(X, rd(ld(X, Y), mult(X, Z))) = rd(rd(Y, Z), X).
7.79/7.99	Proof:
7.79/7.99	  mult(X, rd(ld(X, Y), mult(X, Z)))
7.79/7.99	= { by lemma 13 }
7.79/7.99	  rd(rd(mult(X, ld(X, Y)), Z), X)
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  rd(rd(Y, Z), X)
7.79/7.99	
7.79/7.99	Lemma 35: rd(ld(X, Y), mult(X, Z)) = ld(X, rd(rd(Y, Z), X)).
7.79/7.99	Proof:
7.79/7.99	  rd(ld(X, Y), mult(X, Z))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  ld(X, mult(X, rd(ld(X, Y), mult(X, Z))))
7.79/7.99	= { by lemma 34 }
7.79/7.99	  ld(X, rd(rd(Y, Z), X))
7.79/7.99	
7.79/7.99	Lemma 36: mult(mult(X, rd(ld(X, Y), Z)), X) = rd(Y, ld(X, Z)).
7.79/7.99	Proof:
7.79/7.99	  mult(mult(X, rd(ld(X, Y), Z)), X)
7.79/7.99	= { by lemma 18 }
7.79/7.99	  rd(mult(X, ld(X, Y)), ld(X, Z))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  rd(Y, ld(X, Z))
7.79/7.99	
7.79/7.99	Lemma 37: rd(?, mult(rd(X, Y), ?)) = rd(Y, X).
7.79/7.99	Proof:
7.79/7.99	  rd(?, mult(rd(X, Y), ?))
7.79/7.99	= { by lemma 17 }
7.79/7.99	  rd(Y, mult(rd(X, Y), Y))
7.79/7.99	= { by axiom 3 (f03) }
7.79/7.99	  rd(Y, X)
7.79/7.99	
7.79/7.99	Lemma 38: mult(ld(X, X), mult(ld(X, X), Y)) = Y.
7.79/7.99	Proof:
7.79/7.99	  mult(ld(X, X), mult(ld(X, X), Y))
7.79/7.99	= { by lemma 29 }
7.79/7.99	  ld(ld(X, X), mult(ld(X, X), Y))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  Y
7.79/7.99	
7.79/7.99	Lemma 39: ld(mult(mult(Y, Z), Y), mult(Y, mult(Z, mult(Y, X)))) = X.
7.79/7.99	Proof:
7.79/7.99	  ld(mult(mult(Y, Z), Y), mult(Y, mult(Z, mult(Y, X))))
7.79/7.99	= { by axiom 2 (f05) }
7.79/7.99	  ld(mult(mult(Y, Z), Y), mult(mult(mult(Y, Z), Y), X))
7.79/7.99	= { by axiom 1 (f02) }
7.79/7.99	  X
7.79/7.99	
7.79/7.99	Lemma 40: ld(mult(mult(X, Y), X), mult(X, Z)) = ld(X, ld(Y, Z)).
7.79/7.99	Proof:
7.79/7.99	  ld(mult(mult(X, Y), X), mult(X, Z))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  ld(mult(mult(X, Y), X), mult(X, mult(Y, ld(Y, Z))))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  ld(mult(mult(X, Y), X), mult(X, mult(Y, mult(X, ld(X, ld(Y, Z))))))
7.79/7.99	= { by lemma 39 }
7.79/7.99	  ld(X, ld(Y, Z))
7.79/7.99	
7.79/7.99	Lemma 41: ld(mult(Y, X), mult(X, Z)) = ld(X, ld(ld(X, Y), Z)).
7.79/7.99	Proof:
7.79/7.99	  ld(mult(Y, X), mult(X, Z))
7.79/7.99	= { by axiom 5 (f01) }
7.79/7.99	  ld(mult(mult(X, ld(X, Y)), X), mult(X, Z))
7.79/7.99	= { by lemma 40 }
7.79/7.99	  ld(X, ld(ld(X, Y), Z))
7.79/7.99	
7.79/7.99	Lemma 42: rd(X, X) = ld(X, X).
7.79/7.99	Proof:
7.79/7.99	  rd(X, X)
7.79/7.99	= { by lemma 37 }
7.79/7.99	  rd(?, mult(rd(X, X), ?))
7.79/7.99	= { by lemma 17 }
7.79/7.99	  rd(ld(X, ?), mult(rd(X, X), ld(X, ?)))
7.79/7.99	= { by lemma 31 }
7.79/7.99	  rd(ld(X, ?), mult(rd(X, X), mult(rd(?, mult(X, ?)), ?)))
7.79/7.99	= { by lemma 27 }
7.79/7.99	  rd(ld(X, ?), ld(rd(X, X), mult(rd(?, mult(X, ?)), ?)))
7.79/7.99	= { by lemma 14 }
7.79/7.99	  rd(ld(X, ?), ld(mult(X, rd(?, mult(X, ?))), mult(rd(?, mult(X, ?)), ?)))
7.79/7.99	= { by lemma 41 }
7.79/7.99	  rd(ld(X, ?), ld(rd(?, mult(X, ?)), ld(ld(rd(?, mult(X, ?)), X), ?)))
7.79/7.99	= { by lemma 27 }
7.79/7.99	  rd(ld(X, ?), mult(rd(mult(X, ?), ?), ld(ld(rd(?, mult(X, ?)), X), ?)))
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  rd(ld(X, ?), mult(X, ld(ld(rd(?, mult(X, ?)), X), ?)))
7.79/7.99	= { by lemma 27 }
7.79/7.99	  rd(ld(X, ?), mult(X, ld(mult(rd(mult(X, ?), ?), X), ?)))
7.79/7.99	= { by axiom 4 (f04) }
7.79/7.99	  rd(ld(X, ?), mult(X, ld(mult(X, X), ?)))
7.79/7.99	= { by lemma 35 }
7.79/7.99	  ld(X, rd(rd(?, ld(mult(X, X), ?)), X))
7.79/7.99	= { by lemma 7 }
7.79/7.99	  ld(X, rd(mult(X, X), X))
7.79/7.99	= { by axiom 4 (f04) }
7.79/8.00	  ld(X, X)
7.79/8.00	
7.79/8.00	Lemma 43: mult(ld(X, X), ld(X, Z)) = mult(X, ld(mult(X, X), Z)).
7.79/8.00	Proof:
7.79/8.00	  mult(ld(X, X), ld(X, Z))
7.79/8.00	= { by lemma 42 }
7.79/8.00	  mult(rd(X, X), ld(X, Z))
7.79/8.00	= { by lemma 31 }
7.79/8.00	  mult(rd(X, X), mult(rd(?, mult(X, ?)), Z))
7.79/8.00	= { by lemma 22 }
7.79/8.00	  mult(rd(X, X), mult(rd(ld(X, ?), ?), Z))
7.79/8.00	= { by lemma 27 }
7.79/8.00	  ld(rd(X, X), mult(rd(ld(X, ?), ?), Z))
7.79/8.00	= { by lemma 19 }
7.79/8.00	  ld(mult(X, rd(ld(X, ?), ?)), mult(rd(ld(X, ?), ?), Z))
7.79/8.00	= { by lemma 41 }
7.79/8.00	  ld(rd(ld(X, ?), ?), ld(ld(rd(ld(X, ?), ?), X), Z))
7.79/8.00	= { by lemma 27 }
7.79/8.00	  mult(rd(?, ld(X, ?)), ld(ld(rd(ld(X, ?), ?), X), Z))
7.79/8.00	= { by lemma 7 }
7.79/8.00	  mult(X, ld(ld(rd(ld(X, ?), ?), X), Z))
7.79/8.00	= { by lemma 27 }
7.79/8.00	  mult(X, ld(mult(rd(?, ld(X, ?)), X), Z))
7.79/8.00	= { by lemma 7 }
7.79/8.00	  mult(X, ld(mult(X, X), Z))
7.79/8.00	
7.79/8.00	Lemma 44: ld(ld(X, Y), ld(X, Z)) = mult(X, ld(mult(Y, X), Z)).
