0.04/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.04/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n014.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   : 180
0.12/0.33	% DateTime   : Thu Aug 29 09:44:09 EDT 2019
0.12/0.33	% CPUTime    : 
0.18/0.52	% SZS status Theorem
0.18/0.52	
0.18/0.52	% SZS output start Proof
0.18/0.52	Take the following subset of the input axioms:
0.40/0.61	  fof(f01, axiom, ![A]: A=ld(A, mult(A, A))).
0.40/0.61	  fof(f02, axiom, ![A]: A=rd(mult(A, A), A)).
0.40/0.61	  fof(f03, axiom, ![B, A]: ld(A, mult(A, B))=mult(A, ld(A, B))).
0.40/0.61	  fof(f04, axiom, ![B, A]: mult(rd(A, B), B)=rd(mult(A, B), B)).
0.40/0.61	  fof(f05, axiom, ![B, A, D, C]: ld(ld(A, B), mult(ld(A, B), mult(C, D)))=mult(ld(A, mult(A, C)), D)).
0.40/0.61	  fof(f06, axiom, ![B, A, D, C]: rd(mult(mult(A, B), rd(C, D)), rd(C, D))=mult(A, rd(mult(B, D), D))).
0.40/0.61	  fof(f07, axiom, ![B, A]: rd(mult(rd(A, A), B), B)=ld(A, mult(A, ld(B, B)))).
0.40/0.61	  fof(goals, conjecture, ![X3, X4, X5]: (mult(X3, ld(X4, mult(X4, X5)))=mult(X3, X5) & mult(rd(mult(X3, X4), X4), X5)=mult(X3, X5))).
0.40/0.61	
0.40/0.61	Now clausify the problem and encode Horn clauses using encoding 3 of
0.40/0.61	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.40/0.61	We repeatedly replace C & s=t => u=v by the two clauses:
0.40/0.61	  fresh(y, y, x1...xn) = u
0.40/0.61	  C => fresh(s, t, x1...xn) = v
0.40/0.61	where fresh is a fresh function symbol and x1..xn are the free
0.40/0.61	variables of u and v.
0.40/0.61	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.40/0.61	input problem has no model of domain size 1).
0.40/0.61	
0.40/0.61	The encoding turns the above axioms into the following unit equations and goals:
0.40/0.61	
0.40/0.61	Axiom 1 (f01): X = ld(X, mult(X, X)).
0.40/0.61	Axiom 2 (f07): rd(mult(rd(X, X), Y), Y) = ld(X, mult(X, ld(Y, Y))).
0.40/0.61	Axiom 3 (f02): X = rd(mult(X, X), X).
0.40/0.61	Axiom 4 (f06): rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)) = mult(X, rd(mult(Y, W), W)).
0.40/0.61	Axiom 5 (f03): ld(X, mult(X, Y)) = mult(X, ld(X, Y)).
0.40/0.61	Axiom 6 (f05): ld(ld(X, Y), mult(ld(X, Y), mult(Z, W))) = mult(ld(X, mult(X, Z)), W).
0.40/0.62	Axiom 7 (f04): mult(rd(X, Y), Y) = rd(mult(X, Y), Y).
0.40/0.62	
0.40/0.62	Lemma 8: mult(rd(X, X), X) = X.
0.40/0.62	Proof:
0.40/0.62	  mult(rd(X, X), X)
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  rd(mult(X, X), X)
0.40/0.62	= { by axiom 3 (f02) }
0.40/0.62	  X
0.40/0.62	
0.40/0.62	Lemma 9: mult(X, ld(X, X)) = X.
0.40/0.62	Proof:
0.40/0.62	  mult(X, ld(X, X))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  ld(X, mult(X, X))
0.40/0.62	= { by axiom 1 (f01) }
0.40/0.62	  X
0.40/0.62	
0.40/0.62	Lemma 10: mult(X, ld(X, ld(X, X))) = ld(X, X).
0.40/0.62	Proof:
0.40/0.62	  mult(X, ld(X, ld(X, X)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  ld(X, mult(X, ld(X, X)))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  ld(X, X)
0.40/0.62	
0.40/0.62	Lemma 11: rd(X, X) = ld(X, X).
0.40/0.62	Proof:
0.40/0.62	  rd(X, X)
0.40/0.62	= { by lemma 8 }
0.40/0.62	  rd(mult(rd(X, X), X), X)
0.40/0.62	= { by axiom 2 (f07) }
0.40/0.62	  ld(X, mult(X, ld(X, X)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(X, ld(X, ld(X, X)))
0.40/0.62	= { by lemma 10 }
0.40/0.62	  ld(X, X)
0.40/0.62	
0.40/0.62	Lemma 12: mult(rd(ld(X, X), Y), Y) = mult(X, ld(X, ld(Y, Y))).
