TSTP Solution File: GEO300+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GEO300+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 23:28:33 EDT 2023
% Result : Theorem 18.32s 2.89s
% Output : Proof 18.32s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO300+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.35 % Computer : n026.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 23:36:51 EDT 2023
% 0.14/0.35 % CPUTime :
% 18.32/2.89 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 18.32/2.89
% 18.32/2.89 % SZS status Theorem
% 18.32/2.89
% 18.32/2.89 % SZS output start Proof
% 18.32/2.89 Take the following subset of the input axioms:
% 18.32/2.90 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(vd1186, Vd1195) & (ron(vd1185, Vd1195) & rline(Vd1195)))) & (vangle(vd1179, vd1178, vd1180)=vangle(vd1186, vd1185, vd1187) & (vf(vd1178, vd1180)=vf(vd1185, vd1187) & (vf(vd1178, vd1179)=vf(vd1185, vd1186) & (?[Vd1191]: (vd1187=Vd1191 & rpoint(Vd1191)) & (?[Vd1190]: (vd1186=Vd1190 & rpoint(Vd1190)) & (?[Vd1189]: (vd1185=Vd1189 & rpoint(Vd1189)) & (vd1179!=vd1180 & (vd1178!=vd1180 & (vd1178!=vd1179 & (?[Vd1184]: (vd1180=Vd1184 & rpoint(Vd1184)) & (?[Vd1183]: (vd1179=Vd1183 & rpoint(Vd1183)) & ?[Vd1182]: (vd1178=Vd1182 & rpoint(Vd1182)))))))))))))).
% 18.32/2.90 fof('holds(330, 1259, 0)', axiom, rR(vd1187, vd1185, vd1201)).
% 18.32/2.90 fof('holds(331, 1260, 0)', conjecture, vf(vd1185, vd1201)=vplus(vf(vd1185, vd1187), vf(vd1187, vd1201))).
% 18.32/2.90 fof('qe(s3(plural(271)))', axiom, ?[Vd1205]: (vd1201=Vd1205 & rpoint(Vd1205))).
% 18.32/2.90 fof('qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))', axiom, ![Vd828, Vd829, Vd830]: ((rR(Vd829, Vd828, Vd830) & (?[Vd834]: (Vd830=Vd834 & rpoint(Vd834)) & (?[Vd833]: (Vd829=Vd833 & rpoint(Vd833)) & ?[Vd832]: (Vd828=Vd832 & rpoint(Vd832))))) => vplus(vf(Vd828, Vd829), vf(Vd829, Vd830))=vf(Vd828, Vd830))).
% 18.32/2.90
% 18.32/2.90 Now clausify the problem and encode Horn clauses using encoding 3 of
% 18.32/2.90 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 18.32/2.90 We repeatedly replace C & s=t => u=v by the two clauses:
% 18.32/2.90 fresh(y, y, x1...xn) = u
% 18.32/2.90 C => fresh(s, t, x1...xn) = v
% 18.32/2.90 where fresh is a fresh function symbol and x1..xn are the free
% 18.32/2.90 variables of u and v.
% 18.32/2.90 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 18.32/2.90 input problem has no model of domain size 1).
% 18.32/2.90
% 18.32/2.90 The encoding turns the above axioms into the following unit equations and goals:
% 18.32/2.90
% 18.32/2.90 Axiom 1 (qe(s3(plural(271)))): vd1201 = vd1205.
% 18.32/2.90 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)))))))))))))))_3): vd1187 = vd1191.
% 18.32/2.90 Axiom 3 (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)))))))))))))))_2): vd1185 = vd1189.
% 18.32/2.90 Axiom 4 (qe(s3(plural(271)))_1): rpoint(vd1205) = true2.
% 18.32/2.90 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)))))))))))))))_9): rpoint(vd1191) = true2.
% 18.32/2.90 Axiom 6 (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.
% 18.32/2.90 Axiom 7 (holds(330, 1259, 0)): rR(vd1187, vd1185, vd1201) = true2.
% 18.32/2.90 Axiom 8 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh60(X, X, Y, Z, W) = vf(W, Y).
% 18.32/2.90 Axiom 9 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh466(X, X, Y, Z, W) = vplus(vf(W, Z), vf(Z, Y)).
% 18.32/2.90 Axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh465(X, X, Y, Z, W) = fresh466(rpoint(Y), true2, Y, Z, W).
% 18.32/2.90 Axiom 11 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh464(X, X, Y, Z, W) = fresh465(rpoint(Z), true2, Y, Z, W).
% 18.32/2.90 Axiom 12 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))): fresh464(rpoint(X), true2, Y, Z, X) = fresh60(rR(Z, X, Y), true2, Y, Z, X).
% 18.32/2.90
% 18.32/2.90 Goal 1 (holds(331, 1260, 0)): vf(vd1185, vd1201) = vplus(vf(vd1185, vd1187), vf(vd1187, vd1201)).
% 18.32/2.90 Proof:
% 18.32/2.90 vf(vd1185, vd1201)
% 18.32/2.90 = { by axiom 8 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) R->L }
% 18.32/2.90 fresh60(true2, true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 7 (holds(330, 1259, 0)) R->L }
% 18.32/2.90 fresh60(rR(vd1187, vd1185, vd1201), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 12 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) R->L }
% 18.32/2.90 fresh464(rpoint(vd1185), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 3 (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)))))))))))))))_2) }
% 18.32/2.90 fresh464(rpoint(vd1189), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 6 (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) }
% 18.32/2.90 fresh464(true2, true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 11 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) }
% 18.32/2.90 fresh465(rpoint(vd1187), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { 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)))))))))))))))_3) }
% 18.32/2.90 fresh465(rpoint(vd1191), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { 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)))))))))))))))_9) }
% 18.32/2.90 fresh465(true2, true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 10 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) }
% 18.32/2.90 fresh466(rpoint(vd1201), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 1 (qe(s3(plural(271)))) }
% 18.32/2.90 fresh466(rpoint(vd1205), true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 4 (qe(s3(plural(271)))_1) }
% 18.32/2.90 fresh466(true2, true2, vd1201, vd1187, vd1185)
% 18.32/2.90 = { by axiom 9 (qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))) }
% 18.32/2.90 vplus(vf(vd1185, vd1187), vf(vd1187, vd1201))
% 18.32/2.90 % SZS output end Proof
% 18.32/2.90
% 18.32/2.90 RESULT: Theorem (the conjecture is true).
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