0.11/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.34	% Computer   : n017.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 10:14:04 EDT 2019
0.13/0.34	% CPUTime    : 
0.19/0.48	% SZS status Unsatisfiable
0.19/0.48	
0.19/0.48	% SZS output start Proof
0.19/0.48	Take the following subset of the input axioms:
0.19/0.48	  fof(prove_order4, negated_conjecture, multiply(a, multiply(a, multiply(a, a)))!=identity).
0.19/0.48	  fof(single_axiom, axiom, ![Y, X, Z]: multiply(Y, multiply(multiply(Y, multiply(multiply(Y, Y), multiply(X, Z))), multiply(Z, multiply(Z, Z))))=X).
0.19/0.48	  fof(single_axiom2, axiom, multiply(identity, identity)=identity).
0.19/0.48	
0.19/0.48	Now clausify the problem and encode Horn clauses using encoding 3 of
0.19/0.48	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.19/0.48	We repeatedly replace C & s=t => u=v by the two clauses:
0.19/0.48	  fresh(y, y, x1...xn) = u
0.19/0.48	  C => fresh(s, t, x1...xn) = v
0.19/0.48	where fresh is a fresh function symbol and x1..xn are the free
0.19/0.48	variables of u and v.
0.19/0.48	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.19/0.48	input problem has no model of domain size 1).
0.19/0.48	
0.19/0.48	The encoding turns the above axioms into the following unit equations and goals:
0.19/0.48	
0.19/0.48	Axiom 1 (single_axiom2): multiply(identity, identity) = identity.
0.19/0.56	Axiom 2 (single_axiom): multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(Y, Z))), multiply(Z, multiply(Z, Z)))) = Y.
0.19/0.56	
0.19/0.56	Lemma 3: multiply(Y, multiply(multiply(Y, multiply(multiply(Y, Y), multiply(X, identity))), identity)) = X.
0.19/0.56	Proof:
0.19/0.56	  multiply(Y, multiply(multiply(Y, multiply(multiply(Y, Y), multiply(X, identity))), identity))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(Y, multiply(multiply(Y, multiply(multiply(Y, Y), multiply(X, identity))), multiply(identity, identity)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(Y, multiply(multiply(Y, multiply(multiply(Y, Y), multiply(X, identity))), multiply(identity, multiply(identity, identity))))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  X
0.19/0.56	
0.19/0.56	Lemma 4: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))) = multiply(X, multiply(multiply(X, Y), identity)).
0.19/0.56	Proof:
0.19/0.56	  multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity)))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, identity))), identity))), multiply(identity, multiply(identity, identity))))
0.19/0.56	= { by lemma 3 }
0.19/0.56	  multiply(X, multiply(multiply(X, Y), multiply(identity, multiply(identity, identity))))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(X, multiply(multiply(X, Y), multiply(identity, identity)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(X, multiply(multiply(X, Y), identity))
0.19/0.56	
0.19/0.56	Lemma 5: multiply(multiply(Y, Y), multiply(multiply(Y, multiply(multiply(Y, X), identity)), identity)) = X.
0.19/0.56	Proof:
0.19/0.56	  multiply(multiply(Y, Y), multiply(multiply(Y, multiply(multiply(Y, X), identity)), identity))
0.19/0.56	= { by lemma 4 }
0.19/0.56	  multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(Y, Y)), multiply(X, identity))), identity))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(Y, Y)), multiply(X, identity))), multiply(identity, identity)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(multiply(multiply(Y, Y), multiply(Y, Y)), multiply(X, identity))), multiply(identity, multiply(identity, identity))))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  X
0.19/0.56	
0.19/0.56	Lemma 6: multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, Y))), multiply(Y, multiply(Y, Y)))) = X.
0.19/0.56	Proof:
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, Y))), multiply(Y, multiply(Y, Y))))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  X
0.19/0.56	
0.19/0.56	Lemma 7: multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity)) = X.
0.19/0.56	Proof:
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))
0.19/0.56	= { by lemma 3 }
0.19/0.56	  X
0.19/0.56	
0.19/0.56	Lemma 8: multiply(identity, multiply(multiply(identity, X), identity)) = multiply(identity, multiply(identity, multiply(X, identity))).
0.19/0.56	Proof:
0.19/0.56	  multiply(identity, multiply(multiply(identity, X), identity))
0.19/0.56	= { by lemma 3 }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))), identity))
0.19/0.56	= { by lemma 7 }
0.19/0.56	  multiply(identity, multiply(multiply(identity, identity), multiply(X, identity)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(identity, multiply(identity, multiply(X, identity)))
0.19/0.56	
0.19/0.56	Lemma 9: multiply(identity, multiply(identity, multiply(multiply(multiply(identity, X), identity), identity))) = X.
