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
0.12/0.33	% Computer   : n004.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 960
0.12/0.33	% WCLimit    : 120
0.12/0.33	% DateTime   : Thu Jul  2 08:01:58 EDT 2020
0.12/0.34	% CPUTime    : 
14.08/2.12	% SZS status Theorem
14.08/2.12	
14.08/2.12	% SZS output start Proof
14.08/2.12	Take the following subset of the input axioms:
14.08/2.12	  fof(f01, axiom, ![B, A]: mult(A, ld(A, B))=B).
14.08/2.12	  fof(f02, axiom, ![B, A]: B=ld(A, mult(A, B))).
14.08/2.12	  fof(f03, axiom, ![B, A]: A=mult(rd(A, B), B)).
14.08/2.12	  fof(f04, axiom, ![B, A]: A=rd(mult(A, B), B)).
14.08/2.12	  fof(f05, axiom, ![C, B, A]: mult(mult(mult(A, B), C), B)=mult(A, mult(B, mult(C, B)))).
14.08/2.12	  fof(goals, conjecture, ![X0, X1]: (mult(X0, ld(X1, X1))=X0 & X0=mult(ld(X1, X1), X0))).
14.08/2.12	
14.08/2.12	Now clausify the problem and encode Horn clauses using encoding 3 of
14.08/2.12	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
14.08/2.12	We repeatedly replace C & s=t => u=v by the two clauses:
14.08/2.12	  fresh(y, y, x1...xn) = u
14.08/2.12	  C => fresh(s, t, x1...xn) = v
14.08/2.12	where fresh is a fresh function symbol and x1..xn are the free
14.08/2.12	variables of u and v.
14.08/2.12	A predicate p(X) is encoded as p(X)=true (this is sound, because the
14.08/2.12	input problem has no model of domain size 1).
14.08/2.12	
14.08/2.12	The encoding turns the above axioms into the following unit equations and goals:
14.08/2.12	
14.08/2.12	Axiom 1 (f03): X = mult(rd(X, Y), Y).
14.08/2.12	Axiom 2 (f02): X = ld(Y, mult(Y, X)).
14.08/2.12	Axiom 3 (f04): X = rd(mult(X, Y), Y).
14.08/2.12	Axiom 4 (f01): mult(X, ld(X, Y)) = Y.
14.25/2.16	Axiom 5 (f05): mult(mult(mult(X, Y), Z), Y) = mult(X, mult(Y, mult(Z, Y))).
14.25/2.16	
14.25/2.16	Lemma 6: rd(X, ld(Y, X)) = Y.
14.25/2.16	Proof:
14.25/2.16	  rd(X, ld(Y, X))
14.25/2.16	= { by axiom 4 (f01) }
14.25/2.16	  rd(mult(Y, ld(Y, X)), ld(Y, X))
14.25/2.16	= { by axiom 3 (f04) }
14.25/2.16	  Y
14.25/2.16	
14.25/2.16	Lemma 7: mult(rd(Z, Y), mult(Y, mult(X, Y))) = mult(mult(Z, X), Y).
14.25/2.16	Proof:
14.25/2.16	  mult(rd(Z, Y), mult(Y, mult(X, Y)))
14.25/2.16	= { by axiom 5 (f05) }
14.25/2.16	  mult(mult(mult(rd(Z, Y), Y), X), Y)
14.25/2.16	= { by axiom 1 (f03) }
14.25/2.16	  mult(mult(Z, X), Y)
14.25/2.16	
14.25/2.16	Lemma 8: ld(rd(Y, Z), mult(X, Z)) = mult(Z, mult(ld(Y, X), Z)).
14.25/2.16	Proof:
14.25/2.16	  ld(rd(Y, Z), mult(X, Z))
14.25/2.16	= { by axiom 4 (f01) }
14.25/2.16	  ld(rd(Y, Z), mult(mult(Y, ld(Y, X)), Z))
14.25/2.16	= { by lemma 7 }
14.25/2.16	  ld(rd(Y, Z), mult(rd(Y, Z), mult(Z, mult(ld(Y, X), Z))))
14.25/2.16	= { by axiom 2 (f02) }
14.25/2.16	  mult(Z, mult(ld(Y, X), Z))
14.25/2.16	
14.25/2.16	Lemma 9: mult(Y, mult(ld(X, rd(X, Y)), Y)) = Y.
14.25/2.16	Proof:
14.25/2.16	  mult(Y, mult(ld(X, rd(X, Y)), Y))
14.25/2.16	= { by lemma 8 }
14.25/2.16	  ld(rd(X, Y), mult(rd(X, Y), Y))
14.25/2.16	= { by axiom 2 (f02) }
14.25/2.16	  Y
14.25/2.16	
14.25/2.16	Lemma 10: mult(ld(Y, rd(Y, X)), X) = ld(X, X).
