0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n018.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 09:19:06 EDT 2019
0.12/0.33	% CPUTime    : 
0.18/0.42	% SZS status Unsatisfiable
0.18/0.42	
0.18/0.42	% SZS output start Proof
0.18/0.42	Take the following subset of the input axioms:
0.18/0.42	  fof(additive_inverse, axiom, ![X]: add(X, inverse(X))=n1).
0.18/0.42	  fof(multiply_add, axiom, ![X, Y]: Y=multiply(add(X, Y), Y)).
0.18/0.42	  fof(multiply_add_property, axiom, ![X, Y, Z]: multiply(X, add(Y, Z))=add(multiply(Y, X), multiply(Z, X))).
0.18/0.42	  fof(pixley1, axiom, ![X, Y]: pixley(X, X, Y)=Y).
0.18/0.42	  fof(pixley2, axiom, ![X, Y]: pixley(X, Y, Y)=X).
0.18/0.42	  fof(pixley3, axiom, ![X, Y]: X=pixley(X, Y, X)).
0.18/0.42	  fof(pixley_defn, axiom, ![X, Y, Z]: pixley(X, Y, Z)=add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z)))).
0.18/0.42	  fof(prove_equal_identity, negated_conjecture, multiply(b, inverse(b))!=multiply(a, inverse(a))).
0.18/0.42	
0.18/0.42	Now clausify the problem and encode Horn clauses using encoding 3 of
0.18/0.42	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.18/0.42	We repeatedly replace C & s=t => u=v by the two clauses:
0.18/0.42	  fresh(y, y, x1...xn) = u
0.18/0.42	  C => fresh(s, t, x1...xn) = v
0.18/0.42	where fresh is a fresh function symbol and x1..xn are the free
0.18/0.42	variables of u and v.
0.18/0.42	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.18/0.42	input problem has no model of domain size 1).
0.18/0.42	
0.18/0.42	The encoding turns the above axioms into the following unit equations and goals:
0.18/0.42	
0.18/0.42	Axiom 1 (pixley1): pixley(X, X, Y) = Y.
0.18/0.42	Axiom 2 (pixley2): pixley(X, Y, Y) = X.
0.18/0.42	Axiom 3 (pixley_defn): pixley(X, Y, Z) = add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z))).
0.18/0.42	Axiom 4 (multiply_add_property): multiply(X, add(Y, Z)) = add(multiply(Y, X), multiply(Z, X)).
0.18/0.42	Axiom 5 (additive_inverse): add(X, inverse(X)) = n1.
0.18/0.42	Axiom 6 (multiply_add): X = multiply(add(Y, X), X).
0.18/0.44	Axiom 7 (pixley3): X = pixley(X, Y, X).
0.18/0.44	
0.18/0.44	Lemma 8: multiply(n1, inverse(X)) = inverse(X).
0.18/0.44	Proof:
0.18/0.44	  multiply(n1, inverse(X))
0.18/0.44	= { by axiom 5 (additive_inverse) }
0.18/0.44	  multiply(add(X, inverse(X)), inverse(X))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  inverse(X)
0.18/0.44	
0.18/0.44	Lemma 9: multiply(X, add(Y, add(Z, X))) = add(multiply(Y, X), X).
0.18/0.44	Proof:
0.18/0.44	  multiply(X, add(Y, add(Z, X)))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(multiply(Y, X), multiply(add(Z, X), X))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(multiply(Y, X), X)
0.18/0.44	
0.18/0.44	Lemma 10: add(multiply(X, inverse(Y)), multiply(Z, add(X, inverse(Y)))) = pixley(X, Y, Z).
0.18/0.44	Proof:
0.18/0.44	  add(multiply(X, inverse(Y)), multiply(Z, add(X, inverse(Y))))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(multiply(X, inverse(Y)), add(multiply(X, Z), multiply(inverse(Y), Z)))
0.18/0.44	= { by axiom 3 (pixley_defn) }
0.18/0.44	  pixley(X, Y, Z)
0.18/0.44	
0.18/0.44	Lemma 11: add(multiply(Y, inverse(Y)), multiply(X, n1)) = X.