0.40/0.62	Proof:
0.40/0.62	  mult(rd(ld(X, X), Y), Y)
0.40/0.62	= { by lemma 11 }
0.40/0.62	  mult(rd(rd(X, X), Y), Y)
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  rd(mult(rd(X, X), Y), Y)
0.40/0.62	= { by axiom 2 (f07) }
0.40/0.62	  ld(X, mult(X, ld(Y, Y)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(X, ld(X, ld(Y, Y)))
0.40/0.62	
0.40/0.62	Lemma 13: mult(rd(mult(X, Y), Z), Z) = mult(X, mult(rd(Y, Z), Z)).
0.40/0.62	Proof:
0.40/0.62	  mult(rd(mult(X, Y), Z), Z)
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  rd(mult(mult(X, Y), Z), Z)
0.40/0.62	= { by axiom 3 (f02) }
0.40/0.62	  rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), Z)
0.40/0.62	= { by lemma 8 }
0.40/0.62	  rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), mult(rd(Z, Z), Z))
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  rd(mult(mult(X, Y), rd(mult(Z, Z), Z)), rd(mult(Z, Z), Z))
0.40/0.62	= { by axiom 4 (f06) }
0.40/0.62	  mult(X, rd(mult(Y, Z), Z))
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  mult(X, mult(rd(Y, Z), Z))
0.40/0.62	
0.40/0.62	Lemma 14: mult(X, mult(X, ld(X, ld(Y, Y)))) = mult(rd(X, Y), Y).
0.40/0.62	Proof:
0.40/0.62	  mult(X, mult(X, ld(X, ld(Y, Y))))
0.40/0.62	= { by lemma 12 }
0.40/0.62	  mult(X, mult(rd(ld(X, X), Y), Y))
0.40/0.62	= { by lemma 13 }
0.40/0.62	  mult(rd(mult(X, ld(X, X)), Y), Y)
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(rd(X, Y), Y)
0.40/0.62	
0.40/0.62	Lemma 15: mult(ld(X, Y), ld(ld(X, Y), mult(Z, W))) = mult(mult(X, ld(X, Z)), W).
0.40/0.62	Proof:
0.40/0.62	  mult(ld(X, Y), ld(ld(X, Y), mult(Z, W)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  ld(ld(X, Y), mult(ld(X, Y), mult(Z, W)))
0.40/0.62	= { by axiom 6 (f05) }
0.40/0.62	  mult(ld(X, mult(X, Z)), W)
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(mult(X, ld(X, Z)), W)
0.40/0.62	
0.40/0.62	Lemma 16: mult(ld(X, Z), ld(ld(X, Z), Y)) = mult(ld(X, ?), ld(ld(X, ?), Y)).
0.40/0.62	Proof:
0.40/0.62	  mult(ld(X, Z), ld(ld(X, Z), Y))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(ld(X, Z), ld(ld(X, Z), mult(Y, ld(Y, Y))))
0.40/0.62	= { by lemma 15 }
0.40/0.62	  mult(mult(X, ld(X, Y)), ld(Y, Y))
0.40/0.62	= { by lemma 15 }
0.40/0.62	  mult(ld(X, ?), ld(ld(X, ?), mult(Y, ld(Y, Y))))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.62	
0.40/0.62	Lemma 17: mult(ld(X, ?), ld(ld(X, ?), Y)) = mult(X, ld(X, Y)).
0.40/0.62	Proof:
0.40/0.62	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.62	= { by lemma 16 }
0.40/0.62	  mult(ld(X, mult(X, X)), ld(ld(X, mult(X, X)), Y))
0.40/0.62	= { by axiom 1 (f01) }
0.40/0.62	  mult(X, ld(ld(X, mult(X, X)), Y))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(X, ld(mult(X, ld(X, X)), Y))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(X, ld(X, Y))
0.40/0.62	
0.40/0.62	Lemma 18: mult(X, mult(X, ld(X, Y))) = mult(X, Y).
0.40/0.62	Proof:
0.40/0.62	  mult(X, mult(X, ld(X, Y)))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(mult(X, ld(X, X)), mult(X, ld(X, Y)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(ld(X, mult(X, X)), mult(X, ld(X, Y)))
0.40/0.62	= { by lemma 17 }
0.40/0.62	  mult(ld(X, mult(X, X)), mult(ld(X, ?), ld(ld(X, ?), Y)))
0.40/0.62	= { by lemma 16 }
0.40/0.62	  mult(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), ld(ld(X, mult(X, X)), Y)))
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(ld(X, mult(X, X)), ld(ld(X, mult(X, X)), mult(ld(X, mult(X, X)), Y)))
0.40/0.62	= { by lemma 15 }
0.40/0.62	  mult(mult(X, ld(X, ld(X, mult(X, X)))), Y)
0.40/0.62	= { by axiom 1 (f01) }
0.40/0.62	  mult(mult(X, ld(X, X)), Y)
0.40/0.62	= { by lemma 9 }
0.40/0.62	  mult(X, Y)
0.40/0.62	
0.40/0.62	Lemma 19: mult(rd(X, Y), Y) = mult(X, ld(Y, Y)).
