0.08/0.15	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.08/0.15	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.14/0.37	% Computer   : n008.cluster.edu
0.14/0.37	% Model      : x86_64 x86_64
0.14/0.37	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.14/0.37	% Memory     : 8042.1875MB
0.14/0.37	% OS         : Linux 3.10.0-693.el7.x86_64
0.14/0.37	% CPULimit   : 180
0.14/0.37	% DateTime   : Thu Aug 29 10:54:38 EDT 2019
0.14/0.37	% CPUTime    : 
0.21/0.44	% SZS status Unsatisfiable
0.21/0.44	
0.21/0.44	% SZS output start Proof
0.21/0.44	Take the following subset of the input axioms:
0.21/0.44	  fof(identity, axiom, ![A]: identity=double_divide(A, inverse(A))).
0.21/0.44	  fof(inverse, axiom, ![A]: double_divide(A, identity)=inverse(A)).
0.21/0.44	  fof(multiply, axiom, ![A, B]: double_divide(double_divide(B, A), identity)=multiply(A, B)).
0.21/0.44	  fof(prove_these_axioms_3, negated_conjecture, multiply(a3, multiply(b3, c3))!=multiply(multiply(a3, b3), c3)).
0.21/0.44	  fof(single_axiom, axiom, ![A, B, C]: double_divide(double_divide(A, double_divide(double_divide(B, double_divide(A, C)), double_divide(identity, C))), double_divide(identity, identity))=B).
0.21/0.44	
0.21/0.44	Now clausify the problem and encode Horn clauses using encoding 3 of
0.21/0.44	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.21/0.44	We repeatedly replace C & s=t => u=v by the two clauses:
0.21/0.44	  fresh(y, y, x1...xn) = u
0.21/0.44	  C => fresh(s, t, x1...xn) = v
0.21/0.44	where fresh is a fresh function symbol and x1..xn are the free
0.21/0.44	variables of u and v.
0.21/0.44	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.21/0.44	input problem has no model of domain size 1).
0.21/0.44	
0.21/0.44	The encoding turns the above axioms into the following unit equations and goals:
0.21/0.44	
0.21/0.44	Axiom 1 (multiply): double_divide(double_divide(X, Y), identity) = multiply(Y, X).
0.21/0.44	Axiom 2 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(X, Z)), double_divide(identity, Z))), double_divide(identity, identity)) = Y.
0.21/0.44	Axiom 3 (inverse): double_divide(X, identity) = inverse(X).
0.21/0.44	Axiom 4 (identity): identity = double_divide(X, inverse(X)).
0.21/0.44	
0.21/0.44	Lemma 5: double_divide(double_divide(Y, double_divide(double_divide(X, inverse(Y)), inverse(identity))), inverse(identity)) = X.
0.21/0.44	Proof:
0.21/0.44	  double_divide(double_divide(Y, double_divide(double_divide(X, inverse(Y)), inverse(identity))), inverse(identity))
0.21/0.44	= { by axiom 3 (inverse) }
0.21/0.44	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, identity)), inverse(identity))), inverse(identity))
0.21/0.44	= { by axiom 3 (inverse) }
0.21/0.44	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, identity)), double_divide(identity, identity))), inverse(identity))
0.21/0.44	= { by axiom 3 (inverse) }
0.21/0.44	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, identity)), double_divide(identity, identity))), double_divide(identity, identity))
0.21/0.44	= { by axiom 2 (single_axiom) }
0.21/0.44	  X
0.21/0.44	
0.21/0.44	Lemma 6: double_divide(inverse(X), inverse(identity)) = X.
0.21/0.44	Proof:
0.21/0.44	  double_divide(inverse(X), inverse(identity))
0.21/0.44	= { by axiom 3 (inverse) }
0.21/0.44	  double_divide(double_divide(X, identity), inverse(identity))
0.21/0.44	= { by axiom 4 (identity) }
0.21/0.45	  double_divide(double_divide(X, double_divide(identity, inverse(identity))), inverse(identity))
0.21/0.45	= { by axiom 4 (identity) }
0.21/0.45	  double_divide(double_divide(X, double_divide(double_divide(X, inverse(X)), inverse(identity))), inverse(identity))
0.21/0.45	= { by lemma 5 }
0.21/0.45	  X
0.21/0.45	
0.21/0.45	Lemma 7: inverse(inverse(X)) = multiply(identity, X).
