0.02/0.03	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.02/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.23	% Computer   : n141.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 04:57:54 CDT 2018
0.03/0.24	% CPUTime    : 
11.24/11.46	% SZS status Theorem
11.24/11.46	
11.33/11.51	% SZS output start Proof
11.33/11.51	Take the following subset of the input axioms:
11.33/11.54	  fof(f01, axiom, ![B, A]: B=mult(A, ld(A, B))).
11.33/11.54	  fof(f02, axiom, ![B, A]: ld(A, mult(A, B))=B).
11.33/11.54	  fof(f03, axiom, ![B, A]: mult(rd(A, B), B)=A).
11.33/11.54	  fof(f04, axiom, ![B, A]: rd(mult(A, B), B)=A).
11.33/11.54	  fof(f05, axiom, ![A]: mult(A, unit)=A).
11.33/11.54	  fof(f06, axiom, ![A]: mult(unit, A)=A).
11.33/11.54	  fof(f07, axiom,
11.33/11.54	      ![B, A, C]:
11.33/11.54	        mult(mult(A, mult(mult(B, C), B)), C)=mult(mult(A, B),
11.33/11.54	                                                   mult(mult(C, B), C))).
11.33/11.54	  fof(f08, axiom, ![B, A]: mult(A, mult(B, A))=mult(mult(A, B), A)).
11.33/11.54	  fof(f09, axiom, ![A]: mult(f(A), f(A))=A).
11.33/11.54	  fof(f10, axiom,
11.33/11.54	      ![X0, X1, X2]:
11.33/11.54	        (mult(mult(mult(X1, X0), X1), X2)=mult(X1, mult(X0, mult(X1, X2)))
11.33/11.54	           <= mult(mult(mult(X0, X1), X2), X1)=mult(X0,
11.33/11.54	                                                    mult(X1, mult(X2, X1))))).
11.33/11.54	  fof(f12, axiom,
11.33/11.54	      ![X6, X7, X8]:
11.33/11.54	        (mult(mult(X6, X7), mult(X8, X6))=mult(X6, mult(mult(X7, X8), X6))
11.33/11.54	           => mult(mult(mult(X6, X7), X6), X8)=mult(X6,
11.33/11.54	                                                    mult(X7, mult(X6, X8))))).
11.33/11.54	  fof(goals, conjecture,
11.33/11.54	      mult(a, mult(b, mult(a, c)))=mult(mult(mult(a, b), a), c)).
11.33/11.54	
11.33/11.54	Now clausify the problem and encode Horn clauses using encoding 3 of
11.33/11.54	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
11.33/11.54	We repeatedly replace C & s=t => u=v by the two clauses:
11.33/11.54	  $$fresh(y, y, x1...xn) = u
11.33/11.54	  C => $$fresh(s, t, x1...xn) = v
11.33/11.54	where $$fresh is a fresh function symbol and x1..xn are the free
11.33/11.54	variables of u and v.
11.33/11.54	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
11.33/11.54	input problem has no model of domain size 1).
11.33/11.54	
11.33/11.54	The encoding turns the above axioms into the following unit equations and goals:
11.33/11.54	
11.33/11.54	Axiom 1 (f10): $$fresh3(X, X, Y, Z, W) = mult(Z, mult(Y, mult(Z, W))).
11.33/11.54	Axiom 3 (f12): $$fresh(X, X, Y, Z, W) = mult(Y, mult(Z, mult(Y, W))).
11.33/11.54	Axiom 4 (f06): mult(unit, X) = X.
11.33/11.54	Axiom 5 (f03): mult(rd(X, Y), Y) = X.
11.33/11.54	Axiom 6 (f09): mult(f(X), f(X)) = X.
11.33/11.54	Axiom 7 (f10): $$fresh3(mult(mult(mult(X, Y), Z), Y), mult(X, mult(Y, mult(Z, Y))), X, Y, Z) = mult(mult(mult(Y, X), Y), Z).
11.33/11.54	Axiom 9 (f04): rd(mult(X, Y), Y) = X.
11.33/11.54	Axiom 10 (f05): mult(X, unit) = X.
11.33/11.54	Axiom 11 (f12): $$fresh(mult(mult(X, Y), mult(Z, X)), mult(X, mult(mult(Y, Z), X)), X, Y, Z) = mult(mult(mult(X, Y), X), Z).
11.33/11.54	Axiom 12 (f02): ld(X, mult(X, Y)) = Y.
11.33/11.54	Axiom 13 (f07): mult(mult(X, mult(mult(Y, Z), Y)), Z) = mult(mult(X, Y), mult(mult(Z, Y), Z)).
11.33/11.54	Axiom 14 (f08): mult(X, mult(Y, X)) = mult(mult(X, Y), X).
11.33/11.54	Axiom 15 (f01): X = mult(Y, ld(Y, X)).
