0.04/0.07 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.04/0.08 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof 0.08/0.27 % Computer : n002.cluster.edu 0.08/0.27 % Model : x86_64 x86_64 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.08/0.27 % Memory : 8042.1875MB 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64 0.08/0.27 % CPULimit : 1200 0.08/0.27 % WCLimit : 120 0.08/0.27 % DateTime : Tue Jul 13 10:24:33 EDT 2021 0.08/0.27 % CPUTime : 280.52/35.77 % SZS status Theorem 280.52/35.77 280.52/35.78 % SZS output start Proof 280.52/35.78 Take the following subset of the input axioms: 280.52/35.78 fof(ax1_1123, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))). 280.52/35.78 fof(ax1_153, axiom, ![OBJ]: ~(tptpcol_1_65536(OBJ) & tptpcol_1_1(OBJ))). 280.52/35.78 fof(ax1_164, axiom, ![TERM]: ((executionbyfiringsquad(TERM) & mtvisible(c_cyclistsmt)) => tptp_9_720(TERM, f_relationallexistsfn(TERM, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)))). 280.52/35.78 fof(ax1_165, axiom, mtvisible(c_cyclistsmt) => relationallexists(c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)). 280.52/35.78 fof(ax1_167, axiom, ![OBJ]: ~(setorcollection(OBJ) & individual(OBJ))). 280.52/35.78 fof(ax1_243, axiom, genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt)). 280.52/35.78 fof(ax1_254, axiom, genlmt(c_tptp_spindleheadmt, c_cyclistsmt)). 280.52/35.78 fof(ax1_289, axiom, ![OBJ]: ~(collection(OBJ) & individual(OBJ))). 280.52/35.78 fof(ax1_297, axiom, ![TERM, PRED, INDEPCOL, DEPCOL]: (isa(f_relationallexistsfn(TERM, PRED, INDEPCOL, DEPCOL), DEPCOL) <= (isa(TERM, INDEPCOL) & relationallexists(PRED, INDEPCOL, DEPCOL)))). 280.52/35.78 fof(ax1_3, axiom, ![OBJ]: ~(intangible(OBJ) & partiallytangible(OBJ))). 280.52/35.78 fof(ax1_363, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (disjointwith(COL1, COL2) & isa(OBJ, COL2)))). 280.52/35.78 fof(ax1_488, axiom, ![OBJ]: ~(tptpcol_3_98305(OBJ) & tptpcol_3_114688(OBJ))). 280.52/35.78 fof(ax1_521, axiom, ![X]: ~affiliatedwith(X, X)). 280.52/35.78 fof(ax1_698, axiom, ![X]: ~objectfoundinlocation(X, X)). 280.52/35.78 fof(ax1_783, axiom, ![X]: (tptpcol_16_29490(X) <= isa(X, c_tptpcol_16_29490))). 280.52/35.78 fof(ax1_901, axiom, ![X]: ~borderson(X, X)). 280.52/35.78 fof(ax1_919, axiom, ![X]: (executionbyfiringsquad(X) => isa(X, c_executionbyfiringsquad))). 280.52/35.78 fof(ax1_94, axiom, executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90)). 280.52/35.78 fof(query94, conjecture, ?[X]: (mtvisible(c_tptp_member3633_mt) => (tptp_9_720(c_tptpexecutionbyfiringsquad_90, X) & tptpcol_16_29490(X)))). 280.52/35.78 280.52/35.78 Now clausify the problem and encode Horn clauses using encoding 3 of 280.52/35.78 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf. 280.52/35.78 We repeatedly replace C & s=t => u=v by the two clauses: 280.52/35.78 fresh(y, y, x1...xn) = u 280.52/35.78 C => fresh(s, t, x1...xn) = v 280.52/35.78 where fresh is a fresh function symbol and x1..xn are the free 280.52/35.78 variables of u and v. 280.52/35.78 A predicate p(X) is encoded as p(X)=true (this is sound, because the 280.52/35.78 input problem has no model of domain size 1). 280.52/35.78 280.52/35.78 The encoding turns the above axioms into the following unit equations and goals: 280.52/35.78 280.52/35.78 Axiom 1 (query94): mtvisible(c_tptp_member3633_mt) = true2. 280.52/35.78 Axiom 2 (ax1_94): executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90) = true2. 280.52/35.78 Axiom 3 (ax1_254): genlmt(c_tptp_spindleheadmt, c_cyclistsmt) = true2. 280.52/35.78 Axiom 4 (ax1_243): genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt) = true2. 280.52/35.78 Axiom 5 (ax1_165): fresh648(X, X) = true2. 280.52/35.78 Axiom 6 (ax1_164): fresh822(X, X, Y) = true2. 280.52/35.78 Axiom 7 (ax1_1123): fresh680(X, X, Y) = true2. 280.52/35.78 Axiom 8 (ax1_165): fresh648(mtvisible(c_cyclistsmt), true2) = relationallexists(c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490). 280.52/35.78 Axiom 9 (ax1_783): fresh206(X, X, Y) = true2. 280.52/35.78 Axiom 10 (ax1_919): fresh74(X, X, Y) = true2. 280.52/35.78 Axiom 11 (ax1_164): fresh821(X, X, Y) = fresh822(mtvisible(c_cyclistsmt), true2, Y). 280.52/35.78 Axiom 12 (ax1_1123): fresh681(X, X, Y, Z) = mtvisible(Z). 280.52/35.78 Axiom 13 (ax1_919): fresh74(executionbyfiringsquad(X), true2, X) = isa(X, c_executionbyfiringsquad). 280.52/35.78 Axiom 14 (ax1_1123): fresh681(mtvisible(X), true2, X, Y) = fresh680(genlmt(X, Y), true2, Y). 280.52/35.78 Axiom 15 (ax1_783): fresh206(isa(X, c_tptpcol_16_29490), true2, X) = tptpcol_16_29490(X). 