0.08/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.08/0.14 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.14/0.35 % Computer : n025.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 180 0.14/0.35 % DateTime : Thu Aug 29 10:01:45 EDT 2019 0.14/0.35 % CPUTime : 69.00/69.19 % SZS status Theorem 69.00/69.19 69.00/69.19 % SZS output start Proof 69.00/69.19 Take the following subset of the input axioms: 69.00/69.20 fof(ax2_1249, axiom, ![OBJ]: ~(tptpcol_1_65536(OBJ) & tptpcol_1_1(OBJ))). 69.00/69.20 fof(ax2_1271, axiom, ![OBJ]: ~(partiallytangible(OBJ) & intangible(OBJ))). 69.00/69.20 fof(ax2_1745, axiom, ![OBJ]: ~(intangible(OBJ) & partiallytangible(OBJ))). 69.00/69.20 fof(ax2_1803, axiom, ![OBJ]: ~(tptpcol_1_65536(OBJ) & tptpcol_1_1(OBJ))). 69.00/69.20 fof(ax2_2129, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL2) & (disjointwith(COL1, COL2) & isa(OBJ, COL1)))). 69.00/69.20 fof(ax2_220, axiom, ![OBJ]: ~(setorcollection(OBJ) & individual(OBJ))). 69.00/69.20 fof(ax2_2346, axiom, ![OBJ]: ~(tptpcol_3_114688(OBJ) & tptpcol_3_98305(OBJ))). 69.00/69.20 fof(ax2_2498, axiom, ![OBJ]: ~(waitinglist(OBJ) & partiallytangible(OBJ))). 69.00/69.20 fof(ax2_2792, axiom, ![OBJ]: ~(thermalenergy(OBJ) & partiallytangible(OBJ))). 69.00/69.20 fof(ax2_3089, axiom, ![OBJ]: ~(collection(OBJ) & individual(OBJ))). 69.00/69.20 fof(ax2_3226, axiom, ![OBJ]: ~(collection(OBJ) & individual(OBJ))). 69.00/69.20 fof(ax2_3854, axiom, ![OBJ]: ~(tptpcol_3_98305(OBJ) & tptpcol_3_114688(OBJ))). 69.00/69.20 fof(ax2_4139, axiom, mtvisible(c_englishmt) => prettystring(f_instancewithrelationtofn(c_footballteam, c_affiliatedwith, c_beloitcollege), s_thefootballteamwhohasbeenaffiliatedwithbeloitcollege)). 69.00/69.20 fof(ax2_4279, axiom, ![OBJ]: ~(collection(OBJ) & set_mathematical(OBJ))). 69.00/69.20 fof(ax2_4519, axiom, ![X, Y]: ~(temporaryparts(X, Y) & temporaryparts(Y, X))). 69.00/69.20 fof(ax2_4520, axiom, ![X]: ~temporaryparts(X, X)). 69.00/69.20 fof(ax2_4585, axiom, ![X, Y]: ~(along_underspecifiedpath(X, Y) & along_underspecifiedpath(Y, X))). 69.00/69.20 fof(ax2_4586, axiom, ![X]: ~along_underspecifiedpath(X, X)). 69.00/69.20 fof(ax2_4598, axiom, ![X, Y]: ~(typicallycomparestowrtslotfnlessthanbasicprice(Y, X) & typicallycomparestowrtslotfnlessthanbasicprice(X, Y))). 69.00/69.20 fof(ax2_4599, axiom, ![X]: ~typicallycomparestowrtslotfnlessthanbasicprice(X, X)). 69.00/69.20 fof(ax2_4627, axiom, ![X, Y]: ~(properphysicalparts(Y, X) & properphysicalparts(X, Y))). 69.00/69.20 fof(ax2_4628, axiom, ![X]: ~properphysicalparts(X, X)). 69.00/69.20 fof(ax2_4678, axiom, ![X, Y]: ~(northof(Y, X) & northof(X, Y))). 69.00/69.20 fof(ax2_4679, axiom, ![X]: ~northof(X, X)). 69.00/69.20 fof(ax2_4838, axiom, ![X, Y]: ~(temporallyfinishedby(X, Y) & temporallyfinishedby(Y, X))). 69.00/69.20 fof(ax2_4839, axiom, ![X]: ~temporallyfinishedby(X, X)). 69.00/69.20 fof(ax2_4929, axiom, ![X, Y]: ~(for_underspecifiedlocation(Y, X) & for_underspecifiedlocation(X, Y))). 