0.03/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.13	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.13/0.35	% Computer   : n010.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 10:19:36 EDT 2019
0.13/0.35	% CPUTime    : 
0.20/0.50	% SZS status Unsatisfiable
0.20/0.50	
0.20/0.50	% SZS output start Proof
0.20/0.50	Take the following subset of the input axioms:
0.20/0.52	  fof(additive_id1, axiom, ![X]: X=add(X, additive_identity)).
0.20/0.52	  fof(additive_inverse1, axiom, ![X]: add(X, inverse(X))=multiplicative_identity).
0.20/0.52	  fof(commutativity_of_add, axiom, ![X, Y]: add(X, Y)=add(Y, X)).
0.20/0.52	  fof(commutativity_of_multiply, axiom, ![X, Y]: multiply(X, Y)=multiply(Y, X)).
0.20/0.52	  fof(distributivity1, axiom, ![X, Y, Z]: multiply(add(X, Y), add(X, Z))=add(X, multiply(Y, Z))).
0.20/0.52	  fof(distributivity2, axiom, ![X, Y, Z]: multiply(X, add(Y, Z))=add(multiply(X, Y), multiply(X, Z))).
0.20/0.52	  fof(multiplicative_id1, axiom, ![X]: multiply(X, multiplicative_identity)=X).
0.20/0.52	  fof(multiplicative_inverse1, axiom, ![X]: multiply(X, inverse(X))=additive_identity).
0.20/0.52	  fof(prove_associativity, negated_conjecture, multiply(a, multiply(b, c))!=multiply(multiply(a, b), c)).
0.20/0.52	
0.20/0.52	Now clausify the problem and encode Horn clauses using encoding 3 of
0.20/0.52	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.20/0.52	We repeatedly replace C & s=t => u=v by the two clauses:
0.20/0.52	  fresh(y, y, x1...xn) = u
0.20/0.52	  C => fresh(s, t, x1...xn) = v
0.20/0.52	where fresh is a fresh function symbol and x1..xn are the free
0.20/0.52	variables of u and v.
0.20/0.52	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.20/0.52	input problem has no model of domain size 1).
0.20/0.52	
0.20/0.52	The encoding turns the above axioms into the following unit equations and goals:
0.20/0.52	
0.20/0.52	Axiom 1 (commutativity_of_multiply): multiply(X, Y) = multiply(Y, X).
0.20/0.52	Axiom 2 (additive_inverse1): add(X, inverse(X)) = multiplicative_identity.
0.20/0.52	Axiom 3 (distributivity2): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
0.20/0.52	Axiom 4 (multiplicative_inverse1): multiply(X, inverse(X)) = additive_identity.
0.20/0.52	Axiom 5 (commutativity_of_add): add(X, Y) = add(Y, X).
0.20/0.52	Axiom 6 (distributivity1): multiply(add(X, Y), add(X, Z)) = add(X, multiply(Y, Z)).
0.20/0.52	Axiom 7 (multiplicative_id1): multiply(X, multiplicative_identity) = X.
0.20/0.52	Axiom 8 (additive_id1): X = add(X, additive_identity).
0.20/0.52	
0.20/0.52	Lemma 9: multiply(multiplicative_identity, X) = X.
0.20/0.52	Proof:
0.20/0.52	  multiply(multiplicative_identity, X)
0.20/0.52	= { by axiom 1 (commutativity_of_multiply) }
0.20/0.52	  multiply(X, multiplicative_identity)
0.20/0.52	= { by axiom 7 (multiplicative_id1) }
0.20/0.52	  X
0.20/0.52	
0.20/0.52	Lemma 10: add(additive_identity, X) = X.
0.20/0.52	Proof:
0.20/0.52	  add(additive_identity, X)
0.20/0.52	= { by axiom 5 (commutativity_of_add) }
0.20/0.52	  add(X, additive_identity)
0.20/0.52	= { by axiom 8 (additive_id1) }
0.20/0.52	  X
0.20/0.52	
0.20/0.52	Lemma 11: multiply(X, add(Y, inverse(X))) = multiply(X, Y).
