0.05/0.10	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.05/0.10	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.10/0.30	% Computer   : n020.cluster.edu
0.10/0.30	% Model      : x86_64 x86_64
0.10/0.30	% CPU        : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.10/0.30	% Memory     : 8042.1875MB
0.10/0.30	% OS         : Linux 3.10.0-693.el7.x86_64
0.10/0.30	% CPULimit   : 1200
0.10/0.30	% WCLimit    : 120
0.10/0.30	% DateTime   : Tue Jul 13 16:28:21 EDT 2021
0.10/0.31	% CPUTime    : 
2.48/0.67	% SZS status Theorem
2.48/0.67	
2.86/0.69	% SZS output start Proof
2.86/0.69	Take the following subset of the input axioms:
2.86/0.69	  fof('ass(cond(140, 0), 0)', axiom, ![Vd208, Vd209]: (greater(Vd208, Vd209) => less(Vd209, Vd208))).
2.86/0.69	  fof('ass(cond(189, 0), 0)', axiom, ![Vd295, Vd296]: greater(vplus(Vd295, Vd296), Vd295)).
2.86/0.69	  fof('ass(cond(270, 0), 0)', axiom, ![Vd418, Vd419]: vmul(Vd419, Vd418)=vmul(Vd418, Vd419)).
2.86/0.69	  fof('ass(cond(33, 0), 0)', axiom, ![Vd46, Vd47, Vd48]: vplus(Vd46, vplus(Vd47, Vd48))=vplus(vplus(Vd46, Vd47), Vd48)).
2.86/0.69	  fof('ass(cond(61, 0), 0)', axiom, ![Vd78, Vd79]: vplus(Vd78, Vd79)=vplus(Vd79, Vd78)).
2.86/0.69	  fof('def(cond(conseq(axiom(3)), 12), 1)', axiom, ![Vd198, Vd199]: (less(Vd199, Vd198) <=> ?[Vd201]: Vd198=vplus(Vd199, Vd201))).
2.86/0.69	  fof('holds(conjunct1(314), 510, 0)', axiom, greater(vd508, vd509)).
2.86/0.69	  fof('holds(conjunct1(315), 514, 0)', axiom, greater(vmul(vd508, vd511), vmul(vd509, vd511))).
2.86/0.69	  fof('holds(conjunct2(314), 513, 0)', axiom, greater(vd511, vd512)).
2.86/0.69	  fof('holds(conjunct2(315), 515, 1)', axiom, greater(vmul(vd511, vd509), vmul(vd512, vd509))).
2.86/0.69	  fof('holds(conseq_conjunct2(315), 516, 0)', conjecture, greater(vmul(vd508, vd511), vmul(vd509, vd512))).
2.86/0.69	
2.86/0.69	Now clausify the problem and encode Horn clauses using encoding 3 of
2.86/0.69	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
2.86/0.69	We repeatedly replace C & s=t => u=v by the two clauses:
2.86/0.69	  fresh(y, y, x1...xn) = u
2.86/0.69	  C => fresh(s, t, x1...xn) = v
2.86/0.69	where fresh is a fresh function symbol and x1..xn are the free
2.86/0.69	variables of u and v.
2.86/0.69	A predicate p(X) is encoded as p(X)=true (this is sound, because the
2.86/0.69	input problem has no model of domain size 1).
2.86/0.69	
2.86/0.69	The encoding turns the above axioms into the following unit equations and goals:
2.86/0.69	
2.86/0.69	Axiom 1 (holds(conjunct1(314), 510, 0)): greater(vd508, vd509) = true2.
2.86/0.69	Axiom 2 (holds(conjunct2(314), 513, 0)): greater(vd511, vd512) = true2.
2.86/0.69	Axiom 3 (ass(cond(270, 0), 0)): vmul(X, Y) = vmul(Y, X).
2.86/0.69	Axiom 4 (ass(cond(61, 0), 0)): vplus(X, Y) = vplus(Y, X).
2.86/0.69	Axiom 5 (ass(cond(140, 0), 0)): fresh40(X, X, Y, Z) = true2.
