0.03/0.13	% Problem    : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.03/0.14	% Command    : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
0.13/0.34	% Computer   : n009.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   : 1200
0.13/0.34	% WCLimit    : 120
0.13/0.34	% DateTime   : Tue Jul 13 13:26:57 EDT 2021
0.13/0.34	% CPUTime    : 
45.82/6.24	% SZS status Theorem
45.82/6.24	
45.82/6.25	% SZS output start Proof
45.82/6.25	Take the following subset of the input axioms:
45.82/6.25	  fof('and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))', axiom, vd1288!=vd1289 & (vd1289!=vd1287 & (vd1288!=vd1287 & (?[Vd1291]: (rpoint(Vd1291) & Vd1291=vd1287) & (?[Vd1292]: (rpoint(Vd1292) & vd1288=Vd1292) & (?[Vd1293]: (rpoint(Vd1293) & vd1289=Vd1293) & vf(vd1287, vd1288)=vf(vd1287, vd1289))))))).
45.82/6.25	  fof('and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))', axiom, rR(vd1289, vd1287, vd1302) & (rpoint(vd1303) & (rR(vd1288, vd1287, vd1299) & vd1303=vd1302))).
45.82/6.25	  fof('pred(347, 0)', axiom, rline(vd1297)).
45.82/6.25	  fof('pred(conjunct2(349), 0)', conjecture, ron(vd1302, vd1297)).
45.82/6.25	  fof('pred(s1(plural(347)), 0)', axiom, ron(vd1287, vd1297)).
45.82/6.25	  fof('pred(s2(plural(347)), 0)', axiom, ron(vd1289, vd1297)).
45.82/6.25	  fof('qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))', axiom, ![Vd352, Vd353, Vd354, Vd359, Vd360]: (ron(Vd354, Vd359) <= (ron(Vd353, Vd359) & (ron(Vd352, Vd359) & (rR(Vd353, Vd352, Vd354) & (?[Vd356]: (rpoint(Vd356) & Vd352=Vd356) & (?[Vd357]: (Vd357=Vd353 & rpoint(Vd357)) & (?[Vd358]: (Vd358=Vd354 & rpoint(Vd358)) & (rline(Vd360) & Vd360=Vd359))))))))).
45.82/6.25	
45.82/6.25	Now clausify the problem and encode Horn clauses using encoding 3 of
45.82/6.25	http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
45.82/6.25	We repeatedly replace C & s=t => u=v by the two clauses:
45.82/6.25	  fresh(y, y, x1...xn) = u
45.82/6.25	  C => fresh(s, t, x1...xn) = v
45.82/6.25	where fresh is a fresh function symbol and x1..xn are the free
45.82/6.25	variables of u and v.
45.82/6.25	A predicate p(X) is encoded as p(X)=true (this is sound, because the
45.82/6.25	input problem has no model of domain size 1).
45.82/6.25	
45.82/6.25	The encoding turns the above axioms into the following unit equations and goals:
45.82/6.25	
45.82/6.25	Axiom 1 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))): vd1303 = vd1302.
45.82/6.25	Axiom 2 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_2): vd1291 = vd1287.
45.82/6.25	Axiom 3 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))): vd1289 = vd1293.
45.82/6.25	Axiom 4 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_1): rpoint(vd1303) = true2.
45.82/6.25	Axiom 5 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_4): rpoint(vd1291) = true2.
45.82/6.25	Axiom 6 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_6): rpoint(vd1293) = true2.
45.82/6.25	Axiom 7 (pred(347, 0)): rline(vd1297) = true2.
45.82/6.25	Axiom 8 (pred(s1(plural(347)), 0)): ron(vd1287, vd1297) = true2.
45.82/6.25	Axiom 9 (pred(s2(plural(347)), 0)): ron(vd1289, vd1297) = true2.
45.82/6.25	Axiom 10 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_2): rR(vd1289, vd1287, vd1302) = true2.