11.33/11.54	
11.33/11.54	Lemma 16: $$fresh3(?, ?, Z, Y, W) = $$fresh(?, ?, Y, Z, W).
11.33/11.54	Proof:
11.33/11.54	  $$fresh3(?, ?, Z, Y, W)
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  mult(Y, mult(Z, mult(Y, W)))
11.33/11.54	= { by axiom 3 (f12) }
11.33/11.54	  $$fresh(?, ?, Y, Z, W)
11.33/11.54	
11.33/11.54	Lemma 17: rd(X, X) = unit.
11.33/11.54	Proof:
11.33/11.54	  rd(X, X)
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  rd(mult(unit, X), X)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  unit
11.33/11.54	
11.33/11.54	Lemma 18: mult(f(X), X) = mult(X, f(X)).
11.33/11.54	Proof:
11.33/11.54	  mult(f(X), X)
11.33/11.54	= { by axiom 6 (f09) }
11.33/11.54	  mult(f(X), mult(f(X), f(X)))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(f(X), f(X)), f(X))
11.33/11.54	= { by axiom 6 (f09) }
11.33/11.54	  mult(X, f(X))
11.33/11.54	
11.33/11.54	Lemma 19: mult(mult(X, Y), Y) = mult(X, mult(Y, Y)).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, Y), Y)
11.33/11.54	= { by axiom 10 (f05) }
11.33/11.54	  mult(mult(X, mult(Y, unit)), Y)
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(mult(X, mult(mult(unit, Y), unit)), Y)
11.33/11.54	= { by axiom 13 (f07) }
11.33/11.54	  mult(mult(X, unit), mult(mult(Y, unit), Y))
11.33/11.54	= { by axiom 10 (f05) }
11.33/11.54	  mult(X, mult(mult(Y, unit), Y))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(X, mult(Y, mult(unit, Y)))
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(X, mult(Y, Y))
11.33/11.54	
11.33/11.54	Lemma 20: mult(X, mult(Y, X)) = $$fresh(?, ?, X, Y, unit).
11.33/11.54	Proof:
11.33/11.54	  mult(X, mult(Y, X))
11.33/11.54	= { by axiom 10 (f05) }
11.33/11.54	  mult(X, mult(Y, mult(X, unit)))
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  $$fresh3(?, ?, Y, X, unit)
11.33/11.54	= { by lemma 16 }
11.33/11.54	  $$fresh(?, ?, X, Y, unit)
11.33/11.54	
11.33/11.54	Lemma 21: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, X), Y)
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(mult(X, mult(unit, X)), Y)
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(mult(X, unit), X), Y)
11.33/11.54	= { by axiom 11 (f12) }
11.33/11.54	  $$fresh(mult(mult(X, unit), mult(Y, X)), mult(X, mult(mult(unit, Y), X)), X, unit, Y)
11.33/11.54	= { by axiom 10 (f05) }
11.33/11.54	  $$fresh(mult(X, mult(Y, X)), mult(X, mult(mult(unit, Y), X)), X, unit, Y)
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  $$fresh(mult(X, mult(Y, X)), mult(X, mult(Y, X)), X, unit, Y)
11.33/11.54	= { by axiom 3 (f12) }
11.33/11.54	  mult(X, mult(unit, mult(X, Y)))
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(X, mult(X, Y))
11.33/11.54	
11.33/11.54	Lemma 22: rd(mult(X, Y), X) = mult(X, rd(Y, X)).
11.33/11.54	Proof:
11.33/11.54	  rd(mult(X, Y), X)
11.33/11.54	= { by axiom 5 (f03) }
11.33/11.54	  rd(mult(X, mult(rd(Y, X), X)), X)
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  rd(mult(mult(X, rd(Y, X)), X), X)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  mult(X, rd(Y, X))
11.33/11.54	
11.33/11.54	Lemma 23: mult(X, rd(unit, X)) = unit.
11.33/11.54	Proof:
11.33/11.54	  mult(X, rd(unit, X))
11.33/11.54	= { by lemma 22 }
11.33/11.54	  rd(mult(X, unit), X)
11.33/11.54	= { by axiom 10 (f05) }
11.33/11.54	  rd(X, X)
11.33/11.54	= { by lemma 17 }
11.33/11.54	  unit
11.33/11.54	
11.33/11.54	Lemma 24: ld(X, unit) = rd(unit, X).
11.33/11.54	Proof:
11.33/11.54	  ld(X, unit)
11.33/11.54	= { by lemma 23 }
11.33/11.54	  ld(X, mult(X, rd(unit, X)))
11.33/11.54	= { by axiom 12 (f02) }
11.33/11.54	  rd(unit, X)
11.33/11.54	
11.33/11.54	Lemma 25: mult(X, mult(ld(X, Y), X)) = mult(Y, X).
