0.12/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.12/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n012.cluster.edu
0.13/0.34	% Model      : x86_64 x86_64
0.13/0.34	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.34	% Memory     : 8042.1875MB
0.13/0.34	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.34	% CPULimit   : 180
0.13/0.34	% DateTime   : Thu Aug 29 10:23:12 EDT 2019
0.13/0.34	% CPUTime    : 
0.13/0.38	% SZS status Unsatisfiable
0.13/0.38	
0.13/0.38	% SZS output start Proof
0.13/0.38	Take the following subset of the input axioms:
0.13/0.39	  fof(multiply, axiom, ![A, B]: inverse(double_divide(B, A))=multiply(A, B)).
0.13/0.39	  fof(prove_these_axioms_2, negated_conjecture, a2!=multiply(multiply(inverse(b2), b2), a2)).
0.13/0.39	  fof(single_axiom, axiom, ![A, B, C]: inverse(double_divide(inverse(double_divide(A, inverse(double_divide(B, double_divide(A, C))))), C))=B).
0.13/0.39	
0.13/0.39	Now clausify the problem and encode Horn clauses using encoding 3 of
0.13/0.39	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.13/0.39	We repeatedly replace C & s=t => u=v by the two clauses:
0.13/0.39	  fresh(y, y, x1...xn) = u
0.13/0.39	  C => fresh(s, t, x1...xn) = v
0.13/0.39	where fresh is a fresh function symbol and x1..xn are the free
0.13/0.39	variables of u and v.
0.13/0.39	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.13/0.39	input problem has no model of domain size 1).
0.13/0.39	
0.13/0.39	The encoding turns the above axioms into the following unit equations and goals:
0.13/0.39	
0.13/0.39	Axiom 1 (multiply): inverse(double_divide(X, Y)) = multiply(Y, X).
0.13/0.40	Axiom 2 (single_axiom): inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z)) = Y.
0.13/0.40	
0.13/0.40	Lemma 3: multiply(Z, multiply(multiply(double_divide(X, Z), Y), X)) = Y.
0.13/0.40	Proof:
0.13/0.40	  multiply(Z, multiply(multiply(double_divide(X, Z), Y), X))
0.13/0.40	= { by axiom 1 (multiply) }
0.13/0.40	  multiply(Z, multiply(inverse(double_divide(Y, double_divide(X, Z))), X))
0.13/0.40	= { by axiom 1 (multiply) }
0.13/0.40	  multiply(Z, inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))))
0.13/0.40	= { by axiom 1 (multiply) }
0.13/0.40	  inverse(double_divide(inverse(double_divide(X, inverse(double_divide(Y, double_divide(X, Z))))), Z))
0.13/0.40	= { by axiom 2 (single_axiom) }
0.13/0.40	  Y
0.13/0.40	
0.13/0.40	Lemma 4: multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X) = multiply(Z, multiply(W, Y)).
0.13/0.40	Proof:
0.13/0.40	  multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)
0.13/0.40	= { by lemma 3 }
0.13/0.40	  multiply(Z, multiply(multiply(double_divide(Y, Z), multiply(multiply(double_divide(X, double_divide(Y, Z)), W), X)), Y))
0.13/0.40	= { by lemma 3 }
0.13/0.40	  multiply(Z, multiply(W, Y))
0.13/0.40	
0.13/0.40	Lemma 5: multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y))) = X.
0.13/0.40	Proof:
0.13/0.40	  multiply(double_divide(Y, Z), multiply(Z, multiply(X, Y)))
0.13/0.40	= { by lemma 4 }
0.13/0.40	  multiply(double_divide(Y, Z), multiply(multiply(double_divide(?, double_divide(Y, Z)), X), ?))
0.13/0.40	= { by lemma 3 }
0.13/0.40	  X
0.13/0.40	
0.13/0.40	Lemma 6: multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), Y) = X.
0.13/0.40	Proof:
0.13/0.40	  multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), Y)
0.13/0.40	= { by lemma 5 }
0.13/0.40	  multiply(double_divide(multiply(Y, Z), double_divide(Z, X)), multiply(double_divide(Z, X), multiply(X, multiply(Y, Z))))
0.13/0.40	= { by lemma 5 }
0.13/0.40	  X
0.13/0.40	
0.13/0.40	Lemma 7: multiply(double_divide(X, W), multiply(W, Z)) = double_divide(multiply(X, ?), double_divide(?, Z)).