7.79/8.00	Proof:
7.79/8.00	  ld(ld(X, Y), ld(X, Z))
7.79/8.00	= { by axiom 5 (f01) }
7.79/8.00	  ld(ld(X, Y), ld(X, mult(mult(Y, X), ld(mult(Y, X), Z))))
7.79/8.00	= { by lemma 10 }
7.79/8.00	  ld(ld(X, Y), mult(ld(X, Y), mult(X, ld(mult(Y, X), Z))))
7.79/8.00	= { by axiom 1 (f02) }
7.79/8.00	  mult(X, ld(mult(Y, X), Z))
7.79/8.00	
7.79/8.00	Lemma 45: mult(ld(X, X), mult(X, X)) = mult(X, X).
7.79/8.00	Proof:
7.79/8.00	  mult(ld(X, X), mult(X, X))
7.79/8.00	= { by axiom 4 (f04) }
7.79/8.00	  rd(mult(mult(ld(X, X), mult(X, X)), ?), ?)
7.79/8.00	= { by lemma 42 }
7.79/8.00	  rd(mult(mult(rd(X, X), mult(X, X)), ?), ?)
7.79/8.00	= { by axiom 3 (f03) }
7.79/8.00	  rd(mult(mult(rd(X, X), mult(X, mult(rd(X, X), X))), ?), ?)
7.79/8.00	= { by axiom 2 (f05) }
7.79/8.00	  rd(mult(mult(mult(mult(rd(X, X), X), rd(X, X)), X), ?), ?)
7.79/8.00	= { by axiom 3 (f03) }
7.79/8.00	  rd(mult(mult(mult(X, rd(X, X)), X), ?), ?)
7.79/8.00	= { by axiom 2 (f05) }
7.79/8.00	  rd(mult(X, mult(rd(X, X), mult(X, ?))), ?)
7.79/8.00	= { by lemma 42 }
7.79/8.00	  rd(mult(X, mult(ld(X, X), mult(X, ?))), ?)
7.79/8.00	= { by lemma 9 }
7.79/8.00	  rd(mult(mult(X, X), ?), ?)
7.79/8.00	= { by axiom 4 (f04) }
7.79/8.00	  mult(X, X)
7.79/8.00	
7.79/8.00	Lemma 46: rd(mult(X, mult(X, X)), X) = mult(X, X).
7.79/8.00	Proof:
7.79/8.00	  rd(mult(X, mult(X, X)), X)
7.79/8.00	= { by lemma 45 }
7.79/8.00	  rd(mult(X, mult(ld(X, X), mult(X, X))), X)
7.79/8.00	= { by lemma 8 }
7.79/8.00	  mult(mult(X, ld(X, X)), X)
7.79/8.00	= { by axiom 5 (f01) }
7.79/8.00	  mult(X, X)
7.79/8.00	
7.79/8.00	Lemma 47: mult(rd(mult(X, Y), Z), ld(X, W)) = mult(X, mult(rd(Y, mult(X, Z)), W)).
7.79/8.00	Proof:
7.79/8.00	  mult(rd(mult(X, Y), Z), ld(X, W))
7.79/8.00	= { by lemma 12 }
7.79/8.00	  mult(mult(mult(X, rd(Y, mult(X, Z))), X), ld(X, W))
7.79/8.00	= { by lemma 11 }
7.79/8.00	  mult(X, mult(ld(X, mult(X, rd(Y, mult(X, Z)))), W))
7.79/8.00	= { by axiom 1 (f02) }
7.79/8.00	  mult(X, mult(rd(Y, mult(X, Z)), W))
7.79/8.00	
7.79/8.00	Lemma 48: mult(rd(X, Y), rd(Y, mult(rd(X, Y), Z))) = rd(rd(X, Z), rd(X, Y)).
7.79/8.00	Proof:
7.79/8.00	  mult(rd(X, Y), rd(Y, mult(rd(X, Y), Z)))
7.79/8.00	= { by lemma 13 }
7.79/8.00	  rd(rd(mult(rd(X, Y), Y), Z), rd(X, Y))
7.79/8.00	= { by axiom 3 (f03) }
7.79/8.00	  rd(rd(X, Z), rd(X, Y))
7.79/8.00	
7.79/8.00	Lemma 49: mult(X, ld(mult(X, X), X)) = ld(X, X).
7.79/8.00	Proof:
7.79/8.00	  mult(X, ld(mult(X, X), X))
7.79/8.00	= { by axiom 5 (f01) }
7.79/8.00	  mult(X, ld(mult(X, X), mult(ld(X, X), ld(ld(X, X), X))))
7.79/8.00	= { by lemma 43 }
7.79/8.00	  mult(ld(X, X), ld(X, mult(ld(X, X), ld(ld(X, X), X))))
7.79/8.00	= { by lemma 31 }
7.79/8.00	  mult(ld(X, X), mult(rd(?, mult(X, ?)), mult(ld(X, X), ld(ld(X, X), X))))
7.79/8.00	= { by axiom 2 (f05) }
7.79/8.00	  mult(mult(mult(ld(X, X), rd(?, mult(X, ?))), ld(X, X)), ld(ld(X, X), X))
7.79/8.00	= { by lemma 32 }
7.79/8.00	  mult(mult(rd(?, mult(X, ?)), ld(X, X)), ld(ld(X, X), X))
7.79/8.00	= { by lemma 31 }
7.79/8.00	  mult(ld(X, ld(X, X)), ld(ld(X, X), X))
7.79/8.00	= { by lemma 42 }
7.79/8.00	  mult(ld(X, rd(X, X)), ld(ld(X, X), X))
7.79/8.00	= { by lemma 26 }
7.79/8.00	  ld(X, ld(ld(X, X), X))
7.79/8.00	= { by lemma 41 }
7.79/8.00	  ld(mult(X, X), mult(X, X))
7.79/8.00	= { by lemma 42 }
7.79/8.00	  rd(mult(X, X), mult(X, X))
7.79/8.00	= { by axiom 1 (f02) }
7.79/8.00	  ld(X, mult(X, rd(mult(X, X), mult(X, X))))
7.79/8.00	= { by lemma 13 }
7.79/8.00	  ld(X, rd(rd(mult(X, mult(X, X)), X), X))
7.79/8.00	= { by lemma 35 }
7.79/8.00	  rd(ld(X, mult(X, mult(X, X))), mult(X, X))
7.79/8.00	= { by lemma 31 }
7.79/8.00	  rd(mult(rd(?, mult(X, ?)), mult(X, mult(X, X))), mult(X, X))
7.79/8.00	= { by lemma 17 }
7.79/8.00	  rd(mult(rd(X, mult(X, X)), mult(X, mult(X, X))), mult(X, X))
7.79/8.00	= { by lemma 46 }
7.79/8.00	  rd(mult(rd(X, rd(mult(X, mult(X, X)), X)), mult(X, mult(X, X))), mult(X, X))
7.79/8.00	= { by lemma 46 }
7.79/8.00	  rd(mult(rd(X, rd(mult(X, mult(X, X)), X)), mult(X, mult(X, X))), rd(mult(X, mult(X, X)), X))
7.79/8.00	= { by lemma 33 }
7.79/8.00	  mult(mult(rd(X, rd(mult(X, mult(X, X)), X)), rd(mult(X, mult(X, X)), X)), rd(X, rd(mult(X, mult(X, X)), X)))
7.79/8.00	= { by axiom 3 (f03) }
7.79/8.00	  mult(X, rd(X, rd(mult(X, mult(X, X)), X)))
7.79/8.00	= { by lemma 46 }
7.79/8.00	  mult(X, rd(X, mult(X, X)))
7.79/8.00	= { by lemma 14 }
7.79/8.00	  rd(X, X)
7.79/8.00	= { by lemma 42 }
7.79/8.00	  ld(X, X)
7.79/8.00	
7.79/8.00	Lemma 50: ld(mult(X, X), X) = ld(X, ld(X, X)).