45.82/6.25	Axiom 11 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh439(X, X, Y, Z) = true2.
45.82/6.25	Axiom 12 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh438(X, X, Y, Z, W) = fresh439(rpoint(Y), true2, Z, W).
45.82/6.25	Axiom 13 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh437(X, X, Y, Z, W) = ron(Z, W).
45.82/6.25	Axiom 14 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh436(X, X, Y, Z, W, V) = fresh437(rpoint(Z), true2, Y, Z, W).
45.82/6.25	Axiom 15 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh435(X, X, Y, Z, W, V) = fresh438(rpoint(V), true2, Y, Z, W).
45.82/6.25	Axiom 16 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh433(X, X, Y, Z, W, V) = fresh434(rline(W), true2, Y, Z, W, V).
45.82/6.25	Axiom 17 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh434(X, X, Y, Z, W, V) = fresh436(ron(Y, W), true2, Y, Z, W, V).
45.82/6.25	Axiom 18 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))): fresh433(rR(X, Y, Z), true2, X, Z, W, Y) = fresh435(ron(Y, W), true2, X, Z, W, Y).
45.82/6.25	
45.82/6.25	Goal 1 (pred(conjunct2(349), 0)): ron(vd1302, vd1297) = true2.
45.82/6.25	Proof:
45.82/6.25	  ron(vd1302, vd1297)
45.82/6.25	= { by axiom 13 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
45.82/6.25	  fresh437(true2, true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 4 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_1) R->L }
45.82/6.25	  fresh437(rpoint(vd1303), true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 1 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))) }
45.82/6.25	  fresh437(rpoint(vd1302), true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 14 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
45.82/6.25	  fresh436(true2, true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 9 (pred(s2(plural(347)), 0)) R->L }
45.82/6.25	  fresh436(ron(vd1289, vd1297), true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 17 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
45.82/6.25	  fresh434(true2, true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 7 (pred(347, 0)) R->L }
45.82/6.25	  fresh434(rline(vd1297), true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 16 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) R->L }
45.82/6.25	  fresh433(true2, true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 10 (and(pred(conjunct2(348), 4), and(holds(conjunct2(348), 1304, 0), and(pred(conjunct2(348), 1), holds(conjunct1(348), 1301, 0))))_2) R->L }
45.82/6.25	  fresh433(rR(vd1289, vd1287, vd1302), true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 18 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
45.82/6.25	  fresh435(ron(vd1287, vd1297), true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 8 (pred(s1(plural(347)), 0)) }
45.82/6.25	  fresh435(true2, true2, vd1289, vd1302, vd1297, vd1287)
45.82/6.25	= { by axiom 15 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
45.82/6.25	  fresh438(rpoint(vd1287), true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 2 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_2) R->L }
45.82/6.25	  fresh438(rpoint(vd1291), true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 5 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_4) }
45.82/6.25	  fresh438(true2, true2, vd1289, vd1302, vd1297)
45.82/6.25	= { by axiom 12 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
45.82/6.25	  fresh439(rpoint(vd1289), true2, vd1302, vd1297)
45.82/6.25	= { by axiom 3 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))) }
45.82/6.25	  fresh439(rpoint(vd1293), true2, vd1302, vd1297)
45.82/6.25	= { by axiom 6 (and(holds(conjunct2(345), 1294, 0), and(pred(conjunct1(345), 9), and(pred(conjunct1(345), 8), and(pred(conjunct1(345), 7), and(qe(s3(plural(345))), and(qe(s2(plural(345))), qe(s1(plural(345)))))))))_6) }
45.82/6.25	  fresh439(true2, true2, vd1302, vd1297)
45.82/6.25	= { by axiom 11 (qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))) }
45.82/6.25	  true2
45.82/6.25	% SZS output end Proof
45.82/6.25	
45.82/6.25	RESULT: Theorem (the conjecture is true).
45.82/6.28	EOF