14.25/2.16	Proof:
14.25/2.16	  mult(ld(Y, rd(Y, X)), X)
14.25/2.16	= { by axiom 2 (f02) }
14.25/2.16	  ld(X, mult(X, mult(ld(Y, rd(Y, X)), X)))
14.25/2.17	= { by lemma 9 }
14.25/2.17	  ld(X, X)
14.25/2.17	
14.25/2.17	Lemma 11: rd(mult(Z, mult(Y, X)), Y) = mult(mult(Z, Y), rd(X, Y)).
14.25/2.17	Proof:
14.25/2.17	  rd(mult(Z, mult(Y, X)), Y)
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  rd(mult(Z, mult(Y, mult(rd(X, Y), Y))), Y)
14.25/2.17	= { by axiom 5 (f05) }
14.25/2.17	  rd(mult(mult(mult(Z, Y), rd(X, Y)), Y), Y)
14.25/2.17	= { by axiom 3 (f04) }
14.25/2.17	  mult(mult(Z, Y), rd(X, Y))
14.25/2.17	
14.25/2.17	Lemma 12: mult(mult(Z, Y), rd(ld(Y, X), Y)) = rd(mult(Z, X), Y).
14.25/2.17	Proof:
14.25/2.17	  mult(mult(Z, Y), rd(ld(Y, X), Y))
14.25/2.17	= { by lemma 11 }
14.25/2.17	  rd(mult(Z, mult(Y, ld(Y, X))), Y)
14.25/2.17	= { by axiom 4 (f01) }
14.25/2.17	  rd(mult(Z, X), Y)
14.25/2.17	
14.25/2.17	Lemma 13: ld(rd(X, Y), X) = Y.
14.25/2.17	Proof:
14.25/2.17	  ld(rd(X, Y), X)
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  ld(rd(X, Y), mult(rd(X, Y), Y))
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  Y
14.25/2.17	
14.25/2.17	Lemma 14: ld(Y, rd(Y, X)) = ld(?, rd(?, X)).
14.25/2.17	Proof:
14.25/2.17	  ld(Y, rd(Y, X))
14.25/2.17	= { by axiom 3 (f04) }
14.25/2.17	  rd(mult(ld(Y, rd(Y, X)), X), X)
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(ld(X, X), X)
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(mult(ld(?, rd(?, X)), X), X)
14.25/2.17	= { by axiom 3 (f04) }
14.25/2.17	  ld(?, rd(?, X))
14.25/2.17	
14.25/2.17	Lemma 15: mult(Y, ld(?, rd(?, X))) = rd(Y, X).
14.25/2.17	Proof:
14.25/2.17	  mult(Y, ld(?, rd(?, X)))
14.25/2.17	= { by lemma 14 }
14.25/2.17	  mult(Y, ld(Y, rd(Y, X)))
14.25/2.17	= { by axiom 4 (f01) }
14.25/2.17	  rd(Y, X)
14.25/2.17	
14.25/2.17	Lemma 16: ld(?, rd(?, ld(Y, X))) = ld(X, Y).
14.25/2.17	Proof:
14.25/2.17	  ld(?, rd(?, ld(Y, X)))
14.25/2.17	= { by lemma 14 }
14.25/2.17	  ld(X, rd(X, ld(Y, X)))
14.25/2.17	= { by lemma 6 }
14.25/2.17	  ld(X, Y)
14.25/2.17	
14.25/2.17	Lemma 17: rd(Z, ld(Y, X)) = mult(Z, ld(X, Y)).
14.25/2.17	Proof:
14.25/2.17	  rd(Z, ld(Y, X))
14.25/2.17	= { by lemma 15 }
14.25/2.17	  mult(Z, ld(?, rd(?, ld(Y, X))))
14.25/2.17	= { by lemma 16 }
14.25/2.17	  mult(Z, ld(X, Y))
14.25/2.17	
14.25/2.17	Lemma 18: mult(mult(Y, ld(X, X)), X) = mult(rd(Y, X), mult(X, X)).
14.25/2.17	Proof:
14.25/2.17	  mult(mult(Y, ld(X, X)), X)
14.25/2.17	= { by lemma 13 }
14.25/2.17	  mult(mult(Y, ld(X, X)), ld(rd(?, X), ?))
14.25/2.17	= { by lemma 17 }
14.25/2.17	  rd(mult(Y, ld(X, X)), ld(?, rd(?, X)))
14.25/2.17	= { by lemma 12 }
14.25/2.17	  mult(mult(Y, ld(?, rd(?, X))), rd(ld(ld(?, rd(?, X)), ld(X, X)), ld(?, rd(?, X))))
14.25/2.17	= { by lemma 15 }
14.25/2.17	  mult(rd(Y, X), rd(ld(ld(?, rd(?, X)), ld(X, X)), ld(?, rd(?, X))))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  mult(rd(Y, X), rd(ld(ld(?, rd(?, X)), mult(ld(?, rd(?, X)), X)), ld(?, rd(?, X))))
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  mult(rd(Y, X), rd(X, ld(?, rd(?, X))))
14.25/2.17	= { by lemma 17 }
14.25/2.17	  mult(rd(Y, X), mult(X, ld(rd(?, X), ?)))
