0.00/0.11	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.11/0.11	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.11/0.32	% Computer   : n027.cluster.edu
0.11/0.32	% Model      : x86_64 x86_64
0.11/0.32	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.11/0.32	% Memory     : 8042.1875MB
0.11/0.32	% OS         : Linux 3.10.0-693.el7.x86_64
0.11/0.32	% CPULimit   : 1200
0.11/0.32	% WCLimit    : 120
0.11/0.32	% DateTime   : Tue Jul 13 16:29:25 EDT 2021
0.11/0.32	% CPUTime    : 
0.16/0.56	% SZS status Theorem
0.16/0.56	
0.16/0.56	% SZS output start Proof
0.16/0.56	Take the following subset of the input axioms:
0.16/0.56	  fof('ass(cond(299, 0), 2)', axiom, ![Vd456, Vd457, Vd458]: (greater(Vd457, Vd458) => greater(vmul(Vd457, Vd456), vmul(Vd458, Vd456)))).
0.16/0.56	  fof('holds(conjunct1(314), 510, 0)', axiom, greater(vd508, vd509)).
0.16/0.56	  fof('holds(conjunct1(315), 514, 0)', conjecture, greater(vmul(vd508, vd511), vmul(vd509, vd511))).
0.16/0.56	
0.16/0.56	Now clausify the problem and encode Horn clauses using encoding 3 of
0.16/0.56	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
0.16/0.56	We repeatedly replace C & s=t => u=v by the two clauses:
0.16/0.56	  fresh(y, y, x1...xn) = u
0.16/0.56	  C => fresh(s, t, x1...xn) = v
0.16/0.56	where fresh is a fresh function symbol and x1..xn are the free
0.16/0.56	variables of u and v.
0.16/0.56	A predicate p(X) is encoded as p(X)=true (this is sound, because the
0.16/0.56	input problem has no model of domain size 1).
0.16/0.56	
0.16/0.56	The encoding turns the above axioms into the following unit equations and goals:
0.16/0.56	
0.16/0.56	Axiom 1 (holds(conjunct1(314), 510, 0)): greater(vd508, vd509) = true2.
0.16/0.56	Axiom 2 (ass(cond(299, 0), 2)): fresh26(X, X, Y, Z, W) = true2.
0.16/0.56	Axiom 3 (ass(cond(299, 0), 2)): fresh26(greater(X, Y), true2, Z, X, Y) = greater(vmul(X, Z), vmul(Y, Z)).
0.16/0.56	
0.16/0.56	Goal 1 (holds(conjunct1(315), 514, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd511)) = true2.
0.16/0.56	Proof:
0.16/0.56	  greater(vmul(vd508, vd511), vmul(vd509, vd511))
0.16/0.56	= { by axiom 3 (ass(cond(299, 0), 2)) R->L }
0.16/0.56	  fresh26(greater(vd508, vd509), true2, vd511, vd508, vd509)
0.16/0.56	= { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
0.16/0.56	  fresh26(greater(vd508, vd509), greater(vd508, vd509), vd511, vd508, vd509)
0.16/0.56	= { by axiom 2 (ass(cond(299, 0), 2)) }
0.16/0.56	  true2
0.16/0.56	% SZS output end Proof
0.16/0.56	
0.16/0.56	RESULT: Theorem (the conjecture is true).
0.16/0.57	EOF