11.33/11.54	Proof:
11.33/11.54	  mult(X, mult(ld(X, Y), X))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(X, ld(X, Y)), X)
11.33/11.54	= { by axiom 15 (f01) }
11.33/11.54	  mult(Y, X)
11.33/11.54	
11.33/11.54	Lemma 26: mult(f(X), mult(f(X), Y)) = mult(X, Y).
11.33/11.54	Proof:
11.33/11.54	  mult(f(X), mult(f(X), Y))
11.33/11.54	= { by lemma 21 }
11.33/11.54	  mult(mult(f(X), f(X)), Y)
11.33/11.54	= { by axiom 6 (f09) }
11.33/11.54	  mult(X, Y)
11.33/11.54	
11.33/11.54	Lemma 27: mult(X, rd(f(X), X)) = f(X).
11.33/11.54	Proof:
11.33/11.54	  mult(X, rd(f(X), X))
11.33/11.54	= { by lemma 22 }
11.33/11.54	  rd(mult(X, f(X)), X)
11.33/11.54	= { by lemma 18 }
11.33/11.54	  rd(mult(f(X), X), X)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  f(X)
11.33/11.54	
11.33/11.54	Lemma 28: ld(X, f(X)) = rd(f(X), X).
11.33/11.54	Proof:
11.33/11.54	  ld(X, f(X))
11.33/11.54	= { by lemma 27 }
11.33/11.54	  ld(X, mult(X, rd(f(X), X)))
11.33/11.54	= { by axiom 12 (f02) }
11.33/11.54	  rd(f(X), X)
11.33/11.54	
11.33/11.54	Lemma 29: mult(rd(X, Y), mult(Y, Y)) = mult(X, Y).
11.33/11.54	Proof:
11.33/11.54	  mult(rd(X, Y), mult(Y, Y))
11.33/11.54	= { by lemma 19 }
11.33/11.54	  mult(mult(rd(X, Y), Y), Y)
11.33/11.54	= { by axiom 5 (f03) }
11.33/11.54	  mult(X, Y)
11.33/11.54	
11.33/11.54	Lemma 30: rd(mult(X, mult(Y, Y)), Y) = mult(X, Y).
11.33/11.54	Proof:
11.33/11.54	  rd(mult(X, mult(Y, Y)), Y)
11.33/11.54	= { by lemma 19 }
11.33/11.54	  rd(mult(mult(X, Y), Y), Y)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  mult(X, Y)
11.33/11.54	
11.33/11.54	Lemma 31: rd(mult(X, mult(X, Y)), Y) = mult(X, X).
11.33/11.54	Proof:
11.33/11.54	  rd(mult(X, mult(X, Y)), Y)
11.33/11.54	= { by lemma 21 }
11.33/11.54	  rd(mult(mult(X, X), Y), Y)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  mult(X, X)
11.33/11.54	
11.33/11.54	Lemma 32: ld(f(X), mult(X, Y)) = mult(f(X), Y).
11.33/11.54	Proof:
11.33/11.54	  ld(f(X), mult(X, Y))
11.33/11.54	= { by lemma 26 }
11.33/11.54	  ld(f(X), mult(f(X), mult(f(X), Y)))
11.33/11.54	= { by axiom 12 (f02) }
11.33/11.54	  mult(f(X), Y)
11.33/11.54	
11.33/11.54	Lemma 33: rd(mult(X, Y), f(Y)) = mult(X, f(Y)).
11.33/11.54	Proof:
11.33/11.54	  rd(mult(X, Y), f(Y))
11.33/11.54	= { by axiom 6 (f09) }
11.33/11.54	  rd(mult(X, mult(f(Y), f(Y))), f(Y))
11.33/11.54	= { by lemma 30 }
11.33/11.54	  mult(X, f(Y))
11.33/11.54	
11.33/11.54	Lemma 34: mult(mult(X, mult(Y, X)), Y) = $$fresh(?, ?, X, Y, Y).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, mult(Y, X)), Y)
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(mult(X, Y), X), Y)
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(mult(unit, mult(mult(X, Y), X)), Y)
11.33/11.54	= { by axiom 13 (f07) }
11.33/11.54	  mult(mult(unit, X), mult(mult(Y, X), Y))
11.33/11.54	= { by axiom 4 (f06) }
11.33/11.54	  mult(X, mult(mult(Y, X), Y))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(X, mult(Y, mult(X, Y)))
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  $$fresh3(?, ?, Y, X, Y)
11.33/11.54	= { by lemma 16 }
11.33/11.54	  $$fresh(?, ?, X, Y, Y)
11.33/11.54	
11.33/11.54	Lemma 35: rd(rd(X, Y), Y) = rd(X, mult(Y, Y)).
