0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.34	% Computer   : n026.cluster.edu
0.12/0.34	% Model      : x86_64 x86_64
0.12/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.34	% Memory     : 8042.1875MB
0.12/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.34	% CPULimit   : 960
0.12/0.34	% WCLimit    : 120
0.12/0.34	% DateTime   : Thu Jul  2 07:27:39 EDT 2020
0.12/0.34	% CPUTime    : 
74.56/9.79	% SZS status Theorem
74.56/9.79	
74.56/9.80	% SZS output start Proof
74.56/9.80	Take the following subset of the input axioms:
76.04/9.93	  fof(f01, axiom, ![A, B]: B=mult(A, ld(A, B))).
76.04/9.93	  fof(f02, axiom, ![A, B]: ld(A, mult(A, B))=B).
76.04/9.93	  fof(f03, axiom, ![A, B]: A=mult(rd(A, B), B)).
76.04/9.94	  fof(f04, axiom, ![A, B]: A=rd(mult(A, B), B)).
76.04/9.94	  fof(f05, axiom, ![A]: mult(A, unit)=A).
76.04/9.94	  fof(f06, axiom, ![A]: A=mult(unit, A)).
76.04/9.94	  fof(f07, axiom, ![A, C, B]: mult(mult(A, mult(mult(B, C), B)), C)=mult(mult(A, B), mult(mult(C, B), C))).
76.04/9.94	  fof(f08, axiom, ![A, B]: mult(mult(A, B), A)=mult(A, mult(B, A))).
76.04/9.94	  fof(f09, axiom, ![A]: A=mult(f(A), f(A))).
76.04/9.94	  fof(f10, axiom, ![X0, X1, X2]: (mult(X0, mult(X1, mult(X2, X1)))=mult(mult(mult(X0, X1), X2), X1) => mult(mult(mult(X1, X0), X1), X2)=mult(X1, mult(X0, mult(X1, X2))))).
76.04/9.94	  fof(f12, axiom, ![X6, X7, X8]: (mult(mult(mult(X6, X7), X6), X8)=mult(X6, mult(X7, mult(X6, X8))) <= mult(X6, mult(mult(X7, X8), X6))=mult(mult(X6, X7), mult(X8, X6)))).
76.04/9.94	  fof(goals, conjecture, mult(a, mult(b, mult(a, c)))=mult(mult(mult(a, b), a), c)).
76.04/9.94	
76.04/9.94	Now clausify the problem and encode Horn clauses using encoding 3 of
76.04/9.94	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
76.04/9.94	We repeatedly replace C & s=t => u=v by the two clauses:
76.04/9.94	  fresh(y, y, x1...xn) = u
76.04/9.94	  C => fresh(s, t, x1...xn) = v
76.04/9.94	where fresh is a fresh function symbol and x1..xn are the free
76.04/9.94	variables of u and v.
76.04/9.94	A predicate p(X) is encoded as p(X)=true (this is sound, because the
76.04/9.94	input problem has no model of domain size 1).
76.04/9.94	
76.04/9.94	The encoding turns the above axioms into the following unit equations and goals:
76.04/9.94	
76.04/9.94	Axiom 1 (f10): fresh2(X, X, Y, Z, W) = mult(Z, mult(Y, mult(Z, W))).
76.04/9.94	Axiom 2 (f11): fresh3(X, X, Y, Z, W) = mult(mult(mult(Y, Z), Y), W).
76.04/9.94	Axiom 3 (f12): fresh(X, X, Y, Z, W) = mult(Y, mult(Z, mult(Y, W))).
76.04/9.94	Axiom 4 (f01): X = mult(Y, ld(Y, X)).
76.04/9.94	Axiom 5 (f09): X = mult(f(X), f(X)).
76.04/9.94	Axiom 6 (f03): X = mult(rd(X, Y), Y).
76.04/9.94	Axiom 7 (f12): fresh(mult(X, mult(mult(Y, Z), X)), mult(mult(X, Y), mult(Z, X)), X, Y, Z) = mult(mult(mult(X, Y), X), Z).
76.04/9.94	Axiom 8 (f08): mult(mult(X, Y), X) = mult(X, mult(Y, X)).
76.04/9.94	Axiom 9 (f02): ld(X, mult(X, Y)) = Y.
76.04/9.94	Axiom 10 (f10): fresh2(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), X, Y, Z) = mult(mult(mult(Y, X), Y), Z).
76.04/9.94	Axiom 11 (f05): mult(X, unit) = X.
76.04/9.94	Axiom 12 (f04): X = rd(mult(X, Y), Y).
76.04/9.94	Axiom 13 (f07): mult(mult(X, mult(mult(Y, Z), Y)), Z) = mult(mult(X, Y), mult(mult(Z, Y), Z)).
76.04/9.97	Axiom 14 (f06): X = mult(unit, X).
76.04/9.97	
76.04/9.97	Lemma 15: fresh2(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), X, Y, Z) = fresh3(?, ?, Y, X, Z).
76.04/9.97	Proof:
76.04/9.97	  fresh2(mult(X, mult(Y, mult(Z, Y))), mult(mult(mult(X, Y), Z), Y), X, Y, Z)
76.04/9.97	= { by axiom 10 (f10) }
76.04/9.97	  mult(mult(mult(Y, X), Y), Z)
76.04/9.97	= { by axiom 2 (f11) }
76.04/9.97	  fresh3(?, ?, Y, X, Z)
76.04/9.97	
76.04/9.97	Lemma 16: fresh2(?, ?, Y, Z, X) = fresh(?, ?, Z, Y, X).
76.04/9.97	Proof:
76.04/9.97	  fresh2(?, ?, Y, Z, X)
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  mult(Z, mult(Y, mult(Z, X)))
76.04/9.97	= { by axiom 3 (f12) }
76.04/9.97	  fresh(?, ?, Z, Y, X)
76.04/9.97	
76.04/9.97	Lemma 17: fresh(?, ?, Y, Z, ld(Y, X)) = mult(Y, mult(Z, X)).