7.79/8.00	Proof:
7.79/8.00	  ld(mult(X, X), X)
7.79/8.00	= { by axiom 1 (f02) }
7.79/8.00	  ld(X, mult(X, ld(mult(X, X), X)))
7.79/8.00	= { by lemma 49 }
7.79/8.00	  ld(X, ld(X, X))
7.79/8.00	
7.79/8.00	Lemma 51: mult(X, rd(Y, mult(X, ld(Z, mult(X, Y))))) = rd(Z, X).
7.79/8.00	Proof:
7.79/8.00	  mult(X, rd(Y, mult(X, ld(Z, mult(X, Y)))))
7.79/8.00	= { by lemma 13 }
7.79/8.00	  rd(rd(mult(X, Y), ld(Z, mult(X, Y))), X)
7.79/8.00	= { by lemma 7 }
7.79/8.00	  rd(Z, X)
7.79/8.00	
7.79/8.00	Lemma 52: rd(X, mult(Y, ld(Z, mult(Y, X)))) = ld(Y, rd(Z, Y)).
7.79/8.00	Proof:
7.79/8.00	  rd(X, mult(Y, ld(Z, mult(Y, X))))
7.79/8.00	= { by axiom 1 (f02) }
7.79/8.00	  ld(Y, mult(Y, rd(X, mult(Y, ld(Z, mult(Y, X))))))
7.79/8.00	= { by lemma 51 }
7.79/8.00	  ld(Y, rd(Z, Y))
7.79/8.00	
7.79/8.00	Lemma 53: mult(mult(rd(X, Y), Z), rd(X, Y)) = mult(rd(X, Y), rd(Z, rd(Y, X))).
7.79/8.00	Proof:
7.79/8.00	  mult(mult(rd(X, Y), Z), rd(X, Y))
7.79/8.00	= { by lemma 23 }
7.79/8.00	  rd(mult(rd(X, Y), mult(Z, X)), Y)
7.79/8.00	= { by lemma 27 }
7.79/8.00	  rd(ld(rd(Y, X), mult(Z, X)), Y)
7.79/8.00	= { by lemma 24 }
7.79/8.00	  rd(mult(ld(rd(Y, X), rd(Z, rd(Y, X))), mult(rd(Y, X), X)), Y)
7.79/8.00	= { by lemma 27 }
7.79/8.00	  rd(mult(mult(rd(X, Y), rd(Z, rd(Y, X))), mult(rd(Y, X), X)), Y)
7.79/8.00	= { by axiom 3 (f03) }
7.79/8.00	  rd(mult(mult(rd(X, Y), rd(Z, rd(Y, X))), Y), Y)
7.79/8.00	= { by axiom 4 (f04) }
7.79/8.00	  mult(rd(X, Y), rd(Z, rd(Y, X)))
7.79/8.00	
7.79/8.00	Lemma 54: mult(mult(ld(X, X), Y), ld(X, X)) = mult(ld(X, X), rd(Y, ld(X, X))).
7.79/8.00	Proof:
7.79/8.00	  mult(mult(ld(X, X), Y), ld(X, X))
7.79/8.00	= { by lemma 28 }
7.79/8.00	  mult(mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y), ld(X, X))
7.79/8.00	= { by lemma 28 }
7.79/8.00	  mult(mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y), rd(ld(X, rd(X, X)), ld(X, rd(X, X))))
7.79/8.00	= { by lemma 53 }
7.79/8.00	  mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), rd(Y, rd(ld(X, rd(X, X)), ld(X, rd(X, X)))))
7.79/8.00	= { by lemma 28 }
7.79/8.00	  mult(ld(X, X), rd(Y, rd(ld(X, rd(X, X)), ld(X, rd(X, X)))))
7.79/8.00	= { by lemma 28 }
7.79/8.01	  mult(ld(X, X), rd(Y, ld(X, X)))
7.79/8.01	
7.79/8.01	Lemma 55: mult(ld(X, X), mult(X, Y)) = mult(X, mult(ld(X, X), Y)).
7.79/8.01	Proof:
7.79/8.01	  mult(ld(X, X), mult(X, Y))
7.79/8.01	= { by lemma 29 }
7.79/8.01	  ld(ld(X, X), mult(X, Y))
7.79/8.01	= { by axiom 4 (f04) }
7.79/8.01	  ld(ld(X, X), mult(rd(mult(X, ?), ?), Y))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  ld(ld(X, X), ld(rd(?, mult(X, ?)), Y))
7.79/8.01	= { by lemma 16 }
7.79/8.01	  ld(ld(X, X), ld(ld(X, rd(X, X)), Y))
7.79/8.01	= { by lemma 42 }
7.79/8.01	  ld(ld(X, X), ld(ld(X, ld(X, X)), Y))
7.79/8.01	= { by lemma 31 }
7.79/8.01	  ld(ld(X, X), ld(mult(rd(?, mult(X, ?)), ld(X, X)), Y))
7.79/8.01	= { by lemma 32 }
7.79/8.01	  ld(ld(X, X), ld(mult(mult(ld(X, X), rd(?, mult(X, ?))), ld(X, X)), Y))
7.79/8.01	= { by axiom 5 (f01) }
7.79/8.01	  ld(ld(X, X), ld(mult(mult(ld(X, X), rd(?, mult(X, ?))), ld(X, X)), mult(ld(X, X), ld(ld(X, X), Y))))
7.79/8.01	= { by lemma 40 }
7.79/8.01	  ld(ld(X, X), ld(ld(X, X), ld(rd(?, mult(X, ?)), ld(ld(X, X), Y))))
7.79/8.01	= { by lemma 29 }
7.79/8.01	  ld(ld(X, X), mult(ld(X, X), ld(rd(?, mult(X, ?)), ld(ld(X, X), Y))))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  ld(ld(X, X), mult(ld(X, X), mult(rd(mult(X, ?), ?), ld(ld(X, X), Y))))
7.79/8.01	= { by axiom 4 (f04) }
7.79/8.01	  ld(ld(X, X), mult(ld(X, X), mult(X, ld(ld(X, X), Y))))
7.79/8.01	= { by lemma 29 }
7.79/8.01	  ld(ld(X, X), mult(ld(X, X), mult(X, mult(ld(X, X), Y))))
7.79/8.01	= { by axiom 1 (f02) }
7.79/8.01	  mult(X, mult(ld(X, X), Y))
7.79/8.01	
7.79/8.01	Lemma 56: mult(rd(X, Y), ld(mult(Z, rd(X, Y)), X)) = ld(mult(rd(Y, X), Z), Y).
7.79/8.01	Proof:
7.79/8.01	  mult(rd(X, Y), ld(mult(Z, rd(X, Y)), X))
7.79/8.01	= { by lemma 44 }
7.79/8.01	  ld(ld(rd(X, Y), Z), ld(rd(X, Y), X))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  ld(mult(rd(Y, X), Z), ld(rd(X, Y), X))
7.79/8.01	= { by lemma 6 }
7.79/8.01	  ld(mult(rd(Y, X), Z), Y)
7.79/8.01	
7.79/8.01	Lemma 57: mult(rd(X, Y), rd(Y, X)) = mult(rd(Y, X), rd(X, Y)).
7.79/8.01	Proof:
7.79/8.01	  mult(rd(X, Y), rd(Y, X))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  ld(rd(Y, X), rd(Y, X))
7.79/8.01	= { by lemma 42 }
7.79/8.01	  rd(rd(Y, X), rd(Y, X))
7.79/8.01	= { by lemma 21 }
7.79/8.01	  mult(rd(Y, X), rd(X, Y))
7.79/8.01	
7.79/8.01	Lemma 58: rd(mult(rd(X, Y), Z), rd(X, Y)) = mult(rd(X, Y), mult(Z, rd(Y, X))).