11.33/11.54	Proof:
11.33/11.54	  rd(rd(X, Y), Y)
11.33/11.54	= { by axiom 9 (f04) }
11.33/11.54	  rd(mult(rd(rd(X, Y), Y), mult(Y, Y)), mult(Y, Y))
11.33/11.54	= { by lemma 29 }
11.33/11.54	  rd(mult(rd(X, Y), Y), mult(Y, Y))
11.33/11.54	= { by axiom 5 (f03) }
11.33/11.54	  rd(X, mult(Y, Y))
11.33/11.54	
11.33/11.54	Lemma 36: ld(Y, $$fresh(?, ?, Y, X, Z)) = mult(X, mult(Y, Z)).
11.33/11.54	Proof:
11.33/11.54	  ld(Y, $$fresh(?, ?, Y, X, Z))
11.33/11.54	= { by lemma 16 }
11.33/11.54	  ld(Y, $$fresh3(?, ?, X, Y, Z))
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  ld(Y, mult(Y, mult(X, mult(Y, Z))))
11.33/11.54	= { by axiom 12 (f02) }
11.33/11.54	  mult(X, mult(Y, Z))
11.33/11.54	
11.33/11.54	Lemma 37: $$fresh(?, ?, Y, X, ld(Y, Z)) = mult(Y, mult(X, Z)).
11.33/11.54	Proof:
11.33/11.54	  $$fresh(?, ?, Y, X, ld(Y, Z))
11.33/11.54	= { by lemma 16 }
11.33/11.54	  $$fresh3(?, ?, X, Y, ld(Y, Z))
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  mult(Y, mult(X, mult(Y, ld(Y, Z))))
11.33/11.54	= { by axiom 15 (f01) }
11.33/11.54	  mult(Y, mult(X, Z))
11.33/11.54	
11.33/11.54	Lemma 38: mult(mult(X, Y), mult(X, X)) = $$fresh(?, ?, X, Y, X).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, Y), mult(X, X))
11.33/11.54	= { by lemma 19 }
11.33/11.54	  mult(mult(mult(X, Y), X), X)
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(X, mult(Y, X)), X)
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(X, mult(mult(Y, X), X))
11.33/11.54	= { by lemma 19 }
11.33/11.54	  mult(X, mult(Y, mult(X, X)))
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  $$fresh3(?, ?, Y, X, X)
11.33/11.54	= { by lemma 16 }
11.33/11.54	  $$fresh(?, ?, X, Y, X)
11.33/11.54	
11.33/11.54	Lemma 39: mult(mult(X, mult(Y, Y)), Y) = mult(mult(X, Y), mult(Y, Y)).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, mult(Y, Y)), Y)
11.33/11.54	= { by lemma 19 }
11.33/11.54	  mult(mult(mult(X, Y), Y), Y)
11.33/11.54	= { by lemma 19 }
11.33/11.54	  mult(mult(X, Y), mult(Y, Y))
11.33/11.54	
11.33/11.54	Lemma 40: mult($$fresh(?, ?, X, Y, unit), Y) = $$fresh(?, ?, X, Y, Y).
11.33/11.54	Proof:
11.33/11.54	  mult($$fresh(?, ?, X, Y, unit), Y)
11.33/11.54	= { by lemma 20 }
11.33/11.54	  mult(mult(X, mult(Y, X)), Y)
11.33/11.54	= { by lemma 34 }
11.33/11.54	  $$fresh(?, ?, X, Y, Y)
11.33/11.54	
11.33/11.54	Lemma 41: mult(X, mult(mult(Y, mult(X, Z)), X)) = mult($$fresh(?, ?, X, Y, Z), X).
11.33/11.54	Proof:
11.33/11.54	  mult(X, mult(mult(Y, mult(X, Z)), X))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(X, mult(Y, mult(X, Z))), X)
11.33/11.54	= { by axiom 1 (f10) }
11.33/11.54	  mult($$fresh3(?, ?, Y, X, Z), X)
11.33/11.54	= { by lemma 16 }
11.33/11.54	  mult($$fresh(?, ?, X, Y, Z), X)
11.33/11.54	
11.33/11.54	Lemma 42: mult(mult(X, mult(Z, Y)), ld(Y, Z)) = mult(mult(X, Y), mult(ld(Y, Z), Z)).
11.33/11.54	Proof:
11.33/11.54	  mult(mult(X, mult(Z, Y)), ld(Y, Z))
11.33/11.54	= { by axiom 15 (f01) }
11.33/11.54	  mult(mult(X, mult(mult(Y, ld(Y, Z)), Y)), ld(Y, Z))
11.33/11.54	= { by axiom 13 (f07) }
11.33/11.54	  mult(mult(X, Y), mult(mult(ld(Y, Z), Y), ld(Y, Z)))
11.33/11.54	= { by axiom 14 (f08) }
11.33/11.54	  mult(mult(X, Y), mult(ld(Y, Z), mult(Y, ld(Y, Z))))
11.33/11.54	= { by axiom 15 (f01) }
11.33/11.55	  mult(mult(X, Y), mult(ld(Y, Z), Z))
11.33/11.55	
11.33/11.55	Lemma 43: mult(X, mult(ld(X, Y), Y)) = mult(Y, Y).