0.13/0.40	Proof:
0.13/0.40	  multiply(double_divide(X, W), multiply(W, Z))
0.13/0.40	= { by lemma 6 }
0.13/0.40	  multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, ?), double_divide(?, Z)), X)))
0.13/0.40	= { by lemma 5 }
0.13/0.40	  double_divide(multiply(X, ?), double_divide(?, Z))
0.13/0.40	
0.13/0.40	Lemma 8: double_divide(multiply(X, ?), double_divide(?, multiply(Y, X))) = Y.
0.13/0.40	Proof:
0.13/0.40	  double_divide(multiply(X, ?), double_divide(?, multiply(Y, X)))
0.13/0.40	= { by lemma 7 }
0.13/0.40	  multiply(double_divide(X, ?), multiply(?, multiply(Y, X)))
0.13/0.40	= { by lemma 5 }
0.13/0.40	  Y
0.13/0.40	
0.13/0.40	Lemma 9: multiply(double_divide(?, multiply(X, Y)), multiply(Y, ?)) = inverse(X).
0.13/0.40	Proof:
0.13/0.40	  multiply(double_divide(?, multiply(X, Y)), multiply(Y, ?))
0.13/0.40	= { by axiom 1 (multiply) }
0.13/0.40	  inverse(double_divide(multiply(Y, ?), double_divide(?, multiply(X, Y))))
0.13/0.40	= { by lemma 8 }
0.13/0.40	  inverse(X)
0.13/0.40	
0.13/0.40	Lemma 10: double_divide(multiply(multiply(Y, multiply(Z, X)), ?), double_divide(?, Z)) = double_divide(X, Y).
0.13/0.40	Proof:
0.13/0.40	  double_divide(multiply(multiply(Y, multiply(Z, X)), ?), double_divide(?, Z))
0.13/0.40	= { by lemma 7 }
0.13/0.40	  multiply(double_divide(multiply(Y, multiply(Z, X)), ?), multiply(?, Z))
0.13/0.40	= { by lemma 5 }
0.13/0.40	  multiply(double_divide(multiply(Y, multiply(Z, X)), ?), multiply(?, multiply(double_divide(X, Y), multiply(Y, multiply(Z, X)))))
0.13/0.40	= { by lemma 5 }
0.13/0.40	  double_divide(X, Y)
0.13/0.40	
0.13/0.40	Lemma 11: multiply(double_divide(?, X), multiply(multiply(Y, multiply(X, Z)), ?)) = multiply(Y, Z).
0.13/0.40	Proof:
0.13/0.40	  multiply(double_divide(?, X), multiply(multiply(Y, multiply(X, Z)), ?))
0.13/0.40	= { by axiom 1 (multiply) }
0.13/0.41	  inverse(double_divide(multiply(multiply(Y, multiply(X, Z)), ?), double_divide(?, X)))
0.13/0.41	= { by lemma 10 }
0.13/0.41	  inverse(double_divide(Z, Y))
0.13/0.41	= { by axiom 1 (multiply) }
0.13/0.41	  multiply(Y, Z)
0.13/0.41	
0.13/0.41	Lemma 12: multiply(double_divide(?, double_divide(?, X)), Y) = multiply(X, Y).
0.13/0.41	Proof:
0.13/0.41	  multiply(double_divide(?, double_divide(?, X)), Y)
0.13/0.41	= { by lemma 11 }
0.13/0.41	  multiply(double_divide(?, X), multiply(multiply(double_divide(?, double_divide(?, X)), multiply(X, Y)), ?))
0.13/0.41	= { by lemma 3 }
0.13/0.41	  multiply(X, Y)
0.13/0.41	
0.13/0.41	Lemma 13: multiply(double_divide(?, X), ?) = inverse(X).
0.13/0.41	Proof:
0.13/0.41	  multiply(double_divide(?, X), ?)
0.13/0.41	= { by axiom 1 (multiply) }
0.13/0.41	  inverse(double_divide(?, double_divide(?, X)))
0.13/0.41	= { by lemma 9 }
0.13/0.41	  multiply(double_divide(?, multiply(double_divide(?, double_divide(?, X)), ?)), multiply(?, ?))
0.13/0.41	= { by lemma 12 }
0.13/0.41	  multiply(double_divide(?, multiply(X, ?)), multiply(?, ?))
0.13/0.41	= { by lemma 9 }
0.13/0.41	  inverse(X)
0.13/0.41	
0.13/0.41	Lemma 14: multiply(multiply(X, Y), ?) = multiply(X, multiply(Y, ?)).
