0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof 0.12/0.34 % Computer : n003.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1200 0.12/0.34 % WCLimit : 120 0.12/0.34 % DateTime : Tue Jul 13 13:26:09 EDT 2021 0.19/0.34 % CPUTime : 16.18/2.40 % SZS status Theorem 16.18/2.40 16.18/2.41 % SZS output start Proof 16.18/2.41 Take the following subset of the input axioms: 16.18/2.41 fof('and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))', axiom, vangle(vd1179, vd1178, vd1180)=vangle(vd1186, vd1185, vd1187) & (?[Vd1191]: (rpoint(Vd1191) & Vd1191=vd1187) & (?[Vd1190]: (rpoint(Vd1190) & vd1186=Vd1190) & (?[Vd1189]: (rpoint(Vd1189) & Vd1189=vd1185) & (vd1179!=vd1180 & (vd1178!=vd1180 & (vd1178!=vd1179 & (?[Vd1184]: (vd1180=Vd1184 & rpoint(Vd1184)) & (?[Vd1183]: (rpoint(Vd1183) & Vd1183=vd1179) & (?[Vd1182]: (rpoint(Vd1182) & Vd1182=vd1178) & (vf(vd1178, vd1179)=vf(vd1185, vd1186) & (vf(vd1185, vd1187)=vf(vd1178, vd1180) & ~?[Vd1195]: (ron(vd1187, Vd1195) & (ron(vd1186, Vd1195) & (ron(vd1185, Vd1195) & rline(Vd1195)))))))))))))))). 16.18/2.41 fof('holds(323, 1254, 0)', axiom, rR(vd1201, vd1185, vd1187)). 16.18/2.41 fof('holds(324, 1255, 0)', conjecture, vplus(vf(vd1185, vd1201), vf(vd1201, vd1187))=vf(vd1185, vd1187)). 16.18/2.41 fof('qe(s3(plural(271)))', axiom, ?[Vd1205]: (vd1201=Vd1205 & rpoint(Vd1205))). 16.18/2.41 fof('qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))', axiom, ![Vd828, Vd829, Vd830]: (vplus(vf(Vd828, Vd829), vf(Vd829, Vd830))=vf(Vd828, Vd830) <= (?[Vd834]: (Vd830=Vd834 & rpoint(Vd834)) & (?[Vd833]: (Vd833=Vd829 & rpoint(Vd833)) & (?[Vd832]: (rpoint(Vd832) & Vd832=Vd828) & rR(Vd829, Vd828, Vd830)))))). 16.18/2.41 16.18/2.41 Now clausify the problem and encode Horn clauses using encoding 3 of 16.18/2.41 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 16.18/2.41 We repeatedly replace C & s=t => u=v by the two clauses: 16.18/2.41 fresh(y, y, x1...xn) = u 16.18/2.41 C => fresh(s, t, x1...xn) = v 16.18/2.41 where fresh is a fresh function symbol and x1..xn are the free 16.18/2.41 variables of u and v. 16.18/2.41 A predicate p(X) is encoded as p(X)=true (this is sound, because the 16.18/2.41 input problem has no model of domain size 1). 16.18/2.41 16.18/2.41 The encoding turns the above axioms into the following unit equations and goals: 16.18/2.41 16.18/2.41 Axiom 1 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))): vd1191 = vd1187. 16.18/2.41 Axiom 2 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_6): vd1189 = vd1185. 16.18/2.41 Axiom 3 (qe(s3(plural(271)))): vd1201 = vd1205. 16.18/2.41 Axiom 4 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_9): rpoint(vd1191) = true2. 16.18/2.41 Axiom 5 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_11): rpoint(vd1189) = true2. 16.18/2.41 Axiom 6 (qe(s3(plural(271)))_1): rpoint(vd1205) = true2. 16.18/2.41 Axiom 7 (holds(323, 1254, 0)): rR(vd1201, vd1185, vd1187) = true2. 16.18/2.41 Axiom 8 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh325(X, X, Y, Z, W) = vf(Y, W). 16.18/2.41 Axiom 9 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh323(X, X, Y, Z, W) = vplus(vf(Y, Z), vf(Z, W)). 16.18/2.41 Axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh324(X, X, Y, Z, W) = fresh325(rpoint(Y), true2, Y, Z, W). 16.18/2.41 Axiom 11 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh322(X, X, Y, Z, W) = fresh323(rpoint(Z), true2, Y, Z, W). 16.18/2.41 Axiom 12 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh322(rR(X, Y, Z), true2, Y, X, Z) = fresh324(rpoint(Z), true2, Y, X, Z). 16.18/2.41 16.18/2.41 Goal 1 (holds(324, 1255, 0)): vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) = vf(vd1185, vd1187). 16.18/2.41 Proof: 16.18/2.41 vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) 16.18/2.41 = { by axiom 9 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) R->L } 16.18/2.41 fresh323(true2, true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 6 (qe(s3(plural(271)))_1) R->L } 16.18/2.41 fresh323(rpoint(vd1205), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 3 (qe(s3(plural(271)))) R->L } 16.18/2.41 fresh323(rpoint(vd1201), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 11 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) R->L } 16.18/2.41 fresh322(true2, true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 7 (holds(323, 1254, 0)) R->L } 16.18/2.41 fresh322(rR(vd1201, vd1185, vd1187), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 12 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 16.18/2.41 fresh324(rpoint(vd1187), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 1 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))) R->L } 16.18/2.41 fresh324(rpoint(vd1191), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 4 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_9) } 16.18/2.41 fresh324(true2, true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 16.18/2.41 fresh325(rpoint(vd1185), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 2 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_6) R->L } 16.18/2.41 fresh325(rpoint(vd1189), true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 5 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_11) } 16.18/2.41 fresh325(true2, true2, vd1185, vd1201, vd1187) 16.18/2.41 = { by axiom 8 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 16.18/2.41 vf(vd1185, vd1187) 16.18/2.41 % SZS output end Proof 16.18/2.41 16.18/2.41 RESULT: Theorem (the conjecture is true). 16.18/2.43 EOF