76.04/9.97	Proof:
76.04/9.97	  fresh(?, ?, Y, Z, ld(Y, X))
76.04/9.97	= { by lemma 16 }
76.04/9.97	  fresh2(?, ?, Z, Y, ld(Y, X))
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  mult(Y, mult(Z, mult(Y, ld(Y, X))))
76.04/9.97	= { by axiom 4 (f01) }
76.04/9.97	  mult(Y, mult(Z, X))
76.04/9.97	
76.04/9.97	Lemma 18: mult(X, mult(Y, X)) = fresh2(?, ?, Y, X, unit).
76.04/9.97	Proof:
76.04/9.97	  mult(X, mult(Y, X))
76.04/9.97	= { by axiom 11 (f05) }
76.04/9.97	  mult(X, mult(Y, mult(X, unit)))
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  fresh2(?, ?, Y, X, unit)
76.04/9.97	
76.04/9.97	Lemma 19: mult(mult(Y, Y), X) = mult(Y, mult(Y, X)).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(Y, Y), X)
76.04/9.97	= { by axiom 11 (f05) }
76.04/9.97	  mult(mult(mult(Y, unit), Y), X)
76.04/9.97	= { by axiom 7 (f12) }
76.04/9.97	  fresh(mult(Y, mult(mult(unit, X), Y)), mult(mult(Y, unit), mult(X, Y)), Y, unit, X)
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  fresh(mult(Y, mult(X, Y)), mult(mult(Y, unit), mult(X, Y)), Y, unit, X)
76.04/9.97	= { by axiom 11 (f05) }
76.04/9.97	  fresh(mult(Y, mult(X, Y)), mult(Y, mult(X, Y)), Y, unit, X)
76.04/9.97	= { by axiom 3 (f12) }
76.04/9.97	  mult(Y, mult(unit, mult(Y, X)))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(Y, mult(Y, X))
76.04/9.97	
76.04/9.97	Lemma 20: mult(Y, mult(Y, X)) = fresh2(?, ?, unit, Y, X).
76.04/9.97	Proof:
76.04/9.97	  mult(Y, mult(Y, X))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(Y, mult(unit, mult(Y, X)))
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  fresh2(?, ?, unit, Y, X)
76.04/9.97	
76.04/9.97	Lemma 21: rd(mult(Y, mult(Y, X)), X) = mult(Y, Y).
76.04/9.97	Proof:
76.04/9.97	  rd(mult(Y, mult(Y, X)), X)
76.04/9.97	= { by lemma 19 }
76.04/9.97	  rd(mult(mult(Y, Y), X), X)
76.04/9.97	= { by axiom 12 (f04) }
76.04/9.97	  mult(Y, Y)
76.04/9.97	
76.04/9.97	Lemma 22: mult(Y, fresh(?, ?, Z, Y, X)) = fresh(?, ?, Y, Z, mult(Z, X)).
76.04/9.97	Proof:
76.04/9.97	  mult(Y, fresh(?, ?, Z, Y, X))
76.04/9.97	= { by lemma 16 }
76.04/9.97	  mult(Y, fresh2(?, ?, Y, Z, X))
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  mult(Y, mult(Z, mult(Y, mult(Z, X))))
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  fresh2(?, ?, Z, Y, mult(Z, X))
76.04/9.97	= { by lemma 16 }
76.04/9.97	  fresh(?, ?, Y, Z, mult(Z, X))
76.04/9.97	
76.04/9.97	Lemma 23: mult(mult(Z, mult(Y, Z)), X) = fresh3(?, ?, Z, Y, X).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(Z, mult(Y, Z)), X)
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  mult(mult(mult(Z, Y), Z), X)
76.04/9.97	= { by axiom 2 (f11) }
76.04/9.97	  fresh3(?, ?, Z, Y, X)
76.04/9.97	
76.04/9.97	Lemma 24: mult(mult(X, mult(Y, mult(Z, Y))), Z) = mult(mult(X, Y), mult(Z, mult(Y, Z))).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(X, mult(Y, mult(Z, Y))), Z)
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  mult(mult(X, mult(mult(Y, Z), Y)), Z)
76.04/9.97	= { by axiom 13 (f07) }
76.04/9.97	  mult(mult(X, Y), mult(mult(Z, Y), Z))
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  mult(mult(X, Y), mult(Z, mult(Y, Z)))
76.04/9.97	
76.04/9.97	Lemma 25: fresh3(?, ?, Y, X, X) = fresh(?, ?, Y, X, X).
76.04/9.97	Proof:
76.04/9.97	  fresh3(?, ?, Y, X, X)
76.04/9.97	= { by lemma 23 }
76.04/9.97	  mult(mult(Y, mult(X, Y)), X)
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(mult(unit, mult(Y, mult(X, Y))), X)
76.04/9.97	= { by lemma 24 }
76.04/9.97	  mult(mult(unit, Y), mult(X, mult(Y, X)))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(Y, mult(X, mult(Y, X)))
76.04/9.97	= { by axiom 3 (f12) }
76.04/9.97	  fresh(?, ?, Y, X, X)
76.04/9.97	
76.04/9.97	Lemma 26: mult(fresh(?, ?, Z, Y, unit), X) = fresh3(?, ?, Z, Y, X).
76.04/9.97	Proof:
76.04/9.97	  mult(fresh(?, ?, Z, Y, unit), X)
76.04/9.97	= { by lemma 16 }
76.04/9.97	  mult(fresh2(?, ?, Y, Z, unit), X)
76.04/9.97	= { by lemma 18 }
76.04/9.97	  mult(mult(Z, mult(Y, Z)), X)
76.04/9.97	= { by lemma 23 }
76.04/9.97	  fresh3(?, ?, Z, Y, X)
76.04/9.97	
76.04/9.97	Lemma 27: mult(Z, mult(mult(Y, mult(Z, X)), Z)) = mult(fresh(?, ?, Z, Y, X), Z).
