TSTP Solution File: CSR044+1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR044+1 : TPTP v8.1.2. Released v3.4.0.
% 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 : n018.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 21:41:18 EDT 2023
% Result : Theorem 0.21s 0.50s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR044+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 08:52:17 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.50 Command-line arguments: --lhs-weight 9 --flip-ordering --complete-subsets --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.50
% 0.21/0.50 % SZS status Theorem
% 0.21/0.50
% 0.21/0.50 % SZS output start Proof
% 0.21/0.50 Take the following subset of the input axioms:
% 0.21/0.50 fof(just1, axiom, ![TERM, INDEPCOL, PRED, DEPCOL]: ((isa(TERM, INDEPCOL) & relationallexists(PRED, INDEPCOL, DEPCOL)) => isa(f_relationallexistsfn(TERM, PRED, INDEPCOL, DEPCOL), DEPCOL))).
% 0.21/0.50 fof(just10, axiom, ![TERM2]: ((mtvisible(c_cyclistsmt) & executionbyfiringsquad(TERM2)) => tptp_9_720(TERM2, f_relationallexistsfn(TERM2, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)))).
% 0.21/0.50 fof(just11, axiom, mtvisible(c_cyclistsmt) => relationallexists(c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)).
% 0.21/0.50 fof(just12, axiom, executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90)).
% 0.21/0.50 fof(just13, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.21/0.50 fof(just31, axiom, ![X]: (isa(X, c_tptpcol_16_29490) => tptpcol_16_29490(X))).
% 0.21/0.50 fof(just34, axiom, ![X2]: (executionbyfiringsquad(X2) => isa(X2, c_executionbyfiringsquad))).
% 0.21/0.50 fof(just48, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))).
% 0.21/0.50 fof(just8, axiom, genlmt(c_tptp_spindleheadmt, c_cyclistsmt)).
% 0.21/0.50 fof(just9, axiom, genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt)).
% 0.21/0.50 fof(query44, conjecture, ?[X2]: (mtvisible(c_tptp_member3633_mt) => (tptp_9_720(c_tptpexecutionbyfiringsquad_90, X2) & tptpcol_16_29490(X2)))).
% 0.21/0.50
% 0.21/0.50 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.21/0.50 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.21/0.50 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.21/0.50 fresh(y, y, x1...xn) = u
% 0.21/0.50 C => fresh(s, t, x1...xn) = v
% 0.21/0.50 where fresh is a fresh function symbol and x1..xn are the free
% 0.21/0.50 variables of u and v.
% 0.21/0.50 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.21/0.50 input problem has no model of domain size 1).
% 0.21/0.50
% 0.21/0.50 The encoding turns the above axioms into the following unit equations and goals:
% 0.21/0.50
% 0.21/0.50 Axiom 1 (query44): mtvisible(c_tptp_member3633_mt) = true2.
% 0.21/0.50 Axiom 2 (just12): executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90) = true2.
% 0.21/0.50 Axiom 3 (just8): genlmt(c_tptp_spindleheadmt, c_cyclistsmt) = true2.
% 0.21/0.50 Axiom 4 (just9): genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt) = true2.
% 0.21/0.50 Axiom 5 (just11): fresh53(X, X) = true2.
% 0.21/0.50 Axiom 6 (just10): fresh57(X, X, Y) = true2.
% 0.21/0.50 Axiom 7 (just11): fresh53(mtvisible(c_cyclistsmt), true2) = relationallexists(c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490).
% 0.21/0.50 Axiom 8 (just31): fresh29(X, X, Y) = true2.
% 0.21/0.50 Axiom 9 (just34): fresh26(X, X, Y) = true2.
% 0.21/0.50 Axiom 10 (just48): fresh11(X, X, Y) = true2.
% 0.21/0.50 Axiom 11 (just10): fresh56(X, X, Y) = fresh57(mtvisible(c_cyclistsmt), true2, Y).
% 0.21/0.50 Axiom 12 (just34): fresh26(executionbyfiringsquad(X), true2, X) = isa(X, c_executionbyfiringsquad).
% 0.21/0.50 Axiom 13 (just48): fresh12(X, X, Y, Z) = mtvisible(Z).
% 0.21/0.50 Axiom 14 (just31): fresh29(isa(X, c_tptpcol_16_29490), true2, X) = tptpcol_16_29490(X).
% 0.21/0.50 Axiom 15 (just48): fresh12(mtvisible(X), true2, X, Y) = fresh11(genlmt(X, Y), true2, Y).