0.18/0.44	Proof:
0.18/0.44	  add(multiply(Y, inverse(Y)), multiply(X, n1))
0.18/0.44	= { by axiom 5 (additive_inverse) }
0.18/0.44	  add(multiply(Y, inverse(Y)), multiply(X, add(Y, inverse(Y))))
0.18/0.44	= { by lemma 10 }
0.18/0.44	  pixley(Y, Y, X)
0.18/0.44	= { by axiom 1 (pixley1) }
0.18/0.44	  X
0.18/0.44	
0.18/0.44	Lemma 12: add(multiply(X, multiply(Y, n1)), multiply(Y, n1)) = multiply(multiply(Y, n1), add(X, Y)).
0.18/0.44	Proof:
0.18/0.44	  add(multiply(X, multiply(Y, n1)), multiply(Y, n1))
0.18/0.44	= { by lemma 9 }
0.18/0.44	  multiply(multiply(Y, n1), add(X, add(multiply(?, inverse(?)), multiply(Y, n1))))
0.18/0.44	= { by lemma 11 }
0.18/0.44	  multiply(multiply(Y, n1), add(X, Y))
0.18/0.44	
0.18/0.44	Lemma 13: multiply(X, add(add(Y, X), Z)) = add(X, multiply(Z, X)).
0.18/0.44	Proof:
0.18/0.44	  multiply(X, add(add(Y, X), Z))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(multiply(add(Y, X), X), multiply(Z, X))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(X, multiply(Z, X))
0.18/0.44	
0.18/0.44	Lemma 14: multiply(inverse(X), add(n1, n1)) = add(inverse(X), inverse(X)).
0.18/0.44	Proof:
0.18/0.44	  multiply(inverse(X), add(n1, n1))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(multiply(n1, inverse(X)), multiply(n1, inverse(X)))
0.18/0.44	= { by lemma 8 }
0.18/0.44	  add(inverse(X), multiply(n1, inverse(X)))
0.18/0.44	= { by lemma 8 }
0.18/0.44	  add(inverse(X), inverse(X))
0.18/0.44	
0.18/0.44	Lemma 15: multiply(multiply(Y, add(Z, X)), multiply(X, Y)) = multiply(X, Y).
0.18/0.44	Proof:
0.18/0.44	  multiply(multiply(Y, add(Z, X)), multiply(X, Y))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  multiply(add(multiply(Z, Y), multiply(X, Y)), multiply(X, Y))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  multiply(X, Y)
0.18/0.44	
0.18/0.44	Lemma 16: add(inverse(n1), multiply(X, n1)) = X.
0.18/0.44	Proof:
0.18/0.44	  add(inverse(n1), multiply(X, n1))
0.18/0.44	= { by lemma 8 }
0.18/0.44	  add(multiply(n1, inverse(n1)), multiply(X, n1))
0.18/0.44	= { by axiom 5 (additive_inverse) }
0.18/0.44	  add(multiply(n1, inverse(n1)), multiply(X, add(n1, inverse(n1))))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(multiply(n1, inverse(n1)), add(multiply(n1, X), multiply(inverse(n1), X)))
0.18/0.44	= { by axiom 3 (pixley_defn) }
0.18/0.44	  pixley(n1, n1, X)
0.18/0.44	= { by axiom 1 (pixley1) }
0.18/0.44	  X
0.18/0.44	
0.18/0.44	Lemma 17: add(X, n1) = add(?, n1).
0.18/0.44	Proof:
0.18/0.44	  add(X, n1)
0.18/0.44	= { by lemma 16 }
0.18/0.44	  add(inverse(n1), multiply(add(X, n1), n1))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(inverse(n1), n1)
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(inverse(n1), multiply(add(?, n1), n1))
0.18/0.44	= { by lemma 16 }
0.18/0.44	  add(?, n1)
0.18/0.44	
0.18/0.44	Lemma 18: multiply(n1, add(inverse(X), inverse(X))) = multiply(inverse(X), add(?, n1)).