69.00/69.20 fof(ax2_4930, axiom, ![X]: ~for_underspecifiedlocation(X, X)). 69.00/69.20 fof(ax2_494, axiom, ![OBJ]: ~(individual(OBJ) & setorcollection(OBJ))). 69.00/69.20 fof(ax2_4990, axiom, ![X, Y]: ~(spatiallycontains(Y, X) & spatiallycontains(X, Y))). 69.00/69.20 fof(ax2_4991, axiom, ![X]: ~spatiallycontains(X, X)). 69.00/69.20 fof(ax2_5005, axiom, ![X, Y]: ~(permanentlynorthwestof(Y, X) & permanentlynorthwestof(X, Y))). 69.00/69.20 fof(ax2_5006, axiom, ![X]: ~permanentlynorthwestof(X, X)). 69.00/69.20 fof(ax2_5123, axiom, ![X, Y]: ~(suborgs_materialsupport(X, Y) & suborgs_materialsupport(Y, X))). 69.00/69.20 fof(ax2_5124, axiom, ![X]: ~suborgs_materialsupport(X, X)). 69.00/69.20 fof(ax2_5283, axiom, ![X, Y]: ~(contiguousafter_tempstage(Y, X) & contiguousafter_tempstage(X, Y))). 69.00/69.20 fof(ax2_5284, axiom, ![X]: ~contiguousafter_tempstage(X, X)). 69.00/69.20 fof(ax2_5337, axiom, ![X, Y]: ~(negligiblewrt(X, Y) & negligiblewrt(Y, X))). 69.00/69.20 fof(ax2_5338, axiom, ![X]: ~negligiblewrt(X, X)). 69.00/69.20 fof(ax2_5370, axiom, ![X, Y]: ~(under_underspecifiedlocation(Y, X) & under_underspecifiedlocation(X, Y))). 69.00/69.20 fof(ax2_5371, axiom, ![X]: ~under_underspecifiedlocation(X, X)). 69.00/69.20 fof(ax2_5423, axiom, ![X, Y]: ~(lessthan(Y, X) & lessthan(X, Y))). 69.00/69.20 fof(ax2_5424, axiom, ![X]: ~lessthan(X, X)). 69.00/69.20 fof(ax2_5430, axiom, ![X, Y]: ~(typicallycomparestowrtslotfnlessthanwidthofobject(X, Y) & typicallycomparestowrtslotfnlessthanwidthofobject(Y, X))). 69.00/69.20 fof(ax2_5431, axiom, ![X]: ~typicallycomparestowrtslotfnlessthanwidthofobject(X, X)). 69.00/69.20 fof(ax2_5492, axiom, ![X, Y]: ~(owns(X, Y) & owns(Y, X))). 69.00/69.20 fof(ax2_5493, axiom, ![X]: ~owns(X, X)). 69.00/69.20 fof(ax2_5700, axiom, ![X, Y]: ~(formofcondition(X, Y) & formofcondition(Y, X))). 69.00/69.20 fof(ax2_5701, axiom, ![X]: ~formofcondition(X, X)). 69.00/69.20 fof(ax2_5741, axiom, ![X, Y]: ~(uniquepropersubsituationtypes(X, Y) & uniquepropersubsituationtypes(Y, X))). 69.00/69.20 fof(ax2_5742, axiom, ![X]: ~uniquepropersubsituationtypes(X, X)). 69.00/69.20 fof(ax2_5831, axiom, ![X, Y]: ~(after(X, Y) & after(Y, X))). 69.00/69.20 fof(ax2_5832, axiom, ![X]: ~after(X, X)). 69.00/69.20 fof(ax2_5905, axiom, ![X, Y]: ~(properpartofspaceregion_inverse(X, Y) & properpartofspaceregion_inverse(Y, X))). 69.00/69.20 fof(ax2_5906, axiom, ![X]: ~properpartofspaceregion_inverse(X, X)). 69.00/69.20 fof(ax2_6012, axiom, ![X, Y]: ~(westof(Y, X) & westof(X, Y))). 69.00/69.20 fof(ax2_6013, axiom, ![X]: ~westof(X, X)). 69.00/69.20 fof(ax2_6286, axiom, ![X, Y]: ~(physicallycontains(Y, X) & physicallycontains(X, Y))). 69.00/69.20 fof(ax2_6287, axiom, ![X]: ~physicallycontains(X, X)). 69.00/69.20 fof(ax2_6439, axiom, ![X]: ~sisters(X, X)). 69.00/69.20 fof(ax2_6548, axiom, ![X, Y]: ~(outof_underspecifiedcontainer(Y, X) & outof_underspecifiedcontainer(X, Y))). 