280.52/35.78 Axiom 16 (ax1_164): fresh821(executionbyfiringsquad(X), true2, X) = tptp_9_720(X, f_relationallexistsfn(X, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)). 280.52/35.78 Axiom 17 (ax1_297): fresh583(X, X, Y, Z, W, V) = isa(f_relationallexistsfn(Y, W, Z, V), V). 280.52/35.78 Axiom 18 (ax1_297): fresh582(X, X, Y, Z, W, V) = true2. 280.52/35.78 Axiom 19 (ax1_297): fresh583(relationallexists(X, Y, Z), true2, W, Y, X, Z) = fresh582(isa(W, Y), true2, W, Y, X, Z). 280.52/35.78 280.52/35.78 Lemma 20: mtvisible(c_cyclistsmt) = true2. 280.52/35.78 Proof: 280.52/35.78 mtvisible(c_cyclistsmt) 280.52/35.78 = { by axiom 12 (ax1_1123) R->L } 280.52/35.78 fresh681(true2, true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 7 (ax1_1123) R->L } 280.52/35.78 fresh681(fresh680(true2, true2, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 4 (ax1_243) R->L } 280.52/35.78 fresh681(fresh680(genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 14 (ax1_1123) R->L } 280.52/35.78 fresh681(fresh681(mtvisible(c_tptp_member3633_mt), true2, c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 1 (query94) } 280.52/35.78 fresh681(fresh681(true2, true2, c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 12 (ax1_1123) } 280.52/35.78 fresh681(mtvisible(c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt) 280.52/35.78 = { by axiom 14 (ax1_1123) } 280.52/35.78 fresh680(genlmt(c_tptp_spindleheadmt, c_cyclistsmt), true2, c_cyclistsmt) 280.52/35.78 = { by axiom 3 (ax1_254) } 280.52/35.78 fresh680(true2, true2, c_cyclistsmt) 280.52/35.78 = { by axiom 7 (ax1_1123) } 280.52/35.78 true2 280.52/35.78 280.52/35.78 Goal 1 (query94_1): tuple2(tptpcol_16_29490(X), tptp_9_720(c_tptpexecutionbyfiringsquad_90, X)) = tuple2(true2, true2). 280.52/35.78 The goal is true when: 280.52/35.78 X = f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490) 280.52/35.78 280.52/35.78 Proof: 280.52/35.78 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490))) 280.52/35.78 = { by axiom 16 (ax1_164) R->L } 280.52/35.78 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh821(executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90), true2, c_tptpexecutionbyfiringsquad_90)) 280.52/35.79 = { by axiom 2 (ax1_94) } 280.52/35.79 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh821(true2, true2, c_tptpexecutionbyfiringsquad_90)) 280.52/35.79 = { by axiom 11 (ax1_164) } 280.52/35.79 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh822(mtvisible(c_cyclistsmt), true2, c_tptpexecutionbyfiringsquad_90)) 280.52/35.79 = { by lemma 20 } 280.52/35.79 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh822(true2, true2, c_tptpexecutionbyfiringsquad_90)) 280.52/35.79 = { by axiom 6 (ax1_164) } 280.52/35.79 tuple2(tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 15 (ax1_783) R->L } 280.52/35.79 tuple2(fresh206(isa(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490), c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 17 (ax1_297) R->L } 280.52/35.79 tuple2(fresh206(fresh583(true2, true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 5 (ax1_165) R->L } 280.52/35.79 tuple2(fresh206(fresh583(fresh648(true2, true2), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by lemma 20 R->L } 280.52/35.79 tuple2(fresh206(fresh583(fresh648(mtvisible(c_cyclistsmt), true2), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 8 (ax1_165) } 280.52/35.79 tuple2(fresh206(fresh583(relationallexists(c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 19 (ax1_297) } 280.52/35.79 tuple2(fresh206(fresh582(isa(c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 13 (ax1_919) R->L } 280.52/35.79 tuple2(fresh206(fresh582(fresh74(executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90), true2, c_tptpexecutionbyfiringsquad_90), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 2 (ax1_94) } 280.52/35.79 tuple2(fresh206(fresh582(fresh74(true2, true2, c_tptpexecutionbyfiringsquad_90), true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 10 (ax1_919) } 280.52/35.79 tuple2(fresh206(fresh582(true2, true2, c_tptpexecutionbyfiringsquad_90, c_executionbyfiringsquad, c_tptp_9_720, c_tptpcol_16_29490), true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 18 (ax1_297) } 280.52/35.79 tuple2(fresh206(true2, true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2) 280.52/35.79 = { by axiom 9 (ax1_783) } 280.52/35.79 tuple2(true2, true2) 280.52/35.79 % SZS output end Proof 280.52/35.79 280.52/35.79 RESULT: Theorem (the conjecture is true). 280.52/35.82 EOF