0.40/0.62	Proof:
0.40/0.62	  mult(rd(X, Y), Y)
0.40/0.62	= { by lemma 14 }
0.40/0.62	  mult(X, mult(X, ld(X, ld(Y, Y))))
0.40/0.62	= { by lemma 18 }
0.40/0.62	  mult(X, ld(Y, Y))
0.40/0.62	
0.40/0.62	Lemma 20: mult(X, mult(rd(Y, rd(Z, W)), rd(Z, W))) = mult(X, mult(rd(Y, W), W)).
0.40/0.62	Proof:
0.40/0.62	  mult(X, mult(rd(Y, rd(Z, W)), rd(Z, W)))
0.40/0.62	= { by lemma 13 }
0.40/0.62	  mult(rd(mult(X, Y), rd(Z, W)), rd(Z, W))
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W))
0.40/0.62	= { by axiom 4 (f06) }
0.40/0.62	  mult(X, rd(mult(Y, W), W))
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  mult(X, mult(rd(Y, W), W))
0.40/0.62	
0.40/0.62	Lemma 21: mult(ld(X, X), mult(rd(X, Y), Y)) = mult(rd(X, Y), Y).
0.40/0.62	Proof:
0.40/0.62	  mult(ld(X, X), mult(rd(X, Y), Y))
0.40/0.62	= { by lemma 11 }
0.40/0.62	  mult(rd(X, X), mult(rd(X, Y), Y))
0.40/0.62	= { by lemma 13 }
0.40/0.62	  mult(rd(mult(rd(X, X), X), Y), Y)
0.40/0.62	= { by lemma 8 }
0.40/0.62	  mult(rd(X, Y), Y)
0.40/0.62	
0.40/0.62	Lemma 22: mult(rd(X, rd(Y, Z)), rd(Y, Z)) = mult(rd(X, Z), Z).
0.40/0.62	Proof:
0.40/0.62	  mult(rd(X, rd(Y, Z)), rd(Y, Z))
0.40/0.62	= { by lemma 21 }
0.40/0.62	  mult(ld(X, X), mult(rd(X, rd(Y, Z)), rd(Y, Z)))
0.40/0.62	= { by lemma 20 }
0.40/0.62	  mult(ld(X, X), mult(rd(X, Z), Z))
0.40/0.62	= { by lemma 21 }
0.40/0.62	  mult(rd(X, Z), Z)
0.40/0.62	
0.40/0.62	Lemma 23: mult(rd(rd(X, Y), Y), Y) = rd(X, Y).
0.40/0.62	Proof:
0.40/0.62	  mult(rd(rd(X, Y), Y), Y)
0.40/0.62	= { by lemma 22 }
0.40/0.62	  mult(rd(rd(X, Y), rd(X, Y)), rd(X, Y))
0.40/0.62	= { by lemma 8 }
0.40/0.62	  rd(X, Y)
0.40/0.62	
0.40/0.62	Lemma 24: mult(mult(X, mult(Y, ld(W, W))), rd(Z, W)) = mult(mult(X, Y), rd(Z, W)).
0.40/0.62	Proof:
0.40/0.62	  mult(mult(X, mult(Y, ld(W, W))), rd(Z, W))
0.40/0.62	= { by lemma 19 }
0.40/0.62	  mult(mult(X, mult(rd(Y, W), W)), rd(Z, W))
0.40/0.62	= { by axiom 7 (f04) }
0.40/0.62	  mult(mult(X, rd(mult(Y, W), W)), rd(Z, W))
0.40/0.62	= { by axiom 4 (f06) }
0.40/0.62	  mult(rd(mult(mult(X, Y), rd(Z, W)), rd(Z, W)), rd(Z, W))
0.40/0.62	= { by lemma 13 }
0.40/0.62	  mult(mult(X, Y), mult(rd(rd(Z, W), rd(Z, W)), rd(Z, W)))
0.40/0.62	= { by lemma 20 }
0.40/0.62	  mult(mult(X, Y), mult(rd(rd(Z, W), W), W))
0.40/0.62	= { by lemma 23 }
0.40/0.62	  mult(mult(X, Y), rd(Z, W))
0.40/0.62	
0.40/0.62	Lemma 25: ld(ld(X, X), ld(X, X)) = ld(X, X).