0.19/0.56	Proof:
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, X), identity), identity)))
0.19/0.56	= { by lemma 8 }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, X), identity)), identity))
0.19/0.56	= { by lemma 8 }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(X, identity))), identity))
0.19/0.56	= { by lemma 7 }
0.19/0.56	  X
0.19/0.56	
0.19/0.56	Lemma 10: multiply(identity, multiply(multiply(identity, X), multiply(multiply(Y, multiply(Y, Y)), multiply(multiply(Y, multiply(Y, Y)), multiply(Y, multiply(Y, Y)))))) = multiply(identity, multiply(identity, multiply(X, Y))).
0.19/0.56	Proof:
0.19/0.56	  multiply(identity, multiply(multiply(identity, X), multiply(multiply(Y, multiply(Y, Y)), multiply(multiply(Y, multiply(Y, Y)), multiply(Y, multiply(Y, Y))))))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, Y))), multiply(Y, multiply(Y, Y))))), multiply(multiply(Y, multiply(Y, Y)), multiply(multiply(Y, multiply(Y, Y)), multiply(Y, multiply(Y, Y))))))
0.19/0.56	= { by lemma 6 }
0.19/0.56	  multiply(identity, multiply(multiply(identity, identity), multiply(X, Y)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(identity, multiply(identity, multiply(X, Y)))
0.19/0.56	
0.19/0.56	Lemma 11: multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X)))) = multiply(identity, X).
0.19/0.56	Proof:
0.19/0.56	  multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))
0.19/0.56	= { by lemma 9 }
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))), identity), identity)))
0.19/0.56	= { by axiom 1 (single_axiom2) }
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X))))), identity), identity)))
0.19/0.56	= { by lemma 5 }
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(multiply(X, multiply(X, X)), multiply(multiply(X, multiply(X, X)), multiply(X, multiply(X, X)))))), identity)), identity)), identity), identity)))
0.19/0.56	= { by lemma 10 }
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(identity, X))), identity)), identity)), identity), identity)))
0.19/0.56	= { by lemma 5 }
0.19/0.56	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(identity, X)), identity), identity)))
0.19/0.56	= { by lemma 9 }
0.19/0.56	  multiply(identity, X)
0.19/0.56	
0.19/0.56	Lemma 12: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))) = multiply(X, multiply(multiply(X, Y), multiply(identity, Z))).
0.19/0.56	Proof:
0.19/0.56	  multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z)))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(Y, Z))), multiply(Z, multiply(Z, Z))))), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))))
0.19/0.56	= { by axiom 2 (single_axiom) }
0.19/0.56	  multiply(X, multiply(multiply(X, Y), multiply(multiply(Z, multiply(Z, Z)), multiply(multiply(Z, multiply(Z, Z)), multiply(Z, multiply(Z, Z))))))
0.19/0.56	= { by lemma 11 }
0.19/0.56	  multiply(X, multiply(multiply(X, Y), multiply(identity, Z)))
0.19/0.56	
0.19/0.56	Lemma 13: multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), Y)) = multiply(X, multiply(multiply(X, identity), Y)).
0.19/0.56	Proof:
0.19/0.56	  multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), Y))
0.19/0.56	= { by lemma 6 }
0.19/0.56	  multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(identity, multiply(multiply(identity, multiply(identity, multiply(Y, ?))), multiply(?, multiply(?, ?))))))
0.19/0.56	= { by lemma 12 }
0.19/0.56	  multiply(X, multiply(multiply(X, identity), multiply(identity, multiply(multiply(identity, multiply(identity, multiply(Y, ?))), multiply(?, multiply(?, ?))))))
0.19/0.56	= { by lemma 6 }
0.19/0.57	  multiply(X, multiply(multiply(X, identity), Y))
0.19/0.57	
0.19/0.57	Lemma 14: multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))) = X.
0.19/0.57	Proof:
0.19/0.57	  multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity))))
0.19/0.57	= { by lemma 8 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(identity, multiply(X, identity)), identity)))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, identity), multiply(X, identity)), identity)))
0.19/0.57	= { by lemma 8 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, identity))), identity))
0.19/0.57	= { by lemma 3 }
0.19/0.57	  X
0.19/0.57	
0.19/0.57	Lemma 15: multiply(identity, multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y)) = multiply(identity, multiply(identity, multiply(multiply(X, identity), identity))).
