0.07/0.12	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.07/0.13	% 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 13:41:34 EDT 2019
0.13/0.34	% CPUTime    : 
164.03/164.38	% SZS status Unsatisfiable
164.03/164.38	
164.03/164.39	% SZS output start Proof
164.03/164.39	Take the following subset of the input axioms:
179.53/179.90	  fof(a_times_b_is_c, negated_conjecture, multiply(a, b)=c).
179.53/179.90	  fof(associativity_for_addition, axiom, ![X, Y, Z]: add(X, add(Y, Z))=add(add(X, Y), Z)).
179.53/179.90	  fof(associativity_for_multiplication, axiom, ![X, Y, Z]: multiply(X, multiply(Y, Z))=multiply(multiply(X, Y), Z)).
179.53/179.90	  fof(commutativity_for_addition, axiom, ![X, Y]: add(Y, X)=add(X, Y)).
179.53/179.90	  fof(distribute1, axiom, ![X, Y, Z]: multiply(X, add(Y, Z))=add(multiply(X, Y), multiply(X, Z))).
179.53/179.90	  fof(distribute2, axiom, ![X, Y, Z]: add(multiply(X, Z), multiply(Y, Z))=multiply(add(X, Y), Z)).
179.53/179.90	  fof(left_additive_identity, axiom, ![X]: X=add(additive_identity, X)).
179.53/179.90	  fof(left_additive_inverse, axiom, ![X]: add(additive_inverse(X), X)=additive_identity).
179.53/179.90	  fof(prove_commutativity, negated_conjecture, multiply(b, a)!=c).
179.53/179.90	  fof(right_additive_identity, axiom, ![X]: add(X, additive_identity)=X).
179.53/179.90	  fof(right_additive_inverse, axiom, ![X]: additive_identity=add(X, additive_inverse(X))).
179.53/179.90	  fof(x_fourthed_is_x, hypothesis, ![X]: multiply(X, multiply(X, multiply(X, X)))=X).
179.53/179.90	
179.53/179.90	Now clausify the problem and encode Horn clauses using encoding 3 of
179.53/179.90	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
179.53/179.90	We repeatedly replace C & s=t => u=v by the two clauses:
179.53/179.90	  fresh(y, y, x1...xn) = u
179.53/179.90	  C => fresh(s, t, x1...xn) = v
179.53/179.90	where fresh is a fresh function symbol and x1..xn are the free
179.53/179.90	variables of u and v.
179.53/179.90	A predicate p(X) is encoded as p(X)=true (this is sound, because the
179.53/179.90	input problem has no model of domain size 1).
179.53/179.90	
179.53/179.90	The encoding turns the above axioms into the following unit equations and goals:
179.53/179.90	
179.53/179.90	Axiom 1 (associativity_for_addition): add(X, add(Y, Z)) = add(add(X, Y), Z).
179.53/179.90	Axiom 2 (associativity_for_multiplication): multiply(X, multiply(Y, Z)) = multiply(multiply(X, Y), Z).
179.53/179.90	Axiom 3 (left_additive_identity): X = add(additive_identity, X).
179.53/179.90	Axiom 4 (left_additive_inverse): add(additive_inverse(X), X) = additive_identity.
179.53/179.90	Axiom 5 (distribute2): add(multiply(X, Y), multiply(Z, Y)) = multiply(add(X, Z), Y).
179.53/179.90	Axiom 6 (right_additive_identity): add(X, additive_identity) = X.
179.53/179.90	Axiom 7 (distribute1): multiply(X, add(Y, Z)) = add(multiply(X, Y), multiply(X, Z)).
179.53/179.90	Axiom 8 (right_additive_inverse): additive_identity = add(X, additive_inverse(X)).
179.53/179.90	Axiom 9 (commutativity_for_addition): add(X, Y) = add(Y, X).
179.53/179.90	Axiom 10 (a_times_b_is_c): multiply(a, b) = c.
180.10/180.41	EOF