0.20/0.52	Proof:
0.20/0.52	  multiply(X, add(Y, inverse(X)))
0.20/0.52	= { by axiom 5 (commutativity_of_add) }
0.20/0.52	  multiply(X, add(inverse(X), Y))
0.20/0.52	= { by axiom 3 (distributivity2) }
0.20/0.52	  add(multiply(X, inverse(X)), multiply(X, Y))
0.20/0.52	= { by axiom 4 (multiplicative_inverse1) }
0.20/0.52	  add(additive_identity, multiply(X, Y))
0.20/0.52	= { by lemma 10 }
0.20/0.52	  multiply(X, Y)
0.20/0.52	
0.20/0.52	Lemma 12: multiply(X, additive_identity) = additive_identity.
0.20/0.52	Proof:
0.20/0.52	  multiply(X, additive_identity)
0.20/0.52	= { by lemma 11 }
0.20/0.52	  multiply(X, add(additive_identity, inverse(X)))
0.20/0.52	= { by lemma 10 }
0.20/0.52	  multiply(X, inverse(X))
0.20/0.52	= { by axiom 4 (multiplicative_inverse1) }
0.20/0.52	  additive_identity
0.20/0.52	
0.20/0.52	Lemma 13: add(X, multiplicative_identity) = multiplicative_identity.
0.20/0.52	Proof:
0.20/0.52	  add(X, multiplicative_identity)
0.20/0.52	= { by axiom 5 (commutativity_of_add) }
0.20/0.52	  add(multiplicative_identity, X)
0.20/0.52	= { by lemma 9 }
0.20/0.52	  multiply(multiplicative_identity, add(multiplicative_identity, X))
0.20/0.52	= { by axiom 8 (additive_id1) }
0.20/0.52	  multiply(add(multiplicative_identity, additive_identity), add(multiplicative_identity, X))
0.20/0.52	= { by axiom 6 (distributivity1) }
0.20/0.52	  add(multiplicative_identity, multiply(additive_identity, X))
0.20/0.52	= { by axiom 1 (commutativity_of_multiply) }
0.20/0.52	  add(multiplicative_identity, multiply(X, additive_identity))
0.20/0.52	= { by lemma 12 }
0.20/0.52	  add(multiplicative_identity, additive_identity)
0.20/0.52	= { by axiom 8 (additive_id1) }
0.20/0.52	  multiplicative_identity
0.20/0.52	
0.20/0.52	Lemma 14: add(X, multiply(X, Y)) = multiply(X, add(Y, multiplicative_identity)).
0.20/0.52	Proof:
0.20/0.52	  add(X, multiply(X, Y))
0.20/0.52	= { by axiom 7 (multiplicative_id1) }
0.20/0.52	  add(multiply(X, multiplicative_identity), multiply(X, Y))
0.20/0.52	= { by axiom 3 (distributivity2) }
0.20/0.52	  multiply(X, add(multiplicative_identity, Y))
0.20/0.52	= { by axiom 5 (commutativity_of_add) }
0.20/0.52	  multiply(X, add(Y, multiplicative_identity))
0.20/0.52	
0.20/0.52	Lemma 15: multiply(X, add(inverse(X), Y)) = multiply(X, Y).
0.20/0.52	Proof:
0.20/0.52	  multiply(X, add(inverse(X), Y))
0.20/0.52	= { by axiom 5 (commutativity_of_add) }
0.20/0.52	  multiply(X, add(Y, inverse(X)))
0.20/0.52	= { by lemma 11 }
0.20/0.52	  multiply(X, Y)
0.20/0.52	
0.20/0.52	Lemma 16: add(X, multiply(Y, inverse(X))) = add(X, Y).
0.20/0.52	Proof:
0.20/0.52	  add(X, multiply(Y, inverse(X)))
0.20/0.52	= { by axiom 1 (commutativity_of_multiply) }
0.20/0.52	  add(X, multiply(inverse(X), Y))
0.20/0.52	= { by axiom 6 (distributivity1) }
0.20/0.52	  multiply(add(X, inverse(X)), add(X, Y))
0.20/0.52	= { by axiom 2 (additive_inverse1) }
0.20/0.52	  multiply(multiplicative_identity, add(X, Y))
0.20/0.52	= { by lemma 9 }
0.38/0.54	  add(X, Y)
0.38/0.54	
0.38/0.54	Goal 1 (prove_associativity): multiply(a, multiply(b, c)) = multiply(multiply(a, b), c).