0.21/0.45	Proof:
0.21/0.45	  inverse(inverse(X))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  double_divide(inverse(X), identity)
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  double_divide(double_divide(X, identity), identity)
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  multiply(identity, X)
0.21/0.45	
0.21/0.45	Lemma 8: double_divide(multiply(identity, X), inverse(identity)) = inverse(X).
0.21/0.45	Proof:
0.21/0.45	  double_divide(multiply(identity, X), inverse(identity))
0.21/0.45	= { by lemma 7 }
0.21/0.45	  double_divide(inverse(inverse(X)), inverse(identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  inverse(X)
0.21/0.45	
0.21/0.45	Lemma 9: double_divide(double_divide(identity, X), inverse(identity)) = multiply(identity, X).
0.21/0.45	Proof:
0.21/0.45	  double_divide(double_divide(identity, X), inverse(identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  double_divide(double_divide(identity, double_divide(inverse(X), inverse(identity))), inverse(identity))
0.21/0.45	= { by lemma 8 }
0.21/0.45	  double_divide(double_divide(identity, double_divide(double_divide(multiply(identity, X), inverse(identity)), inverse(identity))), inverse(identity))
0.21/0.45	= { by lemma 5 }
0.21/0.45	  multiply(identity, X)
0.21/0.45	
0.21/0.45	Lemma 10: multiply(identity, identity) = identity.
0.21/0.45	Proof:
0.21/0.45	  multiply(identity, identity)
0.21/0.45	= { by lemma 9 }
0.21/0.45	  double_divide(double_divide(identity, identity), inverse(identity))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  double_divide(inverse(identity), inverse(identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  identity
0.21/0.45	
0.21/0.45	Lemma 11: multiply(identity, double_divide(X, Y)) = inverse(multiply(Y, X)).
0.21/0.45	Proof:
0.21/0.45	  multiply(identity, double_divide(X, Y))
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  double_divide(double_divide(double_divide(X, Y), identity), identity)
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  double_divide(multiply(Y, X), identity)
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  inverse(multiply(Y, X))
0.21/0.45	
0.21/0.45	Lemma 12: inverse(double_divide(X, Y)) = multiply(Y, X).
0.21/0.45	Proof:
0.21/0.45	  inverse(double_divide(X, Y))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  double_divide(double_divide(X, Y), identity)
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  multiply(Y, X)
0.21/0.45	
0.21/0.45	Lemma 13: inverse(identity) = identity.
0.21/0.45	Proof:
0.21/0.45	  inverse(identity)
0.21/0.45	= { by lemma 8 }
0.21/0.45	  double_divide(multiply(identity, identity), inverse(identity))
0.21/0.45	= { by lemma 10 }
0.21/0.45	  double_divide(identity, inverse(identity))
0.21/0.45	= { by axiom 4 (identity) }
0.21/0.45	  identity
0.21/0.45	
0.21/0.45	Lemma 14: multiply(identity, X) = X.
0.21/0.45	Proof:
0.21/0.45	  multiply(identity, X)
0.21/0.45	= { by lemma 7 }
0.21/0.45	  inverse(inverse(X))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  double_divide(inverse(X), identity)
0.21/0.45	= { by lemma 13 }
0.21/0.45	  double_divide(inverse(X), inverse(identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  X
0.21/0.45	
0.21/0.45	Lemma 15: double_divide(identity, X) = inverse(X).
0.21/0.45	Proof:
0.21/0.45	  double_divide(identity, X)
0.21/0.45	= { by lemma 5 }
0.21/0.45	  double_divide(double_divide(identity, double_divide(double_divide(double_divide(identity, X), inverse(identity)), inverse(identity))), inverse(identity))
0.21/0.45	= { by lemma 9 }
0.21/0.45	  double_divide(double_divide(identity, double_divide(multiply(identity, X), inverse(identity))), inverse(identity))
0.21/0.45	= { by lemma 9 }
0.21/0.45	  multiply(identity, double_divide(multiply(identity, X), inverse(identity)))
0.21/0.45	= { by lemma 11 }
0.21/0.45	  inverse(multiply(inverse(identity), multiply(identity, X)))
0.21/0.45	= { by lemma 12 }
0.21/0.45	  inverse(multiply(inverse(identity), inverse(double_divide(X, identity))))
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  inverse(double_divide(double_divide(inverse(double_divide(X, identity)), inverse(identity)), identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  inverse(double_divide(double_divide(X, identity), identity))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  inverse(inverse(double_divide(X, identity)))
0.21/0.45	= { by lemma 12 }
0.21/0.45	  inverse(multiply(identity, X))
0.21/0.45	= { by lemma 7 }
0.21/0.45	  inverse(inverse(inverse(X)))
0.21/0.45	= { by lemma 7 }
0.21/0.45	  multiply(identity, inverse(X))
0.21/0.45	= { by lemma 14 }
0.21/0.45	  inverse(X)
0.21/0.45	
0.21/0.45	Lemma 16: multiply(multiply(Y, X), inverse(Y)) = X.