76.04/9.97	Proof:
76.04/9.97	  mult(Z, mult(mult(Y, mult(Z, X)), Z))
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  mult(mult(Z, mult(Y, mult(Z, X))), Z)
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  mult(fresh2(?, ?, Y, Z, X), Z)
76.04/9.97	= { by lemma 16 }
76.04/9.97	  mult(fresh(?, ?, Z, Y, X), Z)
76.04/9.97	
76.04/9.97	Lemma 28: mult(mult(Y, X), mult(Y, mult(X, Y))) = mult(Y, fresh(?, ?, X, Y, Y)).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(Y, X), mult(Y, mult(X, Y)))
76.04/9.97	= { by lemma 24 }
76.04/9.97	  mult(mult(Y, mult(X, mult(Y, X))), Y)
76.04/9.97	= { by axiom 1 (f10) }
76.04/9.97	  mult(fresh2(?, ?, X, Y, X), Y)
76.04/9.97	= { by lemma 16 }
76.04/9.97	  mult(fresh(?, ?, Y, X, X), Y)
76.04/9.97	= { by lemma 27 }
76.04/9.97	  mult(Y, mult(mult(X, mult(Y, X)), Y))
76.04/9.97	= { by lemma 18 }
76.04/9.97	  mult(Y, mult(fresh2(?, ?, Y, X, unit), Y))
76.04/9.97	= { by lemma 16 }
76.04/9.97	  mult(Y, mult(fresh(?, ?, X, Y, unit), Y))
76.04/9.97	= { by lemma 26 }
76.04/9.97	  mult(Y, fresh3(?, ?, X, Y, Y))
76.04/9.97	= { by lemma 25 }
76.04/9.97	  mult(Y, fresh(?, ?, X, Y, Y))
76.04/9.97	
76.04/9.97	Lemma 29: mult(mult(Y, X), mult(Y, X)) = fresh(?, ?, Y, X, X).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(Y, X), mult(Y, X))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(mult(Y, X), mult(unit, mult(Y, X)))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(mult(Y, X), mult(Y, X))
76.04/9.97	= { by lemma 21 }
76.04/9.97	  rd(mult(mult(Y, X), mult(mult(Y, X), Y)), Y)
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  rd(mult(mult(Y, X), mult(Y, mult(X, Y))), Y)
76.04/9.97	= { by lemma 28 }
76.04/9.97	  rd(mult(Y, fresh(?, ?, X, Y, Y)), Y)
76.04/9.97	= { by lemma 25 }
76.04/9.97	  rd(mult(Y, fresh3(?, ?, X, Y, Y)), Y)
76.04/9.97	= { by lemma 26 }
76.04/9.97	  rd(mult(Y, mult(fresh(?, ?, X, Y, unit), Y)), Y)
76.04/9.97	= { by lemma 16 }
76.04/9.97	  rd(mult(Y, mult(fresh2(?, ?, Y, X, unit), Y)), Y)
76.04/9.97	= { by lemma 18 }
76.04/9.97	  rd(mult(Y, mult(mult(X, mult(Y, X)), Y)), Y)
76.04/9.97	= { by lemma 27 }
76.04/9.97	  rd(mult(fresh(?, ?, Y, X, X), Y), Y)
76.04/9.97	= { by axiom 12 (f04) }
76.04/9.97	  fresh(?, ?, Y, X, X)
76.04/9.97	
76.04/9.97	Lemma 30: mult(Y, mult(ld(Y, X), X)) = mult(X, X).
76.04/9.97	Proof:
76.04/9.97	  mult(Y, mult(ld(Y, X), X))
76.04/9.97	= { by lemma 17 }
76.04/9.97	  fresh(?, ?, Y, ld(Y, X), ld(Y, X))
76.04/9.97	= { by lemma 29 }
76.04/9.97	  mult(mult(Y, ld(Y, X)), mult(Y, ld(Y, X)))
76.04/9.97	= { by axiom 4 (f01) }
76.04/9.97	  mult(X, mult(Y, ld(Y, X)))
76.04/9.97	= { by axiom 4 (f01) }
76.04/9.97	  mult(X, X)
76.04/9.97	
76.04/9.97	Lemma 31: mult(ld(Y, f(X)), f(X)) = ld(Y, X).
76.04/9.97	Proof:
76.04/9.97	  mult(ld(Y, f(X)), f(X))
76.04/9.97	= { by axiom 9 (f02) }
76.04/9.97	  ld(Y, mult(Y, mult(ld(Y, f(X)), f(X))))
76.04/9.97	= { by lemma 30 }
76.04/9.97	  ld(Y, mult(f(X), f(X)))
76.04/9.97	= { by axiom 5 (f09) }
76.04/9.97	  ld(Y, X)
76.04/9.97	
76.04/9.97	Lemma 32: fresh3(?, ?, Z, ld(Z, Y), X) = mult(mult(Y, Z), X).
76.04/9.97	Proof:
76.04/9.97	  fresh3(?, ?, Z, ld(Z, Y), X)
76.04/9.97	= { by axiom 2 (f11) }
76.04/9.97	  mult(mult(mult(Z, ld(Z, Y)), Z), X)
76.04/9.97	= { by axiom 4 (f01) }
76.04/9.97	  mult(mult(Y, Z), X)
76.04/9.97	
76.04/9.97	Lemma 33: mult(mult(Y, X), X) = mult(Y, mult(X, X)).
76.04/9.97	Proof:
76.04/9.97	  mult(mult(Y, X), X)
76.04/9.97	= { by axiom 11 (f05) }
76.04/9.97	  mult(mult(Y, mult(X, unit)), X)
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(mult(Y, mult(unit, mult(X, unit))), X)
76.04/9.97	= { by lemma 24 }
76.04/9.97	  mult(mult(Y, unit), mult(X, mult(unit, X)))
76.04/9.97	= { by axiom 11 (f05) }
76.04/9.97	  mult(Y, mult(X, mult(unit, X)))
76.04/9.97	= { by axiom 14 (f06) }
76.04/9.97	  mult(Y, mult(X, X))
76.04/9.97	
76.04/9.97	Lemma 34: mult(Y, mult(ld(Y, X), Y)) = mult(X, Y).