0.18/0.44	Proof:
0.18/0.44	  multiply(n1, add(inverse(X), inverse(X)))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  multiply(multiply(add(n1, n1), n1), add(inverse(X), inverse(X)))
0.18/0.44	= { by axiom 5 (additive_inverse) }
0.18/0.44	  multiply(multiply(add(n1, n1), add(X, inverse(X))), add(inverse(X), inverse(X)))
0.18/0.44	= { by lemma 14 }
0.18/0.44	  multiply(multiply(add(n1, n1), add(X, inverse(X))), multiply(inverse(X), add(n1, n1)))
0.18/0.44	= { by lemma 15 }
0.18/0.44	  multiply(inverse(X), add(n1, n1))
0.18/0.44	= { by lemma 17 }
0.18/0.44	  multiply(inverse(X), add(?, n1))
0.18/0.44	
0.18/0.44	Lemma 19: multiply(inverse(X), add(?, n1)) = add(inverse(X), inverse(X)).
0.18/0.44	Proof:
0.18/0.44	  multiply(inverse(X), add(?, n1))
0.18/0.44	= { by lemma 18 }
0.18/0.44	  multiply(n1, add(inverse(X), inverse(X)))
0.18/0.44	= { by axiom 5 (additive_inverse) }
0.18/0.44	  multiply(add(X, inverse(X)), add(inverse(X), inverse(X)))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  multiply(multiply(add(add(?, inverse(X)), add(X, inverse(X))), add(X, inverse(X))), add(inverse(X), inverse(X)))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  multiply(multiply(add(add(?, inverse(X)), add(X, inverse(X))), add(X, inverse(X))), add(multiply(add(?, inverse(X)), inverse(X)), inverse(X)))
0.18/0.44	= { by lemma 9 }
0.18/0.44	  multiply(multiply(add(add(?, inverse(X)), add(X, inverse(X))), add(X, inverse(X))), multiply(inverse(X), add(add(?, inverse(X)), add(X, inverse(X)))))
0.18/0.44	= { by lemma 15 }
0.18/0.44	  multiply(inverse(X), add(add(?, inverse(X)), add(X, inverse(X))))
0.18/0.44	= { by lemma 9 }
0.18/0.44	  add(multiply(add(?, inverse(X)), inverse(X)), inverse(X))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(inverse(X), inverse(X))
0.18/0.44	
0.18/0.44	Lemma 20: add(inverse(n1), add(inverse(X), inverse(X))) = multiply(inverse(X), n1).
0.18/0.44	Proof:
0.18/0.44	  add(inverse(n1), add(inverse(X), inverse(X)))
0.18/0.44	= { by lemma 19 }
0.18/0.44	  add(inverse(n1), multiply(inverse(X), add(?, n1)))
0.18/0.44	= { by lemma 18 }
0.18/0.44	  add(inverse(n1), multiply(n1, add(inverse(X), inverse(X))))
0.18/0.44	= { by axiom 4 (multiply_add_property) }
0.18/0.44	  add(inverse(n1), add(multiply(inverse(X), n1), multiply(inverse(X), n1)))
0.18/0.44	= { by axiom 6 (multiply_add) }
0.18/0.44	  add(inverse(n1), add(multiply(add(?, multiply(inverse(X), n1)), multiply(inverse(X), n1)), multiply(inverse(X), n1)))
0.18/0.44	= { by lemma 12 }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), add(add(?, multiply(inverse(X), n1)), inverse(X))))
0.18/0.44	= { by lemma 13 }
0.18/0.44	  add(inverse(n1), add(multiply(inverse(X), n1), multiply(inverse(X), multiply(inverse(X), n1))))
0.18/0.44	= { by lemma 13 }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), add(add(multiply(?, inverse(?)), multiply(inverse(X), n1)), inverse(X))))
0.18/0.44	= { by lemma 11 }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), add(inverse(X), inverse(X))))
0.18/0.44	= { by lemma 12 }
0.18/0.44	  add(inverse(n1), add(multiply(inverse(X), multiply(inverse(X), n1)), multiply(inverse(X), n1)))
0.18/0.44	= { by lemma 8 }
0.18/0.44	  add(inverse(n1), add(multiply(multiply(n1, inverse(X)), multiply(inverse(X), n1)), multiply(inverse(X), n1)))
0.18/0.44	= { by lemma 9 }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), add(multiply(n1, inverse(X)), add(multiply(n1, n1), multiply(inverse(X), n1)))))
0.18/0.44	= { by axiom 3 (pixley_defn) }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), pixley(n1, X, n1)))
0.18/0.44	= { by axiom 7 (pixley3) }
0.18/0.44	  add(inverse(n1), multiply(multiply(inverse(X), n1), n1))
0.18/0.44	= { by lemma 16 }
0.18/0.45	  multiply(inverse(X), n1)
0.18/0.45	
0.18/0.45	Lemma 21: add(inverse(n1), n1) = add(?, n1).