69.00/69.20 fof(ax2_6549, axiom, ![X]: ~outof_underspecifiedcontainer(X, X)). 69.00/69.20 fof(ax2_6628, axiom, ![X, Y]: ~(allnegligiblewrt(Y, X) & allnegligiblewrt(X, Y))). 69.00/69.20 fof(ax2_6629, axiom, ![X]: ~allnegligiblewrt(X, X)). 69.00/69.20 fof(ax2_6643, axiom, ![X, Y]: ~(properparts(Y, X) & properparts(X, Y))). 69.00/69.20 fof(ax2_6644, axiom, ![X]: ~properparts(X, X)). 69.00/69.20 fof(ax2_7179, axiom, ![X]: ~affiliatedwith(X, X)). 69.00/69.20 fof(ax2_7323, axiom, ![X, Y]: ~(requisitefor(X, Y) & requisitefor(Y, X))). 69.00/69.20 fof(ax2_7324, axiom, ![X]: ~requisitefor(X, X)). 69.00/69.20 fof(ax2_7359, axiom, ![X]: ~objectfoundinlocation(X, X)). 69.00/69.20 fof(ax2_7643, axiom, ![X]: ~borderson(X, X)). 69.00/69.20 fof(ax2_7950, axiom, ![X, Y]: ~(superabstractype(X, Y) & superabstractype(Y, X))). 69.00/69.20 fof(ax2_7951, axiom, ![X]: ~superabstractype(X, X)). 69.00/69.20 fof(ax2_848, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))). 69.00/69.20 fof(query135, conjecture, ?[X]: (prettystring(f_instancewithrelationtofn(c_footballteam, c_affiliatedwith, c_beloitcollege), X) <= mtvisible(c_englishmt))). 69.00/69.20 69.00/69.20 Now clausify the problem and encode Horn clauses using encoding 3 of 69.00/69.20 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 69.00/69.20 We repeatedly replace C & s=t => u=v by the two clauses: 69.00/69.20 fresh(y, y, x1...xn) = u 69.00/69.20 C => fresh(s, t, x1...xn) = v 69.00/69.20 where fresh is a fresh function symbol and x1..xn are the free 69.00/69.20 variables of u and v. 69.00/69.20 A predicate p(X) is encoded as p(X)=true (this is sound, because the 69.00/69.20 input problem has no model of domain size 1). 69.00/69.20 69.00/69.20 The encoding turns the above axioms into the following unit equations and goals: 69.00/69.20 69.00/69.20 Axiom 1 (ax2_4139): fresh3529(X, X) = true2. 69.00/69.20 Axiom 2 (ax2_4139): fresh3529(mtvisible(c_englishmt), true2) = prettystring(f_instancewithrelationtofn(c_footballteam, c_affiliatedwith, c_beloitcollege), s_thefootballteamwhohasbeenaffiliatedwithbeloitcollege). 69.00/69.20 Axiom 3 (query135): mtvisible(c_englishmt) = true2. 69.00/69.20 69.00/69.20 Goal 1 (query135_1): prettystring(f_instancewithrelationtofn(c_footballteam, c_affiliatedwith, c_beloitcollege), X) = true2. 69.00/69.20 The goal is true when: 69.00/69.20 X = s_thefootballteamwhohasbeenaffiliatedwithbeloitcollege 69.00/69.20 69.00/69.20 Proof: 69.00/69.20 prettystring(f_instancewithrelationtofn(c_footballteam, c_affiliatedwith, c_beloitcollege), s_thefootballteamwhohasbeenaffiliatedwithbeloitcollege) 69.00/69.20 = { by axiom 2 (ax2_4139) } 69.00/69.20 fresh3529(mtvisible(c_englishmt), true2) 69.00/69.20 = { by axiom 3 (query135) } 69.00/69.20 fresh3529(true2, true2) 69.00/69.20 = { by axiom 1 (ax2_4139) } 69.00/69.20 true2 69.00/69.20 % SZS output end Proof 69.00/69.20 69.00/69.20 RESULT: Theorem (the conjecture is true). 69.14/69.34 EOF