7.79/8.01	Proof:
7.79/8.01	  rd(mult(rd(X, Y), Z), rd(X, Y))
7.79/8.01	= { by lemma 7 }
7.79/8.01	  rd(rd(X, ld(mult(rd(X, Y), Z), X)), rd(X, Y))
7.79/8.01	= { by lemma 48 }
7.79/8.01	  mult(rd(X, Y), rd(Y, mult(rd(X, Y), ld(mult(rd(X, Y), Z), X))))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  mult(rd(X, Y), rd(Y, mult(rd(X, Y), ld(ld(rd(Y, X), Z), X))))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  mult(rd(X, Y), rd(Y, ld(rd(Y, X), ld(ld(rd(Y, X), Z), X))))
7.79/8.01	= { by lemma 41 }
7.79/8.01	  mult(rd(X, Y), rd(Y, ld(mult(Z, rd(Y, X)), mult(rd(Y, X), X))))
7.79/8.01	= { by axiom 3 (f03) }
7.79/8.01	  mult(rd(X, Y), rd(Y, ld(mult(Z, rd(Y, X)), Y)))
7.79/8.01	= { by lemma 7 }
7.79/8.01	  mult(rd(X, Y), mult(Z, rd(Y, X)))
7.79/8.01	
7.79/8.01	Lemma 59: rd(mult(ld(X, X), Y), ld(X, X)) = mult(ld(X, X), mult(Y, ld(X, X))).
7.79/8.01	Proof:
7.79/8.01	  rd(mult(ld(X, X), Y), ld(X, X))
7.79/8.01	= { by lemma 28 }
7.79/8.01	  rd(mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y), ld(X, X))
7.79/8.01	= { by lemma 28 }
7.79/8.01	  rd(mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), Y), rd(ld(X, rd(X, X)), ld(X, rd(X, X))))
7.79/8.01	= { by lemma 58 }
7.79/8.01	  mult(rd(ld(X, rd(X, X)), ld(X, rd(X, X))), mult(Y, rd(ld(X, rd(X, X)), ld(X, rd(X, X)))))
7.79/8.01	= { by lemma 28 }
7.79/8.01	  mult(ld(X, X), mult(Y, rd(ld(X, rd(X, X)), ld(X, rd(X, X)))))
7.79/8.01	= { by lemma 28 }
7.79/8.01	  mult(ld(X, X), mult(Y, ld(X, X)))
7.79/8.01	
7.79/8.01	Lemma 60: mult(mult(X, ld(Y, Y)), ld(Y, Y)) = rd(X, ld(Y, Y)).
7.79/8.01	Proof:
7.79/8.01	  mult(mult(X, ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by lemma 49 }
7.79/8.01	  mult(mult(X, mult(Y, ld(mult(Y, Y), Y))), ld(Y, Y))
7.79/8.01	= { by lemma 44 }
7.79/8.01	  mult(mult(X, ld(ld(Y, Y), ld(Y, Y))), ld(Y, Y))
7.79/8.01	= { by lemma 30 }
7.79/8.01	  mult(mult(ld(Y, Y), mult(ld(ld(Y, Y), rd(X, ld(Y, Y))), ld(Y, Y))), ld(Y, Y))
7.79/8.01	= { by lemma 52 }
7.79/8.01	  mult(mult(ld(Y, Y), mult(rd(?, mult(ld(Y, Y), ld(X, mult(ld(Y, Y), ?)))), ld(Y, Y))), ld(Y, Y))
7.79/8.01	= { by lemma 59 }
7.79/8.01	  mult(rd(mult(ld(Y, Y), rd(?, mult(ld(Y, Y), ld(X, mult(ld(Y, Y), ?))))), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by lemma 51 }
7.79/8.01	  mult(rd(rd(X, ld(Y, Y)), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by axiom 3 (f03) }
7.79/8.01	  rd(X, ld(Y, Y))
7.79/8.01	
7.79/8.01	Lemma 61: rd(mult(X, ld(Y, mult(X, Z))), Z) = rd(mult(X, ld(Y, mult(X, ?))), ?).
7.79/8.01	Proof:
7.79/8.01	  rd(mult(X, ld(Y, mult(X, Z))), Z)
7.79/8.01	= { by lemma 26 }
7.79/8.01	  rd(mult(X, mult(ld(Y, rd(Y, Y)), mult(X, Z))), Z)
7.79/8.01	= { by lemma 8 }
7.79/8.01	  mult(mult(X, ld(Y, rd(Y, Y))), X)
7.79/8.01	= { by lemma 8 }
7.79/8.01	  rd(mult(X, mult(ld(Y, rd(Y, Y)), mult(X, ?))), ?)
7.79/8.01	= { by lemma 26 }
7.79/8.01	  rd(mult(X, ld(Y, mult(X, ?))), ?)
7.79/8.01	
7.79/8.01	Lemma 62: rd(ld(X, Y), Y) = rd(?, mult(X, ?)).
7.79/8.01	Proof:
7.79/8.01	  rd(ld(X, Y), Y)
7.79/8.01	= { by axiom 1 (f02) }
7.79/8.01	  ld(X, mult(X, rd(ld(X, Y), Y)))
7.79/8.01	= { by lemma 19 }
7.79/8.01	  ld(X, rd(X, X))
7.79/8.01	= { by lemma 19 }
7.79/8.01	  ld(X, mult(X, rd(ld(X, ?), ?)))
7.79/8.01	= { by axiom 1 (f02) }
7.79/8.01	  rd(ld(X, ?), ?)
7.79/8.01	= { by lemma 22 }
7.79/8.01	  rd(?, mult(X, ?))
7.79/8.01	
7.79/8.01	Lemma 63: mult(rd(?, mult(X, ?)), Y) = ld(X, Y).
7.79/8.01	Proof:
7.79/8.01	  mult(rd(?, mult(X, ?)), Y)
7.79/8.01	= { by axiom 1 (f02) }
7.79/8.01	  mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), Y)
7.79/8.01	= { by lemma 7 }
7.79/8.01	  mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), rd(mult(Y, X), ld(Y, mult(Y, X))))
7.79/8.01	= { by axiom 4 (f04) }
7.79/8.01	  mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), rd(mult(Y, X), rd(mult(ld(Y, mult(Y, X)), ?), ?)))
7.79/8.01	= { by lemma 53 }
7.79/8.01	  mult(mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), mult(Y, X)), rd(?, mult(ld(Y, mult(Y, X)), ?)))
7.79/8.01	= { by lemma 7 }
7.79/8.01	  mult(mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), rd(mult(ld(Y, mult(Y, X)), ?), ld(mult(Y, X), mult(ld(Y, mult(Y, X)), ?)))), rd(?, mult(ld(Y, mult(Y, X)), ?)))
7.79/8.01	= { by lemma 18 }
7.79/8.01	  rd(mult(rd(?, mult(ld(Y, mult(Y, X)), ?)), mult(ld(Y, mult(Y, X)), ?)), ld(rd(?, mult(ld(Y, mult(Y, X)), ?)), ld(mult(Y, X), mult(ld(Y, mult(Y, X)), ?))))
7.79/8.01	= { by axiom 3 (f03) }
7.79/8.01	  rd(?, ld(rd(?, mult(ld(Y, mult(Y, X)), ?)), ld(mult(Y, X), mult(ld(Y, mult(Y, X)), ?))))
7.79/8.01	= { by lemma 27 }
7.79/8.01	  rd(?, mult(rd(mult(ld(Y, mult(Y, X)), ?), ?), ld(mult(Y, X), mult(ld(Y, mult(Y, X)), ?))))
7.79/8.01	= { by axiom 4 (f04) }
7.79/8.01	  rd(?, mult(ld(Y, mult(Y, X)), ld(mult(Y, X), mult(ld(Y, mult(Y, X)), ?))))
7.79/8.01	= { by lemma 52 }
7.79/8.01	  ld(ld(Y, mult(Y, X)), rd(mult(Y, X), ld(Y, mult(Y, X))))
7.79/8.01	= { by axiom 1 (f02) }
7.79/8.01	  ld(X, rd(mult(Y, X), ld(Y, mult(Y, X))))
7.79/8.01	= { by lemma 7 }
7.79/8.01	  ld(X, Y)
7.79/8.01	
7.79/8.01	Lemma 64: rd(ld(X, X), ld(Y, Y)) = ld(mult(X, ld(Y, Y)), X).
