0.00/0.04	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.04	% Command    : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn
0.03/0.26	% Computer   : n152.star.cs.uiowa.edu
0.03/0.26	% Model      : x86_64 x86_64
0.03/0.26	% CPU        : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
0.03/0.26	% Memory     : 32218.625MB
0.03/0.26	% OS         : Linux 3.10.0-693.2.2.el7.x86_64
0.03/0.26	% CPULimit   : 300
0.03/0.26	% DateTime   : Sat Jul 14 04:23:26 CDT 2018
0.03/0.26	% CPUTime    : 
0.50/0.74	% SZS status Theorem
0.50/0.74	
0.50/0.74	% SZS output start Proof
0.50/0.74	Take the following subset of the input axioms:
0.50/0.74	  fof('ass(cond(270, 0), 0)', axiom,
0.50/0.74	      ![Vd418, Vd419]: vmul(Vd419, Vd418)=vmul(Vd418, Vd419)).
0.50/0.74	  fof('ass(cond(299, 0), 2)', axiom,
0.50/0.74	      ![Vd456, Vd457, Vd458]:
0.50/0.74	        (greater(Vd457, Vd458)
0.50/0.74	           => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))).
0.50/0.74	  fof('holds(conjunct1(314), 510, 0)', axiom, greater(vd508, vd509)).
0.50/0.74	  fof('holds(conjunct1(315), 514, 0)', conjecture,
0.50/0.74	      greater(vmul(vd508, vd511), vmul(vd509, vd511))).
0.50/0.74	
0.50/0.74	Now clausify the problem and encode Horn clauses using encoding 3 of
0.50/0.74	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.50/0.74	We repeatedly replace C & s=t => u=v by the two clauses:
0.50/0.74	  $$fresh(y, y, x1...xn) = u
0.50/0.74	  C => $$fresh(s, t, x1...xn) = v
0.50/0.74	where $$fresh is a fresh function symbol and x1..xn are the free
0.50/0.74	variables of u and v.
0.50/0.74	A predicate p(X) is encoded as p(X)=$$true (this is sound, because the
0.50/0.74	input problem has no model of domain size 1).
0.50/0.74	
0.50/0.74	The encoding turns the above axioms into the following unit equations and goals:
0.50/0.74	
0.50/0.74	Axiom 16 (ass(cond(299, 0), 2)): $$fresh26(X, X, Y, Z, W) = $$true2.
0.50/0.74	Axiom 59 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
0.50/0.74	Axiom 79 (ass(cond(299, 0), 2)): $$fresh26(greater(X, Y), $$true2, Z, X, Y) = greater(vmul(X, Z), vmul(Y, Z)).
0.50/0.74	Axiom 93 (holds(conjunct1(314), 510, 0)): greater(vd508, vd509) = $$true2.
0.50/0.74	
0.50/0.74	Goal 1 (holds(conjunct1(315), 514, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd511)) = $$true2.
0.50/0.74	Proof:
0.50/0.74	  greater(vmul(vd508, vd511), vmul(vd509, vd511))
0.50/0.74	= { by axiom 59 (ass(cond(270, 0), 0)) }
0.50/0.74	  greater(vmul(vd511, vd508), vmul(vd509, vd511))
0.50/0.74	= { by axiom 59 (ass(cond(270, 0), 0)) }
0.50/0.74	  greater(vmul(vd508, vd511), vmul(vd509, vd511))
0.50/0.74	= { by axiom 79 (ass(cond(299, 0), 2)) }
0.50/0.74	  $$fresh26(greater(vd508, vd509), $$true2, vd511, vd508, vd509)
0.50/0.74	= { by axiom 93 (holds(conjunct1(314), 510, 0)) }
0.50/0.74	  $$fresh26($$true2, $$true2, vd511, vd508, vd509)
0.50/0.74	= { by axiom 16 (ass(cond(299, 0), 2)) }
0.50/0.74	  $$true2
0.50/0.74	% SZS output end Proof
0.50/0.74	
0.50/0.74	RESULT: Theorem (the conjecture is true).
0.50/0.75	EOF