0.18/0.45	Proof:
0.18/0.45	  add(inverse(n1), n1)
0.18/0.45	= { by axiom 6 (multiply_add) }
0.18/0.45	  add(inverse(n1), multiply(add(?, n1), n1))
0.18/0.45	= { by lemma 16 }
0.18/0.45	  add(?, n1)
0.18/0.45	
0.18/0.45	Lemma 22: add(multiply(Y, inverse(X)), inverse(X)) = multiply(inverse(X), add(Y, n1)).
0.18/0.45	Proof:
0.18/0.45	  add(multiply(Y, inverse(X)), inverse(X))
0.18/0.45	= { by lemma 8 }
0.18/0.45	  add(multiply(Y, inverse(X)), multiply(n1, inverse(X)))
0.18/0.45	= { by axiom 4 (multiply_add_property) }
0.18/0.45	  multiply(inverse(X), add(Y, n1))
0.18/0.45	
0.18/0.45	Lemma 23: multiply(inverse(X), add(?, n1)) = multiply(inverse(X), n1).
0.18/0.45	Proof:
0.18/0.45	  multiply(inverse(X), add(?, n1))
0.18/0.45	= { by lemma 21 }
0.18/0.45	  multiply(inverse(X), add(inverse(n1), n1))
0.18/0.45	= { by lemma 22 }
0.18/0.45	  add(multiply(inverse(n1), inverse(X)), inverse(X))
0.18/0.45	= { by lemma 9 }
0.18/0.45	  multiply(inverse(X), add(inverse(n1), add(inverse(X), inverse(X))))
0.18/0.45	= { by lemma 16 }
0.18/0.45	  multiply(add(inverse(n1), multiply(inverse(X), n1)), add(inverse(n1), add(inverse(X), inverse(X))))
0.18/0.45	= { by lemma 20 }
0.18/0.45	  multiply(add(inverse(n1), multiply(inverse(X), n1)), multiply(inverse(X), n1))
0.18/0.45	= { by axiom 6 (multiply_add) }
0.18/0.45	  multiply(inverse(X), n1)
0.18/0.45	
0.18/0.45	Lemma 24: add(inverse(X), inverse(X)) = multiply(inverse(X), n1).
0.18/0.45	Proof:
0.18/0.45	  add(inverse(X), inverse(X))
0.18/0.45	= { by lemma 19 }
0.18/0.45	  multiply(inverse(X), add(?, n1))
0.18/0.45	= { by lemma 23 }
0.18/0.45	  multiply(inverse(X), n1)
0.18/0.45	
0.18/0.45	Lemma 25: multiply(inverse(X), n1) = inverse(X).
0.18/0.45	Proof:
0.18/0.45	  multiply(inverse(X), n1)
0.18/0.45	= { by lemma 20 }
0.18/0.45	  add(inverse(n1), add(inverse(X), inverse(X)))
0.18/0.45	= { by lemma 24 }
0.18/0.45	  add(inverse(n1), multiply(inverse(X), n1))
0.18/0.45	= { by lemma 16 }
0.18/0.45	  inverse(X)
0.18/0.45	
0.18/0.45	Lemma 26: add(inverse(n1), inverse(X)) = inverse(X).
0.18/0.45	Proof:
0.18/0.45	  add(inverse(n1), inverse(X))
0.18/0.45	= { by lemma 25 }
0.18/0.45	  add(inverse(n1), multiply(inverse(X), n1))
0.18/0.45	= { by lemma 16 }
0.18/0.46	  inverse(X)
0.18/0.46	
0.18/0.46	Lemma 27: multiply(X, inverse(X)) = inverse(n1).