76.04/9.97	Proof:
76.04/9.97	  mult(Y, mult(ld(Y, X), Y))
76.04/9.97	= { by axiom 8 (f08) }
76.04/9.97	  mult(mult(Y, ld(Y, X)), Y)
76.04/9.97	= { by axiom 4 (f01) }
76.04/9.97	  mult(X, Y)
76.04/9.97	
76.04/9.97	Lemma 35: fresh(?, ?, ld(Y, X), Y, Y) = mult(mult(ld(Y, X), X), Y).
76.04/9.97	Proof:
76.04/9.97	  fresh(?, ?, ld(Y, X), Y, Y)
76.04/9.97	= { by lemma 25 }
76.04/9.98	  fresh3(?, ?, ld(Y, X), Y, Y)
76.04/9.98	= { by lemma 23 }
76.04/9.98	  mult(mult(ld(Y, X), mult(Y, ld(Y, X))), Y)
76.04/9.98	= { by axiom 4 (f01) }
76.04/9.98	  mult(mult(ld(Y, X), X), Y)
76.04/9.98	
76.04/9.98	Lemma 36: ld(Y, mult(X, Y)) = mult(ld(Y, X), Y).
76.04/9.98	Proof:
76.04/9.98	  ld(Y, mult(X, Y))
76.04/9.98	= { by lemma 34 }
76.04/9.98	  ld(Y, mult(Y, mult(ld(Y, X), Y)))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  mult(ld(Y, X), Y)
76.04/9.98	
76.04/9.98	Lemma 37: ld(X, X) = unit.
76.04/9.98	Proof:
76.04/9.98	  ld(X, X)
76.04/9.98	= { by axiom 11 (f05) }
76.04/9.98	  ld(X, mult(X, unit))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  unit
76.04/9.98	
76.04/9.98	Lemma 38: mult(ld(X, unit), X) = unit.
76.04/9.98	Proof:
76.04/9.98	  mult(ld(X, unit), X)
76.04/9.98	= { by lemma 36 }
76.04/9.98	  ld(X, mult(unit, X))
76.04/9.98	= { by axiom 14 (f06) }
76.04/9.98	  ld(X, X)
76.04/9.98	= { by lemma 37 }
76.04/9.98	  unit
76.04/9.98	
76.04/9.98	Lemma 39: mult(ld(X, f(X)), X) = f(X).
76.04/9.98	Proof:
76.04/9.98	  mult(ld(X, f(X)), X)
76.04/9.98	= { by lemma 36 }
76.04/9.98	  ld(X, mult(f(X), X))
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  ld(X, mult(f(X), mult(f(X), f(X))))
76.04/9.98	= { by axiom 8 (f08) }
76.04/9.98	  ld(X, mult(mult(f(X), f(X)), f(X)))
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  ld(X, mult(X, f(X)))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  f(X)
76.04/9.98	
76.04/9.98	Lemma 40: mult(f(Y), mult(f(Y), X)) = mult(Y, X).
76.04/9.98	Proof:
76.04/9.98	  mult(f(Y), mult(f(Y), X))
76.04/9.98	= { by lemma 19 }
76.04/9.98	  mult(mult(f(Y), f(Y)), X)
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  mult(Y, X)
76.04/9.98	
76.04/9.98	Lemma 41: ld(f(Y), mult(Y, X)) = mult(f(Y), X).
76.04/9.98	Proof:
76.04/9.98	  ld(f(Y), mult(Y, X))
76.04/9.98	= { by lemma 40 }
76.04/9.98	  ld(f(Y), mult(f(Y), mult(f(Y), X)))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  mult(f(Y), X)
76.04/9.98	
76.04/9.98	Lemma 42: mult(f(Y), ld(Y, X)) = ld(f(Y), X).
76.04/9.98	Proof:
76.04/9.98	  mult(f(Y), ld(Y, X))
76.04/9.98	= { by lemma 41 }
76.04/9.98	  ld(f(Y), mult(Y, ld(Y, X)))
76.04/9.98	= { by axiom 4 (f01) }
76.04/9.98	  ld(f(Y), X)
76.04/9.98	
76.04/9.98	Lemma 43: mult(ld(X, f(X)), ld(X, f(X))) = ld(X, unit).
76.04/9.98	Proof:
76.04/9.98	  mult(ld(X, f(X)), ld(X, f(X)))
76.04/9.98	= { by lemma 30 }
76.04/9.98	  mult(X, mult(ld(X, ld(X, f(X))), ld(X, f(X))))
76.04/9.98	= { by lemma 17 }
76.04/9.98	  fresh(?, ?, X, ld(X, ld(X, f(X))), ld(X, ld(X, f(X))))
76.04/9.98	= { by lemma 25 }
76.04/9.98	  fresh3(?, ?, X, ld(X, ld(X, f(X))), ld(X, ld(X, f(X))))
76.04/9.98	= { by lemma 32 }
76.04/9.98	  mult(mult(ld(X, f(X)), X), ld(X, ld(X, f(X))))
76.04/9.98	= { by lemma 39 }
76.04/9.98	  mult(f(X), ld(X, ld(X, f(X))))
76.04/9.98	= { by lemma 42 }
76.04/9.98	  ld(f(X), ld(X, f(X)))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  ld(X, mult(X, ld(f(X), ld(X, f(X)))))
76.04/9.98	= { by lemma 40 }
76.04/9.98	  ld(X, mult(f(X), mult(f(X), ld(f(X), ld(X, f(X))))))
76.04/9.98	= { by axiom 4 (f01) }
76.04/9.98	  ld(X, mult(f(X), ld(X, f(X))))
76.04/9.98	= { by lemma 42 }
76.04/9.98	  ld(X, ld(f(X), f(X)))
76.04/9.98	= { by lemma 37 }
76.04/9.98	  ld(X, unit)
76.04/9.98	
76.04/9.98	Lemma 44: mult(rd(Y, X), mult(X, X)) = mult(Y, X).
76.04/9.98	Proof:
76.04/9.98	  mult(rd(Y, X), mult(X, X))
76.04/9.98	= { by lemma 33 }
76.04/9.98	  mult(mult(rd(Y, X), X), X)
76.04/9.98	= { by axiom 6 (f03) }
76.04/9.98	  mult(Y, X)
76.04/9.98	
76.04/9.98	Lemma 45: rd(rd(Y, X), X) = rd(Y, mult(X, X)).