0.21/0.45	Proof:
0.21/0.45	  multiply(multiply(Y, X), inverse(Y))
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  multiply(double_divide(double_divide(X, Y), identity), inverse(Y))
0.21/0.45	= { by lemma 10 }
0.21/0.45	  multiply(double_divide(double_divide(X, Y), multiply(identity, identity)), inverse(Y))
0.21/0.45	= { by axiom 1 (multiply) }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, Y), multiply(identity, identity))), identity)
0.21/0.45	= { by lemma 6 }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, double_divide(inverse(Y), inverse(identity))), multiply(identity, identity))), identity)
0.21/0.45	= { by lemma 7 }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, double_divide(inverse(Y), inverse(identity))), inverse(inverse(identity)))), identity)
0.21/0.45	= { by lemma 15 }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, double_divide(inverse(Y), inverse(identity))), double_divide(identity, inverse(identity)))), identity)
0.21/0.45	= { by lemma 13 }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, double_divide(inverse(Y), inverse(identity))), double_divide(identity, inverse(identity)))), inverse(identity))
0.21/0.45	= { by lemma 15 }
0.21/0.45	  double_divide(double_divide(inverse(Y), double_divide(double_divide(X, double_divide(inverse(Y), inverse(identity))), double_divide(identity, inverse(identity)))), double_divide(identity, identity))
0.21/0.45	= { by axiom 2 (single_axiom) }
0.21/0.45	  X
0.21/0.45	
0.21/0.45	Lemma 17: double_divide(multiply(Y, X), inverse(identity)) = double_divide(X, Y).
0.21/0.45	Proof:
0.21/0.45	  double_divide(multiply(Y, X), inverse(identity))
0.21/0.45	= { by lemma 12 }
0.21/0.45	  double_divide(inverse(double_divide(X, Y)), inverse(identity))
0.21/0.45	= { by lemma 6 }
0.21/0.45	  double_divide(X, Y)
0.21/0.45	
0.21/0.45	Lemma 18: multiply(Y, double_divide(Y, X)) = inverse(X).
0.21/0.45	Proof:
0.21/0.45	  multiply(Y, double_divide(Y, X))
0.21/0.45	= { by lemma 16 }
0.21/0.45	  multiply(multiply(multiply(X, Y), inverse(X)), double_divide(Y, X))
0.21/0.45	= { by lemma 17 }
0.21/0.45	  multiply(multiply(multiply(X, Y), inverse(X)), double_divide(multiply(X, Y), inverse(identity)))
0.21/0.45	= { by lemma 13 }
0.21/0.45	  multiply(multiply(multiply(X, Y), inverse(X)), double_divide(multiply(X, Y), identity))
0.21/0.45	= { by axiom 3 (inverse) }
0.21/0.45	  multiply(multiply(multiply(X, Y), inverse(X)), inverse(multiply(X, Y)))
0.21/0.45	= { by lemma 16 }
0.21/0.46	  inverse(X)
0.21/0.46	
0.21/0.46	Lemma 19: double_divide(X, Y) = double_divide(Y, X).
