0.04/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.13/0.14	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.35	% Computer   : n026.cluster.edu
0.13/0.35	% Model      : x86_64 x86_64
0.13/0.35	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.13/0.35	% Memory     : 8042.1875MB
0.13/0.35	% OS         : Linux 3.10.0-693.el7.x86_64
0.13/0.35	% CPULimit   : 180
0.13/0.35	% DateTime   : Thu Aug 29 13:25:05 EDT 2019
0.20/0.35	% CPUTime    : 
2.84/3.01	% SZS status Unsatisfiable
2.84/3.01	
2.84/3.02	% SZS output start Proof
2.84/3.02	Take the following subset of the input axioms:
2.88/3.05	  fof(additive_inverse_additive_inverse, axiom, ![X]: X=additive_inverse(additive_inverse(X))).
2.88/3.05	  fof(associativity_for_addition, axiom, ![X, Y, Z]: add(add(X, Y), Z)=add(X, add(Y, Z))).
2.88/3.05	  fof(associator, axiom, ![X, Y, Z]: associator(X, Y, Z)=add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z))))).
2.88/3.05	  fof(commutativity_for_addition, axiom, ![X, Y]: add(Y, X)=add(X, Y)).
2.88/3.05	  fof(distribute1, axiom, ![X, Y, Z]: add(multiply(X, Y), multiply(X, Z))=multiply(X, add(Y, Z))).
2.88/3.05	  fof(distribute2, axiom, ![X, Y, Z]: multiply(add(X, Y), Z)=add(multiply(X, Z), multiply(Y, Z))).
2.88/3.05	  fof(left_additive_identity, axiom, ![X]: add(additive_identity, X)=X).
2.88/3.05	  fof(left_additive_inverse, axiom, ![X]: additive_identity=add(additive_inverse(X), X)).
2.88/3.05	  fof(left_alternative, axiom, ![X, Y]: multiply(multiply(X, X), Y)=multiply(X, multiply(X, Y))).
2.88/3.05	  fof(left_multiplicative_zero, axiom, ![X]: multiply(additive_identity, X)=additive_identity).
2.88/3.05	  fof(prove_flexible_law, negated_conjecture, associator(x, y, x)!=additive_identity).
2.88/3.05	  fof(right_additive_identity, axiom, ![X]: add(X, additive_identity)=X).
2.88/3.05	  fof(right_alternative, axiom, ![X, Y]: multiply(X, multiply(Y, Y))=multiply(multiply(X, Y), Y)).
2.88/3.05	  fof(right_multiplicative_zero, axiom, ![X]: multiply(X, additive_identity)=additive_identity).
2.88/3.05	
2.88/3.05	Now clausify the problem and encode Horn clauses using encoding 3 of
2.88/3.05	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.88/3.05	We repeatedly replace C & s=t => u=v by the two clauses:
2.88/3.05	  fresh(y, y, x1...xn) = u
2.88/3.05	  C => fresh(s, t, x1...xn) = v
2.88/3.05	where fresh is a fresh function symbol and x1..xn are the free
2.88/3.05	variables of u and v.
2.88/3.05	A predicate p(X) is encoded as p(X)=true (this is sound, because the
2.88/3.05	input problem has no model of domain size 1).
2.88/3.05	
2.88/3.05	The encoding turns the above axioms into the following unit equations and goals:
2.88/3.05	
2.88/3.05	Axiom 1 (right_alternative): multiply(X, multiply(Y, Y)) = multiply(multiply(X, Y), Y).
2.88/3.05	Axiom 2 (commutativity_for_addition): add(X, Y) = add(Y, X).
2.88/3.05	Axiom 3 (left_alternative): multiply(multiply(X, X), Y) = multiply(X, multiply(X, Y)).
2.88/3.05	Axiom 4 (distribute2): multiply(add(X, Y), Z) = add(multiply(X, Z), multiply(Y, Z)).
2.88/3.05	Axiom 5 (left_multiplicative_zero): multiply(additive_identity, X) = additive_identity.
2.88/3.05	Axiom 6 (left_additive_inverse): additive_identity = add(additive_inverse(X), X).