14.25/2.17	= { by lemma 13 }
14.25/2.17	  mult(rd(Y, X), mult(X, X))
14.25/2.17	
14.25/2.17	Lemma 19: rd(Y, Y) = ld(Y, Y).
14.25/2.17	Proof:
14.25/2.17	  rd(Y, Y)
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  ld(?, mult(?, rd(Y, Y)))
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  ld(?, mult(mult(rd(?, Y), Y), rd(Y, Y)))
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  ld(?, mult(mult(rd(?, Y), Y), rd(ld(Y, mult(Y, Y)), Y)))
14.25/2.17	= { by lemma 12 }
14.25/2.17	  ld(?, rd(mult(rd(?, Y), mult(Y, Y)), Y))
14.25/2.17	= { by lemma 18 }
14.25/2.17	  ld(?, rd(mult(mult(?, ld(Y, Y)), Y), Y))
14.25/2.17	= { by axiom 3 (f04) }
14.25/2.17	  ld(?, mult(?, ld(Y, Y)))
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  ld(Y, Y)
14.25/2.17	
14.25/2.17	Lemma 20: ld(ld(X, X), X) = X.
14.25/2.17	Proof:
14.25/2.17	  ld(ld(X, X), X)
14.25/2.17	= { by lemma 19 }
14.25/2.17	  ld(rd(X, X), X)
14.25/2.17	= { by lemma 13 }
14.25/2.17	  X
14.25/2.17	
14.25/2.17	Lemma 21: mult(ld(X, X), X) = X.
14.25/2.17	Proof:
14.25/2.17	  mult(ld(X, X), X)
14.25/2.17	= { by lemma 19 }
14.25/2.17	  mult(rd(X, X), X)
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  X
14.25/2.17	
14.25/2.17	Lemma 22: mult(ld(X, X), ld(X, X)) = ld(X, X).
14.25/2.17	Proof:
14.25/2.17	  mult(ld(X, X), ld(X, X))
14.25/2.17	= { by lemma 6 }
14.25/2.17	  rd(X, ld(mult(ld(X, X), ld(X, X)), X))
14.25/2.17	= { by lemma 6 }
14.25/2.17	  rd(X, ld(mult(ld(X, rd(X, ld(X, X))), ld(X, X)), X))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, ld(ld(ld(X, X), ld(X, X)), X))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, ld(ld(mult(ld(?, rd(?, X)), X), ld(X, X)), X))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, ld(ld(mult(ld(?, rd(?, X)), X), mult(ld(?, rd(?, X)), X)), X))
14.25/2.17	= { by lemma 19 }
14.25/2.17	  rd(X, ld(rd(mult(ld(?, rd(?, X)), X), mult(ld(?, rd(?, X)), X)), X))
14.25/2.17	= { by lemma 9 }
14.25/2.17	  rd(X, ld(rd(mult(ld(?, rd(?, X)), X), mult(ld(?, rd(?, X)), X)), mult(X, mult(ld(?, rd(?, X)), X))))
14.25/2.17	= { by lemma 8 }
14.25/2.17	  rd(X, mult(mult(ld(?, rd(?, X)), X), mult(ld(mult(ld(?, rd(?, X)), X), X), mult(ld(?, rd(?, X)), X))))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, mult(ld(X, X), mult(ld(mult(ld(?, rd(?, X)), X), X), mult(ld(?, rd(?, X)), X))))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, mult(ld(X, X), mult(ld(ld(X, X), X), mult(ld(?, rd(?, X)), X))))
14.25/2.17	= { by lemma 20 }
14.25/2.17	  rd(X, mult(ld(X, X), mult(X, mult(ld(?, rd(?, X)), X))))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  rd(X, mult(ld(X, X), mult(X, ld(X, X))))
14.25/2.17	= { by axiom 4 (f01) }
14.25/2.17	  rd(X, mult(ld(X, X), X))
14.25/2.17	= { by lemma 21 }
14.25/2.17	  rd(X, X)
14.25/2.17	= { by lemma 19 }
14.25/2.17	  ld(X, X)
14.25/2.17	
14.25/2.17	Lemma 23: mult(ld(?, rd(?, X)), mult(X, X)) = X.