0.40/0.62	Proof:
0.40/0.62	  ld(ld(X, X), ld(X, X))
0.40/0.62	= { by lemma 10 }
0.40/0.62	  ld(ld(X, X), mult(X, ld(X, ld(X, X))))
0.40/0.62	= { by lemma 12 }
0.40/0.62	  ld(ld(X, X), mult(rd(ld(X, X), X), X))
0.40/0.62	= { by lemma 14 }
0.40/0.62	  ld(ld(X, X), mult(ld(X, X), mult(ld(X, X), ld(ld(X, X), ld(X, X)))))
0.40/0.62	= { by lemma 9 }
0.40/0.62	  ld(ld(X, X), mult(ld(X, X), ld(X, X)))
0.40/0.62	= { by axiom 1 (f01) }
0.40/0.62	  ld(X, X)
0.40/0.62	
0.40/0.62	Lemma 26: mult(mult(X, ld(X, ld(Y, Y))), Y) = mult(ld(X, X), Y).
0.40/0.62	Proof:
0.40/0.62	  mult(mult(X, ld(X, ld(Y, Y))), Y)
0.40/0.62	= { by axiom 5 (f03) }
0.40/0.62	  mult(ld(X, mult(X, ld(Y, Y))), Y)
0.40/0.62	= { by axiom 2 (f07) }
0.40/0.62	  mult(rd(mult(rd(X, X), Y), Y), Y)
0.40/0.62	= { by lemma 13 }
0.40/0.62	  mult(rd(X, X), mult(rd(Y, Y), Y))
0.40/0.62	= { by lemma 11 }
0.40/0.62	  mult(ld(X, X), mult(rd(Y, Y), Y))
0.40/0.62	= { by lemma 8 }
0.40/0.63	  mult(ld(X, X), Y)
0.40/0.63	
0.40/0.63	Lemma 27: mult(ld(X, X), Y) = mult(X, ld(X, Y)).
0.40/0.63	Proof:
0.40/0.63	  mult(ld(X, X), Y)
0.40/0.63	= { by lemma 26 }
0.40/0.63	  mult(mult(X, ld(X, ld(Y, Y))), Y)
0.40/0.63	= { by lemma 11 }
0.40/0.63	  mult(mult(X, ld(X, rd(Y, Y))), Y)
0.40/0.63	= { by lemma 15 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), mult(rd(Y, Y), Y)))
0.40/0.63	= { by lemma 8 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(X, ld(X, Y))
0.40/0.63	
0.40/0.63	Lemma 28: rd(mult(X, ld(X, Y)), Y) = mult(X, ld(X, ld(Y, Y))).
0.40/0.63	Proof:
0.40/0.63	  rd(mult(X, ld(X, Y)), Y)
0.40/0.63	= { by lemma 27 }
0.40/0.63	  rd(mult(ld(X, X), Y), Y)
0.40/0.63	= { by axiom 7 (f04) }
0.40/0.63	  mult(rd(ld(X, X), Y), Y)
0.40/0.63	= { by lemma 12 }
0.40/0.63	  mult(X, ld(X, ld(Y, Y)))
0.40/0.63	
0.40/0.63	Lemma 29: mult(mult(X, ld(X, Y)), Z) = mult(X, ld(X, mult(Y, Z))).
0.40/0.63	Proof:
0.40/0.63	  mult(mult(X, ld(X, Y)), Z)
0.40/0.63	= { by lemma 15 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), mult(Y, Z)))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(X, ld(X, mult(Y, Z)))
0.40/0.63	
0.40/0.63	Lemma 30: mult(mult(rd(X, Y), Y), Y) = mult(X, Y).
0.40/0.63	Proof:
0.40/0.63	  mult(mult(rd(X, Y), Y), Y)
0.40/0.63	= { by axiom 7 (f04) }
0.40/0.63	  mult(rd(mult(X, Y), Y), Y)
0.40/0.63	= { by lemma 13 }
0.40/0.63	  mult(X, mult(rd(Y, Y), Y))
0.40/0.63	= { by lemma 8 }
0.40/0.63	  mult(X, Y)
0.40/0.63	
0.40/0.63	Lemma 31: ld(ld(X, X), mult(X, ld(X, Y))) = mult(X, ld(X, Y)).
0.40/0.63	Proof:
0.40/0.63	  ld(ld(X, X), mult(X, ld(X, Y)))
0.40/0.63	= { by lemma 27 }
0.40/0.63	  ld(ld(X, X), mult(ld(X, X), Y))
0.40/0.63	= { by axiom 5 (f03) }
0.40/0.63	  mult(ld(X, X), ld(ld(X, X), Y))
0.40/0.63	= { by lemma 16 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(X, ld(X, Y))
0.40/0.63	
0.40/0.63	Lemma 32: ld(ld(X, X), mult(X, Y)) = mult(X, Y).