11.33/11.55	Proof:
11.33/11.55	  mult(X, mult(ld(X, Y), Y))
11.33/11.55	= { by lemma 37 }
11.33/11.55	  $$fresh(?, ?, X, ld(X, Y), ld(X, Y))
11.33/11.55	= { by lemma 16 }
11.33/11.55	  $$fresh3(?, ?, ld(X, Y), X, ld(X, Y))
11.33/11.55	= { by axiom 1 (f10) }
11.33/11.55	  mult(X, mult(ld(X, Y), mult(X, ld(X, Y))))
11.33/11.55	= { by axiom 9 (f04) }
11.33/11.55	  mult(X, rd(mult(mult(ld(X, Y), mult(X, ld(X, Y))), X), X))
11.33/11.55	= { by lemma 34 }
11.33/11.55	  mult(X, rd($$fresh(?, ?, ld(X, Y), X, X), X))
11.33/11.55	= { by lemma 22 }
11.33/11.55	  rd(mult(X, $$fresh(?, ?, ld(X, Y), X, X)), X)
11.33/11.55	= { by lemma 40 }
11.33/11.55	  rd(mult(X, mult($$fresh(?, ?, ld(X, Y), X, unit), X)), X)
11.33/11.55	= { by lemma 20 }
11.33/11.55	  rd(mult(X, mult(mult(ld(X, Y), mult(X, ld(X, Y))), X)), X)
11.33/11.55	= { by axiom 14 (f08) }
11.33/11.55	  rd(mult(X, mult(mult(mult(ld(X, Y), X), ld(X, Y)), X)), X)
11.33/11.55	= { by axiom 14 (f08) }
11.33/11.55	  rd(mult(mult(X, mult(mult(ld(X, Y), X), ld(X, Y))), X), X)
11.33/11.55	= { by axiom 13 (f07) }
11.33/11.55	  rd(mult(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), X)), X)
11.33/11.55	= { by axiom 14 (f08) }
11.33/11.55	  rd(mult(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))), X)
11.33/11.55	= { by axiom 15 (f01) }
11.33/11.55	  rd(mult(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))), X)
11.33/11.55	= { by axiom 12 (f02) }
11.33/11.55	  rd(mult(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))), ld(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), X)))
11.33/11.55	= { by axiom 14 (f08) }
11.33/11.55	  rd(mult(mult(X, ld(X, Y)), mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))), ld(mult(X, ld(X, Y)), mult(X, mult(ld(X, Y), X))))
11.33/11.55	= { by lemma 31 }
11.33/11.55	  mult(mult(X, ld(X, Y)), mult(X, ld(X, Y)))
11.33/11.55	= { by axiom 15 (f01) }
11.33/11.55	  mult(Y, mult(X, ld(X, Y)))
11.33/11.55	= { by axiom 15 (f01) }
11.33/11.55	  mult(Y, Y)
11.33/11.55	
11.33/11.55	Lemma 44: ld(X, mult(Y, Y)) = mult(ld(X, Y), Y).
11.33/11.55	Proof:
11.33/11.55	  ld(X, mult(Y, Y))
11.33/11.55	= { by lemma 43 }
11.33/11.55	  ld(X, mult(X, mult(ld(X, Y), Y)))
11.33/11.55	= { by axiom 12 (f02) }
11.33/11.55	  mult(ld(X, Y), Y)
11.33/11.55	
11.33/11.55	Lemma 45: mult(ld(X, f(Y)), f(Y)) = ld(X, Y).
11.33/11.55	Proof:
11.33/11.55	  mult(ld(X, f(Y)), f(Y))
11.33/11.55	= { by lemma 44 }
11.33/11.55	  ld(X, mult(f(Y), f(Y)))
11.33/11.55	= { by axiom 6 (f09) }
11.40/11.59	  ld(X, Y)
11.40/11.59	
11.40/11.59	Lemma 46: mult(X, rd(unit, f(Y))) = rd(X, f(Y)).