76.04/9.98	Proof:
76.04/9.98	  rd(rd(Y, X), X)
76.04/9.98	= { by axiom 12 (f04) }
76.04/9.98	  rd(mult(rd(rd(Y, X), X), mult(X, X)), mult(X, X))
76.04/9.98	= { by lemma 44 }
76.04/9.98	  rd(mult(rd(Y, X), X), mult(X, X))
76.04/9.98	= { by axiom 6 (f03) }
76.04/9.98	  rd(Y, mult(X, X))
76.04/9.98	
76.04/9.98	Lemma 46: mult(rd(Y, f(X)), X) = mult(Y, f(X)).
76.04/9.98	Proof:
76.04/9.98	  mult(rd(Y, f(X)), X)
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  mult(rd(Y, f(X)), mult(f(X), f(X)))
76.04/9.98	= { by lemma 44 }
76.04/9.98	  mult(Y, f(X))
76.04/9.98	
76.04/9.98	Lemma 47: mult(mult(Y, mult(X, X)), X) = mult(mult(Y, X), mult(X, X)).
76.04/9.98	Proof:
76.04/9.98	  mult(mult(Y, mult(X, X)), X)
76.04/9.98	= { by lemma 33 }
76.04/9.98	  mult(mult(mult(Y, X), X), X)
76.04/9.98	= { by lemma 33 }
76.04/9.98	  mult(mult(Y, X), mult(X, X))
76.04/9.98	
76.04/9.98	Lemma 48: mult(mult(Y, f(X)), X) = mult(mult(Y, X), f(X)).
76.04/9.98	Proof:
76.04/9.98	  mult(mult(Y, f(X)), X)
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  mult(mult(Y, f(X)), mult(f(X), f(X)))
76.04/9.98	= { by lemma 47 }
76.04/9.98	  mult(mult(Y, mult(f(X), f(X))), f(X))
76.04/9.98	= { by axiom 5 (f09) }
76.04/9.98	  mult(mult(Y, X), f(X))
76.04/9.98	
76.04/9.98	Lemma 49: ld(Y, fresh(?, ?, Y, Z, X)) = mult(Z, mult(Y, X)).
76.04/9.98	Proof:
76.04/9.98	  ld(Y, fresh(?, ?, Y, Z, X))
76.04/9.98	= { by lemma 16 }
76.04/9.98	  ld(Y, fresh2(?, ?, Z, Y, X))
76.04/9.98	= { by axiom 1 (f10) }
76.04/9.98	  ld(Y, mult(Y, mult(Z, mult(Y, X))))
76.04/9.98	= { by axiom 9 (f02) }
76.04/9.98	  mult(Z, mult(Y, X))
76.04/9.98	
76.04/9.98	Lemma 50: mult(mult(Y, X), mult(Y, Y)) = fresh(?, ?, Y, X, Y).
76.04/9.98	Proof:
76.04/9.98	  mult(mult(Y, X), mult(Y, Y))
76.04/9.98	= { by lemma 33 }
76.04/9.98	  mult(mult(mult(Y, X), Y), Y)
76.04/9.98	= { by axiom 2 (f11) }
76.04/9.98	  fresh3(?, ?, Y, X, Y)
76.04/9.98	= { by lemma 23 }
76.04/9.98	  mult(mult(Y, mult(X, Y)), Y)
76.04/9.98	= { by axiom 8 (f08) }
76.04/9.98	  mult(Y, mult(mult(X, Y), Y))
76.04/9.98	= { by lemma 33 }
76.04/9.98	  mult(Y, mult(X, mult(Y, Y)))
76.04/9.98	= { by axiom 3 (f12) }
76.04/9.98	  fresh(?, ?, Y, X, Y)
76.04/9.98	
76.04/9.98	Lemma 51: rd(mult(mult(Z, Y), mult(X, mult(Y, X))), X) = mult(Z, mult(Y, mult(X, Y))).
76.04/9.98	Proof:
76.04/9.98	  rd(mult(mult(Z, Y), mult(X, mult(Y, X))), X)
76.04/9.98	= { by lemma 24 }
76.04/9.98	  rd(mult(mult(Z, mult(Y, mult(X, Y))), X), X)
76.04/9.98	= { by axiom 12 (f04) }
76.74/9.99	  mult(Z, mult(Y, mult(X, Y)))
76.74/9.99	
76.74/9.99	Lemma 52: mult(mult(Y, ld(X, f(X))), f(X)) = Y.