7.79/8.01	Proof:
7.79/8.01	  rd(ld(X, X), ld(Y, Y))
7.79/8.01	= { by lemma 42 }
7.79/8.01	  rd(rd(X, X), ld(Y, Y))
7.79/8.01	= { by axiom 5 (f01) }
7.79/8.01	  rd(rd(X, mult(ld(Y, Y), ld(ld(Y, Y), X))), ld(Y, Y))
7.79/8.01	= { by lemma 29 }
7.79/8.01	  rd(rd(X, ld(ld(Y, Y), ld(ld(Y, Y), X))), ld(Y, Y))
7.79/8.01	= { by lemma 36 }
7.79/8.01	  rd(mult(mult(ld(Y, Y), rd(ld(ld(Y, Y), X), ld(ld(Y, Y), X))), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by lemma 42 }
7.79/8.01	  rd(mult(mult(ld(Y, Y), ld(ld(ld(Y, Y), X), ld(ld(Y, Y), X))), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by lemma 44 }
7.79/8.01	  rd(mult(mult(ld(Y, Y), mult(ld(Y, Y), ld(mult(X, ld(Y, Y)), X))), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by lemma 38 }
7.79/8.01	  rd(mult(ld(mult(X, ld(Y, Y)), X), ld(Y, Y)), ld(Y, Y))
7.79/8.01	= { by axiom 4 (f04) }
7.79/8.01	  ld(mult(X, ld(Y, Y)), X)
7.79/8.01	
7.79/8.01	Lemma 65: ld(mult(X, ld(mult(Y, X), Y)), Z) = mult(mult(X, ld(mult(Y, X), Y)), Z).
7.79/8.01	Proof:
7.79/8.01	  ld(mult(X, ld(mult(Y, X), Y)), Z)
7.79/8.01	= { by lemma 44 }
7.79/8.01	  ld(ld(ld(X, Y), ld(X, Y)), Z)
7.79/8.01	= { by lemma 29 }
7.79/8.01	  mult(ld(ld(X, Y), ld(X, Y)), Z)
7.79/8.01	= { by lemma 44 }
7.79/8.01	  mult(mult(X, ld(mult(Y, X), Y)), Z)
7.79/8.01	
7.79/8.01	Lemma 66: mult(mult(ld(X, X), Y), mult(ld(X, X), Z)) = mult(ld(X, X), mult(mult(Y, ld(X, X)), Z)).
7.79/8.01	Proof:
7.79/8.01	  mult(mult(ld(X, X), Y), mult(ld(X, X), Z))
7.79/8.01	= { by lemma 29 }
7.79/8.01	  mult(ld(ld(X, X), Y), mult(ld(X, X), Z))
7.79/8.01	= { by lemma 10 }
7.79/8.01	  ld(ld(X, X), mult(mult(Y, ld(X, X)), Z))
7.79/8.01	= { by lemma 29 }
7.85/8.04	  mult(ld(X, X), mult(mult(Y, ld(X, X)), Z))
7.85/8.04	
7.85/8.04	Lemma 67: mult(mult(X, ld(mult(Y, X), Y)), mult(X, ld(mult(Y, X), Y))) = mult(X, ld(mult(Y, X), Y)).
7.85/8.04	Proof:
7.85/8.04	  mult(mult(X, ld(mult(Y, X), Y)), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by axiom 4 (f04) }
7.85/8.04	  mult(mult(X, ld(mult(Y, X), rd(mult(Y, X), X))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 63 }
7.85/8.04	  mult(mult(X, mult(rd(?, mult(mult(Y, X), ?)), rd(mult(Y, X), X))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 62 }
7.85/8.04	  mult(mult(X, mult(rd(ld(mult(Y, X), mult(X, ?)), mult(X, ?)), rd(mult(Y, X), X))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 47 }
7.85/8.04	  mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ld(X, rd(mult(Y, X), X))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 52 }
7.85/8.04	  mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 57 }
7.85/8.04	  mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by lemma 21 }
7.85/8.04	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(X, ld(mult(Y, X), Y)))
7.85/8.04	= { by axiom 4 (f04) }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(X, ld(mult(Y, X), rd(mult(Y, X), X))))
7.85/8.05	= { by lemma 63 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(X, mult(rd(?, mult(mult(Y, X), ?)), rd(mult(Y, X), X))))
7.85/8.05	= { by lemma 62 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(X, mult(rd(ld(mult(Y, X), mult(X, ?)), mult(X, ?)), rd(mult(Y, X), X))))
7.85/8.05	= { by lemma 47 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ld(X, rd(mult(Y, X), X))))
7.85/8.05	= { by lemma 52 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))))
7.85/8.05	= { by lemma 57 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 21 }
7.85/8.05	  mult(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))))
7.85/8.05	= { by lemma 21 }
7.85/8.05	  rd(rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))))
7.85/8.05	= { by lemma 21 }
7.85/8.05	  rd(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), rd(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))))
7.85/8.05	= { by lemma 21 }
7.85/8.05	  rd(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 42 }
7.85/8.05	  ld(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 31 }
7.85/8.05	  mult(rd(?, mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?)), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 17 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 6 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ld(rd(mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?), mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 9 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ld(rd(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), mult(ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ?))), mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by axiom 3 (f03) }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ld(rd(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), mult(ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ld(rd(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), mult(ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), mult(X, ld(mult(Y, X), mult(X, ?))))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by axiom 4 (f04) }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  ld(rd(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?)), mult(X, ld(mult(Y, X), mult(X, ?)))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 33 }
7.85/8.05	  ld(mult(mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?), ?)), rd(?, mult(X, ld(mult(Y, X), mult(X, ?))))), mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 40 }
7.85/8.05	  ld(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), ld(rd(mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ld(rd(mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), mult(rd(?, mult(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), ?)), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 31 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ld(mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?)))
7.85/8.05	= { by lemma 49 }
7.85/8.05	  ld(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?))
7.85/8.05	= { by lemma 27 }
7.85/8.05	  mult(rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))), rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?))
7.85/8.05	= { by lemma 57 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), rd(?, mult(X, ld(mult(Y, X), mult(X, ?)))))
7.85/8.05	= { by lemma 52 }
7.85/8.05	  mult(rd(mult(X, ld(mult(Y, X), mult(X, ?))), ?), ld(X, rd(mult(Y, X), X)))
7.85/8.05	= { by lemma 47 }
7.85/8.05	  mult(X, mult(rd(ld(mult(Y, X), mult(X, ?)), mult(X, ?)), rd(mult(Y, X), X)))
7.85/8.05	= { by lemma 62 }
7.85/8.05	  mult(X, mult(rd(?, mult(mult(Y, X), ?)), rd(mult(Y, X), X)))
7.85/8.05	= { by lemma 63 }
7.85/8.05	  mult(X, ld(mult(Y, X), rd(mult(Y, X), X)))
7.85/8.05	= { by axiom 4 (f04) }
7.85/8.06	  mult(X, ld(mult(Y, X), Y))
7.85/8.06	
7.85/8.06	Lemma 68: mult(mult(X, ld(mult(ld(Y, Y), X), ld(Y, Y))), mult(ld(Y, Y), X)) = rd(X, ld(Y, Y)).