0.13/0.41	Proof:
0.13/0.41	  multiply(multiply(X, Y), ?)
0.13/0.41	= { by lemma 12 }
0.13/0.41	  multiply(multiply(double_divide(?, double_divide(?, X)), Y), ?)
0.13/0.41	= { by lemma 4 }
0.13/0.41	  multiply(X, multiply(Y, ?))
0.13/0.41	
0.13/0.41	Lemma 15: multiply(Y, ?) = multiply(?, Y).
0.13/0.41	Proof:
0.13/0.41	  multiply(Y, ?)
0.13/0.41	= { by lemma 3 }
0.13/0.41	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(Y, ?)), ?))
0.13/0.41	= { by lemma 14 }
0.13/0.41	  multiply(?, multiply(multiply(multiply(double_divide(?, ?), Y), ?), ?))
0.13/0.41	= { by axiom 1 (multiply) }
0.13/0.41	  multiply(?, multiply(multiply(inverse(double_divide(Y, double_divide(?, ?))), ?), ?))
0.13/0.41	= { by lemma 4 }
0.13/0.41	  multiply(multiply(double_divide(Y, double_divide(?, ?)), multiply(inverse(double_divide(Y, double_divide(?, ?))), ?)), Y)
0.13/0.41	= { by lemma 13 }
0.13/0.41	  multiply(multiply(double_divide(Y, double_divide(?, ?)), multiply(multiply(double_divide(?, double_divide(Y, double_divide(?, ?))), ?), ?)), Y)
0.13/0.41	= { by lemma 3 }
0.13/0.41	  multiply(?, Y)
0.13/0.41	
0.13/0.41	Lemma 16: multiply(X, multiply(?, Y)) = multiply(?, multiply(X, Y)).
0.13/0.41	Proof:
0.13/0.41	  multiply(X, multiply(?, Y))
0.13/0.41	= { by lemma 4 }
0.13/0.41	  multiply(multiply(double_divide(?, double_divide(Y, X)), ?), ?)
0.13/0.41	= { by lemma 13 }
0.13/0.41	  multiply(inverse(double_divide(Y, X)), ?)
0.13/0.41	= { by lemma 15 }
0.13/0.41	  multiply(?, inverse(double_divide(Y, X)))
0.13/0.41	= { by axiom 1 (multiply) }
0.13/0.41	  multiply(?, multiply(X, Y))
0.13/0.41	
0.13/0.41	Lemma 17: multiply(?, multiply(X, multiply(double_divide(?, X), Z))) = Z.
0.13/0.41	Proof:
0.13/0.41	  multiply(?, multiply(X, multiply(double_divide(?, X), Z)))
0.13/0.41	= { by lemma 16 }
0.13/0.41	  multiply(X, multiply(?, multiply(double_divide(?, X), Z)))
0.13/0.41	= { by lemma 16 }
0.13/0.41	  multiply(X, multiply(double_divide(?, X), multiply(?, Z)))
0.13/0.41	= { by lemma 15 }
0.13/0.41	  multiply(X, multiply(double_divide(?, X), multiply(Z, ?)))
0.13/0.41	= { by lemma 4 }
0.13/0.41	  multiply(X, multiply(multiply(double_divide(?, double_divide(?, double_divide(?, X))), Z), ?))
0.13/0.41	= { by lemma 12 }
0.13/0.41	  multiply(double_divide(?, double_divide(?, X)), multiply(multiply(double_divide(?, double_divide(?, double_divide(?, X))), Z), ?))
0.13/0.41	= { by lemma 3 }
0.20/0.42	  Z
0.20/0.42	
0.20/0.42	Lemma 18: multiply(X, inverse(multiply(Y, X))) = inverse(Y).
0.20/0.42	Proof:
0.20/0.42	  multiply(X, inverse(multiply(Y, X)))
0.20/0.42	= { by lemma 13 }
0.20/0.42	  multiply(X, multiply(double_divide(?, multiply(Y, X)), ?))
0.20/0.42	= { by lemma 3 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(X, multiply(double_divide(?, multiply(Y, X)), ?))), ?))
0.20/0.42	= { by lemma 11 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(?, multiply(X, multiply(double_divide(?, multiply(Y, X)), ?)))), ?)), ?))
0.20/0.42	= { by lemma 16 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(X, multiply(?, multiply(double_divide(?, multiply(Y, X)), ?)))), ?)), ?))
