0.03/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.12	% Command    : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn
0.12/0.33	% Computer   : n027.cluster.edu
0.12/0.33	% Model      : x86_64 x86_64
0.12/0.33	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.12/0.33	% Memory     : 8042.1875MB
0.12/0.33	% OS         : Linux 3.10.0-693.el7.x86_64
0.12/0.33	% CPULimit   : 180
0.12/0.33	% DateTime   : Thu Aug 29 12:27:24 EDT 2019
0.12/0.33	% CPUTime    : 
0.55/0.74	% SZS status Theorem
0.55/0.74	
0.55/0.74	% SZS output start Proof
0.55/0.74	Take the following subset of the input axioms:
0.55/0.74	  fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
0.55/0.74	  fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd418, Vd419)=vmul(Vd419, Vd418)).
0.55/0.74	  fof('ass(cond(281, 0), 0)', axiom, ![Vd432, Vd433, Vd434]: vmul(Vd432, vplus(Vd433, Vd434))=vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434))).
0.55/0.74	  fof('ass(cond(302, 0), 3)', axiom, ![Vd470, Vd471]: (greater(Vd470, Vd471) => Vd470=vplus(Vd471, vskolem9(Vd470, Vd471)))).
0.55/0.74	  fof('holds(conseq_conjunct1(conseq(304)), 483, 0)', axiom, greater(vd481, vd480)).
0.55/0.74	  fof('holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)', conjecture, greater(vmul(vd481, vd469), vmul(vd480, vd469))).
0.55/0.74	
0.55/0.74	Now clausify the problem and encode Horn clauses using encoding 3 of
0.55/0.74	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.55/0.74	We repeatedly replace C & s=t => u=v by the two clauses:
0.55/0.74	  fresh(y, y, x1...xn) = u
0.55/0.74	  C => fresh(s, t, x1...xn) = v
0.55/0.74	where fresh is a fresh function symbol and x1..xn are the free
0.55/0.74	variables of u and v.
0.55/0.74	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.55/0.74	input problem has no model of domain size 1).
0.55/0.74	
0.55/0.74	The encoding turns the above axioms into the following unit equations and goals:
0.55/0.74	
0.55/0.74	Axiom 1 (ass(cond(302, 0), 3)): fresh7(X, X, Y, Z) = Y.
0.55/0.74	Axiom 2 (holds(conseq_conjunct1(conseq(304)), 483, 0)): greater(vd481, vd480) = true2.
0.55/0.74	Axiom 3 (ass(cond(302, 0), 3)): fresh7(greater(X, Y), true2, X, Y) = vplus(Y, vskolem9(X, Y)).
0.55/0.74	Axiom 4 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
0.55/0.74	Axiom 5 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
0.55/0.74	Axiom 6 (ass(cond(281, 0), 0)): vmul(X, vplus(Y, Z)) = vplus(vmul(X, Y), vmul(X, Z)).
0.55/0.74	
0.55/0.74	Goal 1 (holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)): greater(vmul(vd481, vd469), vmul(vd480, vd469)) = true2.
0.55/0.74	Proof:
0.55/0.74	  greater(vmul(vd481, vd469), vmul(vd480, vd469))
0.55/0.74	= { by axiom 4 (ass(cond(270, 0), 0)) }
0.55/0.74	  greater(vmul(vd469, vd481), vmul(vd480, vd469))
0.55/0.74	= { by axiom 1 (ass(cond(302, 0), 3)) }
0.55/0.74	  greater(vmul(vd469, fresh7(true2, true2, vd481, vd480)), vmul(vd480, vd469))
0.55/0.74	= { by axiom 2 (holds(conseq_conjunct1(conseq(304)), 483, 0)) }
0.55/0.74	  greater(vmul(vd469, fresh7(greater(vd481, vd480), true2, vd481, vd480)), vmul(vd480, vd469))
0.55/0.74	= { by axiom 3 (ass(cond(302, 0), 3)) }
0.55/0.74	  greater(vmul(vd469, vplus(vd480, vskolem9(vd481, vd480))), vmul(vd480, vd469))
0.55/0.74	= { by axiom 6 (ass(cond(281, 0), 0)) }
0.55/0.74	  greater(vplus(vmul(vd469, vd480), vmul(vd469, vskolem9(vd481, vd480))), vmul(vd480, vd469))
0.55/0.74	= { by axiom 4 (ass(cond(270, 0), 0)) }
0.55/0.74	  greater(vplus(vmul(vd469, vd480), vmul(vd469, vskolem9(vd481, vd480))), vmul(vd469, vd480))
0.55/0.74	= { by axiom 5 (ass(cond(189, 0), 0)) }
0.55/0.74	  true2
0.55/0.74	% SZS output end Proof
0.55/0.74	
0.55/0.74	RESULT: Theorem (the conjecture is true).
0.55/0.74	EOF