0.40/0.63	Proof:
0.40/0.63	  ld(ld(X, X), mult(X, Y))
0.40/0.63	= { by lemma 18 }
0.40/0.63	  ld(ld(X, X), mult(X, mult(X, ld(X, Y))))
0.40/0.63	= { by axiom 5 (f03) }
0.40/0.63	  ld(ld(X, X), mult(X, ld(X, mult(X, Y))))
0.40/0.63	= { by lemma 31 }
0.40/0.63	  mult(X, ld(X, mult(X, Y)))
0.40/0.63	= { by axiom 5 (f03) }
0.40/0.63	  mult(X, mult(X, ld(X, Y)))
0.40/0.63	= { by lemma 18 }
0.40/0.63	  mult(X, Y)
0.40/0.63	
0.40/0.63	Lemma 33: mult(mult(X, Z), ld(mult(X, Z), Y)) = mult(X, ld(X, Y)).
0.40/0.63	Proof:
0.40/0.63	  mult(mult(X, Z), ld(mult(X, Z), Y))
0.40/0.63	= { by lemma 32 }
0.40/0.63	  mult(ld(ld(X, X), mult(X, Z)), ld(mult(X, Z), Y))
0.40/0.63	= { by lemma 32 }
0.40/0.63	  mult(ld(ld(X, X), mult(X, Z)), ld(ld(ld(X, X), mult(X, Z)), Y))
0.40/0.63	= { by lemma 16 }
0.40/0.63	  mult(ld(ld(X, X), ?), ld(ld(ld(X, X), ?), Y))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(ld(X, X), ld(ld(X, X), Y))
0.40/0.63	= { by lemma 16 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(X, ld(X, Y))
0.40/0.63	
0.40/0.63	Lemma 34: ld(mult(X, ld(Y, Y)), mult(X, Y)) = mult(X, ld(X, Y)).
0.40/0.63	Proof:
0.40/0.63	  ld(mult(X, ld(Y, Y)), mult(X, Y))
0.40/0.63	= { by lemma 19 }
0.40/0.63	  ld(mult(rd(X, Y), Y), mult(X, Y))
0.40/0.63	= { by lemma 30 }
0.40/0.63	  ld(mult(rd(X, Y), Y), mult(mult(rd(X, Y), Y), Y))
0.40/0.63	= { by axiom 5 (f03) }
0.40/0.63	  mult(mult(rd(X, Y), Y), ld(mult(rd(X, Y), Y), Y))
0.40/0.63	= { by lemma 33 }
0.40/0.63	  mult(mult(mult(rd(X, Y), Y), Y), ld(mult(mult(rd(X, Y), Y), Y), Y))
0.40/0.63	= { by lemma 30 }
0.40/0.63	  mult(mult(X, Y), ld(mult(mult(rd(X, Y), Y), Y), Y))
0.40/0.63	= { by lemma 30 }
0.40/0.63	  mult(mult(X, Y), ld(mult(X, Y), Y))
0.40/0.63	= { by lemma 33 }
0.40/0.63	  mult(X, ld(X, Y))
0.40/0.63	
0.40/0.63	Lemma 35: mult(X, ld(X, mult(Z, ld(mult(X, ld(X, Z)), Y)))) = mult(X, ld(X, Y)).
0.40/0.63	Proof:
0.40/0.63	  mult(X, ld(X, mult(Z, ld(mult(X, ld(X, Z)), Y))))
0.40/0.63	= { by lemma 31 }
0.40/0.63	  mult(X, ld(X, mult(Z, ld(ld(ld(X, X), mult(X, ld(X, Z))), Y))))
0.40/0.63	= { by lemma 29 }
0.40/0.63	  mult(mult(X, ld(X, Z)), ld(ld(ld(X, X), mult(X, ld(X, Z))), Y))
0.40/0.63	= { by lemma 31 }
0.40/0.63	  mult(ld(ld(X, X), mult(X, ld(X, Z))), ld(ld(ld(X, X), mult(X, ld(X, Z))), Y))
0.40/0.63	= { by lemma 16 }
0.40/0.63	  mult(ld(ld(X, X), ?), ld(ld(ld(X, X), ?), Y))
0.40/0.63	= { by lemma 17 }
0.40/0.63	  mult(ld(X, X), ld(ld(X, X), Y))
0.40/0.63	= { by lemma 16 }
0.40/0.63	  mult(ld(X, ?), ld(ld(X, ?), Y))
0.40/0.63	= { by lemma 17 }
0.46/0.63	  mult(X, ld(X, Y))
0.46/0.63	
0.46/0.63	Lemma 36: ld(mult(X, ld(X, Y)), mult(X, ld(X, Y))) = mult(X, ld(X, ld(Y, Y))).