14.25/2.17	Proof:
14.25/2.17	  mult(ld(?, rd(?, X)), mult(X, X))
14.25/2.17	= { by axiom 3 (f04) }
14.25/2.17	  mult(rd(mult(ld(?, rd(?, X)), X), X), mult(X, X))
14.25/2.17	= { by lemma 10 }
14.25/2.17	  mult(rd(ld(X, X), X), mult(X, X))
14.25/2.17	= { by lemma 18 }
14.25/2.17	  mult(mult(ld(X, X), ld(X, X)), X)
14.25/2.17	= { by axiom 4 (f01) }
14.25/2.17	  mult(mult(ld(X, X), ld(X, X)), mult(X, ld(X, X)))
14.25/2.17	= { by lemma 17 }
14.25/2.17	  mult(mult(ld(X, X), ld(X, X)), rd(X, ld(X, X)))
14.25/2.17	= { by lemma 11 }
14.25/2.17	  rd(mult(ld(X, X), mult(ld(X, X), X)), ld(X, X))
14.25/2.17	= { by lemma 21 }
14.25/2.17	  rd(mult(ld(X, X), X), ld(X, X))
14.25/2.17	= { by lemma 17 }
14.25/2.17	  mult(mult(ld(X, X), X), ld(X, X))
14.25/2.17	= { by lemma 21 }
14.25/2.17	  mult(X, ld(X, X))
14.25/2.17	= { by axiom 4 (f01) }
14.25/2.17	  X
14.25/2.17	
14.25/2.17	Lemma 24: ld(ld(X, Y), ld(Y, X)) = mult(ld(Y, X), ld(Y, X)).
14.25/2.17	Proof:
14.25/2.17	  ld(ld(X, Y), ld(Y, X))
14.25/2.17	= { by lemma 16 }
14.25/2.17	  ld(ld(?, rd(?, ld(Y, X))), ld(Y, X))
14.25/2.17	= { by lemma 23 }
14.25/2.17	  ld(ld(?, rd(?, ld(Y, X))), mult(ld(?, rd(?, ld(Y, X))), mult(ld(Y, X), ld(Y, X))))
14.25/2.17	= { by axiom 2 (f02) }
14.25/2.17	  mult(ld(Y, X), ld(Y, X))
14.25/2.17	
14.25/2.17	Lemma 25: mult(Z, mult(ld(Y, rd(X, Z)), Z)) = ld(rd(Y, Z), X).
14.25/2.17	Proof:
14.25/2.17	  mult(Z, mult(ld(Y, rd(X, Z)), Z))
14.25/2.17	= { by lemma 8 }
14.25/2.17	  ld(rd(Y, Z), mult(rd(X, Z), Z))
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  ld(rd(Y, Z), X)
14.25/2.17	
14.25/2.17	Lemma 26: ld(rd(ld(rd(Y, X), rd(Y, X)), X), Y) = mult(X, Y).
14.25/2.17	Proof:
14.25/2.17	  ld(rd(ld(rd(Y, X), rd(Y, X)), X), Y)
14.25/2.17	= { by lemma 25 }
14.25/2.17	  mult(X, mult(ld(ld(rd(Y, X), rd(Y, X)), rd(Y, X)), X))
14.25/2.17	= { by lemma 20 }
14.25/2.17	  mult(X, mult(rd(Y, X), X))
14.25/2.17	= { by axiom 1 (f03) }
14.25/2.17	  mult(X, Y)
14.25/2.17	
14.25/2.17	Lemma 27: rd(ld(rd(Y, X), rd(Y, X)), X) = rd(Y, mult(X, Y)).
14.25/2.17	Proof:
14.25/2.17	  rd(ld(rd(Y, X), rd(Y, X)), X)
14.25/2.17	= { by lemma 6 }
14.25/2.17	  rd(Y, ld(rd(ld(rd(Y, X), rd(Y, X)), X), Y))
14.25/2.17	= { by lemma 26 }
14.25/2.18	  rd(Y, mult(X, Y))
14.25/2.18	
14.25/2.18	Lemma 28: ld(rd(Y, X), rd(Y, X)) = mult(rd(Y, mult(X, Y)), X).
14.25/2.18	Proof:
14.25/2.18	  ld(rd(Y, X), rd(Y, X))
14.25/2.18	= { by axiom 1 (f03) }
14.25/2.18	  mult(rd(ld(rd(Y, X), rd(Y, X)), X), X)
14.25/2.18	= { by lemma 27 }
14.25/2.18	  mult(rd(Y, mult(X, Y)), X)
14.25/2.18	
14.25/2.18	Lemma 29: mult(rd(Y, mult(ld(X, Y), Y)), ld(X, Y)) = ld(X, X).
14.25/2.18	Proof:
14.25/2.18	  mult(rd(Y, mult(ld(X, Y), Y)), ld(X, Y))
14.25/2.18	= { by lemma 28 }
14.25/2.18	  ld(rd(Y, ld(X, Y)), rd(Y, ld(X, Y)))
14.25/2.18	= { by lemma 6 }
14.25/2.18	  ld(X, rd(Y, ld(X, Y)))
14.25/2.18	= { by lemma 17 }
14.25/2.18	  ld(X, mult(Y, ld(Y, X)))
14.25/2.18	= { by axiom 4 (f01) }
14.25/2.18	  ld(X, X)
14.25/2.18	
14.25/2.18	Lemma 30: ld(mult(X, Y), X) = ld(?, rd(?, Y)).