2.88/3.05	Axiom 7 (left_additive_identity): add(additive_identity, X) = X.
2.88/3.05	Axiom 8 (right_multiplicative_zero): multiply(X, additive_identity) = additive_identity.
2.88/3.05	Axiom 9 (additive_inverse_additive_inverse): X = additive_inverse(additive_inverse(X)).
2.88/3.05	Axiom 10 (associativity_for_addition): add(add(X, Y), Z) = add(X, add(Y, Z)).
2.88/3.05	Axiom 11 (associator): associator(X, Y, Z) = add(multiply(multiply(X, Y), Z), additive_inverse(multiply(X, multiply(Y, Z)))).
2.88/3.05	Axiom 12 (distribute1): add(multiply(X, Y), multiply(X, Z)) = multiply(X, add(Y, Z)).
2.88/3.05	Axiom 13 (right_additive_identity): add(X, additive_identity) = X.
2.88/3.05	
2.88/3.05	Lemma 14: add(X, additive_inverse(X)) = additive_identity.
2.88/3.05	Proof:
2.88/3.05	  add(X, additive_inverse(X))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(additive_inverse(X), X)
2.88/3.05	= { by axiom 6 (left_additive_inverse) }
2.88/3.05	  additive_identity
2.88/3.05	
2.88/3.05	Lemma 15: add(X, add(Y, additive_inverse(X))) = Y.
2.88/3.05	Proof:
2.88/3.05	  add(X, add(Y, additive_inverse(X)))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(X, add(additive_inverse(X), Y))
2.88/3.05	= { by axiom 10 (associativity_for_addition) }
2.88/3.05	  add(add(X, additive_inverse(X)), Y)
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(additive_identity, Y)
2.88/3.05	= { by axiom 7 (left_additive_identity) }
2.88/3.05	  Y
2.88/3.05	
2.88/3.05	Lemma 16: add(additive_inverse(multiply(X, Y)), multiply(add(X, Z), Y)) = multiply(Z, Y).
2.88/3.05	Proof:
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(add(X, Z), Y))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(add(Z, X), Y))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(multiply(add(Z, X), Y), additive_inverse(multiply(X, Y)))
2.88/3.05	= { by axiom 4 (distribute2) }
2.88/3.05	  add(add(multiply(Z, Y), multiply(X, Y)), additive_inverse(multiply(X, Y)))
2.88/3.05	= { by axiom 10 (associativity_for_addition) }
2.88/3.05	  add(multiply(Z, Y), add(multiply(X, Y), additive_inverse(multiply(X, Y))))
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(multiply(Z, Y), additive_identity)
2.88/3.05	= { by axiom 13 (right_additive_identity) }
2.88/3.05	  multiply(Z, Y)
2.88/3.05	
2.88/3.05	Lemma 17: additive_inverse(multiply(X, Y)) = multiply(additive_inverse(X), Y).
2.88/3.05	Proof:
2.88/3.05	  additive_inverse(multiply(X, Y))
2.88/3.05	= { by axiom 13 (right_additive_identity) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), additive_identity)
2.88/3.05	= { by axiom 5 (left_multiplicative_zero) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(additive_identity, Y))
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(add(X, additive_inverse(X)), Y))
2.88/3.05	= { by lemma 16 }
2.88/3.05	  multiply(additive_inverse(X), Y)
2.88/3.05	
2.88/3.05	Lemma 18: multiply(additive_inverse(X), Y) = multiply(X, additive_inverse(Y)).