0.20/0.42	= { by lemma 16 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(X, multiply(double_divide(?, multiply(Y, X)), multiply(?, ?)))), ?)), ?))
0.20/0.42	= { by lemma 14 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(X, multiply(multiply(double_divide(?, multiply(Y, X)), ?), ?))), ?)), ?))
0.20/0.42	= { by lemma 11 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(X, multiply(multiply(double_divide(?, X), multiply(multiply(double_divide(?, multiply(Y, X)), multiply(X, ?)), ?)), ?))), ?)), ?))
0.20/0.42	= { by lemma 3 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, multiply(Y, X)), multiply(X, ?)), ?)), ?)), ?))
0.20/0.42	= { by lemma 14 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(double_divide(?, multiply(Y, X)), multiply(multiply(X, ?), ?))), ?)), ?))
0.20/0.42	= { by lemma 14 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(double_divide(?, multiply(Y, X)), multiply(X, multiply(?, ?)))), ?)), ?))
0.20/0.42	= { by lemma 16 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(double_divide(?, multiply(Y, X)), multiply(?, multiply(X, ?)))), ?)), ?))
0.20/0.42	= { by lemma 16 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(?, multiply(double_divide(?, multiply(Y, X)), multiply(X, ?)))), ?)), ?))
0.20/0.42	= { by lemma 11 }
0.20/0.42	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(double_divide(?, multiply(Y, X)), multiply(X, ?))), ?))
0.20/0.42	= { by lemma 3 }
0.20/0.42	  multiply(double_divide(?, multiply(Y, X)), multiply(X, ?))
0.20/0.42	= { by lemma 9 }
0.20/0.42	  inverse(Y)
0.20/0.42	
0.20/0.42	Lemma 19: double_divide(?, double_divide(?, X)) = X.
0.20/0.42	Proof:
0.20/0.42	  double_divide(?, double_divide(?, X))
0.20/0.42	= { by lemma 5 }
0.20/0.42	  multiply(double_divide(?, ?), multiply(?, multiply(double_divide(?, double_divide(?, X)), ?)))
0.20/0.42	= { by lemma 12 }
0.20/0.42	  multiply(double_divide(?, ?), multiply(?, multiply(X, ?)))
0.20/0.42	= { by lemma 5 }
0.20/0.42	  X
0.20/0.42	
0.20/0.42	Lemma 20: double_divide(multiply(X, Y), double_divide(Y, Z)) = double_divide(multiply(X, ?), double_divide(?, Z)).
0.20/0.42	Proof:
0.20/0.42	  double_divide(multiply(X, Y), double_divide(Y, Z))
0.20/0.42	= { by lemma 5 }
0.20/0.42	  multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, Y), double_divide(Y, Z)), X)))
0.20/0.42	= { by lemma 6 }
0.20/0.42	  multiply(double_divide(X, W), multiply(W, Z))
0.20/0.42	= { by lemma 6 }
0.20/0.42	  multiply(double_divide(X, W), multiply(W, multiply(double_divide(multiply(X, ?), double_divide(?, Z)), X)))
0.20/0.42	= { by lemma 5 }
0.20/0.42	  double_divide(multiply(X, ?), double_divide(?, Z))
0.20/0.42	
0.20/0.42	Lemma 21: multiply(double_divide(X, Y), multiply(Z, X)) = multiply(double_divide(?, Y), multiply(Z, ?)).
0.20/0.42	Proof:
0.20/0.42	  multiply(double_divide(X, Y), multiply(Z, X))
0.20/0.42	= { by axiom 1 (multiply) }
0.20/0.42	  inverse(double_divide(multiply(Z, X), double_divide(X, Y)))
0.20/0.42	= { by lemma 20 }
0.20/0.42	  inverse(double_divide(multiply(Z, ?), double_divide(?, Y)))
0.20/0.42	= { by axiom 1 (multiply) }
0.20/0.42	  multiply(double_divide(?, Y), multiply(Z, ?))
0.20/0.42	
0.20/0.42	Lemma 22: double_divide(X, double_divide(X, Y)) = double_divide(?, double_divide(?, Y)).
0.20/0.42	Proof:
0.20/0.42	  double_divide(X, double_divide(X, Y))
0.20/0.42	= { by lemma 10 }
0.20/0.42	  double_divide(multiply(multiply(double_divide(X, Y), multiply(Z, X)), ?), double_divide(?, Z))
0.20/0.42	= { by lemma 21 }
0.20/0.42	  double_divide(multiply(multiply(double_divide(?, Y), multiply(Z, ?)), ?), double_divide(?, Z))
0.20/0.42	= { by lemma 10 }
0.20/0.42	  double_divide(?, double_divide(?, Y))
0.20/0.42	
0.20/0.42	Lemma 23: double_divide(Y, double_divide(?, Y)) = ?.