14.25/2.18	Proof:
14.25/2.18	  ld(mult(X, Y), X)
14.25/2.18	= { by axiom 3 (f04) }
14.25/2.18	  ld(mult(X, Y), rd(mult(X, Y), Y))
14.25/2.18	= { by lemma 14 }
14.25/2.18	  ld(?, rd(?, Y))
14.25/2.18	
14.25/2.18	Lemma 31: ld(X, ld(X, X)) = ld(?, rd(?, X)).
14.25/2.18	Proof:
14.25/2.18	  ld(X, ld(X, X))
14.25/2.18	= { by lemma 19 }
14.25/2.18	  ld(X, rd(X, X))
14.25/2.18	= { by lemma 14 }
14.25/2.18	  ld(?, rd(?, X))
14.25/2.18	
14.25/2.18	Lemma 32: ld(mult(X, Z), rd(mult(X, Y), Z)) = rd(ld(Z, Y), Z).
14.25/2.18	Proof:
14.25/2.18	  ld(mult(X, Z), rd(mult(X, Y), Z))
14.25/2.18	= { by lemma 12 }
14.25/2.18	  ld(mult(X, Z), mult(mult(X, Z), rd(ld(Z, Y), Z)))
14.25/2.18	= { by axiom 2 (f02) }
14.25/2.18	  rd(ld(Z, Y), Z)
14.25/2.18	
14.25/2.18	Lemma 33: mult(ld(ld(Y, X), X), ld(X, Y)) = mult(ld(X, Y), Y).
14.25/2.18	Proof:
14.25/2.18	  mult(ld(ld(Y, X), X), ld(X, Y))
14.25/2.18	= { by lemma 17 }
14.25/2.18	  rd(ld(ld(Y, X), X), ld(Y, X))
14.25/2.18	= { by lemma 32 }
14.25/2.18	  ld(mult(ld(X, X), ld(Y, X)), rd(mult(ld(X, X), X), ld(Y, X)))
14.25/2.18	= { by axiom 4 (f01) }
14.25/2.18	  ld(mult(ld(X, mult(Y, ld(Y, X))), ld(Y, X)), rd(mult(ld(X, X), X), ld(Y, X)))
14.25/2.18	= { by lemma 17 }
14.25/2.18	  ld(mult(ld(X, rd(Y, ld(X, Y))), ld(Y, X)), rd(mult(ld(X, X), X), ld(Y, X)))
14.25/2.18	= { by lemma 17 }
14.25/2.18	  ld(rd(ld(X, rd(Y, ld(X, Y))), ld(X, Y)), rd(mult(ld(X, X), X), ld(Y, X)))
14.25/2.18	= { by lemma 6 }
14.25/2.18	  ld(rd(ld(rd(Y, ld(X, Y)), rd(Y, ld(X, Y))), ld(X, Y)), rd(mult(ld(X, X), X), ld(Y, X)))
14.25/2.18	= { by lemma 21 }
14.25/2.18	  ld(rd(ld(rd(Y, ld(X, Y)), rd(Y, ld(X, Y))), ld(X, Y)), rd(X, ld(Y, X)))
14.25/2.18	= { by lemma 6 }
14.25/2.18	  ld(rd(ld(rd(Y, ld(X, Y)), rd(Y, ld(X, Y))), ld(X, Y)), Y)
14.25/2.18	= { by lemma 26 }
14.25/2.19	  mult(ld(X, Y), Y)
14.25/2.19	
14.25/2.19	Lemma 34: mult(ld(Y, Y), mult(ld(Y, Y), X)) = ld(ld(Y, Y), X).