11.40/11.59	Proof:
11.40/11.59	  mult(X, rd(unit, f(Y)))
11.40/11.59	= { by axiom 5 (f03) }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(Y, f(Y))), rd(unit, f(Y)))
11.40/11.59	= { by lemma 18 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), rd(unit, f(Y)))
11.40/11.59	= { by lemma 24 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(f(Y), unit))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(f(Y), ld(f(Y), mult(f(Y), unit))))
11.40/11.59	= { by axiom 10 (f05) }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(f(Y), ld(f(Y), f(Y))))
11.40/11.59	= { by lemma 27 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(f(Y), ld(f(Y), mult(Y, rd(f(Y), Y)))))
11.40/11.59	= { by lemma 32 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(f(Y), mult(f(Y), rd(f(Y), Y))))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), rd(f(Y), Y))
11.40/11.59	= { by lemma 28 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), Y)), ld(Y, f(Y)))
11.40/11.59	= { by lemma 42 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), Y), mult(ld(Y, f(Y)), f(Y)))
11.40/11.59	= { by lemma 28 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), Y), mult(rd(f(Y), Y), f(Y)))
11.40/11.59	= { by lemma 33 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), Y), rd(mult(rd(f(Y), Y), Y), f(Y)))
11.40/11.59	= { by axiom 5 (f03) }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), Y), rd(f(Y), f(Y)))
11.40/11.59	= { by lemma 17 }
11.40/11.59	  mult(mult(rd(X, mult(Y, f(Y))), Y), unit)
11.40/11.59	= { by axiom 10 (f05) }
11.40/11.59	  mult(rd(X, mult(Y, f(Y))), Y)
11.40/11.59	= { by lemma 30 }
11.40/11.59	  rd(mult(rd(X, mult(Y, f(Y))), mult(Y, Y)), Y)
11.40/11.59	= { by axiom 6 (f09) }
11.40/11.59	  rd(mult(rd(X, mult(Y, f(Y))), mult(Y, Y)), mult(f(Y), f(Y)))
11.40/11.59	= { by lemma 35 }
11.40/11.59	  rd(rd(mult(rd(X, mult(Y, f(Y))), mult(Y, Y)), f(Y)), f(Y))
11.40/11.59	= { by lemma 19 }
11.40/11.59	  rd(rd(mult(mult(rd(X, mult(Y, f(Y))), Y), Y), f(Y)), f(Y))
11.40/11.59	= { by lemma 33 }
11.40/11.59	  rd(mult(mult(rd(X, mult(Y, f(Y))), Y), f(Y)), f(Y))
11.40/11.59	= { by axiom 6 (f09) }
11.40/11.59	  rd(mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), f(Y))), f(Y)), f(Y))
11.40/11.59	= { by lemma 39 }
11.40/11.59	  rd(mult(mult(rd(X, mult(Y, f(Y))), f(Y)), mult(f(Y), f(Y))), f(Y))
11.40/11.59	= { by lemma 36 }
11.40/11.59	  rd(ld(f(Y), $$fresh(?, ?, f(Y), mult(rd(X, mult(Y, f(Y))), f(Y)), f(Y))), f(Y))
11.40/11.59	= { by lemma 38 }
11.40/11.59	  rd(ld(f(Y), mult(mult(f(Y), mult(rd(X, mult(Y, f(Y))), f(Y))), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by axiom 14 (f08) }
11.40/11.59	  rd(ld(f(Y), mult(mult(mult(f(Y), rd(X, mult(Y, f(Y)))), f(Y)), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by axiom 7 (f10) }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(mult(mult(rd(X, mult(Y, f(Y))), f(Y)), mult(f(Y), f(Y))), f(Y)), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 39 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(mult(mult(rd(X, mult(Y, f(Y))), f(Y)), f(Y)), mult(f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 19 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(mult(rd(X, mult(Y, f(Y))), mult(f(Y), f(Y))), mult(f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 19 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(rd(X, mult(Y, f(Y))), mult(mult(f(Y), f(Y)), mult(f(Y), f(Y)))), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 38 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(rd(X, mult(Y, f(Y))), $$fresh(?, ?, f(Y), f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(mult(f(Y), f(Y)), f(Y)))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 21 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(rd(X, mult(Y, f(Y))), $$fresh(?, ?, f(Y), f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(f(Y), mult(f(Y), f(Y))))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by axiom 1 (f10) }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(rd(X, mult(Y, f(Y))), $$fresh(?, ?, f(Y), f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), $$fresh3(?, ?, f(Y), f(Y), f(Y))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 16 }
11.40/11.59	  rd(ld(f(Y), $$fresh3(mult(rd(X, mult(Y, f(Y))), $$fresh(?, ?, f(Y), f(Y), f(Y))), mult(rd(X, mult(Y, f(Y))), $$fresh(?, ?, f(Y), f(Y), f(Y))), rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by axiom 1 (f10) }
11.40/11.59	  rd(ld(f(Y), mult(f(Y), mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(f(Y), f(Y)))))), f(Y))
11.40/11.59	= { by axiom 1 (f10) }
11.40/11.59	  rd(ld(f(Y), $$fresh3(?, ?, rd(X, mult(Y, f(Y))), f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 16 }
11.40/11.59	  rd(ld(f(Y), $$fresh(?, ?, f(Y), rd(X, mult(Y, f(Y))), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 36 }
11.40/11.59	  rd(mult(rd(X, mult(Y, f(Y))), mult(f(Y), mult(f(Y), f(Y)))), f(Y))
11.40/11.59	= { by lemma 26 }
11.40/11.59	  rd(mult(rd(X, mult(Y, f(Y))), mult(Y, f(Y))), f(Y))
11.40/11.59	= { by axiom 5 (f03) }
11.40/11.59	  rd(X, f(Y))
11.40/11.59	
11.40/11.59	Lemma 47: mult(X, rd(unit, Y)) = rd(X, Y).