0.21/0.46	Proof:
0.21/0.46	  double_divide(X, Y)
0.21/0.46	= { by lemma 16 }
0.21/0.46	  multiply(multiply(X, double_divide(X, Y)), inverse(X))
0.21/0.46	= { by lemma 18 }
0.21/0.46	  multiply(inverse(Y), inverse(X))
0.21/0.46	= { by axiom 3 (inverse) }
0.21/0.46	  multiply(double_divide(Y, identity), inverse(X))
0.21/0.46	= { by axiom 1 (multiply) }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(Y, identity)), identity)
0.21/0.46	= { by axiom 2 (single_axiom) }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(identity, double_divide(double_divide(Y, double_divide(identity, inverse(X))), double_divide(identity, inverse(X)))), double_divide(identity, identity)), identity)), identity)
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(inverse(double_divide(double_divide(Y, double_divide(identity, inverse(X))), double_divide(identity, inverse(X)))), double_divide(identity, identity)), identity)), identity)
0.21/0.46	= { by lemma 12 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(multiply(double_divide(identity, inverse(X)), double_divide(Y, double_divide(identity, inverse(X)))), double_divide(identity, identity)), identity)), identity)
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(multiply(double_divide(identity, inverse(X)), double_divide(Y, double_divide(identity, inverse(X)))), inverse(identity)), identity)), identity)
0.21/0.46	= { by lemma 17 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(Y, double_divide(identity, inverse(X))), double_divide(identity, inverse(X))), identity)), identity)
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(Y, inverse(inverse(X))), double_divide(identity, inverse(X))), identity)), identity)
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(Y, inverse(inverse(X))), inverse(inverse(X))), identity)), identity)
0.21/0.46	= { by lemma 13 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(Y, inverse(inverse(X))), inverse(inverse(X))), inverse(identity))), identity)
0.21/0.46	= { by lemma 13 }
0.21/0.46	  double_divide(double_divide(inverse(X), double_divide(double_divide(double_divide(Y, inverse(inverse(X))), inverse(inverse(X))), inverse(identity))), inverse(identity))
0.21/0.46	= { by lemma 5 }
0.21/0.46	  double_divide(Y, inverse(inverse(X)))
0.21/0.46	= { by lemma 7 }
0.21/0.46	  double_divide(Y, multiply(identity, X))
0.21/0.46	= { by lemma 14 }
0.21/0.46	  double_divide(Y, X)
0.21/0.46	
0.21/0.46	Lemma 20: multiply(X, Y) = multiply(Y, X).
0.21/0.46	Proof:
0.21/0.46	  multiply(X, Y)
0.21/0.46	= { by axiom 1 (multiply) }
0.21/0.46	  double_divide(double_divide(Y, X), identity)
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(double_divide(X, Y), identity)
0.21/0.46	= { by axiom 1 (multiply) }
0.21/0.46	  multiply(Y, X)
0.21/0.46	
0.21/0.46	Lemma 21: double_divide(inverse(X), inverse(Y)) = multiply(X, Y).
0.21/0.46	Proof:
0.21/0.46	  double_divide(inverse(X), inverse(Y))
0.21/0.46	= { by lemma 18 }
0.21/0.46	  double_divide(inverse(X), multiply(X, double_divide(X, Y)))
0.21/0.46	= { by lemma 17 }
0.21/0.46	  double_divide(multiply(multiply(X, double_divide(X, Y)), inverse(X)), inverse(identity))
0.21/0.46	= { by lemma 16 }
0.21/0.46	  double_divide(double_divide(X, Y), inverse(identity))
0.21/0.46	= { by lemma 13 }
0.21/0.46	  double_divide(double_divide(X, Y), identity)
0.21/0.46	= { by axiom 3 (inverse) }
0.21/0.46	  inverse(double_divide(X, Y))
0.21/0.46	= { by lemma 12 }
0.21/0.46	  multiply(Y, X)
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(X, Y)
0.21/0.46	
0.21/0.46	Lemma 22: multiply(X, inverse(Y)) = double_divide(Y, inverse(X)).
0.21/0.46	Proof:
0.21/0.46	  multiply(X, inverse(Y))
0.21/0.46	= { by lemma 21 }
0.21/0.46	  double_divide(inverse(X), inverse(inverse(Y)))
0.21/0.46	= { by lemma 7 }
0.21/0.46	  double_divide(inverse(X), multiply(identity, Y))
0.21/0.46	= { by lemma 14 }
0.21/0.46	  double_divide(inverse(X), Y)
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(Y, inverse(X))
0.21/0.46	
0.21/0.46	Lemma 23: double_divide(double_divide(Y, Z), inverse(X)) = multiply(X, multiply(Y, Z)).