2.88/3.05	Proof:
2.88/3.05	  multiply(additive_inverse(X), Y)
2.88/3.05	= { by axiom 13 (right_additive_identity) }
2.88/3.05	  add(multiply(additive_inverse(X), Y), additive_identity)
2.88/3.05	= { by lemma 17 }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), additive_identity)
2.88/3.05	= { by axiom 8 (right_multiplicative_zero) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(X, additive_identity))
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(X, add(Y, additive_inverse(Y))))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(X, add(additive_inverse(Y), Y)))
2.88/3.05	= { by axiom 2 (commutativity_for_addition) }
2.88/3.05	  add(multiply(X, add(additive_inverse(Y), Y)), additive_inverse(multiply(X, Y)))
2.88/3.05	= { by axiom 12 (distribute1) }
2.88/3.05	  add(add(multiply(X, additive_inverse(Y)), multiply(X, Y)), additive_inverse(multiply(X, Y)))
2.88/3.05	= { by axiom 10 (associativity_for_addition) }
2.88/3.05	  add(multiply(X, additive_inverse(Y)), add(multiply(X, Y), additive_inverse(multiply(X, Y))))
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(multiply(X, additive_inverse(Y)), additive_identity)
2.88/3.05	= { by axiom 13 (right_additive_identity) }
2.88/3.05	  multiply(X, additive_inverse(Y))
2.88/3.05	
2.88/3.05	Lemma 19: additive_inverse(multiply(X, Y)) = multiply(X, additive_inverse(Y)).
2.88/3.05	Proof:
2.88/3.05	  additive_inverse(multiply(X, Y))
2.88/3.05	= { by axiom 13 (right_additive_identity) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), additive_identity)
2.88/3.05	= { by axiom 5 (left_multiplicative_zero) }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(additive_identity, Y))
2.88/3.05	= { by lemma 14 }
2.88/3.05	  add(additive_inverse(multiply(X, Y)), multiply(add(X, additive_inverse(X)), Y))
2.88/3.05	= { by lemma 16 }
2.88/3.05	  multiply(additive_inverse(X), Y)
2.88/3.05	= { by lemma 18 }
2.88/3.09	  multiply(X, additive_inverse(Y))
2.88/3.09	
2.88/3.09	Goal 1 (prove_flexible_law): associator(x, y, x) = additive_identity.
2.88/3.09	Proof:
2.88/3.09	  associator(x, y, x)
2.88/3.09	= { by lemma 15 }
2.88/3.09	  associator(x, add(x, add(y, additive_inverse(x))), x)
2.88/3.09	= { by axiom 11 (associator) }
2.88/3.09	  add(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), x), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 13 (right_additive_identity) }
2.88/3.09	  add(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(x, additive_identity)), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 14 }
2.88/3.09	  add(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(x, add(add(y, additive_inverse(x)), additive_inverse(add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 10 (associativity_for_addition) }
2.88/3.09	  add(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(add(x, add(y, additive_inverse(x))), additive_inverse(add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  add(add(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(x, add(y, additive_inverse(x)))), multiply(multiply(x, add(x, add(y, additive_inverse(x)))), additive_inverse(add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 1 (right_alternative) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), multiply(multiply(x, add(x, add(y, additive_inverse(x)))), additive_inverse(add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 19 }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(multiply(x, add(x, add(y, additive_inverse(x)))), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(add(multiply(x, x), multiply(x, add(y, additive_inverse(x)))), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(add(multiply(x, add(y, additive_inverse(x))), multiply(x, x)), add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 4 (distribute2) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(add(multiply(multiply(x, add(y, additive_inverse(x))), add(y, additive_inverse(x))), multiply(multiply(x, x), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 1 (right_alternative) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(add(multiply(x, multiply(add(y, additive_inverse(x)), add(y, additive_inverse(x)))), multiply(multiply(x, x), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 3 (left_alternative) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(add(multiply(x, multiply(add(y, additive_inverse(x)), add(y, additive_inverse(x)))), multiply(x, multiply(x, add(y, additive_inverse(x))))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(x, add(multiply(add(y, additive_inverse(x)), add(y, additive_inverse(x))), multiply(x, add(y, additive_inverse(x))))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 4 (distribute2) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(add(y, additive_inverse(x)), x), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 19 }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), multiply(x, additive_inverse(multiply(add(x, add(y, additive_inverse(x))), add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 19 }