76.74/9.99	Proof:
76.74/9.99	  mult(mult(Y, ld(X, f(X))), f(X))
76.74/9.99	= { by lemma 46 }
76.74/9.99	  mult(rd(mult(Y, ld(X, f(X))), f(X)), X)
76.74/9.99	= { by axiom 12 (f04) }
76.74/9.99	  rd(mult(mult(rd(mult(Y, ld(X, f(X))), f(X)), X), X), X)
76.74/9.99	= { by lemma 46 }
76.74/9.99	  rd(mult(mult(mult(Y, ld(X, f(X))), f(X)), X), X)
76.74/9.99	= { by axiom 5 (f09) }
76.74/9.99	  rd(mult(mult(mult(Y, ld(X, f(X))), f(X)), mult(f(X), f(X))), X)
76.74/9.99	= { by lemma 49 }
76.74/9.99	  rd(ld(f(X), fresh(?, ?, f(X), mult(mult(Y, ld(X, f(X))), f(X)), f(X))), X)
76.74/9.99	= { by lemma 50 }
76.74/9.99	  rd(ld(f(X), mult(mult(f(X), mult(mult(Y, ld(X, f(X))), f(X))), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 23 }
76.74/9.99	  rd(ld(f(X), fresh3(?, ?, f(X), mult(Y, ld(X, f(X))), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 15 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), mult(f(X), mult(mult(f(X), f(X)), f(X)))), mult(mult(mult(mult(Y, ld(X, f(X))), f(X)), mult(f(X), f(X))), f(X)), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 19 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), mult(f(X), mult(f(X), mult(f(X), f(X))))), mult(mult(mult(mult(Y, ld(X, f(X))), f(X)), mult(f(X), f(X))), f(X)), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by axiom 3 (f12) }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(mult(mult(mult(Y, ld(X, f(X))), f(X)), mult(f(X), f(X))), f(X)), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 47 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(mult(mult(mult(Y, ld(X, f(X))), f(X)), f(X)), mult(f(X), f(X))), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 33 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(mult(mult(Y, ld(X, f(X))), mult(f(X), f(X))), mult(f(X), f(X))), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 33 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(mult(Y, ld(X, f(X))), mult(mult(f(X), f(X)), mult(f(X), f(X)))), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 50 }
76.74/9.99	  rd(ld(f(X), fresh2(mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(mult(Y, ld(X, f(X))), fresh(?, ?, f(X), f(X), f(X))), mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by axiom 1 (f10) }
76.74/9.99	  rd(ld(f(X), mult(f(X), mult(mult(Y, ld(X, f(X))), mult(f(X), mult(f(X), f(X)))))), X)
76.74/9.99	= { by axiom 1 (f10) }
76.74/9.99	  rd(ld(f(X), fresh2(?, ?, mult(Y, ld(X, f(X))), f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 16 }
76.74/9.99	  rd(ld(f(X), fresh(?, ?, f(X), mult(Y, ld(X, f(X))), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 49 }
76.74/9.99	  rd(mult(mult(Y, ld(X, f(X))), mult(f(X), mult(f(X), f(X)))), X)
76.74/9.99	= { by lemma 40 }
76.74/9.99	  rd(mult(mult(Y, ld(X, f(X))), mult(X, f(X))), X)
76.74/9.99	= { by lemma 39 }
76.74/9.99	  rd(mult(mult(Y, ld(X, f(X))), mult(X, mult(ld(X, f(X)), X))), X)
76.74/9.99	= { by lemma 51 }
76.74/9.99	  mult(Y, mult(ld(X, f(X)), mult(X, ld(X, f(X)))))
76.74/9.99	= { by axiom 4 (f01) }
76.74/9.99	  mult(Y, mult(ld(X, f(X)), f(X)))
76.74/9.99	= { by lemma 31 }
76.74/9.99	  mult(Y, ld(X, X))
76.74/9.99	= { by lemma 37 }
76.74/9.99	  mult(Y, unit)
76.74/9.99	= { by axiom 11 (f05) }
76.74/9.99	  Y
76.74/9.99	
76.74/9.99	Lemma 53: rd(Y, ld(X, f(X))) = mult(Y, f(X)).
76.74/9.99	Proof:
76.74/9.99	  rd(Y, ld(X, f(X)))
76.74/9.99	= { by lemma 52 }
76.74/10.00	  mult(mult(rd(Y, ld(X, f(X))), ld(X, f(X))), f(X))
76.74/10.00	= { by axiom 6 (f03) }
76.74/10.00	  mult(Y, f(X))
76.74/10.00	
76.74/10.00	Lemma 54: ld(rd(X, Y), X) = Y.
76.74/10.00	Proof:
76.74/10.00	  ld(rd(X, Y), X)
76.74/10.00	= { by axiom 6 (f03) }
76.74/10.00	  ld(rd(X, Y), mult(rd(X, Y), Y))
76.74/10.00	= { by axiom 9 (f02) }
76.74/10.00	  Y
76.74/10.00	
76.74/10.00	Lemma 55: mult(rd(Y, X), mult(X, Y)) = mult(Y, Y).
76.74/10.00	Proof:
76.74/10.00	  mult(rd(Y, X), mult(X, Y))
76.74/10.00	= { by lemma 54 }
76.74/10.00	  mult(rd(Y, X), mult(ld(rd(Y, X), Y), Y))
76.74/10.00	= { by lemma 30 }
76.74/10.01	  mult(Y, Y)
76.74/10.01	
76.74/10.01	Lemma 56: mult(ld(Y, unit), X) = ld(Y, X).
76.74/10.01	Proof:
76.74/10.01	  mult(ld(Y, unit), X)
76.74/10.01	= { by lemma 54 }
76.74/10.01	  mult(ld(rd(X, ld(Y, unit)), X), X)
76.74/10.01	= { by lemma 43 }
76.74/10.01	  mult(ld(rd(X, mult(ld(Y, f(Y)), ld(Y, f(Y)))), X), X)
76.74/10.01	= { by lemma 45 }
76.74/10.01	  mult(ld(rd(rd(X, ld(Y, f(Y))), ld(Y, f(Y))), X), X)
76.74/10.01	= { by lemma 53 }
76.74/10.01	  mult(ld(mult(rd(X, ld(Y, f(Y))), f(Y)), X), X)
76.74/10.01	= { by lemma 53 }
76.74/10.01	  mult(ld(mult(mult(X, f(Y)), f(Y)), X), X)
76.74/10.01	= { by lemma 33 }
76.74/10.01	  mult(ld(mult(X, mult(f(Y), f(Y))), X), X)
76.74/10.01	= { by axiom 5 (f09) }
76.74/10.01	  mult(ld(mult(X, Y), X), X)
76.74/10.01	= { by axiom 12 (f04) }
76.74/10.01	  mult(ld(mult(X, rd(mult(Y, ld(Y, X)), ld(Y, X))), X), X)
76.74/10.01	= { by axiom 4 (f01) }
76.74/10.01	  mult(ld(mult(X, rd(X, ld(Y, X))), X), X)
76.74/10.01	= { by axiom 12 (f04) }
76.74/10.01	  mult(ld(rd(mult(mult(X, rd(X, ld(Y, X))), ld(Y, X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 54 }
76.74/10.01	  mult(ld(rd(mult(mult(X, rd(X, ld(Y, X))), ld(rd(X, ld(Y, X)), X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 32 }
76.74/10.01	  mult(ld(rd(fresh3(?, ?, rd(X, ld(Y, X)), ld(rd(X, ld(Y, X)), X), ld(rd(X, ld(Y, X)), X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 25 }
76.74/10.01	  mult(ld(rd(fresh(?, ?, rd(X, ld(Y, X)), ld(rd(X, ld(Y, X)), X), ld(rd(X, ld(Y, X)), X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 17 }
76.74/10.01	  mult(ld(rd(mult(rd(X, ld(Y, X)), mult(ld(rd(X, ld(Y, X)), X), X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 54 }
76.74/10.01	  mult(ld(rd(mult(rd(X, ld(Y, X)), mult(ld(Y, X), X)), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 55 }
76.74/10.01	  mult(ld(rd(mult(X, X), ld(Y, X)), X), X)
76.74/10.01	= { by lemma 55 }
76.74/10.01	  mult(ld(rd(mult(rd(X, rd(ld(Y, X), X)), mult(rd(ld(Y, X), X), X)), ld(Y, X)), X), X)
76.74/10.01	= { by axiom 6 (f03) }
76.74/10.01	  mult(ld(rd(mult(rd(X, rd(ld(Y, X), X)), ld(Y, X)), ld(Y, X)), X), X)
76.74/10.01	= { by axiom 12 (f04) }
76.74/10.01	  mult(ld(rd(X, rd(ld(Y, X), X)), X), X)
76.74/10.01	= { by lemma 54 }
76.74/10.01	  mult(rd(ld(Y, X), X), X)
76.74/10.01	= { by axiom 6 (f03) }
76.74/10.01	  ld(Y, X)
76.74/10.01	
76.74/10.01	Lemma 57: mult(Y, ld(X, f(X))) = rd(Y, f(X)).