0.18/0.46	Proof:
0.18/0.46	  multiply(X, inverse(X))
0.18/0.46	= { by lemma 26 }
0.18/0.46	  multiply(X, add(inverse(n1), inverse(X)))
0.18/0.46	= { by axiom 4 (multiply_add_property) }
0.18/0.46	  add(multiply(inverse(n1), X), multiply(inverse(X), X))
0.18/0.46	= { by axiom 6 (multiply_add) }
0.18/0.46	  multiply(add(multiply(inverse(n1), inverse(X)), add(multiply(inverse(n1), X), multiply(inverse(X), X))), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by axiom 3 (pixley_defn) }
0.18/0.46	  multiply(pixley(inverse(n1), X, X), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by axiom 2 (pixley2) }
0.18/0.46	  multiply(inverse(n1), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by lemma 25 }
0.18/0.46	  multiply(multiply(inverse(n1), n1), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by lemma 24 }
0.18/0.46	  multiply(add(inverse(n1), inverse(n1)), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by lemma 14 }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(inverse(n1), X), multiply(inverse(X), X)))
0.18/0.46	= { by axiom 4 (multiply_add_property) }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), multiply(X, add(inverse(n1), inverse(X))))
0.18/0.46	= { by axiom 2 (pixley2) }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), pixley(multiply(X, add(inverse(n1), inverse(X))), n1, n1))
0.18/0.46	= { by lemma 10 }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(n1, add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by axiom 5 (additive_inverse) }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(add(inverse(n1), inverse(inverse(n1))), add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by lemma 26 }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(add(inverse(n1), add(inverse(n1), inverse(inverse(n1)))), add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by axiom 5 (additive_inverse) }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(add(inverse(n1), n1), add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by lemma 21 }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(add(?, n1), add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by lemma 17 }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(add(n1, n1), add(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)))))
0.18/0.46	= { by axiom 4 (multiply_add_property) }
0.18/0.46	  multiply(multiply(inverse(n1), add(n1, n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), add(multiply(multiply(X, add(inverse(n1), inverse(X))), add(n1, n1)), multiply(inverse(n1), add(n1, n1)))))
0.18/0.46	= { by lemma 9 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(inverse(n1), add(n1, n1))), multiply(inverse(n1), add(n1, n1)))
0.18/0.46	= { by lemma 17 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(inverse(n1), add(?, n1))), multiply(inverse(n1), add(n1, n1)))
0.18/0.46	= { by lemma 23 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), multiply(inverse(n1), n1)), multiply(inverse(n1), add(n1, n1)))
0.18/0.46	= { by lemma 25 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), inverse(n1)), multiply(inverse(n1), add(n1, n1)))
0.18/0.46	= { by lemma 17 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), inverse(n1)), multiply(inverse(n1), add(?, n1)))
0.18/0.46	= { by lemma 23 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), inverse(n1)), multiply(inverse(n1), n1))
0.18/0.46	= { by lemma 25 }
0.18/0.46	  add(multiply(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), inverse(n1)), inverse(n1))
0.18/0.46	= { by lemma 22 }
0.18/0.46	  multiply(inverse(n1), add(multiply(multiply(X, add(inverse(n1), inverse(X))), inverse(n1)), n1))
0.18/0.46	= { by lemma 17 }
0.18/0.46	  multiply(inverse(n1), add(?, n1))
0.18/0.46	= { by lemma 23 }
0.18/0.46	  multiply(inverse(n1), n1)
0.18/0.46	= { by lemma 25 }
0.18/0.46	  inverse(n1)
0.18/0.46	
0.18/0.46	Goal 1 (prove_equal_identity): multiply(b, inverse(b)) = multiply(a, inverse(a)).
0.18/0.46	Proof:
0.18/0.46	  multiply(b, inverse(b))
0.18/0.46	= { by lemma 27 }
0.18/0.46	  inverse(n1)
0.18/0.46	= { by lemma 27 }
0.18/0.46	  multiply(a, inverse(a))
0.18/0.46	% SZS output end Proof
0.18/0.46	
0.18/0.46	RESULT: Unsatisfiable (the axioms are contradictory).
0.18/0.46	EOF