11.40/11.59	Proof:
11.40/11.59	  mult(X, rd(unit, Y))
11.40/11.59	= { by axiom 6 (f09) }
11.40/11.59	  mult(X, rd(unit, mult(f(Y), f(Y))))
11.40/11.59	= { by lemma 31 }
11.40/11.59	  mult(X, rd(unit, rd(mult(f(Y), mult(f(Y), rd(unit, f(Y)))), rd(unit, f(Y)))))
11.40/11.59	= { by lemma 23 }
11.40/11.59	  mult(X, rd(unit, rd(mult(f(Y), unit), rd(unit, f(Y)))))
11.40/11.59	= { by axiom 10 (f05) }
11.40/11.59	  mult(X, rd(unit, rd(f(Y), rd(unit, f(Y)))))
11.40/11.59	= { by lemma 24 }
11.40/11.59	  mult(X, ld(rd(f(Y), rd(unit, f(Y))), unit))
11.40/11.59	= { by lemma 23 }
11.40/11.59	  mult(X, ld(rd(f(Y), rd(unit, f(Y))), mult(f(Y), rd(unit, f(Y)))))
11.40/11.59	= { by lemma 29 }
11.40/11.59	  mult(X, ld(rd(f(Y), rd(unit, f(Y))), mult(rd(f(Y), rd(unit, f(Y))), mult(rd(unit, f(Y)), rd(unit, f(Y))))))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  mult(X, mult(rd(unit, f(Y)), rd(unit, f(Y))))
11.40/11.59	= { by lemma 19 }
11.40/11.59	  mult(mult(X, rd(unit, f(Y))), rd(unit, f(Y)))
11.40/11.59	= { by lemma 46 }
11.40/11.59	  rd(mult(X, rd(unit, f(Y))), f(Y))
11.40/11.59	= { by lemma 46 }
11.40/11.59	  rd(rd(X, f(Y)), f(Y))
11.40/11.59	= { by lemma 35 }
11.40/11.59	  rd(X, mult(f(Y), f(Y)))
11.40/11.59	= { by axiom 6 (f09) }
11.40/11.59	  rd(X, Y)
11.40/11.59	
11.40/11.59	Lemma 48: ld(mult(Y, X), Y) = rd(unit, X).
11.40/11.59	Proof:
11.40/11.59	  ld(mult(Y, X), Y)
11.40/11.59	= { by axiom 9 (f04) }
11.40/11.59	  ld(mult(Y, X), rd(mult(Y, X), X))
11.40/11.59	= { by lemma 47 }
11.40/11.59	  ld(mult(Y, X), mult(mult(Y, X), rd(unit, X)))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  rd(unit, X)
11.40/11.59	
11.40/11.59	Lemma 49: mult(rd(unit, X), Y) = ld(X, Y).
11.40/11.59	Proof:
11.40/11.59	  mult(rd(unit, X), Y)
11.40/11.59	= { by lemma 48 }
11.40/11.59	  mult(ld(mult(Y, X), Y), Y)
11.40/11.59	= { by lemma 44 }
11.40/11.59	  ld(mult(Y, X), mult(Y, Y))
11.40/11.59	= { by lemma 43 }
11.40/11.59	  ld(mult(Y, X), mult(X, mult(ld(X, Y), Y)))
11.40/11.59	= { by lemma 37 }
11.40/11.59	  ld(mult(Y, X), $$fresh(?, ?, X, ld(X, Y), ld(X, Y)))
11.40/11.59	= { by lemma 40 }
11.40/11.59	  ld(mult(Y, X), mult($$fresh(?, ?, X, ld(X, Y), unit), ld(X, Y)))
11.40/11.59	= { by lemma 20 }
11.40/11.59	  ld(mult(Y, X), mult(mult(X, mult(ld(X, Y), X)), ld(X, Y)))
11.40/11.59	= { by lemma 25 }
11.40/11.59	  ld(mult(Y, X), mult(mult(Y, X), ld(X, Y)))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  ld(X, Y)
11.40/11.59	
11.40/11.59	Lemma 50: ld(ld(X, Y), X) = mult(ld(Y, X), X).