2.86/0.69	Axiom 6 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh6(X, X, Y, Z) = Y.
2.86/0.69	Axiom 7 (ass(cond(189, 0), 0)): greater(vplus(X, Y), X) = true2.
2.86/0.69	Axiom 8 (ass(cond(33, 0), 0)): vplus(X, vplus(Y, Z)) = vplus(vplus(X, Y), Z).
2.86/0.69	Axiom 9 (ass(cond(140, 0), 0)): fresh40(greater(X, Y), true2, X, Y) = less(Y, X).
2.86/0.69	Axiom 10 (def(cond(conseq(axiom(3)), 12), 1)_1): fresh6(less(X, Y), true2, Y, X) = vplus(X, vd201(Y, X)).
2.86/0.69	Axiom 11 (holds(conjunct1(315), 514, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd511)) = true2.
2.86/0.69	Axiom 12 (holds(conjunct2(315), 515, 1)): greater(vmul(vd511, vd509), vmul(vd512, vd509)) = true2.
2.86/0.69	
2.86/0.69	Lemma 13: greater(vd511, vd512) = greater(vd508, vd509).
2.86/0.69	Proof:
2.86/0.69	  greater(vd511, vd512)
2.86/0.69	= { by axiom 2 (holds(conjunct2(314), 513, 0)) }
2.86/0.69	  true2
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
2.86/0.69	  greater(vd508, vd509)
2.86/0.69	
2.86/0.69	Lemma 14: fresh40(X, X, Y, Z) = greater(vd511, vd512).
2.86/0.69	Proof:
2.86/0.69	  fresh40(X, X, Y, Z)
2.86/0.69	= { by axiom 5 (ass(cond(140, 0), 0)) }
2.86/0.69	  true2
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
2.86/0.69	  greater(vd508, vd509)
2.86/0.69	= { by lemma 13 R->L }
2.86/0.69	  greater(vd511, vd512)
2.86/0.69	
2.86/0.69	Lemma 15: greater(vmul(vd508, vd511), vmul(vd509, vd511)) = greater(vd511, vd512).
2.86/0.69	Proof:
2.86/0.69	  greater(vmul(vd508, vd511), vmul(vd509, vd511))
2.86/0.69	= { by axiom 11 (holds(conjunct1(315), 514, 0)) }
2.86/0.69	  true2
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
2.86/0.69	  greater(vd508, vd509)
2.86/0.69	= { by lemma 13 R->L }
2.86/0.69	  greater(vd511, vd512)
2.86/0.69	
2.86/0.69	Lemma 16: greater(vmul(vd511, vd509), vmul(vd512, vd509)) = greater(vmul(vd508, vd511), vmul(vd509, vd511)).
2.86/0.69	Proof:
2.86/0.69	  greater(vmul(vd511, vd509), vmul(vd512, vd509))
2.86/0.69	= { by axiom 12 (holds(conjunct2(315), 515, 1)) }
2.86/0.69	  true2
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) R->L }
2.86/0.69	  greater(vd508, vd509)
2.86/0.69	= { by lemma 13 R->L }
2.86/0.69	  greater(vd511, vd512)
2.86/0.69	= { by lemma 15 R->L }
2.86/0.69	  greater(vmul(vd508, vd511), vmul(vd509, vd511))
2.86/0.69	
2.86/0.69	Lemma 17: fresh40(greater(X, Y), greater(vd511, vd512), X, Y) = less(Y, X).
2.86/0.69	Proof:
2.86/0.69	  fresh40(greater(X, Y), greater(vd511, vd512), X, Y)
2.86/0.69	= { by lemma 13 }
2.86/0.69	  fresh40(greater(X, Y), greater(vd508, vd509), X, Y)
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) }
2.86/0.69	  fresh40(greater(X, Y), true2, X, Y)
2.86/0.69	= { by axiom 9 (ass(cond(140, 0), 0)) }
2.86/0.69	  less(Y, X)
2.86/0.69	
2.86/0.69	Lemma 18: fresh6(less(X, Y), greater(vd511, vd512), Y, X) = vplus(X, vd201(Y, X)).