% 0.21/0.50 Axiom 16 (just10): fresh56(executionbyfiringsquad(X), true2, X) = tptp_9_720(X, f_relationallexistsfn(X, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)).
% 0.21/0.50 Axiom 17 (just1): fresh55(X, X, Y, Z, W, V) = true2.
% 0.21/0.50 Axiom 18 (just1): fresh54(X, X, Y, Z, W, V) = isa(f_relationallexistsfn(Y, W, Z, V), V).
% 0.21/0.50 Axiom 19 (just1): fresh54(relationallexists(X, Y, Z), true2, W, Y, X, Z) = fresh55(isa(W, Y), true2, W, Y, X, Z).
% 0.21/0.50
% 0.21/0.50 Lemma 20: mtvisible(c_cyclistsmt) = true2.
% 0.21/0.50 Proof:
% 0.21/0.50 mtvisible(c_cyclistsmt)
% 0.21/0.50 = { by axiom 13 (just48) R->L }
% 0.21/0.50 fresh12(true2, true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 10 (just48) R->L }
% 0.21/0.50 fresh12(fresh11(true2, true2, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 4 (just9) R->L }
% 0.21/0.50 fresh12(fresh11(genlmt(c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 15 (just48) R->L }
% 0.21/0.50 fresh12(fresh12(mtvisible(c_tptp_member3633_mt), true2, c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 1 (query44) }
% 0.21/0.50 fresh12(fresh12(true2, true2, c_tptp_member3633_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 13 (just48) }
% 0.21/0.50 fresh12(mtvisible(c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt)
% 0.21/0.50 = { by axiom 15 (just48) }
% 0.21/0.50 fresh11(genlmt(c_tptp_spindleheadmt, c_cyclistsmt), true2, c_cyclistsmt)
% 0.21/0.50 = { by axiom 3 (just8) }
% 0.21/0.50 fresh11(true2, true2, c_cyclistsmt)
% 0.21/0.50 = { by axiom 10 (just48) }
% 0.21/0.50 true2
% 0.21/0.50
% 0.21/0.50 Goal 1 (query44_1): tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, X), tptpcol_16_29490(X)) = tuple2(true2, true2).
% 0.21/0.50 The goal is true when:
% 0.21/0.50 X = f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)
% 0.21/0.50
% 0.21/0.50 Proof:
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), tptpcol_16_29490(f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)))
% 0.21/0.51 = { by axiom 14 (just31) R->L }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(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)))
% 0.21/0.51 = { by axiom 18 (just1) R->L }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh54(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)))
% 0.21/0.51 = { by axiom 5 (just11) R->L }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh54(fresh53(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)))
% 0.21/0.51 = { by lemma 20 R->L }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh54(fresh53(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)))
% 0.21/0.51 = { by axiom 7 (just11) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh54(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)))
% 0.21/0.51 = { by axiom 19 (just1) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh55(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)))
% 0.21/0.51 = { by axiom 12 (just34) R->L }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh55(fresh26(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)))
% 0.21/0.51 = { by axiom 2 (just12) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh55(fresh26(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)))
% 0.21/0.51 = { by axiom 9 (just34) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(fresh55(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)))
% 0.21/0.51 = { by axiom 17 (just1) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), fresh29(true2, true2, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)))
% 0.21/0.51 = { by axiom 8 (just31) }
% 0.21/0.51 tuple2(tptp_9_720(c_tptpexecutionbyfiringsquad_90, f_relationallexistsfn(c_tptpexecutionbyfiringsquad_90, c_tptp_9_720, c_executionbyfiringsquad, c_tptpcol_16_29490)), true2)
% 0.21/0.51 = { by axiom 16 (just10) R->L }
% 0.21/0.51 tuple2(fresh56(executionbyfiringsquad(c_tptpexecutionbyfiringsquad_90), true2, c_tptpexecutionbyfiringsquad_90), true2)
% 0.21/0.51 = { by axiom 2 (just12) }
% 0.21/0.51 tuple2(fresh56(true2, true2, c_tptpexecutionbyfiringsquad_90), true2)
% 0.21/0.51 = { by axiom 11 (just10) }
% 0.21/0.51 tuple2(fresh57(mtvisible(c_cyclistsmt), true2, c_tptpexecutionbyfiringsquad_90), true2)
% 0.21/0.51 = { by lemma 20 }
% 0.21/0.51 tuple2(fresh57(true2, true2, c_tptpexecutionbyfiringsquad_90), true2)
% 0.21/0.51 = { by axiom 6 (just10) }
% 0.21/0.51 tuple2(true2, true2)
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51
% 0.21/0.51 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------