0.46/0.63	Proof:
0.46/0.63	  ld(mult(X, ld(X, Y)), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 27 }
0.46/0.63	  ld(mult(ld(X, X), Y), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 26 }
0.46/0.63	  ld(mult(mult(X, ld(X, ld(Y, Y))), Y), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 28 }
0.46/0.63	  ld(mult(rd(mult(X, ld(X, Y)), Y), Y), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 13 }
0.46/0.63	  ld(mult(X, mult(rd(ld(X, Y), Y), Y)), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  ld(mult(X, mult(ld(X, Y), ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 25 }
0.46/0.63	  ld(mult(X, mult(ld(X, Y), ld(ld(Y, Y), ld(Y, Y)))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  ld(mult(X, mult(rd(ld(X, Y), ld(Y, Y)), ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by axiom 7 (f04) }
0.46/0.63	  ld(mult(X, rd(mult(ld(X, Y), ld(Y, Y)), ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by axiom 4 (f06) }
0.46/0.63	  ld(rd(mult(mult(X, ld(X, Y)), rd(?, ld(Y, Y))), rd(?, ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 27 }
0.46/0.63	  ld(rd(mult(mult(ld(X, X), Y), rd(?, ld(Y, Y))), rd(?, ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by axiom 4 (f06) }
0.46/0.63	  ld(mult(ld(X, X), rd(mult(Y, ld(Y, Y)), ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 27 }
0.46/0.63	  ld(mult(X, ld(X, rd(mult(Y, ld(Y, Y)), ld(Y, Y)))), mult(X, ld(X, Y)))
0.46/0.63	= { by axiom 7 (f04) }
0.46/0.63	  ld(mult(X, ld(X, mult(rd(Y, ld(Y, Y)), ld(Y, Y)))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  ld(mult(X, ld(X, mult(Y, ld(ld(Y, Y), ld(Y, Y))))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 29 }
0.46/0.63	  ld(mult(mult(X, ld(X, Y)), ld(ld(Y, Y), ld(Y, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 17 }
0.46/0.63	  ld(mult(mult(X, ld(X, Y)), ld(ld(Y, Y), ld(Y, Y))), mult(ld(X, ?), ld(ld(X, ?), Y)))
0.46/0.63	= { by lemma 9 }
0.46/0.63	  ld(mult(mult(X, ld(X, Y)), ld(ld(Y, Y), ld(Y, Y))), mult(ld(X, ?), ld(ld(X, ?), mult(Y, ld(Y, Y)))))
0.46/0.63	= { by lemma 15 }
0.46/0.63	  ld(mult(mult(X, ld(X, Y)), ld(ld(Y, Y), ld(Y, Y))), mult(mult(X, ld(X, Y)), ld(Y, Y)))
0.46/0.63	= { by lemma 34 }
0.46/0.63	  mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), ld(Y, Y)))
0.46/0.63	= { by lemma 29 }
0.46/0.63	  mult(X, ld(X, mult(Y, ld(mult(X, ld(X, Y)), ld(Y, Y)))))
0.46/0.63	= { by lemma 35 }
0.46/0.63	  mult(X, ld(X, ld(Y, Y)))
0.46/0.63	
0.46/0.63	Lemma 37: rd(mult(X, Y), mult(X, ld(X, Y))) = mult(X, ld(Y, Y)).
0.46/0.63	Proof:
0.46/0.63	  rd(mult(X, Y), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 18 }
0.46/0.63	  rd(mult(X, mult(X, ld(X, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by axiom 7 (f04) }
0.46/0.63	  mult(rd(X, mult(X, ld(X, Y))), mult(X, ld(X, Y)))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(X, ld(mult(X, ld(X, Y)), mult(X, ld(X, Y))))
0.46/0.63	= { by lemma 36 }
0.46/0.63	  mult(X, mult(X, ld(X, ld(Y, Y))))
0.46/0.63	= { by lemma 14 }
0.46/0.63	  mult(rd(X, Y), Y)
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(X, ld(Y, Y))
0.46/0.63	
0.46/0.63	Lemma 38: mult(X, mult(Y, ld(Y, ld(Z, Z)))) = mult(X, ld(Z, Z)).
0.46/0.63	Proof:
0.46/0.63	  mult(X, mult(Y, ld(Y, ld(Z, Z))))
0.46/0.63	= { by lemma 36 }
0.46/0.63	  mult(X, ld(mult(Y, ld(Y, Z)), mult(Y, ld(Y, Z))))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(rd(X, mult(Y, ld(Y, Z))), mult(Y, ld(Y, Z)))
0.46/0.63	= { by lemma 22 }
0.46/0.63	  mult(rd(X, rd(mult(Y, Z), mult(Y, ld(Y, Z)))), rd(mult(Y, Z), mult(Y, ld(Y, Z))))
0.46/0.63	= { by lemma 37 }
0.46/0.63	  mult(rd(X, mult(Y, ld(Z, Z))), rd(mult(Y, Z), mult(Y, ld(Y, Z))))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(rd(X, mult(rd(Y, Z), Z)), rd(mult(Y, Z), mult(Y, ld(Y, Z))))
0.46/0.63	= { by axiom 7 (f04) }
0.46/0.63	  mult(rd(X, rd(mult(Y, Z), Z)), rd(mult(Y, Z), mult(Y, ld(Y, Z))))
0.46/0.63	= { by lemma 37 }
0.46/0.63	  mult(rd(X, rd(mult(Y, Z), Z)), mult(Y, ld(Z, Z)))
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(rd(X, rd(mult(Y, Z), Z)), mult(rd(Y, Z), Z))
0.46/0.63	= { by axiom 7 (f04) }
0.46/0.63	  mult(rd(X, rd(mult(Y, Z), Z)), rd(mult(Y, Z), Z))
0.46/0.63	= { by lemma 22 }
0.46/0.63	  mult(rd(X, Z), Z)
0.46/0.63	= { by lemma 19 }
0.46/0.63	  mult(X, ld(Z, Z))
0.46/0.63	
0.46/0.63	Lemma 39: mult(X, ld(X, ld(X, Y))) = ld(X, Y).