7.85/8.06	Proof:
7.85/8.06	  mult(mult(X, ld(mult(ld(Y, Y), X), ld(Y, Y))), mult(ld(Y, Y), X))
7.85/8.06	= { by lemma 29 }
7.85/8.06	  mult(mult(X, ld(ld(ld(Y, Y), X), ld(Y, Y))), mult(ld(Y, Y), X))
7.85/8.06	= { by lemma 29 }
7.85/8.06	  mult(mult(X, ld(ld(ld(Y, Y), X), ld(Y, Y))), ld(ld(Y, Y), X))
7.85/8.06	= { by axiom 1 (f02) }
7.85/8.06	  ld(ld(Y, Y), mult(ld(Y, Y), mult(mult(X, ld(ld(ld(Y, Y), X), ld(Y, Y))), ld(ld(Y, Y), X))))
7.85/8.06	= { by axiom 4 (f04) }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(ld(Y, Y), mult(mult(X, ld(ld(ld(Y, Y), X), ld(Y, Y))), ld(ld(Y, Y), X))), ld(Y, Y)), ld(Y, Y)))
7.85/8.06	= { by axiom 5 (f01) }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(ld(Y, Y), mult(mult(mult(ld(Y, Y), ld(ld(Y, Y), X)), ld(ld(ld(Y, Y), X), ld(Y, Y))), ld(ld(Y, Y), X))), ld(Y, Y)), ld(Y, Y)))
7.85/8.06	= { by lemma 11 }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(ld(Y, Y), mult(mult(ld(ld(Y, Y), X), mult(ld(ld(ld(Y, Y), X), ld(Y, Y)), ld(Y, Y))), ld(ld(Y, Y), X))), ld(Y, Y)), ld(Y, Y)))
7.85/8.06	= { by lemma 8 }
7.85/8.06	  ld(ld(Y, Y), rd(rd(mult(ld(Y, Y), mult(mult(mult(ld(ld(Y, Y), X), mult(ld(ld(ld(Y, Y), X), ld(Y, Y)), ld(Y, Y))), ld(ld(Y, Y), X)), mult(ld(Y, Y), ?))), ?), ld(Y, Y)))
7.85/8.06	= { by axiom 2 (f05) }
7.85/8.06	  ld(ld(Y, Y), rd(rd(mult(ld(Y, Y), mult(ld(ld(Y, Y), X), mult(mult(ld(ld(ld(Y, Y), X), ld(Y, Y)), ld(Y, Y)), mult(ld(ld(Y, Y), X), mult(ld(Y, Y), ?))))), ?), ld(Y, Y)))
7.85/8.06	= { by lemma 9 }
7.85/8.06	  ld(ld(Y, Y), rd(rd(mult(ld(Y, Y), mult(ld(ld(Y, Y), X), mult(ld(Y, Y), mult(ld(ld(Y, Y), ld(ld(ld(Y, Y), X), ld(Y, Y))), mult(ld(Y, Y), mult(ld(ld(Y, Y), X), mult(ld(Y, Y), ?))))))), ?), ld(Y, Y)))
7.85/8.06	= { by lemma 9 }
7.85/8.06	  ld(ld(Y, Y), rd(rd(mult(ld(Y, Y), mult(ld(ld(Y, Y), X), mult(ld(Y, Y), mult(ld(ld(Y, Y), ld(ld(ld(Y, Y), X), ld(Y, Y))), mult(mult(X, ld(Y, Y)), ?))))), ?), ld(Y, Y)))
7.85/8.06	= { by lemma 9 }
7.85/8.06	  ld(ld(Y, Y), rd(rd(mult(mult(X, ld(Y, Y)), mult(ld(ld(Y, Y), ld(ld(ld(Y, Y), X), ld(Y, Y))), mult(mult(X, ld(Y, Y)), ?))), ?), ld(Y, Y)))
7.85/8.06	= { by lemma 8 }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(mult(X, ld(Y, Y)), ld(ld(Y, Y), ld(ld(ld(Y, Y), X), ld(Y, Y)))), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by lemma 11 }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(ld(Y, Y), mult(ld(ld(Y, Y), X), ld(ld(ld(Y, Y), X), ld(Y, Y)))), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by axiom 5 (f01) }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(ld(Y, Y), ld(Y, Y)), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by lemma 43 }
7.85/8.06	  ld(ld(Y, Y), rd(mult(mult(Y, ld(mult(Y, Y), Y)), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by lemma 29 }
7.85/8.06	  mult(ld(Y, Y), rd(mult(mult(Y, ld(mult(Y, Y), Y)), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by lemma 50 }
7.85/8.06	  mult(ld(Y, Y), rd(mult(mult(Y, ld(Y, ld(Y, Y))), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by axiom 5 (f01) }
7.85/8.06	  mult(ld(Y, Y), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), ld(Y, Y)))
7.85/8.06	= { by lemma 59 }
7.85/8.06	  mult(ld(Y, Y), mult(ld(Y, Y), mult(mult(X, ld(Y, Y)), ld(Y, Y))))
7.85/8.06	= { by lemma 38 }
7.85/8.06	  mult(mult(X, ld(Y, Y)), ld(Y, Y))
7.85/8.06	= { by lemma 60 }
8.81/9.04	  rd(X, ld(Y, Y))
8.81/9.04	
8.81/9.04	Lemma 69: mult(ld(X, X), ld(mult(Y, ld(X, X)), Y)) = ld(Y, Y).
8.81/9.04	Proof:
8.81/9.04	  mult(ld(X, X), ld(mult(Y, ld(X, X)), Y))
8.81/9.04	= { by lemma 44 }
8.81/9.04	  ld(ld(ld(X, X), Y), ld(ld(X, X), Y))
8.81/9.04	= { by lemma 29 }
8.81/9.04	  ld(mult(ld(X, X), Y), ld(ld(X, X), Y))
8.81/9.04	= { by lemma 29 }
8.81/9.04	  ld(mult(ld(X, X), Y), mult(ld(X, X), Y))
8.81/9.04	= { by lemma 38 }
8.81/9.04	  mult(ld(X, X), mult(ld(X, X), ld(mult(ld(X, X), Y), mult(ld(X, X), Y))))
8.81/9.04	= { by axiom 3 (f03) }
8.81/9.04	  mult(ld(X, X), mult(ld(X, X), ld(mult(rd(mult(ld(X, X), Y), ld(X, X)), ld(X, X)), mult(ld(X, X), Y))))
8.81/9.04	= { by lemma 41 }
8.81/9.04	  mult(ld(X, X), mult(ld(X, X), ld(ld(X, X), ld(ld(ld(X, X), rd(mult(ld(X, X), Y), ld(X, X))), Y))))
8.81/9.04	= { by axiom 5 (f01) }
8.81/9.04	  mult(ld(X, X), ld(ld(ld(X, X), rd(mult(ld(X, X), Y), ld(X, X))), Y))
8.81/9.04	= { by lemma 29 }
8.81/9.04	  ld(ld(X, X), ld(ld(ld(X, X), rd(mult(ld(X, X), Y), ld(X, X))), Y))
8.81/9.04	= { by lemma 41 }
8.81/9.04	  ld(mult(rd(mult(ld(X, X), Y), ld(X, X)), ld(X, X)), mult(ld(X, X), Y))
8.81/9.04	= { by lemma 56 }
8.81/9.04	  mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))
8.81/9.04	= { by lemma 67 }
8.81/9.04	  mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))))
8.81/9.04	= { by lemma 65 }
8.81/9.04	  ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))))
8.81/9.04	= { by axiom 4 (f04) }
8.81/9.04	  rd(mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 55 }
8.81/9.04	  rd(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by axiom 4 (f04) }
8.81/9.04	  rd(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 31 }
8.81/9.04	  rd(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(?, mult(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ?)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 22 }
8.81/9.04	  rd(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ?), ?), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 20 }
8.81/9.04	  rd(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?)), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 47 }
8.81/9.04	  rd(mult(mult(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), ld(rd(ld(X, X), mult(ld(X, X), Y)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 52 }
8.81/9.04	  rd(mult(mult(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(?, mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))))), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 21 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(ld(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 65 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X)))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 67 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by axiom 4 (f04) }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 31 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(?, mult(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ?)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 22 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ?), ?), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 20 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), mult(rd(ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?)), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 47 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), ld(rd(ld(X, X), mult(ld(X, X), Y)), rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), rd(ld(X, X), mult(ld(X, X), Y))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 52 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(mult(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(?, mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 21 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by axiom 1 (f02) }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ld(?, mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 30 }
8.81/9.04	  rd(mult(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(?, mult(ld(?, rd(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ?)), mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.04	= { by lemma 27 }
8.81/9.05	  rd(ld(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(?, mult(ld(?, rd(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ?)), mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 3 (f03) }
8.81/9.05	  rd(ld(mult(rd(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ?), ?), mult(?, mult(ld(?, rd(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ?)), mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 34 }
8.81/9.05	  rd(ld(mult(mult(?, rd(ld(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)))), ?), mult(?, mult(ld(?, rd(rd(rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?), rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), ?)), mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 35 }
8.81/9.05	  rd(ld(mult(mult(?, rd(ld(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)))), ?), mult(?, mult(rd(ld(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?)), mult(?, rd(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(rd(ld(X, X), mult(ld(X, X), Y)), ?))), ?))), mult(?, mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 39 }