2.88/3.09	  add(add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x))))), multiply(x, multiply(add(x, add(y, additive_inverse(x))), additive_inverse(add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  add(multiply(x, add(multiply(add(x, add(y, additive_inverse(x))), add(x, add(y, additive_inverse(x)))), multiply(add(x, add(y, additive_inverse(x))), additive_inverse(add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(add(x, add(y, additive_inverse(x))), additive_inverse(add(y, additive_inverse(x)))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 10 (associativity_for_addition) }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, add(add(y, additive_inverse(x)), additive_inverse(add(y, additive_inverse(x))))))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 14 }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), add(x, additive_identity))), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by axiom 13 (right_additive_identity) }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x)), additive_inverse(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 17 }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x)), multiply(additive_inverse(x), multiply(add(x, add(y, additive_inverse(x))), x)))
2.88/3.09	= { by lemma 18 }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x)), multiply(x, additive_inverse(multiply(add(x, add(y, additive_inverse(x))), x))))
2.88/3.09	= { by lemma 17 }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x)), multiply(x, multiply(additive_inverse(add(x, add(y, additive_inverse(x)))), x)))
2.88/3.09	= { by lemma 18 }
2.88/3.09	  add(multiply(x, multiply(add(x, add(y, additive_inverse(x))), x)), multiply(x, multiply(add(x, add(y, additive_inverse(x))), additive_inverse(x))))
2.88/3.09	= { by axiom 12 (distribute1) }
2.88/3.09	  multiply(x, add(multiply(add(x, add(y, additive_inverse(x))), x), multiply(add(x, add(y, additive_inverse(x))), additive_inverse(x))))
2.88/3.09	= { by lemma 18 }
2.88/3.09	  multiply(x, add(multiply(add(x, add(y, additive_inverse(x))), x), multiply(additive_inverse(add(x, add(y, additive_inverse(x)))), x)))
2.88/3.09	= { by axiom 4 (distribute2) }
2.88/3.09	  multiply(x, multiply(add(add(x, add(y, additive_inverse(x))), additive_inverse(add(x, add(y, additive_inverse(x))))), x))
2.88/3.09	= { by axiom 10 (associativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(x, add(add(y, additive_inverse(x)), additive_inverse(add(x, add(y, additive_inverse(x)))))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(x, add(add(y, additive_inverse(x)), additive_inverse(add(add(y, additive_inverse(x)), x)))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(x, add(additive_inverse(add(add(y, additive_inverse(x)), x)), add(y, additive_inverse(x)))), x))
2.88/3.09	= { by axiom 10 (associativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(x, additive_inverse(add(add(y, additive_inverse(x)), x))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(x, additive_inverse(add(x, add(y, additive_inverse(x))))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 9 (additive_inverse_additive_inverse) }
2.88/3.09	  multiply(x, multiply(add(add(x, additive_inverse(add(x, additive_inverse(additive_inverse(add(y, additive_inverse(x))))))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(x, additive_inverse(add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), x))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by lemma 15 }
2.88/3.09	  multiply(x, multiply(add(add(additive_inverse(add(y, additive_inverse(x))), add(add(x, additive_inverse(add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), x))), additive_inverse(additive_inverse(add(y, additive_inverse(x)))))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(additive_inverse(add(y, additive_inverse(x))), add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), add(x, additive_inverse(add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), x))))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 10 (associativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(additive_inverse(add(y, additive_inverse(x))), add(add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), x), additive_inverse(add(additive_inverse(additive_inverse(add(y, additive_inverse(x)))), x)))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by lemma 14 }
2.88/3.09	  multiply(x, multiply(add(add(additive_inverse(add(y, additive_inverse(x))), additive_identity), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 13 (right_additive_identity) }
2.88/3.09	  multiply(x, multiply(add(additive_inverse(add(y, additive_inverse(x))), add(y, additive_inverse(x))), x))
2.88/3.09	= { by axiom 2 (commutativity_for_addition) }
2.88/3.09	  multiply(x, multiply(add(add(y, additive_inverse(x)), additive_inverse(add(y, additive_inverse(x)))), x))
2.88/3.09	= { by lemma 14 }
2.88/3.09	  multiply(x, multiply(additive_identity, x))
2.88/3.09	= { by axiom 5 (left_multiplicative_zero) }
2.88/3.09	  multiply(x, additive_identity)
2.88/3.09	= { by axiom 8 (right_multiplicative_zero) }
2.88/3.09	  additive_identity
2.88/3.09	% SZS output end Proof
2.88/3.09	
2.88/3.09	RESULT: Unsatisfiable (the axioms are contradictory).
2.88/3.09	EOF