0.20/0.42	Proof:
0.20/0.42	  double_divide(Y, double_divide(?, Y))
0.20/0.42	= { by lemma 3 }
0.20/0.42	  double_divide(multiply(?, multiply(multiply(double_divide(?, ?), Y), ?)), double_divide(?, Y))
0.20/0.42	= { by lemma 14 }
0.20/0.42	  double_divide(multiply(multiply(?, multiply(double_divide(?, ?), Y)), ?), double_divide(?, Y))
0.20/0.42	= { by lemma 7 }
0.20/0.42	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), Y)), ?), multiply(?, Y))
0.20/0.42	= { by lemma 17 }
0.20/0.42	  multiply(double_divide(multiply(?, multiply(double_divide(?, ?), Y)), ?), multiply(?, multiply(?, multiply(?, multiply(double_divide(?, ?), Y)))))
0.20/0.42	= { by lemma 5 }
0.20/0.43	  ?
0.20/0.43	
0.20/0.43	Lemma 24: multiply(X, Y) = multiply(Y, X).
0.20/0.43	Proof:
0.20/0.43	  multiply(X, Y)
0.20/0.43	= { by lemma 3 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(X, Y)), ?))
0.20/0.43	= { by lemma 11 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(?, multiply(X, Y))), ?)), ?))
0.20/0.43	= { by lemma 15 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(multiply(X, Y), ?)), ?)), ?))
0.20/0.43	= { by axiom 1 (multiply) }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), inverse(double_divide(?, multiply(X, Y)))), ?)), ?))
0.20/0.43	= { by lemma 18 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(?, inverse(multiply(double_divide(?, multiply(X, Y)), ?)))), ?)), ?))
0.20/0.43	= { by lemma 13 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), multiply(multiply(double_divide(?, ?), multiply(?, inverse(inverse(multiply(X, Y))))), ?)), ?))
0.20/0.43	= { by lemma 11 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), inverse(inverse(multiply(X, Y)))), ?))
0.20/0.43	= { by lemma 3 }
0.20/0.43	  inverse(inverse(multiply(X, Y)))
0.20/0.43	= { by lemma 19 }
0.20/0.43	  inverse(inverse(multiply(X, double_divide(?, double_divide(?, Y)))))
0.20/0.43	= { by lemma 22 }
0.20/0.43	  inverse(inverse(multiply(X, double_divide(X, double_divide(X, Y)))))
0.20/0.43	= { by lemma 13 }
0.20/0.43	  inverse(multiply(double_divide(?, multiply(X, double_divide(X, double_divide(X, Y)))), ?))
0.20/0.43	= { by lemma 19 }
0.20/0.43	  inverse(multiply(double_divide(?, double_divide(?, double_divide(?, multiply(X, double_divide(X, double_divide(X, Y)))))), ?))
0.20/0.43	= { by lemma 22 }
0.20/0.43	  inverse(multiply(double_divide(multiply(X, double_divide(X, double_divide(X, Y))), double_divide(multiply(X, double_divide(X, double_divide(X, Y))), double_divide(?, multiply(X, double_divide(X, double_divide(X, Y)))))), ?))
0.20/0.43	= { by lemma 23 }
0.20/0.43	  inverse(multiply(double_divide(multiply(X, double_divide(X, double_divide(X, Y))), ?), ?))
0.20/0.43	= { by lemma 23 }
0.20/0.43	  inverse(multiply(double_divide(multiply(X, double_divide(X, double_divide(X, Y))), double_divide(double_divide(X, double_divide(X, Y)), double_divide(?, double_divide(X, double_divide(X, Y))))), ?))
0.20/0.43	= { by lemma 20 }
0.20/0.43	  inverse(multiply(double_divide(multiply(X, ?), double_divide(?, double_divide(?, double_divide(X, double_divide(X, Y))))), ?))
0.20/0.43	= { by lemma 15 }
0.20/0.43	  inverse(multiply(double_divide(multiply(?, X), double_divide(?, double_divide(?, double_divide(X, double_divide(X, Y))))), ?))
0.20/0.43	= { by lemma 19 }
0.20/0.43	  inverse(multiply(double_divide(multiply(?, X), double_divide(X, double_divide(X, Y))), ?))