0.19/0.57	Proof:
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y))
0.19/0.57	= { by lemma 5 }
0.19/0.57	  multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y))), identity)), identity))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y))), identity)), identity))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, identity), multiply(X, multiply(Y, multiply(Y, Y)))), Y))), identity)), identity))
0.19/0.57	= { by lemma 10 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(multiply(identity, identity), multiply(X, multiply(Y, multiply(Y, Y))))), multiply(multiply(Y, multiply(Y, Y)), multiply(multiply(Y, multiply(Y, Y)), multiply(Y, multiply(Y, Y)))))), identity)), identity))
0.19/0.57	= { by axiom 2 (single_axiom) }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(X, identity)), identity))
0.19/0.57	= { by lemma 7 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(X, identity)), identity), identity))), identity)))
0.19/0.57	= { by lemma 9 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))
0.19/0.57	
0.19/0.57	Lemma 16: multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y) = multiply(identity, multiply(multiply(X, identity), identity)).
0.19/0.57	Proof:
0.19/0.57	  multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y)
0.19/0.57	= { by lemma 9 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(identity, multiply(X, multiply(Y, multiply(Y, Y)))), Y)), identity), identity)))
0.19/0.57	= { by lemma 15 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(identity, multiply(multiply(X, identity), identity))), identity), identity)))
0.19/0.57	= { by lemma 9 }
0.19/0.57	  multiply(identity, multiply(multiply(X, identity), identity))
0.19/0.57	
0.19/0.57	Lemma 17: multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(X, identity), identity)), Z))) = multiply(X, multiply(identity, multiply(identity, Z))).
0.19/0.57	Proof:
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(X, identity), identity)), Z)))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, multiply(multiply(identity, identity), multiply(multiply(identity, multiply(multiply(X, identity), identity)), Z)))
0.19/0.57	= { by lemma 16 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, identity), multiply(multiply(multiply(identity, multiply(X, multiply(?, multiply(?, ?)))), ?), Z)))
0.19/0.57	= { by lemma 13 }
0.19/0.57	  multiply(multiply(identity, identity), multiply(multiply(multiply(identity, identity), multiply(identity, identity)), multiply(multiply(multiply(identity, multiply(X, multiply(?, multiply(?, ?)))), ?), Z)))
0.19/0.57	= { by lemma 12 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(X, multiply(?, multiply(?, ?)))), ?)), multiply(identity, Z)))
0.19/0.57	= { by lemma 15 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(identity, multiply(multiply(X, identity), identity))), multiply(identity, Z)))
0.19/0.57	= { by lemma 15 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, multiply(multiply(identity, multiply(X, multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))))))), multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))))), multiply(identity, Z)))
0.19/0.57	= { by lemma 15 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(X, multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))))))), identity), identity)))
0.19/0.57	= { by lemma 9 }
0.19/0.57	  multiply(X, multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))), multiply(multiply(identity, Z), multiply(multiply(identity, Z), multiply(identity, Z))))))
0.19/0.57	= { by lemma 11 }
0.19/0.57	  multiply(X, multiply(identity, multiply(identity, Z)))
0.19/0.57	
0.19/0.57	Lemma 18: multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity))) = identity.
0.19/0.57	Proof:
0.19/0.57	  multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity)))
0.19/0.57	= { by lemma 5 }
0.19/0.57	  multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity)))), identity)), identity))
0.19/0.57	= { by lemma 13 }
0.19/0.57	  multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(X, X), multiply(multiply(X, identity), identity)))), identity)), identity))
0.19/0.57	= { by lemma 12 }
0.19/0.57	  multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, multiply(X, X)), multiply(identity, multiply(multiply(X, identity), identity)))), identity)), identity))
0.19/0.57	= { by lemma 5 }
0.19/0.57	  multiply(multiply(X, multiply(X, X)), multiply(identity, multiply(multiply(X, identity), identity)))
0.19/0.57	= { by lemma 14 }
0.19/0.57	  multiply(multiply(X, multiply(X, multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))))), multiply(identity, multiply(multiply(X, identity), identity)))
0.19/0.57	= { by lemma 17 }
0.19/0.57	  multiply(multiply(X, multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(X, identity), identity)), multiply(identity, multiply(multiply(X, identity), identity)))))), multiply(identity, multiply(multiply(X, identity), identity)))
0.19/0.57	= { by lemma 17 }
0.19/0.57	  multiply(multiply(identity, multiply(identity, multiply(multiply(identity, multiply(multiply(X, identity), identity)), multiply(multiply(identity, multiply(multiply(X, identity), identity)), multiply(identity, multiply(multiply(X, identity), identity)))))), multiply(identity, multiply(multiply(X, identity), identity)))
0.19/0.57	= { by lemma 16 }
0.19/0.57	  multiply(identity, multiply(multiply(identity, identity), identity))
0.19/0.57	= { by lemma 8 }
0.19/0.57	  multiply(identity, multiply(identity, multiply(identity, identity)))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, multiply(identity, identity))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(identity, identity)
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  identity
0.19/0.57	
0.19/0.57	Lemma 19: multiply(X, multiply(multiply(X, multiply(multiply(X, X), identity)), identity)) = identity.