76.74/10.01	Proof:
76.74/10.01	  mult(Y, ld(X, f(X)))
76.74/10.01	= { by axiom 12 (f04) }
76.74/10.01	  rd(mult(mult(Y, ld(X, f(X))), f(X)), f(X))
76.74/10.01	= { by lemma 52 }
76.74/10.01	  rd(Y, f(X))
76.74/10.01	
76.74/10.01	Lemma 58: mult(Y, ld(X, unit)) = rd(Y, X).
76.74/10.01	Proof:
76.74/10.01	  mult(Y, ld(X, unit))
76.74/10.01	= { by lemma 43 }
76.74/10.01	  mult(Y, mult(ld(X, f(X)), ld(X, f(X))))
76.74/10.01	= { by lemma 33 }
76.74/10.01	  mult(mult(Y, ld(X, f(X))), ld(X, f(X)))
76.74/10.01	= { by lemma 57 }
76.95/10.01	  rd(mult(Y, ld(X, f(X))), f(X))
76.95/10.01	= { by lemma 57 }
76.95/10.01	  rd(rd(Y, f(X)), f(X))
76.95/10.01	= { by lemma 45 }
76.95/10.01	  rd(Y, mult(f(X), f(X)))
76.95/10.01	= { by axiom 5 (f09) }
76.95/10.01	  rd(Y, X)
76.95/10.01	
76.95/10.01	Lemma 59: rd(unit, X) = ld(X, unit).
76.95/10.01	Proof:
76.95/10.01	  rd(unit, X)
76.95/10.01	= { by lemma 38 }
76.95/10.01	  rd(mult(ld(X, unit), X), X)
76.95/10.01	= { by axiom 12 (f04) }
76.95/10.01	  ld(X, unit)
76.95/10.01	
76.95/10.01	Lemma 60: mult(Y, mult(X, Y)) = fresh3(?, ?, Y, X, unit).
76.95/10.01	Proof:
76.95/10.01	  mult(Y, mult(X, Y))
76.95/10.01	= { by axiom 8 (f08) }
76.95/10.01	  mult(mult(Y, X), Y)
76.95/10.01	= { by axiom 11 (f05) }
76.95/10.01	  mult(mult(mult(Y, X), Y), unit)
76.95/10.01	= { by axiom 2 (f11) }
77.83/10.15	  fresh3(?, ?, Y, X, unit)
77.83/10.15	
77.83/10.15	Goal 1 (goals): mult(a, mult(b, mult(a, c))) = mult(mult(mult(a, b), a), c).
77.83/10.15	Proof:
77.83/10.15	  mult(a, mult(b, mult(a, c)))
77.83/10.15	= { by axiom 3 (f12) }
77.83/10.15	  fresh(?, ?, a, b, c)
77.83/10.15	= { by lemma 16 }
77.83/10.15	  fresh2(?, ?, b, a, c)
77.83/10.15	= { by axiom 1 (f10) }
77.83/10.15	  mult(a, mult(b, mult(a, c)))
77.83/10.15	= { by axiom 1 (f10) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(b, mult(a, mult(c, a))), b, a, c)
77.83/10.15	= { by lemma 51 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(c, mult(a, c))), c), b, a, c)
77.83/10.15	= { by axiom 4 (f01) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(f(rd(mult(c, mult(a, c)), c)), ld(f(rd(mult(c, mult(a, c)), c)), mult(c, mult(a, c))))), c), b, a, c)
77.83/10.15	= { by axiom 4 (f01) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(c, ld(c, f(rd(mult(c, mult(a, c)), c)))), ld(f(rd(mult(c, mult(a, c)), c)), mult(c, mult(a, c))))), c), b, a, c)
77.83/10.15	= { by axiom 6 (f03) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(c, ld(c, f(rd(mult(c, mult(a, c)), c)))), ld(f(rd(mult(c, mult(a, c)), c)), mult(rd(mult(c, mult(a, c)), c), c)))), c), b, a, c)
77.83/10.15	= { by lemma 41 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(c, ld(c, f(rd(mult(c, mult(a, c)), c)))), mult(f(rd(mult(c, mult(a, c)), c)), c))), c), b, a, c)
77.83/10.15	= { by lemma 34 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(c, ld(c, f(rd(mult(c, mult(a, c)), c)))), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c)))), c), b, a, c)
77.83/10.15	= { by lemma 28 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(c, fresh(?, ?, ld(c, f(rd(mult(c, mult(a, c)), c))), c, c))), c), b, a, c)
77.83/10.15	= { by lemma 29 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(c, mult(mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c)))), c), b, a, c)
77.83/10.15	= { by lemma 33 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c)), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), c), b, a, c)
77.83/10.15	= { by lemma 23 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), fresh3(?, ?, c, ld(c, f(rd(mult(c, mult(a, c)), c))), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), c), b, a, c)
77.83/10.15	= { by lemma 32 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), c), b, a, c)
77.83/10.15	= { by lemma 36 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), ld(c, mult(f(rd(mult(c, mult(a, c)), c)), c)))), c), b, a, c)
77.83/10.15	= { by lemma 56 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(ld(c, unit), mult(f(rd(mult(c, mult(a, c)), c)), c)))), c), b, a, c)
77.83/10.15	= { by axiom 11 (f05) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(ld(c, unit), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), unit)))), c), b, a, c)
77.83/10.15	= { by lemma 38 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(ld(c, unit), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(ld(c, unit), c))))), c), b, a, c)
77.83/10.15	= { by axiom 1 (f10) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), fresh2(?, ?, mult(f(rd(mult(c, mult(a, c)), c)), c), ld(c, unit), c))), c), b, a, c)