0.38/0.54	Proof:
0.38/0.54	  multiply(a, multiply(b, c))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(a, multiply(c, b))
0.38/0.54	= { by axiom 8 (additive_id1) }
0.38/0.54	  add(multiply(a, multiply(c, b)), additive_identity)
0.38/0.54	= { by lemma 12 }
0.38/0.54	  add(multiply(a, multiply(c, b)), multiply(c, additive_identity))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  add(multiply(a, multiply(c, b)), multiply(additive_identity, c))
0.38/0.54	= { by axiom 6 (distributivity1) }
0.38/0.54	  multiply(add(multiply(a, multiply(c, b)), additive_identity), add(multiply(a, multiply(c, b)), c))
0.38/0.54	= { by axiom 8 (additive_id1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(multiply(a, multiply(c, b)), c))
0.38/0.54	= { by axiom 5 (commutativity_of_add) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(c, multiply(a, multiply(c, b))))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(c, multiply(multiply(c, b), a)))
0.38/0.54	= { by axiom 6 (distributivity1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), multiply(add(c, multiply(c, b)), add(c, a)))
0.38/0.54	= { by lemma 14 }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), multiply(multiply(c, add(b, multiplicative_identity)), add(c, a)))
0.38/0.54	= { by lemma 13 }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), multiply(multiply(c, multiplicative_identity), add(c, a)))
0.38/0.54	= { by axiom 7 (multiplicative_id1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), multiply(c, add(c, a)))
0.38/0.54	= { by axiom 8 (additive_id1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), multiply(add(c, additive_identity), add(c, a)))
0.38/0.54	= { by axiom 6 (distributivity1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(c, multiply(additive_identity, a)))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(c, multiply(a, additive_identity)))
0.38/0.54	= { by lemma 12 }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), add(c, additive_identity))
0.38/0.54	= { by axiom 8 (additive_id1) }
0.38/0.54	  multiply(multiply(a, multiply(c, b)), c)
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, multiply(a, multiply(c, b)))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, c)))
0.38/0.54	= { by axiom 8 (additive_id1) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(c, additive_identity))))
0.38/0.54	= { by axiom 4 (multiplicative_inverse1) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(c, multiply(inverse(c), inverse(inverse(c)))))))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(c, multiply(inverse(inverse(c)), inverse(c))))))
0.38/0.54	= { by lemma 16 }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(c, inverse(inverse(c))))))
0.38/0.54	= { by axiom 5 (commutativity_of_add) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(inverse(inverse(c)), c))))
0.38/0.54	= { by axiom 7 (multiplicative_id1) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(inverse(inverse(c)), multiply(c, multiplicative_identity)))))
0.38/0.54	= { by axiom 2 (additive_inverse1) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(inverse(inverse(c)), multiply(c, add(inverse(c), inverse(inverse(c))))))))
0.38/0.54	= { by lemma 15 }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(inverse(inverse(c)), multiply(c, inverse(inverse(c)))))))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, add(inverse(inverse(c)), multiply(inverse(inverse(c)), c)))))
0.38/0.54	= { by lemma 14 }
0.38/0.54	  multiply(c, multiply(a, multiply(b, multiply(inverse(inverse(c)), add(c, multiplicative_identity)))))
0.38/0.54	= { by lemma 13 }
0.38/0.54	  multiply(c, multiply(a, multiply(b, multiply(inverse(inverse(c)), multiplicative_identity))))
0.38/0.54	= { by axiom 7 (multiplicative_id1) }
0.38/0.54	  multiply(c, multiply(a, multiply(b, inverse(inverse(c)))))
0.38/0.54	= { by lemma 15 }
0.38/0.54	  multiply(c, add(inverse(c), multiply(a, multiply(b, inverse(inverse(c))))))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, add(inverse(c), multiply(multiply(b, inverse(inverse(c))), a)))
0.38/0.54	= { by axiom 6 (distributivity1) }
0.38/0.54	  multiply(c, multiply(add(inverse(c), multiply(b, inverse(inverse(c)))), add(inverse(c), a)))
0.38/0.54	= { by lemma 16 }
0.38/0.54	  multiply(c, multiply(add(inverse(c), b), add(inverse(c), a)))
0.38/0.54	= { by axiom 6 (distributivity1) }
0.38/0.54	  multiply(c, add(inverse(c), multiply(b, a)))
0.38/0.54	= { by lemma 15 }
0.38/0.54	  multiply(c, multiply(b, a))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(c, multiply(a, b))
0.38/0.54	= { by axiom 1 (commutativity_of_multiply) }
0.38/0.54	  multiply(multiply(a, b), c)
0.38/0.54	% SZS output end Proof
0.38/0.54	
0.38/0.54	RESULT: Unsatisfiable (the axioms are contradictory).
0.38/0.54	EOF