0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.12 % Command : twee %s --tstp --casc --quiet --explain-encoding --conditional-encoding if --smaller --drop-non-horn 0.12/0.33 % Computer : n016.cluster.edu 0.12/0.33 % Model : x86_64 x86_64 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.33 % Memory : 8042.1875MB 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.33 % CPULimit : 180 0.12/0.33 % DateTime : Thu Aug 29 11:39:38 EDT 2019 0.12/0.34 % CPUTime : 20.43/20.61 % SZS status Theorem 20.43/20.61 20.43/20.61 % SZS output start Proof 20.43/20.61 Take the following subset of the input axioms: 20.43/20.61 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, ~?[Vd1195]: (ron(vd1187, Vd1195) & (ron(vd1185, Vd1195) & (rline(Vd1195) & ron(vd1186, Vd1195)))) & (?[Vd1191]: (Vd1191=vd1187 & rpoint(Vd1191)) & (?[Vd1190]: (rpoint(Vd1190) & vd1186=Vd1190) & (vd1180!=vd1178 & (?[Vd1184]: (Vd1184=vd1180 & rpoint(Vd1184)) & (?[Vd1183]: (vd1179=Vd1183 & rpoint(Vd1183)) & (?[Vd1182]: (vd1178=Vd1182 & rpoint(Vd1182)) & (vd1179!=vd1178 & (vd1180!=vd1179 & (?[Vd1189]: (rpoint(Vd1189) & Vd1189=vd1185) & (vf(vd1185, vd1186)=vf(vd1178, vd1179) & (vf(vd1185, vd1187)=vf(vd1178, vd1180) & vangle(vd1186, vd1185, vd1187)=vangle(vd1179, vd1178, vd1180))))))))))))). 20.43/20.61 fof('holds(291, 1230, 0)', axiom, vd1185=vd1199). 20.43/20.61 fof('holds(314, 1247, 0)', axiom, vf(vd1199, vd1201)=vf(vd1185, vd1187)). 20.43/20.61 fof('holds(323, 1254, 0)', axiom, rR(vd1201, vd1185, vd1187)). 20.43/20.61 fof('holds(324, 1255, 0)', conjecture, vplus(vf(vd1185, vd1201), vf(vd1201, vd1187))=vf(vd1185, vd1187)). 20.43/20.61 fof('qe(s1(plural(271)))', axiom, ?[Vd1203]: (rpoint(Vd1203) & Vd1203=vd1199)). 20.43/20.61 fof('qe(s3(plural(271)))', axiom, ?[Vd1205]: (vd1201=Vd1205 & rpoint(Vd1205))). 20.43/20.61 fof('qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))', axiom, ![Vd829, Vd830, Vd828]: ((rR(Vd829, Vd828, Vd830) & (?[Vd833]: (Vd833=Vd829 & rpoint(Vd833)) & (?[Vd832]: (rpoint(Vd832) & Vd828=Vd832) & ?[Vd834]: (Vd834=Vd830 & rpoint(Vd834))))) => vf(Vd828, Vd830)=vplus(vf(Vd828, Vd829), vf(Vd829, Vd830)))). 20.43/20.61 20.43/20.61 Now clausify the problem and encode Horn clauses using encoding 3 of 20.43/20.61 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 20.43/20.61 We repeatedly replace C & s=t => u=v by the two clauses: 20.43/20.61 fresh(y, y, x1...xn) = u 20.43/20.61 C => fresh(s, t, x1...xn) = v 20.43/20.61 where fresh is a fresh function symbol and x1..xn are the free 20.43/20.61 variables of u and v. 20.43/20.61 A predicate p(X) is encoded as p(X)=true (this is sound, because the 20.43/20.61 input problem has no model of domain size 1). 20.43/20.61 20.43/20.61 The encoding turns the above axioms into the following unit equations and goals: 20.43/20.61 20.43/20.61 Axiom 1 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh266(X, X, Y, Z, W) = vf(W, Z). 20.43/20.61 Axiom 2 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh264(X, X, Y, Z, W) = vplus(vf(W, Y), vf(Y, Z)). 20.43/20.61 Axiom 3 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh265(X, X, Y, Z, W) = fresh266(rpoint(Y), true2, Y, Z, W). 20.43/20.61 Axiom 4 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh263(X, X, Y, Z, W) = fresh264(rpoint(Z), true2, Y, Z, W). 20.43/20.61 Axiom 5 (qe(s1(plural(271)))_1): rpoint(sK37_qe(s1(plural(271)))_Vd1203) = true2. 20.43/20.61 Axiom 6 (qe(s1(plural(271)))): sK37_qe(s1(plural(271)))_Vd1203 = vd1199. 