0.20/0.43	= { by lemma 6 }
0.20/0.43	  inverse(double_divide(X, Y))
0.20/0.43	= { by axiom 1 (multiply) }
0.20/0.43	  multiply(Y, X)
0.20/0.43	
0.20/0.43	Lemma 25: multiply(double_divide(X, Y), X) = multiply(double_divide(?, Y), ?).
0.20/0.43	Proof:
0.20/0.43	  multiply(double_divide(X, Y), X)
0.20/0.43	= { by axiom 1 (multiply) }
0.20/0.43	  inverse(double_divide(X, double_divide(X, Y)))
0.20/0.43	= { by lemma 22 }
0.20/0.43	  inverse(double_divide(?, double_divide(?, Y)))
0.20/0.43	= { by axiom 1 (multiply) }
0.20/0.43	  multiply(double_divide(?, Y), ?)
0.20/0.43	
0.20/0.43	Lemma 26: multiply(double_divide(?, X), X) = inverse(?).
0.20/0.43	Proof:
0.20/0.43	  multiply(double_divide(?, X), X)
0.20/0.43	= { by lemma 17 }
0.20/0.43	  multiply(double_divide(?, multiply(?, multiply(?, multiply(double_divide(?, ?), X)))), X)
0.20/0.43	= { by lemma 3 }
0.20/0.43	  multiply(double_divide(?, multiply(?, multiply(?, multiply(double_divide(?, ?), X)))), multiply(?, multiply(multiply(double_divide(?, ?), X), ?)))
0.20/0.43	= { by lemma 14 }
0.20/0.43	  multiply(double_divide(?, multiply(?, multiply(?, multiply(double_divide(?, ?), X)))), multiply(multiply(?, multiply(double_divide(?, ?), X)), ?))
0.20/0.43	= { by lemma 9 }
0.20/0.43	  inverse(?)
0.20/0.43	
0.20/0.43	Goal 1 (prove_these_axioms_2): a2 = multiply(multiply(inverse(b2), b2), a2).
0.20/0.43	Proof:
0.20/0.43	  a2
0.20/0.43	= { by lemma 3 }
0.20/0.43	  multiply(?, multiply(multiply(double_divide(?, ?), a2), ?))
0.20/0.43	= { by lemma 14 }
0.20/0.43	  multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?)
0.20/0.43	= { by lemma 3 }
0.20/0.43	  multiply(multiply(?, multiply(?, multiply(double_divide(?, ?), a2))), multiply(multiply(double_divide(?, multiply(?, multiply(?, multiply(double_divide(?, ?), a2)))), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?)), ?))
0.20/0.43	= { by lemma 9 }
0.20/0.43	  multiply(multiply(?, multiply(?, multiply(double_divide(?, ?), a2))), multiply(inverse(?), ?))
0.20/0.43	= { by lemma 4 }
0.20/0.43	  multiply(multiply(double_divide(multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?), double_divide(?, multiply(?, multiply(?, multiply(double_divide(?, ?), a2))))), inverse(?)), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 8 }
0.20/0.43	  multiply(multiply(?, inverse(?)), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 13 }
0.20/0.43	  multiply(multiply(?, multiply(double_divide(?, ?), ?)), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 4 }
0.20/0.43	  multiply(multiply(multiply(double_divide(?, double_divide(?, ?)), double_divide(?, ?)), ?), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 26 }
0.20/0.43	  multiply(multiply(inverse(?), ?), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 26 }
0.20/0.43	  multiply(multiply(multiply(double_divide(?, double_divide(?, b2)), double_divide(?, b2)), ?), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 4 }
0.20/0.43	  multiply(multiply(b2, multiply(double_divide(?, b2), ?)), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 13 }
0.20/0.43	  multiply(multiply(b2, inverse(b2)), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 24 }
0.20/0.43	  multiply(multiply(inverse(b2), b2), multiply(multiply(?, multiply(double_divide(?, ?), a2)), ?))
0.20/0.43	= { by lemma 14 }
0.20/0.43	  multiply(multiply(inverse(b2), b2), multiply(?, multiply(multiply(double_divide(?, ?), a2), ?)))
0.20/0.43	= { by lemma 3 }
0.20/0.43	  multiply(multiply(inverse(b2), b2), a2)
0.20/0.43	% SZS output end Proof
0.20/0.43	
0.20/0.43	RESULT: Unsatisfiable (the axioms are contradictory).
0.20/0.43	EOF