14.25/2.19	Proof:
14.25/2.19	  mult(ld(Y, Y), mult(ld(Y, Y), X))
14.25/2.19	= { by lemma 13 }
14.25/2.19	  mult(ld(rd(X, ld(Y, Y)), X), mult(ld(Y, Y), X))
14.25/2.19	= { by lemma 16 }
14.25/2.19	  mult(ld(?, rd(?, ld(X, rd(X, ld(Y, Y))))), mult(ld(Y, Y), X))
14.25/2.19	= { by lemma 30 }
14.25/2.19	  mult(ld(mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y)))), mult(ld(rd(X, ld(Y, Y)), X), X)), mult(ld(Y, Y), X))
14.25/2.19	= { by lemma 13 }
14.25/2.19	  mult(ld(mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y)))), mult(ld(rd(X, ld(Y, Y)), X), X)), mult(ld(rd(X, ld(Y, Y)), X), X))
14.25/2.19	= { by lemma 33 }
14.25/2.19	  mult(ld(ld(mult(ld(rd(X, ld(Y, Y)), X), X), mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y))))), mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y))))), ld(mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y)))), mult(ld(rd(X, ld(Y, Y)), X), X)))
14.25/2.19	= { by axiom 2 (f02) }
14.25/2.19	  mult(ld(ld(X, rd(X, ld(Y, Y))), mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y))))), ld(mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y)))), mult(ld(rd(X, ld(Y, Y)), X), X)))
14.25/2.19	= { by lemma 30 }
14.25/2.19	  mult(ld(ld(X, rd(X, ld(Y, Y))), mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y))))), ld(?, rd(?, ld(X, rd(X, ld(Y, Y))))))
14.25/2.19	= { by lemma 15 }
14.25/2.19	  rd(ld(ld(X, rd(X, ld(Y, Y))), mult(mult(ld(rd(X, ld(Y, Y)), X), X), ld(X, rd(X, ld(Y, Y))))), ld(X, rd(X, ld(Y, Y))))
14.25/2.19	= { by lemma 17 }
14.25/2.19	  rd(ld(ld(X, rd(X, ld(Y, Y))), rd(mult(ld(rd(X, ld(Y, Y)), X), X), ld(rd(X, ld(Y, Y)), X))), ld(X, rd(X, ld(Y, Y))))
14.25/2.19	= { by lemma 33 }
14.25/2.19	  rd(ld(ld(X, rd(X, ld(Y, Y))), rd(mult(ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y))), ld(rd(X, ld(Y, Y)), X)), ld(rd(X, ld(Y, Y)), X))), ld(X, rd(X, ld(Y, Y))))
14.25/2.19	= { by axiom 3 (f04) }
14.25/2.19	  rd(ld(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y))))
14.25/2.19	= { by lemma 32 }
14.25/2.19	  ld(mult(ld(X, rd(X, ld(Y, Y))), ld(X, rd(X, ld(Y, Y)))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 14 }
14.25/2.19	  ld(mult(ld(?, rd(?, ld(Y, Y))), ld(X, rd(X, ld(Y, Y)))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 14 }
14.25/2.19	  ld(mult(ld(?, rd(?, ld(Y, Y))), ld(?, rd(?, ld(Y, Y)))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 15 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(Y, Y)), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 13 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(rd(ld(?, rd(?, ld(Y, Y))), ld(Y, Y)), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 15 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(mult(ld(?, rd(?, ld(Y, Y))), ld(?, rd(?, ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 31 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(mult(ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y))), ld(?, rd(?, ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 31 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(mult(ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y))), ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 24 }
14.25/2.19	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(ld(ld(ld(ld(Y, Y), ld(Y, Y)), ld(Y, Y)), ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.19	= { by lemma 20 }
14.25/2.20	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(ld(ld(Y, Y), ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 23 }
14.25/2.20	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(ld(mult(ld(?, rd(?, ld(Y, Y))), mult(ld(Y, Y), ld(Y, Y))), ld(ld(Y, Y), ld(ld(Y, Y), ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 31 }
14.25/2.20	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(ld(mult(ld(?, rd(?, ld(Y, Y))), mult(ld(Y, Y), ld(Y, Y))), ld(?, rd(?, ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 30 }
14.25/2.20	  ld(rd(ld(?, rd(?, ld(Y, Y))), ld(ld(?, rd(?, mult(ld(Y, Y), ld(Y, Y)))), ld(?, rd(?, ld(Y, Y))))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 6 }
14.25/2.20	  ld(ld(?, rd(?, mult(ld(Y, Y), ld(Y, Y)))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 22 }
14.25/2.20	  ld(ld(?, rd(?, ld(Y, Y))), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 16 }
14.25/2.20	  ld(ld(Y, Y), rd(mult(ld(X, rd(X, ld(Y, Y))), ld(ld(X, rd(X, ld(Y, Y))), rd(X, ld(Y, Y)))), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by axiom 4 (f01) }
14.25/2.20	  ld(ld(Y, Y), rd(rd(X, ld(Y, Y)), ld(X, rd(X, ld(Y, Y)))))
14.25/2.20	= { by lemma 17 }
14.25/2.20	  ld(ld(Y, Y), mult(rd(X, ld(Y, Y)), ld(rd(X, ld(Y, Y)), X)))
14.25/2.20	= { by axiom 4 (f01) }
14.25/2.20	  ld(ld(Y, Y), X)
14.25/2.20	
14.25/2.20	Lemma 35: mult(mult(Z, rd(Y, X)), X) = mult(rd(Z, X), mult(X, Y)).
14.25/2.20	Proof:
14.25/2.20	  mult(mult(Z, rd(Y, X)), X)
14.25/2.20	= { by lemma 7 }
14.25/2.20	  mult(rd(Z, X), mult(X, mult(rd(Y, X), X)))
14.25/2.20	= { by axiom 1 (f03) }
14.25/2.20	  mult(rd(Z, X), mult(X, Y))
14.25/2.20	
14.25/2.20	Lemma 36: rd(mult(Z, Y), mult(Y, mult(X, Y))) = rd(rd(Z, X), Y).
