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 : n005.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 04:44:54 CDT 2018 0.02/0.24 % CPUTime : 25.19/25.39 % SZS status Theorem 25.19/25.39 25.19/25.39 % SZS output start Proof 25.19/25.39 Take the following subset of the input axioms: 25.22/25.42 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)))))))))))))))', 25.22/25.42 axiom, 25.22/25.42 ~?[Vd1195]: 25.22/25.42 (ron(vd1187, Vd1195) 25.22/25.42 & (ron(vd1186, Vd1195) & (rline(Vd1195) & ron(vd1185, Vd1195)))) 25.22/25.42 & (?[Vd1191]: (rpoint(Vd1191) & Vd1191=vd1187) 25.22/25.42 & (?[Vd1190]: (rpoint(Vd1190) & Vd1190=vd1186) 25.22/25.42 & (?[Vd1189]: (Vd1189=vd1185 & rpoint(Vd1189)) 25.22/25.42 & (vd1179!=vd1180 25.22/25.42 & (?[Vd1184]: (vd1180=Vd1184 & rpoint(Vd1184)) 25.22/25.42 & (?[Vd1182]: (rpoint(Vd1182) & vd1178=Vd1182) 25.22/25.42 & (?[Vd1183]: (Vd1183=vd1179 & rpoint(Vd1183)) 25.22/25.42 & (vd1179!=vd1178 25.22/25.42 & (vd1178!=vd1180 25.22/25.42 & (vf(vd1178, vd1179)=vf(vd1185, vd1186) 25.22/25.42 & (vf(vd1178, vd1180)=vf(vd1185, vd1187) 25.22/25.42 & vangle(vd1186, vd1185, 25.22/25.42 vd1187)=vangle(vd1179, vd1178, 25.22/25.42 vd1180))))))))))))). 25.22/25.42 fof('holds(291, 1230, 0)', axiom, vd1199=vd1185). 25.22/25.42 fof('holds(314, 1247, 0)', axiom, 25.22/25.42 vf(vd1185, vd1187)=vf(vd1199, vd1201)). 25.22/25.42 fof('holds(323, 1254, 0)', axiom, rR(vd1201, vd1185, vd1187)). 25.22/25.42 fof('holds(324, 1255, 0)', conjecture, 25.22/25.42 vf(vd1185, vd1187)=vplus(vf(vd1185, vd1201), vf(vd1201, vd1187))). 25.22/25.42 fof('qe(s1(plural(271)))', axiom, 25.22/25.42 ?[Vd1203]: (vd1199=Vd1203 & rpoint(Vd1203))). 25.22/25.42 fof('qe(s3(plural(271)))', axiom, 25.22/25.42 ?[Vd1205]: (Vd1205=vd1201 & rpoint(Vd1205))). 25.22/25.42 fof('qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))', axiom, 25.22/25.42 ![Vd828, Vd829, Vd830]: 25.22/25.42 ((?[Vd832]: (rpoint(Vd832) & Vd832=Vd828) 25.22/25.42 & (?[Vd833]: (rpoint(Vd833) & Vd833=Vd829) 25.22/25.42 & (?[Vd834]: (Vd834=Vd830 & rpoint(Vd834)) 25.22/25.42 & rR(Vd829, Vd828, Vd830)))) 25.22/25.42 => vplus(vf(Vd828, Vd829), vf(Vd829, Vd830))=vf(Vd828, Vd830))). 25.22/25.42 25.22/25.42 Now clausify the problem and encode Horn clauses using encoding 3 of 25.22/25.42 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 25.22/25.42 We repeatedly replace C & s=t => u=v by the two clauses: 25.22/25.42 $$fresh(y, y, x1...xn) = u 25.22/25.42 C => $$fresh(s, t, x1...xn) = v 25.22/25.42 where $$fresh is a fresh function symbol and x1..xn are the free 25.22/25.42 variables of u and v. 25.22/25.42 A predicate p(X) is encoded as p(X)=$$true (this is sound, because the 25.22/25.42 input problem has no model of domain size 1). 25.22/25.42 25.22/25.42 The encoding turns the above axioms into the following unit equations and goals: 25.22/25.42 25.22/25.42 Axiom 175 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): $$fresh267(X, X, Y, Z, W) = vf(Y, W). 25.22/25.42 Axiom 176 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): $$fresh265(X, X, Y, Z, W) = vplus(vf(Y, Z), vf(Z, W)). 25.22/25.42 Axiom 177 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): $$fresh268(X, X, Y, Z, W) = $$fresh267(rpoint(Y), $$true2, Y, Z, W). 25.22/25.42 Axiom 178 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): $$fresh266(X, X, Y, Z, W) = $$fresh265(rpoint(Z), $$true2, Y, Z, W). 25.22/25.42 Axiom 491 (holds(291, 1230, 0)): vd1199 = vd1185. 25.22/25.42 Axiom 500 (qe(s3(plural(271)))_1): rpoint(sK39_qe(s3(plural(271)))_Vd1205) = $$true2. 25.22/25.42 Axiom 501 (qe(s3(plural(271)))): sK39_qe(s3(plural(271)))_Vd1205 = vd1201. 25.22/25.42 Axiom 505 (holds(323, 1254, 0)): rR(vd1201, vd1185, vd1187) = $$true2. 25.22/25.42 Axiom 534 (qe(s1(plural(271)))_1): rpoint(sK29_qe(s1(plural(271)))_Vd1203) = $$true2. 