0.21/0.46	Proof:
0.21/0.46	  double_divide(double_divide(Y, Z), inverse(X))
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(inverse(X), double_divide(Y, Z))
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(double_divide(Y, Z), inverse(X))
0.21/0.46	= { by lemma 22 }
0.21/0.46	  multiply(X, inverse(double_divide(Y, Z)))
0.21/0.46	= { by lemma 15 }
0.21/0.46	  multiply(X, double_divide(identity, double_divide(Y, Z)))
0.21/0.46	= { by lemma 16 }
0.21/0.46	  multiply(multiply(multiply(identity, double_divide(Y, Z)), multiply(X, double_divide(identity, double_divide(Y, Z)))), inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(multiply(multiply(double_divide(Y, Z), identity), multiply(X, double_divide(identity, double_divide(Y, Z)))), inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(multiply(multiply(double_divide(Y, Z), identity), multiply(double_divide(identity, double_divide(Y, Z)), X)), inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(multiply(multiply(double_divide(identity, double_divide(Y, Z)), X), multiply(double_divide(Y, Z), identity)), inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 12 }
0.21/0.46	  multiply(multiply(multiply(double_divide(identity, double_divide(Y, Z)), X), inverse(double_divide(identity, double_divide(Y, Z)))), inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 16 }
0.21/0.46	  multiply(X, inverse(multiply(identity, double_divide(Y, Z))))
0.21/0.46	= { by lemma 22 }
0.21/0.46	  double_divide(multiply(identity, double_divide(Y, Z)), inverse(X))
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(inverse(X), multiply(identity, double_divide(Y, Z)))
0.21/0.46	= { by lemma 11 }
0.21/0.46	  double_divide(inverse(X), inverse(multiply(Z, Y)))
0.21/0.46	= { by lemma 21 }
0.21/0.46	  multiply(X, multiply(Z, Y))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(X, multiply(Y, Z))
0.21/0.46	
0.21/0.46	Lemma 24: multiply(Y, multiply(double_divide(Y, Z), multiply(X, Z))) = X.
0.21/0.46	Proof:
0.21/0.46	  multiply(Y, multiply(double_divide(Y, Z), multiply(X, Z)))
0.21/0.46	= { by lemma 23 }
0.21/0.46	  multiply(Y, double_divide(double_divide(X, Z), inverse(double_divide(Y, Z))))
0.21/0.46	= { by lemma 14 }
0.21/0.46	  multiply(identity, multiply(Y, double_divide(double_divide(X, Z), inverse(double_divide(Y, Z)))))
0.21/0.46	= { by lemma 23 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, Z), inverse(double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 6 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(inverse(Z), inverse(identity))), inverse(double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 18 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(multiply(Y, double_divide(Y, Z)), inverse(identity))), inverse(double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 17 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(double_divide(Y, Z), Y)), inverse(double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 19 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, double_divide(Y, Z))), inverse(double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, double_divide(Y, Z))), double_divide(identity, double_divide(Y, Z)))), inverse(identity))
0.21/0.46	= { by lemma 15 }
0.21/0.46	  double_divide(double_divide(Y, double_divide(double_divide(X, double_divide(Y, double_divide(Y, Z))), double_divide(identity, double_divide(Y, Z)))), double_divide(identity, identity))
0.21/0.46	= { by axiom 2 (single_axiom) }
0.21/0.46	  X
0.21/0.46	
0.21/0.46	Goal 1 (prove_these_axioms_3): multiply(a3, multiply(b3, c3)) = multiply(multiply(a3, b3), c3).
0.21/0.46	Proof:
0.21/0.46	  multiply(a3, multiply(b3, c3))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(a3, multiply(c3, b3))
0.21/0.46	= { by lemma 24 }
0.21/0.46	  multiply(a3, multiply(c3, multiply(double_divide(c3, multiply(b3, a3)), multiply(double_divide(double_divide(c3, multiply(b3, a3)), a3), multiply(b3, a3)))))
0.21/0.46	= { by lemma 24 }
0.21/0.46	  multiply(a3, double_divide(double_divide(c3, multiply(b3, a3)), a3))
0.21/0.46	= { by lemma 19 }
0.21/0.46	  multiply(a3, double_divide(a3, double_divide(c3, multiply(b3, a3))))
0.21/0.46	= { by lemma 20 }
0.21/0.46	  multiply(a3, double_divide(a3, double_divide(c3, multiply(a3, b3))))
0.21/0.46	= { by lemma 18 }
0.21/0.46	  inverse(double_divide(c3, multiply(a3, b3)))
0.21/0.46	= { by lemma 12 }
0.21/0.46	  multiply(multiply(a3, b3), c3)
0.21/0.46	% SZS output end Proof
0.21/0.46	
0.21/0.46	RESULT: Unsatisfiable (the axioms are contradictory).
0.21/0.46	EOF