77.83/10.15	= { by lemma 16 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), rd(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), fresh(?, ?, ld(c, unit), mult(f(rd(mult(c, mult(a, c)), c)), c), c))), c), b, a, c)
77.83/10.15	= { by lemma 58 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), fresh(?, ?, ld(c, unit), mult(f(rd(mult(c, mult(a, c)), c)), c), c))), ld(c, unit)), b, a, c)
77.83/10.15	= { by lemma 59 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), fresh(?, ?, rd(unit, c), mult(f(rd(mult(c, mult(a, c)), c)), c), c))), ld(c, unit)), b, a, c)
77.83/10.15	= { by lemma 16 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), fresh2(?, ?, mult(f(rd(mult(c, mult(a, c)), c)), c), rd(unit, c), c))), ld(c, unit)), b, a, c)
77.83/10.15	= { by axiom 1 (f10) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(rd(unit, c), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(rd(unit, c), c))))), ld(c, unit)), b, a, c)
77.83/10.15	= { by axiom 6 (f03) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(rd(unit, c), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), unit)))), ld(c, unit)), b, a, c)
77.83/10.15	= { by axiom 3 (f12) }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), fresh(?, ?, mult(f(rd(mult(c, mult(a, c)), c)), c), rd(unit, c), unit)), ld(c, unit)), b, a, c)
77.83/10.15	= { by lemma 16 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), fresh2(?, ?, rd(unit, c), mult(f(rd(mult(c, mult(a, c)), c)), c), unit)), ld(c, unit)), b, a, c)
77.83/10.15	= { by lemma 18 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(rd(unit, c), mult(f(rd(mult(c, mult(a, c)), c)), c)))), ld(c, unit)), b, a, c)
77.83/10.15	= { by lemma 59 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), mult(rd(unit, c), mult(f(rd(mult(c, mult(a, c)), c)), c)))), rd(unit, c)), b, a, c)
77.83/10.15	= { by lemma 24 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(f(rd(mult(c, mult(a, c)), c)), c)), mult(rd(unit, c), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), rd(unit, c)))), b, a, c)
77.83/10.15	= { by lemma 34 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), mult(rd(unit, c), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), rd(unit, c)))), b, a, c)
77.83/10.15	= { by lemma 59 }
77.83/10.15	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), mult(ld(c, unit), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), rd(unit, c)))), b, a, c)
77.83/10.15	= { by lemma 59 }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), mult(ld(c, unit), mult(mult(f(rd(mult(c, mult(a, c)), c)), c), ld(c, unit)))), b, a, c)
77.83/10.16	= { by lemma 56 }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), ld(c, mult(mult(f(rd(mult(c, mult(a, c)), c)), c), ld(c, unit)))), b, a, c)
77.83/10.16	= { by lemma 58 }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), ld(c, rd(mult(f(rd(mult(c, mult(a, c)), c)), c), c))), b, a, c)
77.83/10.16	= { by axiom 12 (f04) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), mult(c, mult(ld(c, f(rd(mult(c, mult(a, c)), c))), c))), ld(c, f(rd(mult(c, mult(a, c)), c)))), b, a, c)
77.83/10.16	= { by lemma 24 }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), mult(c, ld(c, f(rd(mult(c, mult(a, c)), c)))))), b, a, c)
77.83/10.16	= { by axiom 4 (f01) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), mult(ld(c, f(rd(mult(c, mult(a, c)), c))), f(rd(mult(c, mult(a, c)), c)))), b, a, c)
77.83/10.16	= { by lemma 31 }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), ld(c, rd(mult(c, mult(a, c)), c))), b, a, c)
77.83/10.16	= { by axiom 6 (f03) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), ld(c, rd(mult(c, mult(rd(mult(a, c), c), c)), c))), b, a, c)
77.83/10.16	= { by axiom 8 (f08) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), ld(c, rd(mult(mult(c, rd(mult(a, c), c)), c), c))), b, a, c)
77.83/10.16	= { by axiom 12 (f04) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), ld(c, mult(c, rd(mult(a, c), c)))), b, a, c)
77.83/10.16	= { by axiom 9 (f02) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), rd(mult(a, c), c)), b, a, c)
77.83/10.16	= { by axiom 12 (f04) }
77.83/10.16	  fresh2(mult(b, mult(a, mult(c, a))), mult(mult(mult(b, a), c), a), b, a, c)
77.83/10.16	= { by lemma 15 }
77.83/10.16	  fresh3(?, ?, a, b, c)
77.83/10.16	= { by lemma 23 }
77.83/10.16	  mult(mult(a, mult(b, a)), c)
77.83/10.16	= { by axiom 8 (f08) }
77.83/10.16	  mult(mult(mult(a, b), a), c)
77.83/10.16	% SZS output end Proof
77.83/10.16	
77.83/10.16	RESULT: Theorem (the conjecture is true).
77.83/10.18	EOF