0.19/0.57	Proof:
0.19/0.57	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), identity)), identity))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(identity, identity))), identity))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(identity, identity))), multiply(identity, identity)))
0.19/0.57	= { by axiom 1 (single_axiom2) }
0.19/0.57	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(identity, identity))), multiply(identity, multiply(identity, identity))))
0.19/0.57	= { by axiom 2 (single_axiom) }
0.19/0.65	  identity
0.19/0.65	
0.19/0.65	Lemma 20: multiply(X, identity) = X.
0.19/0.65	Proof:
0.19/0.65	  multiply(X, identity)
0.19/0.65	= { by lemma 18 }
0.19/0.65	  multiply(X, multiply(multiply(X, identity), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 19 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), identity)), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 18 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), identity), identity))))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), multiply(identity, identity)), identity))))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 19 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), identity)), identity)), identity)), identity))))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 5 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), identity)), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 2 (single_axiom) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, X)), identity)), identity))), multiply(identity, multiply(identity, identity)))), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 19 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(X, multiply(multiply(X, identity), multiply(identity, multiply(identity, identity)))), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(X, multiply(multiply(X, identity), multiply(identity, identity))), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), identity), multiply(multiply(X, multiply(multiply(X, identity), identity)), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 5 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), identity), multiply(multiply(X, multiply(multiply(X, identity), identity)), identity))), identity)), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 13 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), multiply(multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(X, X), multiply(X, X))), multiply(multiply(X, multiply(multiply(X, identity), identity)), identity))), identity)), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 4 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, X)), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity))), identity)), identity)), identity)))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by lemma 5 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity))), identity))), identity))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity))), identity))), multiply(identity, identity)))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(?, multiply(multiply(?, multiply(multiply(?, ?), multiply(multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity))), identity))), multiply(identity, multiply(identity, identity))))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 2 (single_axiom) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, identity), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(identity, identity)), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, identity), identity)), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, identity)), identity)), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, multiply(identity, identity))), identity)), identity))))
0.19/0.65	= { by axiom 1 (single_axiom2) }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, multiply(identity, multiply(identity, identity)))), identity)), identity))))
0.19/0.65	= { by lemma 8 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, multiply(multiply(identity, identity), identity))), identity)), identity))))
0.19/0.65	= { by lemma 6 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(multiply(identity, multiply(identity, multiply(identity, multiply(multiply(X, identity), identity)))), multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))), identity), identity))), identity)), identity))))
0.19/0.65	= { by lemma 14 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(identity, multiply(identity, multiply(multiply(multiply(identity, multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity))))), identity), identity))), identity)), identity))))
0.19/0.65	= { by lemma 9 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(X, X), multiply(multiply(X, multiply(multiply(X, multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))), identity)), identity))))
0.19/0.65	= { by lemma 5 }
0.19/0.65	  multiply(X, multiply(multiply(X, multiply(multiply(X, X), multiply(X, multiply(multiply(X, identity), identity)))), multiply(multiply(multiply(X, identity), identity), multiply(multiply(multiply(X, identity), identity), multiply(multiply(X, identity), identity)))))
0.19/0.65	= { by axiom 2 (single_axiom) }
0.19/0.65	  X
0.19/0.65	
0.19/0.65	Goal 1 (prove_order4): multiply(a, multiply(a, multiply(a, a))) = identity.
0.19/0.65	Proof:
0.19/0.65	  multiply(a, multiply(a, multiply(a, a)))
0.19/0.65	= { by lemma 20 }
0.19/0.65	  multiply(a, multiply(a, multiply(multiply(a, a), identity)))
0.19/0.65	= { by lemma 20 }
0.19/0.65	  multiply(a, multiply(multiply(a, multiply(multiply(a, a), identity)), identity))
0.19/0.65	= { by lemma 19 }
0.19/0.65	  identity
0.19/0.65	% SZS output end Proof
0.19/0.65	
0.19/0.65	RESULT: Unsatisfiable (the axioms are contradictory).
0.19/0.65	EOF