11.40/11.59	Proof:
11.40/11.59	  ld(ld(X, Y), X)
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  ld(Y, mult(Y, ld(ld(X, Y), X)))
11.40/11.59	= { by axiom 15 (f01) }
11.40/11.59	  ld(Y, mult(mult(ld(X, Y), ld(ld(X, Y), Y)), ld(ld(X, Y), X)))
11.40/11.59	= { by axiom 15 (f01) }
11.40/11.59	  ld(Y, mult(mult(ld(X, Y), ld(ld(X, Y), mult(X, ld(X, Y)))), ld(ld(X, Y), X)))
11.40/11.59	= { by lemma 25 }
11.40/11.59	  ld(Y, mult(mult(ld(X, Y), ld(ld(X, Y), mult(ld(X, Y), mult(ld(ld(X, Y), X), ld(X, Y))))), ld(ld(X, Y), X)))
11.40/11.59	= { by axiom 12 (f02) }
11.40/11.59	  ld(Y, mult(mult(ld(X, Y), mult(ld(ld(X, Y), X), ld(X, Y))), ld(ld(X, Y), X)))
11.40/11.59	= { by lemma 34 }
11.40/11.59	  ld(Y, $$fresh(?, ?, ld(X, Y), ld(ld(X, Y), X), ld(ld(X, Y), X)))
11.40/11.59	= { by lemma 37 }
11.40/11.59	  ld(Y, mult(ld(X, Y), mult(ld(ld(X, Y), X), X)))
11.40/11.59	= { by lemma 43 }
11.40/11.59	  ld(Y, mult(X, X))
11.40/11.59	= { by lemma 44 }
11.40/11.63	  mult(ld(Y, X), X)
11.40/11.63	
11.40/11.63	Goal 1 (goals): mult(a, mult(b, mult(a, c))) = mult(mult(mult(a, b), a), c).
11.40/11.63	Proof:
11.40/11.63	  mult(a, mult(b, mult(a, c)))
11.40/11.63	= { by axiom 1 (f10) }
11.40/11.63	  $$fresh3(?, ?, b, a, c)
11.40/11.63	= { by axiom 1 (f10) }
11.40/11.63	  mult(a, mult(b, mult(a, c)))
11.40/11.63	= { by axiom 1 (f10) }
11.40/11.63	  $$fresh3(mult(b, mult(a, mult(c, a))), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 14 (f08) }
11.40/11.63	  $$fresh3(mult(b, mult(mult(a, c), a)), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 5 (f03) }
11.40/11.63	  $$fresh3(mult(rd(mult(b, mult(mult(a, c), a)), a), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 47 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(mult(a, c), a)), rd(unit, a)), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 26 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), mult(f(mult(a, c)), a))), rd(unit, a)), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 48 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), mult(f(mult(a, c)), a))), ld(mult(f(mult(a, c)), a), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 42 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), mult(ld(mult(f(mult(a, c)), a), f(mult(a, c))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 45 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(mult(f(mult(a, c)), a), mult(a, c))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 32 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(ld(f(mult(a, c)), mult(mult(a, c), a)), mult(a, c))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 45 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), mult(ld(ld(f(mult(a, c)), mult(mult(a, c), a)), f(mult(a, c))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 50 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(ld(f(mult(a, c)), ld(f(mult(a, c)), mult(mult(a, c), a))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 15 (f01) }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(ld(f(mult(a, c)), ld(f(mult(a, c)), mult(mult(a, c), ld(mult(a, c), mult(mult(a, c), a))))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 32 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(ld(f(mult(a, c)), mult(f(mult(a, c)), ld(mult(a, c), mult(mult(a, c), a)))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 12 (f02) }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(ld(mult(a, c), mult(mult(a, c), a)), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 49 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), mult(rd(unit, ld(mult(a, c), mult(mult(a, c), a))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 33 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), rd(mult(rd(unit, ld(mult(a, c), mult(mult(a, c), a))), mult(a, c)), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 49 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), rd(ld(ld(mult(a, c), mult(mult(a, c), a)), mult(a, c)), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 50 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), rd(mult(ld(mult(mult(a, c), a), mult(a, c)), mult(a, c)), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 33 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), mult(ld(mult(mult(a, c), a), mult(a, c)), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 48 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), mult(rd(unit, a), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 49 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, mult(f(mult(a, c)), a)), ld(a, f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 42 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, a), mult(ld(a, f(mult(a, c))), f(mult(a, c)))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by lemma 45 }
11.40/11.63	  $$fresh3(mult(mult(mult(b, a), ld(a, mult(a, c))), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 12 (f02) }
11.40/11.63	  $$fresh3(mult(mult(mult(b, a), c), a), mult(b, mult(a, mult(c, a))), b, a, c)
11.40/11.63	= { by axiom 7 (f10) }
11.40/11.63	  mult(mult(mult(a, b), a), c)
11.40/11.63	% SZS output end Proof
11.40/11.63	
11.40/11.63	RESULT: Theorem (the conjecture is true).
11.40/11.64	EOF