0.46/0.63	Proof:
0.46/0.63	  mult(X, ld(X, ld(X, Y)))
0.46/0.63	= { by lemma 17 }
0.46/0.63	  mult(ld(X, ?), ld(ld(X, ?), ld(X, Y)))
0.46/0.63	= { by lemma 16 }
0.46/0.63	  mult(ld(X, Y), ld(ld(X, Y), ld(X, Y)))
0.46/0.63	= { by lemma 9 }
0.46/0.63	  ld(X, Y)
0.46/0.63	
0.46/0.63	Lemma 40: mult(X, ld(X, ld(ld(X, Y), ld(X, Y)))) = ld(ld(X, Y), ld(X, Y)).
0.46/0.63	Proof:
0.46/0.63	  mult(X, ld(X, ld(ld(X, Y), ld(X, Y))))
0.46/0.63	= { by lemma 28 }
0.46/0.63	  rd(mult(X, ld(X, ld(X, Y))), ld(X, Y))
0.46/0.63	= { by lemma 39 }
0.46/0.63	  rd(ld(X, Y), ld(X, Y))
0.46/0.63	= { by lemma 11 }
0.46/0.63	  ld(ld(X, Y), ld(X, Y))
0.46/0.63	
0.46/0.63	Lemma 41: mult(X, ld(X, ld(ld(X, X), Y))) = mult(X, ld(X, Y)).
0.46/0.63	Proof:
0.46/0.63	  mult(X, ld(X, ld(ld(X, X), Y)))
0.46/0.63	= { by lemma 18 }
0.46/0.63	  mult(X, mult(X, ld(X, ld(X, ld(ld(X, X), Y)))))
0.46/0.63	= { by axiom 5 (f03) }
0.46/0.63	  mult(X, ld(X, mult(X, ld(X, ld(ld(X, X), Y)))))
0.46/0.63	= { by lemma 27 }
0.46/0.63	  mult(ld(X, X), mult(X, ld(X, ld(ld(X, X), Y))))
0.46/0.63	= { by lemma 27 }
0.46/0.63	  mult(ld(X, X), mult(ld(X, X), ld(ld(X, X), Y)))
0.46/0.63	= { by lemma 18 }
0.46/0.63	  mult(ld(X, X), Y)
0.46/0.63	= { by lemma 27 }
0.46/0.63	  mult(X, ld(X, Y))
0.46/0.63	
0.46/0.64	Lemma 42: ld(ld(X, X), Y) = mult(X, ld(X, Y)).
0.46/0.64	Proof:
0.46/0.64	  ld(ld(X, X), Y)
0.46/0.64	= { by lemma 39 }
0.46/0.64	  mult(ld(X, X), ld(ld(X, X), ld(ld(X, X), Y)))
0.46/0.64	= { by lemma 27 }
0.46/0.64	  mult(X, ld(X, ld(ld(X, X), ld(ld(X, X), Y))))
0.46/0.64	= { by lemma 41 }
0.46/0.64	  mult(X, ld(X, ld(ld(X, X), Y)))
0.46/0.64	= { by lemma 41 }
0.46/0.64	  mult(X, ld(X, Y))
0.46/0.64	
0.46/0.64	Lemma 43: mult(X, mult(Y, ld(Y, Z))) = mult(X, Z).
