0.00/0.04 % 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 0.02/0.24 % Computer : n059.star.cs.uiowa.edu 0.02/0.24 % Model : x86_64 x86_64 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.02/0.24 % Memory : 32218.625MB 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.02/0.24 % CPULimit : 300 0.02/0.24 % DateTime : Sat Jul 14 04:33:55 CDT 2018 0.02/0.24 % CPUTime : 189.12/189.42 % SZS status Theorem 189.12/189.42 189.12/189.42 % SZS output start Proof 189.12/189.42 Take the following subset of the input axioms: 189.12/189.42 fof(ax2_1237, axiom, 189.12/189.42 mtvisible(c_tptpgeo_member4_mt) 189.12/189.42 => borderson(c_georegion_l4_x36_y50, c_georegion_l4_x37_y50)). 189.12/189.42 fof(ax2_7642, axiom, 189.12/189.42 ![X, Y]: (borderson(Y, X) <= borderson(X, Y))). 189.12/189.42 fof(query147, conjecture, 189.12/189.42 mtvisible(c_tptpgeo_member4_mt) 189.12/189.42 => borderson(c_georegion_l4_x37_y50, c_georegion_l4_x36_y50)). 189.12/189.42 189.12/189.42 Now clausify the problem and encode Horn clauses using encoding 3 of 189.12/189.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 189.12/189.42 We repeatedly replace C & s=t => u=v by the two clauses: 189.12/189.42 $$fresh(y, y, x1...xn) = u 189.12/189.42 C => $$fresh(s, t, x1...xn) = v 189.12/189.42 where $$fresh is a fresh function symbol and x1..xn are the free 189.12/189.42 variables of u and v. 189.12/189.42 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 189.12/189.42 input problem has no model of domain size 1). 189.12/189.42 189.12/189.42 The encoding turns the above axioms into the following unit equations and goals: 189.12/189.42 189.12/189.42 Axiom 108 (ax2_1237): $$fresh4790(X, X) = $$true2. 189.12/189.42 Axiom 4573 (ax2_7642): $$fresh403(X, X, Y, Z) = $$true2. 189.12/189.42 Axiom 7856 (ax2_1237): $$fresh4790(mtvisible(c_tptpgeo_member4_mt), $$true2) = borderson(c_georegion_l4_x36_y50, c_georegion_l4_x37_y50). 189.12/189.42 Axiom 9730 (ax2_7642): $$fresh403(borderson(X, Y), $$true2, X, Y) = borderson(Y, X). 189.12/189.42 Axiom 12917 (query147): mtvisible(c_tptpgeo_member4_mt) = $$true2. 189.12/189.42 189.12/189.42 Goal 1 (query147_1): borderson(c_georegion_l4_x37_y50, c_georegion_l4_x36_y50) = $$true2. 189.12/189.42 Proof: 189.12/189.42 borderson(c_georegion_l4_x37_y50, c_georegion_l4_x36_y50) 189.12/189.42 = { by axiom 9730 (ax2_7642) } 189.12/189.42 $$fresh403(borderson(c_georegion_l4_x36_y50, c_georegion_l4_x37_y50), $$true2, c_georegion_l4_x36_y50, c_georegion_l4_x37_y50) 189.12/189.42 = { by axiom 7856 (ax2_1237) } 189.12/189.42 $$fresh403($$fresh4790(mtvisible(c_tptpgeo_member4_mt), $$true2), $$true2, c_georegion_l4_x36_y50, c_georegion_l4_x37_y50) 189.12/189.42 = { by axiom 12917 (query147) } 189.12/189.42 $$fresh403($$fresh4790($$true2, $$true2), $$true2, c_georegion_l4_x36_y50, c_georegion_l4_x37_y50) 189.12/189.42 = { by axiom 108 (ax2_1237) } 189.12/189.42 $$fresh403($$true2, $$true2, c_georegion_l4_x36_y50, c_georegion_l4_x37_y50) 189.12/189.42 = { by axiom 4573 (ax2_7642) } 189.12/189.42 $$true2 189.12/189.42 % SZS output end Proof 189.12/189.42 189.12/189.42 RESULT: Theorem (the conjecture is true). 189.31/189.60 EOF