0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : twee %s --tstp --casc --quiet --conditional-encoding if --smaller --drop-non-horn 0.03/0.24 % Computer : n129.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 04:39:40 CDT 2018 0.03/0.24 % CPUTime : 94.57/94.79 % SZS status Theorem 94.57/94.79 94.57/94.79 % SZS output start Proof 94.57/94.79 Take the following subset of the input axioms: 94.57/94.79 fof(ax2_2090, axiom, 94.57/94.79 mtvisible(c_tptpgeo_member1_mt) 94.57/94.79 => borderson(c_georegion_l4_x38_y24, c_georegion_l4_x39_y24)). 94.57/94.79 fof(query169, conjecture, 94.57/94.79 borderson(c_georegion_l4_x38_y24, c_georegion_l4_x39_y24) 94.57/94.79 <= mtvisible(c_tptpgeo_member1_mt)). 94.57/94.79 94.57/94.79 Now clausify the problem and encode Horn clauses using encoding 3 of 94.57/94.79 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 94.57/94.79 We repeatedly replace C & s=t => u=v by the two clauses: 94.57/94.79 $$fresh(y, y, x1...xn) = u 94.57/94.79 C => $$fresh(s, t, x1...xn) = v 94.57/94.79 where $$fresh is a fresh function symbol and x1..xn are the free 94.57/94.79 variables of u and v. 94.57/94.79 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 94.57/94.79 input problem has no model of domain size 1). 94.57/94.79 94.57/94.79 The encoding turns the above axioms into the following unit equations and goals: 94.57/94.79 94.57/94.79 Axiom 501 (ax2_2090): $$fresh4419(X, X) = $$true2. 94.57/94.79 Axiom 6488 (ax2_2090): $$fresh4419(mtvisible(c_tptpgeo_member1_mt), $$true2) = borderson(c_georegion_l4_x38_y24, c_georegion_l4_x39_y24). 94.57/94.79 Axiom 12917 (query169): mtvisible(c_tptpgeo_member1_mt) = $$true2. 94.57/94.79 94.57/94.79 Goal 1 (query169_1): borderson(c_georegion_l4_x38_y24, c_georegion_l4_x39_y24) = $$true2. 94.57/94.79 Proof: 94.57/94.79 borderson(c_georegion_l4_x38_y24, c_georegion_l4_x39_y24) 94.57/94.79 = { by axiom 6488 (ax2_2090) } 94.57/94.79 $$fresh4419(mtvisible(c_tptpgeo_member1_mt), $$true2) 94.57/94.79 = { by axiom 12917 (query169) } 94.57/94.79 $$fresh4419($$true2, $$true2) 94.57/94.79 = { by axiom 501 (ax2_2090) } 94.57/94.79 $$true2 94.57/94.79 % SZS output end Proof 94.57/94.79 94.57/94.79 RESULT: Theorem (the conjecture is true). 94.71/94.99 EOF