8.81/9.05	  rd(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 49 }
8.81/9.05	  rd(mult(mult(X, ld(mult(X, X), X)), rd(ld(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 43 }
8.81/9.05	  rd(mult(mult(ld(X, X), ld(X, X)), rd(ld(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(X, X), ld(X, X)), rd(ld(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(ld(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(rd(X, X), mult(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 49 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(rd(X, X), mult(mult(X, ld(mult(X, X), X)), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 43 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(rd(X, X), mult(mult(ld(X, X), ld(X, X)), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(rd(X, X), mult(mult(rd(X, X), ld(X, X)), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(X, X)), rd(rd(X, X), mult(mult(rd(X, X), rd(X, X)), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 13 }
8.81/9.05	  rd(rd(rd(mult(mult(rd(X, X), rd(X, X)), rd(X, X)), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 9 }
8.81/9.05	  rd(rd(rd(mult(rd(X, X), mult(ld(rd(X, X), rd(X, X)), mult(rd(X, X), rd(X, X)))), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 45 }
8.81/9.05	  rd(rd(rd(mult(rd(X, X), mult(rd(X, X), rd(X, X))), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 27 }
8.81/9.05	  rd(rd(rd(ld(rd(X, X), mult(rd(X, X), rd(X, X))), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 21 }
8.81/9.05	  rd(rd(rd(ld(rd(X, X), rd(rd(X, X), rd(X, X))), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 16 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), mult(rd(X, X), rd(X, X))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 1 (f02) }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(?, mult(rd(X, X), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 27 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(?, ld(rd(X, X), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 30 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), mult(ld(rd(X, X), rd(?, rd(X, X))), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 52 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), mult(rd(?, mult(rd(X, X), ld(?, mult(rd(X, X), ?)))), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 58 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, rd(mult(rd(X, X), rd(?, mult(rd(X, X), ld(?, mult(rd(X, X), ?))))), rd(X, X)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 51 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, rd(rd(?, rd(X, X)), rd(X, X)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 5 (f01) }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), ld(rd(X, X), rd(rd(?, rd(X, X)), rd(X, X)))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 4 (f04) }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), rd(mult(ld(rd(X, X), rd(rd(?, rd(X, X)), rd(X, X))), ?), ?)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 25 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), rd(ld(rd(X, X), mult(rd(?, rd(X, X)), ld(rd(X, X), ?))), ?)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 26 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), rd(ld(rd(X, X), mult(rd(?, rd(X, X)), mult(ld(rd(X, X), rd(rd(X, X), rd(X, X))), ?))), ?)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 26 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), rd(mult(ld(rd(X, X), rd(rd(X, X), rd(X, X))), mult(rd(?, rd(X, X)), mult(ld(rd(X, X), rd(rd(X, X), rd(X, X))), ?))), ?)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 8 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), mult(mult(ld(rd(X, X), rd(rd(X, X), rd(X, X))), rd(?, rd(X, X))), ld(rd(X, X), rd(rd(X, X), rd(X, X))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 26 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), mult(ld(rd(X, X), rd(?, rd(X, X))), ld(rd(X, X), rd(rd(X, X), rd(X, X))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(rd(X, X), mult(ld(rd(X, X), rd(?, rd(X, X))), ld(rd(X, X), ld(rd(X, X), rd(X, X))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 30 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(?, mult(?, ld(rd(X, X), ld(rd(X, X), ld(rd(X, X), rd(X, X))))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 1 (f02) }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(rd(X, X), ld(rd(X, X), ld(rd(X, X), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(rd(X, X), ld(rd(X, X), rd(rd(X, X), rd(X, X))))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 16 }
8.81/9.05	  rd(rd(rd(rd(?, mult(rd(X, X), ?)), Y), ld(rd(X, X), rd(?, mult(rd(X, X), ?)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 36 }
8.81/9.05	  rd(mult(mult(rd(X, X), rd(ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y)), rd(?, mult(rd(X, X), ?)))), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 4 (f04) }
8.81/9.05	  rd(mult(mult(rd(mult(rd(X, X), ?), ?), rd(ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y)), rd(?, mult(rd(X, X), ?)))), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 53 }
8.81/9.05	  rd(mult(mult(mult(rd(mult(rd(X, X), ?), ?), ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y))), rd(mult(rd(X, X), ?), ?)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 4 (f04) }
8.81/9.05	  rd(mult(mult(mult(rd(X, X), ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y))), rd(mult(rd(X, X), ?), ?)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 4 (f04) }
8.81/9.05	  rd(mult(mult(mult(rd(X, X), ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y))), rd(X, X)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by axiom 2 (f05) }
8.81/9.05	  rd(mult(rd(X, X), mult(ld(rd(X, X), rd(rd(?, mult(rd(X, X), ?)), Y)), mult(rd(X, X), rd(X, X)))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 9 }
8.81/9.05	  rd(mult(mult(rd(rd(?, mult(rd(X, X), ?)), Y), rd(X, X)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 37 }
8.81/9.05	  rd(mult(mult(rd(rd(X, X), Y), rd(X, X)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(rd(X, X), Y), ld(X, X)), rd(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(mult(mult(rd(rd(X, X), Y), ld(X, X)), ld(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 60 }
8.81/9.05	  rd(rd(rd(rd(X, X), Y), ld(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 42 }
8.81/9.05	  rd(rd(rd(ld(X, X), Y), ld(X, X)), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 68 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(mult(rd(ld(X, X), mult(ld(X, X), Y)), ld(mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y))), ld(X, X))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), Y)))))
8.81/9.05	= { by lemma 68 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), rd(rd(ld(X, X), mult(ld(X, X), Y)), ld(X, X)))
8.81/9.05	= { by lemma 29 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), rd(rd(ld(X, X), ld(ld(X, X), Y)), ld(X, X)))
8.81/9.05	= { by lemma 34 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(ld(ld(X, X), ld(X, X)), mult(ld(X, X), ld(ld(X, X), Y)))))
8.81/9.05	= { by lemma 29 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(mult(ld(X, X), ld(X, X)), mult(ld(X, X), ld(ld(X, X), Y)))))
8.81/9.05	= { by lemma 43 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(mult(X, ld(mult(X, X), X)), mult(ld(X, X), ld(ld(X, X), Y)))))
8.81/9.05	= { by lemma 50 }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(mult(X, ld(X, ld(X, X))), mult(ld(X, X), ld(ld(X, X), Y)))))
8.81/9.05	= { by axiom 5 (f01) }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(ld(X, X), mult(ld(X, X), ld(ld(X, X), Y)))))
8.81/9.05	= { by axiom 5 (f01) }
8.81/9.05	  rd(mult(mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X))), mult(ld(X, X), rd(ld(X, X), Y))), mult(ld(X, X), rd(ld(X, X), Y)))
8.81/9.05	= { by axiom 4 (f04) }
8.81/9.05	  mult(rd(ld(X, X), Y), ld(mult(ld(X, X), rd(ld(X, X), Y)), ld(X, X)))
8.81/9.06	= { by lemma 56 }
8.81/9.06	  ld(mult(rd(Y, ld(X, X)), ld(X, X)), Y)
8.81/9.06	= { by lemma 36 }
8.81/9.06	  ld(mult(mult(mult(X, rd(ld(X, Y), X)), X), ld(X, X)), Y)
8.81/9.06	= { by lemma 11 }
8.81/9.06	  ld(mult(X, mult(ld(X, mult(X, rd(ld(X, Y), X))), X)), Y)
8.81/9.06	= { by axiom 1 (f02) }
8.81/9.06	  ld(mult(X, mult(rd(ld(X, Y), X), X)), Y)
8.81/9.06	= { by axiom 3 (f03) }
8.81/9.06	  ld(mult(X, ld(X, Y)), Y)
8.81/9.06	= { by axiom 5 (f01) }
8.81/9.06	  ld(Y, Y)
8.81/9.06	
8.81/9.06	Lemma 70: ld(mult(X, ld(Y, Y)), X) = ld(X, X).