25.22/25.42 Axiom 535 (qe(s1(plural(271)))): vd1199 = sK29_qe(s1(plural(271)))_Vd1203. 25.22/25.42 Axiom 552 (holds(314, 1247, 0)): vf(vd1185, vd1187) = vf(vd1199, vd1201). 25.22/25.42 Axiom 561 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): $$fresh266(rR(X, Y, Z), $$true2, Y, X, Z) = $$fresh268(rpoint(Z), $$true2, Y, X, Z). 25.22/25.42 Axiom 630 (and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_9): rpoint(sK6_and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_Vd1191) = $$true2. 25.22/25.42 Axiom 634 (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)))))))))))))))_5): sK6_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. 25.22/25.42 25.22/25.42 Lemma 635: vf(vd1185, vd1187) = vf(vd1185, vd1201). 25.22/25.42 Proof: 25.22/25.42 vf(vd1185, vd1187) 25.22/25.42 = { by axiom 552 (holds(314, 1247, 0)) } 25.22/25.42 vf(vd1199, vd1201) 25.22/25.42 = { by axiom 491 (holds(291, 1230, 0)) } 25.22/25.42 vf(vd1185, vd1201) 25.22/25.42 25.22/25.42 Goal 1 (holds(324, 1255, 0)): vf(vd1185, vd1187) = vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)). 25.22/25.42 Proof: 25.22/25.42 vf(vd1185, vd1187) 25.22/25.42 = { by lemma 635 } 25.22/25.42 vf(vd1185, vd1201) 25.22/25.42 = { by lemma 635 } 25.22/25.42 vf(vd1185, vd1187) 25.22/25.42 = { by axiom 175 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 25.22/25.42 $$fresh267($$true2, $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 534 (qe(s1(plural(271)))_1) } 25.22/25.42 $$fresh267(rpoint(sK29_qe(s1(plural(271)))_Vd1203), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 535 (qe(s1(plural(271)))) } 25.22/25.42 $$fresh267(rpoint(vd1199), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 491 (holds(291, 1230, 0)) } 25.22/25.42 $$fresh267(rpoint(vd1185), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 177 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 25.22/25.42 $$fresh268($$true2, $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 630 (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) } 25.22/25.42 $$fresh268(rpoint(sK6_and(neg(neg(conjunct2(conjunct2(conjunct2(plural(comma_conjunct2(268))))))), and(holds(conjunct1(conjunct2(conjunct2(plural(comma_conjunct2(268))))), 1194, 0), and(holds(conjunct1(conjunct2(plural(comma_conjunct2(268)))), 1193, 0), and(holds(conjunct1(plural(comma_conjunct2(268))), 1192, 0), and(qe(s3(plural(comma_conjunct2(268)))), and(qe(s2(plural(comma_conjunct2(268)))), and(qe(s1(plural(comma_conjunct2(268)))), and(pred(comma_conjunct1(268), 9), and(pred(comma_conjunct1(268), 8), and(pred(comma_conjunct1(268), 7), and(qe(s3(plural(268))), and(qe(s2(plural(268))), qe(s1(plural(268)))))))))))))))_Vd1191), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 634 (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)))))))))))))))_5) } 25.22/25.42 $$fresh268(rpoint(vd1187), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 561 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 25.22/25.42 $$fresh266(rR(vd1201, vd1185, vd1187), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 505 (holds(323, 1254, 0)) } 25.22/25.42 $$fresh266($$true2, $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 178 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 25.22/25.42 $$fresh265(rpoint(vd1201), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 501 (qe(s3(plural(271)))) } 25.22/25.42 $$fresh265(rpoint(sK39_qe(s3(plural(271)))_Vd1205), $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 500 (qe(s3(plural(271)))_1) } 25.22/25.42 $$fresh265($$true2, $$true2, vd1185, vd1201, vd1187) 25.22/25.42 = { by axiom 176 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) } 25.22/25.42 vplus(vf(vd1185, vd1201), vf(vd1201, vd1187)) 25.22/25.42 % SZS output end Proof 25.22/25.42 25.22/25.42 RESULT: Theorem (the conjecture is true). 25.22/25.42 EOF