20.43/20.61 Axiom 7 (holds(314, 1247, 0)): vf(vd1199, vd1201) = vf(vd1185, vd1187). 20.43/20.61 Axiom 8 (qe(s3(plural(271)))_1): rpoint(sK25_qe(s3(plural(271)))_Vd1205) = true2. 20.43/20.61 Axiom 9 (qe(s3(plural(271)))): vd1201 = sK25_qe(s3(plural(271)))_Vd1205. 20.43/20.61 Axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh263(rR(X, Y, Z), true2, X, Z, Y) = fresh265(rpoint(Y), true2, X, Z, Y). 20.43/20.61 Axiom 11 (holds(323, 1254, 0)): rR(vd1201, vd1185, vd1187) = true2. 20.43/20.61 Axiom 12 (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(sK12_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) = true2. 20.43/20.61 Axiom 13 (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)))))))))))))))_1): sK12_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. 20.43/20.61 Axiom 14 (holds(291, 1230, 0)): vd1185 = vd1199. 20.43/20.61 20.43/20.61 Lemma 15: vf(vd1185, vd1187) = vf(vd1185, vd1201). 20.43/20.61 Proof: 20.43/20.61 vf(vd1185, vd1187) 20.43/20.61 = { by axiom 7 (holds(314, 1247, 0)) } 20.43/20.61 vf(vd1199, vd1201) 20.43/20.61 = { by axiom 14 (holds(291, 1230, 0)) } 20.43/20.61 vf(vd1185, vd1201) 20.43/20.61 20.43/20.61 Goal 1 (holds(324, 1255, 0)): vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) = vf(vd1185, vd1187). 20.43/20.61 Proof: 20.43/20.61 vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) 20.43/20.61 = { by axiom 2 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 fresh264(?, ?, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 2 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) 20.43/20.61 = { by axiom 2 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 fresh264(true2, true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 12 (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) } 20.43/20.61 fresh264(rpoint(sK12_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), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 13 (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)))))))))))))))_1) } 20.43/20.61 fresh264(rpoint(vd1187), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 4 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 fresh263(true2, true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 11 (holds(323, 1254, 0)) } 20.43/20.61 fresh263(rR(vd1201, vd1185, vd1187), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 fresh265(rpoint(vd1185), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 14 (holds(291, 1230, 0)) } 20.43/20.61 fresh265(rpoint(vd1199), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 6 (qe(s1(plural(271)))) } 20.43/20.61 fresh265(rpoint(sK37_qe(s1(plural(271)))_Vd1203), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 5 (qe(s1(plural(271)))_1) } 20.43/20.61 fresh265(true2, true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 3 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 fresh266(rpoint(vd1201), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 9 (qe(s3(plural(271)))) } 20.43/20.61 fresh266(rpoint(sK25_qe(s3(plural(271)))_Vd1205), true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 8 (qe(s3(plural(271)))_1) } 20.43/20.61 fresh266(true2, true2, vd1201, vd1187, vd1185) 20.43/20.61 = { by axiom 1 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 20.43/20.61 vf(vd1185, vd1187) 20.43/20.61 % SZS output end Proof 20.43/20.61 20.43/20.61 RESULT: Theorem (the conjecture is true). 20.43/20.62 EOF