8.81/9.06	Proof:
8.81/9.06	  ld(mult(X, ld(Y, Y)), X)
8.81/9.06	= { by lemma 64 }
8.81/9.06	  rd(ld(X, X), ld(Y, Y))
8.81/9.06	= { by lemma 68 }
8.81/9.06	  mult(mult(ld(X, X), ld(mult(ld(Y, Y), ld(X, X)), ld(Y, Y))), mult(ld(Y, Y), ld(X, X)))
8.81/9.06	= { by lemma 69 }
8.81/9.06	  mult(ld(ld(Y, Y), ld(Y, Y)), mult(ld(Y, Y), ld(X, X)))
8.81/9.06	= { by lemma 55 }
8.81/9.06	  mult(ld(Y, Y), mult(ld(ld(Y, Y), ld(Y, Y)), ld(X, X)))
8.81/9.06	= { by lemma 44 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(Y, ld(mult(Y, Y), Y)), ld(X, X)))
8.81/9.06	= { by lemma 50 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(Y, ld(Y, ld(Y, Y))), ld(X, X)))
8.81/9.06	= { by axiom 5 (f01) }
8.81/9.06	  mult(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))
8.81/9.06	= { by lemma 38 }
8.81/9.06	  ld(X, X)
8.81/9.06	
8.81/9.06	Lemma 71: ld(X, X) = ld(?, ?).
8.81/9.06	Proof:
8.81/9.06	  ld(X, X)
8.81/9.06	= { by lemma 69 }
8.81/9.06	  mult(ld(Y, Y), ld(mult(X, ld(Y, Y)), X))
8.81/9.06	= { by lemma 67 }
8.81/9.06	  mult(mult(ld(Y, Y), ld(mult(X, ld(Y, Y)), X)), mult(ld(Y, Y), ld(mult(X, ld(Y, Y)), X)))
8.81/9.06	= { by lemma 70 }
8.81/9.06	  mult(mult(ld(Y, Y), ld(X, X)), mult(ld(Y, Y), ld(mult(X, ld(Y, Y)), X)))
8.81/9.06	= { by lemma 66 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(ld(X, X), ld(Y, Y)), ld(mult(X, ld(Y, Y)), X)))
8.81/9.06	= { by lemma 70 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(ld(X, X), ld(Y, Y)), ld(X, X)))
8.81/9.06	= { by lemma 54 }
8.81/9.06	  mult(ld(Y, Y), mult(ld(X, X), rd(ld(Y, Y), ld(X, X))))
8.81/9.06	= { by lemma 64 }
8.81/9.06	  mult(ld(Y, Y), mult(ld(X, X), ld(mult(Y, ld(X, X)), Y)))
8.81/9.06	= { by lemma 69 }
8.81/9.06	  mult(ld(Y, Y), ld(Y, Y))
8.81/9.06	= { by lemma 69 }
8.81/9.06	  mult(ld(Y, Y), mult(ld(?, ?), ld(mult(Y, ld(?, ?)), Y)))
8.81/9.06	= { by lemma 64 }
8.81/9.06	  mult(ld(Y, Y), mult(ld(?, ?), rd(ld(Y, Y), ld(?, ?))))
8.81/9.06	= { by lemma 54 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(ld(?, ?), ld(Y, Y)), ld(?, ?)))
8.81/9.06	= { by lemma 70 }
8.81/9.06	  mult(ld(Y, Y), mult(mult(ld(?, ?), ld(Y, Y)), ld(mult(?, ld(Y, Y)), ?)))
8.81/9.06	= { by lemma 66 }
8.81/9.06	  mult(mult(ld(Y, Y), ld(?, ?)), mult(ld(Y, Y), ld(mult(?, ld(Y, Y)), ?)))
8.81/9.06	= { by lemma 70 }
8.81/9.06	  mult(mult(ld(Y, Y), ld(mult(?, ld(Y, Y)), ?)), mult(ld(Y, Y), ld(mult(?, ld(Y, Y)), ?)))
8.81/9.06	= { by lemma 67 }
8.81/9.06	  mult(ld(Y, Y), ld(mult(?, ld(Y, Y)), ?))
8.81/9.06	= { by lemma 69 }
8.81/9.06	  ld(?, ?)
8.81/9.06	
8.81/9.06	Lemma 72: mult(X, ld(?, ?)) = X.
8.81/9.06	Proof:
8.81/9.06	  mult(X, ld(?, ?))
8.81/9.06	= { by lemma 7 }
8.81/9.06	  rd(X, ld(mult(X, ld(?, ?)), X))
8.81/9.06	= { by lemma 70 }
8.81/9.06	  rd(X, ld(X, X))
8.81/9.06	= { by lemma 7 }
8.81/9.06	  X
8.81/9.06	
8.81/9.06	Lemma 73: rd(X, ld(?, ?)) = X.
8.81/9.06	Proof:
8.81/9.06	  rd(X, ld(?, ?))
8.81/9.06	= { by lemma 72 }
8.81/9.06	  mult(rd(X, ld(?, ?)), ld(?, ?))
8.81/9.06	= { by axiom 3 (f03) }
8.81/9.06	  X
8.81/9.06	
8.81/9.06	Goal 1 (goals): tuple(mult(X, sK1_goals_X1(X)), sK2_goals_X1(X)) = tuple(sK1_goals_X1(X), mult(sK2_goals_X1(X), X)).
8.81/9.06	The goal is true when:
8.81/9.06	  X = ld(?, ?)
8.81/9.06	where "?" stands for an arbitrary term of your choice.
8.81/9.06	
8.81/9.06	Proof:
8.81/9.06	  tuple(mult(ld(?, ?), sK1_goals_X1(ld(?, ?))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 71 }
8.81/9.06	  tuple(mult(ld(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), sK1_goals_X1(ld(?, ?))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 42 }
8.81/9.06	  tuple(mult(rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), sK1_goals_X1(ld(?, ?))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 7 }
8.81/9.06	  tuple(mult(rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), rd(sK1_goals_X1(ld(?, ?)), ld(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 72 }
8.81/9.06	  tuple(mult(rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), rd(sK1_goals_X1(ld(?, ?)), mult(ld(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), ld(?, ?)))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 42 }
8.81/9.06	  tuple(mult(rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), rd(sK1_goals_X1(ld(?, ?)), mult(rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?))), ld(?, ?)))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 48 }
8.81/9.06	  tuple(rd(rd(sK1_goals_X1(ld(?, ?)), ld(?, ?)), rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?)))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 73 }
8.81/9.06	  tuple(rd(sK1_goals_X1(ld(?, ?)), rd(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?)))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 42 }
8.81/9.06	  tuple(rd(sK1_goals_X1(ld(?, ?)), ld(sK1_goals_X1(ld(?, ?)), sK1_goals_X1(ld(?, ?)))), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 71 }
8.81/9.06	  tuple(rd(sK1_goals_X1(ld(?, ?)), ld(?, ?)), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 73 }
8.81/9.06	  tuple(sK1_goals_X1(ld(?, ?)), sK2_goals_X1(ld(?, ?)))
8.81/9.06	= { by lemma 72 }
8.81/9.06	  tuple(sK1_goals_X1(ld(?, ?)), mult(sK2_goals_X1(ld(?, ?)), ld(?, ?)))
8.81/9.06	% SZS output end Proof
8.81/9.06	
8.81/9.06	RESULT: Theorem (the conjecture is true).
8.81/9.06	EOF