14.25/2.20	Proof:
14.25/2.20	  rd(mult(Z, Y), mult(Y, mult(X, Y)))
14.25/2.20	= { by lemma 13 }
14.25/2.20	  rd(mult(Z, Y), mult(Y, mult(ld(rd(rd(mult(Z, Y), Y), X), rd(mult(Z, Y), Y)), Y)))
14.25/2.20	= { by lemma 25 }
14.25/2.20	  rd(mult(Z, Y), ld(rd(rd(rd(mult(Z, Y), Y), X), Y), mult(Z, Y)))
14.25/2.20	= { by lemma 6 }
14.25/2.20	  rd(rd(rd(mult(Z, Y), Y), X), Y)
14.25/2.20	= { by axiom 3 (f04) }
14.88/2.23	  rd(rd(Z, X), Y)
14.88/2.23	
14.88/2.23	Lemma 37: mult(ld(ld(Y, Y), ld(X, X)), ld(X, X)) = ld(ld(Y, Y), ld(X, X)).
14.88/2.23	Proof:
14.88/2.23	  mult(ld(ld(Y, Y), ld(X, X)), ld(X, X))
14.88/2.23	= { by lemma 34 }
14.88/2.23	  mult(mult(ld(Y, Y), mult(ld(Y, Y), ld(X, X))), ld(X, X))
14.88/2.23	= { by lemma 22 }
14.88/2.23	  mult(mult(mult(ld(Y, Y), ld(Y, Y)), mult(ld(Y, Y), ld(X, X))), ld(X, X))
14.88/2.23	= { by lemma 17 }
14.88/2.23	  mult(mult(rd(ld(Y, Y), ld(Y, Y)), mult(ld(Y, Y), ld(X, X))), ld(X, X))
14.88/2.23	= { by lemma 35 }
14.88/2.23	  mult(mult(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), ld(X, X))
14.88/2.23	= { by lemma 17 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), ld(X, X))
14.88/2.23	= { by axiom 1 (f03) }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), mult(rd(ld(X, X), ld(Y, Y)), ld(Y, Y)))
14.88/2.23	= { by axiom 2 (f02) }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), mult(ld(ld(Y, Y), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y)))
14.88/2.23	= { by lemma 17 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(ld(ld(Y, Y), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y)))
14.88/2.23	= { by lemma 34 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), rd(mult(ld(Y, Y), mult(ld(Y, Y), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))))), ld(Y, Y)))
14.88/2.23	= { by lemma 11 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), mult(mult(ld(Y, Y), ld(Y, Y)), rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y))))
14.88/2.23	= { by lemma 22 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), mult(ld(Y, Y), rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y))))
14.88/2.23	= { by lemma 17 }
14.88/2.23	  mult(rd(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y)), mult(ld(Y, Y), mult(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y))))
14.88/2.23	= { by lemma 7 }
14.88/2.23	  mult(mult(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 3 (f04) }
14.88/2.23	  mult(mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(X, ld(Y, Y))), rd(ld(X, X), ld(Y, Y))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 1 (f03) }
14.88/2.23	  mult(mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(ld(X, X), ld(Y, Y))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 3 (f04) }
14.88/2.23	  mult(mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(ld(rd(mult(X, ld(Y, Y)), ld(Y, Y)), X), ld(Y, Y))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 3 (f04) }
14.88/2.23	  mult(mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(ld(rd(mult(X, ld(Y, Y)), ld(Y, Y)), rd(mult(X, ld(Y, Y)), ld(Y, Y))), ld(Y, Y))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by lemma 27 }
14.88/2.23	  mult(mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by lemma 28 }
14.88/2.23	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 3 (f04) }
14.88/2.23	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(X, ld(Y, Y))), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by axiom 1 (f03) }
14.88/2.23	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(ld(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by lemma 19 }
14.88/2.23	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(rd(X, X), ld(Y, Y)))), ld(Y, Y))
14.88/2.23	= { by lemma 36 }
14.88/2.24	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), ld(Y, Y))
14.88/2.24	= { by lemma 28 }
14.88/2.24	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))))), ld(Y, Y))
14.88/2.24	= { by lemma 22 }
14.88/2.24	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))))), ld(Y, Y))
14.88/2.24	= { by lemma 6 }
14.88/2.24	  mult(mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))))), ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))))), ld(Y, Y))
14.88/2.24	= { by lemma 9 }
14.88/2.24	  mult(ld(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))))), ld(Y, Y))
14.88/2.24	= { by lemma 28 }
14.88/2.24	  mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y)))), mult(ld(Y, Y), mult(X, ld(Y, Y))))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), ld(Y, Y))
14.88/2.24	= { by axiom 1 (f03) }
14.88/2.24	  mult(mult(rd(mult(ld(Y, Y), mult(X, ld(Y, Y))), mult(X, ld(Y, Y))), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), ld(Y, Y))
14.88/2.24	= { by axiom 3 (f04) }
14.88/2.24	  mult(mult(ld(Y, Y), rd(mult(X, ld(Y, Y)), mult(ld(Y, Y), mult(X, ld(Y, Y))))), ld(Y, Y))
14.88/2.24	= { by lemma 36 }
14.88/2.24	  mult(mult(ld(Y, Y), rd(rd(X, X), ld(Y, Y))), ld(Y, Y))
14.88/2.24	= { by lemma 19 }
14.88/2.24	  mult(mult(ld(Y, Y), rd(ld(X, X), ld(Y, Y))), ld(Y, Y))
14.88/2.24	= { by lemma 35 }
14.88/2.24	  mult(rd(ld(Y, Y), ld(Y, Y)), mult(ld(Y, Y), ld(X, X)))
14.88/2.24	= { by lemma 17 }
14.88/2.24	  mult(mult(ld(Y, Y), ld(Y, Y)), mult(ld(Y, Y), ld(X, X)))
14.88/2.24	= { by lemma 22 }
14.88/2.24	  mult(ld(Y, Y), mult(ld(Y, Y), ld(X, X)))
14.88/2.24	= { by lemma 34 }
14.88/2.24	  ld(ld(Y, Y), ld(X, X))
14.88/2.24	
14.88/2.24	Lemma 38: ld(Y, Y) = ld(?, ?).