2.86/0.69	Proof:
2.86/0.69	  fresh6(less(X, Y), greater(vd511, vd512), Y, X)
2.86/0.69	= { by lemma 13 }
2.86/0.69	  fresh6(less(X, Y), greater(vd508, vd509), Y, X)
2.86/0.69	= { by axiom 1 (holds(conjunct1(314), 510, 0)) }
2.86/0.69	  fresh6(less(X, Y), true2, Y, X)
2.86/0.69	= { by axiom 10 (def(cond(conseq(axiom(3)), 12), 1)_1) }
2.86/0.70	  vplus(X, vd201(Y, X))
2.86/0.70	
2.86/0.70	Goal 1 (holds(conseq_conjunct2(315), 516, 0)): greater(vmul(vd508, vd511), vmul(vd509, vd512)) = true2.
2.86/0.70	Proof:
2.86/0.70	  greater(vmul(vd508, vd511), vmul(vd509, vd512))
2.86/0.70	= { by axiom 6 (def(cond(conseq(axiom(3)), 12), 1)_1) R->L }
2.86/0.70	  greater(fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd511, vd509), vmul(vd512, vd509)), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(fresh6(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(fresh6(greater(vd511, vd512), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 14 R->L }
2.86/0.70	  greater(fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd511, vd509), vmul(vd512, vd509)), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(fresh6(fresh40(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by axiom 3 (ass(cond(270, 0), 0)) }
2.86/0.70	  greater(fresh6(fresh40(greater(vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 17 }
2.86/0.70	  greater(fresh6(less(vmul(vd511, vd509), vmul(vd508, vd511)), greater(vd511, vd512), vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by lemma 18 }
2.86/0.70	  greater(vplus(vmul(vd511, vd509), vd201(vmul(vd508, vd511), vmul(vd511, vd509))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 4 (ass(cond(61, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd511, vd509)), vmul(vd509, vd512))
2.86/0.70	= { by axiom 6 (def(cond(conseq(axiom(3)), 12), 1)_1) R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd511, vd509), vmul(vd512, vd509)), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(greater(vmul(vd508, vd511), vmul(vd509, vd511)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(greater(vd511, vd512), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 14 R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd511, vd509), vmul(vd512, vd509)), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 16 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vmul(vd508, vd511), vmul(vd509, vd511)), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 15 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd512, vd509)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 3 (ass(cond(270, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(fresh40(greater(vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 17 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), fresh6(less(vmul(vd509, vd512), vmul(vd511, vd509)), greater(vd511, vd512), vmul(vd511, vd509), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by lemma 18 }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vplus(vmul(vd509, vd512), vd201(vmul(vd511, vd509), vmul(vd509, vd512)))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 4 (ass(cond(61, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 4 (ass(cond(61, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vmul(vd509, vd512)), vd201(vmul(vd508, vd511), vmul(vd511, vd509))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 8 (ass(cond(33, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vplus(vmul(vd509, vd512), vd201(vmul(vd508, vd511), vmul(vd511, vd509)))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 4 (ass(cond(61, 0), 0)) }
2.86/0.70	  greater(vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vplus(vd201(vmul(vd508, vd511), vmul(vd511, vd509)), vmul(vd509, vd512))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 8 (ass(cond(33, 0), 0)) }
2.86/0.70	  greater(vplus(vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vd201(vmul(vd508, vd511), vmul(vd511, vd509))), vmul(vd509, vd512)), vmul(vd509, vd512))
2.86/0.70	= { by axiom 4 (ass(cond(61, 0), 0)) R->L }
2.86/0.70	  greater(vplus(vmul(vd509, vd512), vplus(vd201(vmul(vd511, vd509), vmul(vd509, vd512)), vd201(vmul(vd508, vd511), vmul(vd511, vd509)))), vmul(vd509, vd512))
2.86/0.70	= { by axiom 7 (ass(cond(189, 0), 0)) }
2.86/0.70	  true2
2.86/0.70	% SZS output end Proof
2.86/0.70	
2.86/0.70	RESULT: Theorem (the conjecture is true).
2.86/0.71	EOF