0.46/0.64	Proof:
0.46/0.64	  mult(X, mult(Y, ld(Y, Z)))
0.46/0.64	= { by lemma 18 }
0.46/0.64	  mult(X, mult(X, ld(X, mult(Y, ld(Y, Z)))))
0.46/0.64	= { by lemma 27 }
0.46/0.64	  mult(X, mult(X, ld(X, mult(ld(Y, Y), Z))))
0.46/0.64	= { by lemma 29 }
0.46/0.64	  mult(X, mult(mult(X, ld(X, ld(Y, Y))), Z))
0.46/0.64	= { by lemma 36 }
0.46/0.64	  mult(X, mult(ld(mult(X, ld(X, Y)), mult(X, ld(X, Y))), Z))
0.46/0.64	= { by lemma 27 }
0.46/0.64	  mult(X, mult(mult(X, ld(X, Y)), ld(mult(X, ld(X, Y)), Z)))
0.46/0.64	= { by lemma 29 }
0.46/0.64	  mult(X, mult(X, ld(X, mult(Y, ld(mult(X, ld(X, Y)), Z)))))
0.46/0.64	= { by lemma 35 }
0.46/0.64	  mult(X, mult(X, ld(X, Z)))
0.46/0.64	= { by lemma 18 }
0.56/0.73	  mult(X, Z)
0.56/0.73	
0.56/0.73	Goal 1 (goals): tuple(mult(rd(mult(sK3_goals_X3, sK2_goals_X4), sK2_goals_X4), sK1_goals_X5), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5)))) = tuple(mult(sK3_goals_X3, sK1_goals_X5), mult(sK6_goals_X3, sK4_goals_X5)).
0.56/0.73	Proof:
0.56/0.73	  tuple(mult(rd(mult(sK3_goals_X3, sK2_goals_X4), sK2_goals_X4), sK1_goals_X5), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 7 (f04) }
0.56/0.73	  tuple(mult(mult(rd(sK3_goals_X3, sK2_goals_X4), sK2_goals_X4), sK1_goals_X5), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(sK2_goals_X4, sK2_goals_X4)), sK1_goals_X5), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 3 (f02) }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(sK2_goals_X4, sK2_goals_X4)), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 24 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(ld(sK2_goals_X4, sK2_goals_X4), ld(sK1_goals_X5, sK1_goals_X5))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(rd(ld(sK2_goals_X4, sK2_goals_X4), sK1_goals_X5), sK1_goals_X5)), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 22 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(rd(ld(sK2_goals_X4, sK2_goals_X4), rd(sK1_goals_X5, sK1_goals_X5)), rd(sK1_goals_X5, sK1_goals_X5))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 11 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(rd(ld(sK2_goals_X4, sK2_goals_X4), ld(sK1_goals_X5, sK1_goals_X5)), rd(sK1_goals_X5, sK1_goals_X5))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 11 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(rd(ld(sK2_goals_X4, sK2_goals_X4), ld(sK1_goals_X5, sK1_goals_X5)), ld(sK1_goals_X5, sK1_goals_X5))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 12 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(sK2_goals_X4, ld(sK2_goals_X4, ld(ld(sK1_goals_X5, sK1_goals_X5), ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 38 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(ld(sK1_goals_X5, sK1_goals_X5), ld(sK1_goals_X5, sK1_goals_X5))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 40 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 36 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))), mult(sK1_goals_X5, ld(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 5 (f03) }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(ld(sK1_goals_X5, mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))), mult(sK1_goals_X5, ld(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 42 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK1_goals_X5, ld(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 5 (f03) }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 42 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 40 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 33 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 34 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(rd(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 13 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, mult(rd(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 18 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 41 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 18 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, mult(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 9 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 41 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)), mult(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)), mult(rd(mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 7 (f04) }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)), mult(mult(rd(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))), ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 30 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)), mult(sK1_goals_X5, ld(sK1_goals_X5, ld(ld(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5))))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 41 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)), mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 36 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, mult(sK1_goals_X5, ld(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5)))), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 38 }
0.56/0.73	  tuple(mult(mult(sK3_goals_X3, ld(sK1_goals_X5, sK1_goals_X5)), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(mult(rd(sK3_goals_X3, sK1_goals_X5), sK1_goals_X5), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 22 }
0.56/0.73	  tuple(mult(mult(rd(sK3_goals_X3, rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 30 }
0.56/0.73	  tuple(mult(sK3_goals_X3, rd(mult(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 7 (f04) }
0.56/0.73	  tuple(mult(sK3_goals_X3, mult(rd(sK1_goals_X5, sK1_goals_X5), sK1_goals_X5)), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 19 }
0.56/0.73	  tuple(mult(sK3_goals_X3, mult(sK1_goals_X5, ld(sK1_goals_X5, sK1_goals_X5))), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 43 }
0.56/0.73	  tuple(mult(sK3_goals_X3, sK1_goals_X5), mult(sK6_goals_X3, ld(sK5_goals_X4, mult(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by axiom 5 (f03) }
0.56/0.73	  tuple(mult(sK3_goals_X3, sK1_goals_X5), mult(sK6_goals_X3, mult(sK5_goals_X4, ld(sK5_goals_X4, sK4_goals_X5))))
0.56/0.73	= { by lemma 43 }
0.56/0.73	  tuple(mult(sK3_goals_X3, sK1_goals_X5), mult(sK6_goals_X3, sK4_goals_X5))
0.56/0.73	% SZS output end Proof
0.56/0.73	
0.56/0.73	RESULT: Theorem (the conjecture is true).
0.56/0.73	EOF