14.88/2.24	Proof:
14.88/2.24	  ld(Y, Y)
14.88/2.24	= { by lemma 22 }
14.88/2.24	  mult(ld(Y, Y), ld(Y, Y))
14.88/2.24	= { by lemma 24 }
14.88/2.24	  ld(ld(Y, Y), ld(Y, Y))
14.88/2.24	= { by lemma 29 }
14.88/2.24	  mult(rd(ld(X, X), mult(ld(ld(Y, Y), ld(X, X)), ld(X, X))), ld(ld(Y, Y), ld(X, X)))
14.88/2.24	= { by lemma 37 }
14.88/2.24	  mult(rd(ld(X, X), ld(ld(Y, Y), ld(X, X))), ld(ld(Y, Y), ld(X, X)))
14.88/2.24	= { by axiom 1 (f03) }
14.88/2.24	  ld(X, X)
14.88/2.24	= { by axiom 1 (f03) }
14.88/2.24	  mult(rd(ld(X, X), ld(ld(?, ?), ld(X, X))), ld(ld(?, ?), ld(X, X)))
14.88/2.24	= { by lemma 37 }
14.88/2.24	  mult(rd(ld(X, X), mult(ld(ld(?, ?), ld(X, X)), ld(X, X))), ld(ld(?, ?), ld(X, X)))
14.88/2.24	= { by lemma 29 }
14.88/2.24	  ld(ld(?, ?), ld(?, ?))
14.88/2.24	= { by lemma 24 }
14.88/2.24	  mult(ld(?, ?), ld(?, ?))
14.88/2.24	= { by lemma 22 }
14.88/2.24	  ld(?, ?)
14.88/2.24	
14.88/2.24	Goal 1 (goals): tuple(sK2_goals_X0, mult(sK4_goals_X0, ld(sK3_goals_X1, sK3_goals_X1))) = tuple(mult(ld(sK1_goals_X1, sK1_goals_X1), sK2_goals_X0), sK4_goals_X0).
14.88/2.24	Proof:
14.88/2.24	  tuple(sK2_goals_X0, mult(sK4_goals_X0, ld(sK3_goals_X1, sK3_goals_X1)))
14.88/2.24	= { by lemma 21 }
14.88/2.24	  tuple(mult(ld(sK2_goals_X0, sK2_goals_X0), sK2_goals_X0), mult(sK4_goals_X0, ld(sK3_goals_X1, sK3_goals_X1)))
14.88/2.24	= { by lemma 38 }
14.88/2.24	  tuple(mult(ld(?, ?), sK2_goals_X0), mult(sK4_goals_X0, ld(sK3_goals_X1, sK3_goals_X1)))
14.88/2.24	= { by lemma 38 }
14.88/2.24	  tuple(mult(ld(sK1_goals_X1, sK1_goals_X1), sK2_goals_X0), mult(sK4_goals_X0, ld(sK3_goals_X1, sK3_goals_X1)))
14.88/2.24	= { by lemma 38 }
14.88/2.24	  tuple(mult(ld(sK1_goals_X1, sK1_goals_X1), sK2_goals_X0), mult(sK4_goals_X0, ld(?, ?)))
14.88/2.24	= { by lemma 38 }
14.88/2.24	  tuple(mult(ld(sK1_goals_X1, sK1_goals_X1), sK2_goals_X0), mult(sK4_goals_X0, ld(sK4_goals_X0, sK4_goals_X0)))
14.88/2.24	= { by axiom 4 (f01) }
14.88/2.24	  tuple(mult(ld(sK1_goals_X1, sK1_goals_X1), sK2_goals_X0), sK4_goals_X0)
14.88/2.24	% SZS output end Proof
14.88/2.24	
14.88/2.24	RESULT: Theorem (the conjecture is true).
14.88/2.25	EOF