TSTP Solution File: CSR056+1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : CSR056+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 : n020.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 21:41:29 EDT 2023
% Result : Theorem 0.19s 0.45s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CSR056+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
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 07:38:29 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.45 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.45
% 0.19/0.45 % SZS status Theorem
% 0.19/0.45
% 0.19/0.46 % SZS output start Proof
% 0.19/0.46 Take the following subset of the input axioms:
% 0.19/0.46 fof(just10, axiom, ![INS]: ((mtvisible(c_tptp_spindleheadmt) & supplies(INS)) => tptpofobject(INS, f_tptpquantityfn_14(n_232)))).
% 0.19/0.46 fof(just12, axiom, mtvisible(c_cyclistsmt) => artsupplies(c_tptpartsupplies)).
% 0.19/0.46 fof(just13, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.19/0.46 fof(just2, axiom, ![OBJ2]: (artsupplies(OBJ2) => supplies(OBJ2))).
% 0.19/0.46 fof(just47, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))).
% 0.19/0.46 fof(just8, axiom, genlmt(c_tptp_spindleheadmt, c_cyclistsmt)).
% 0.19/0.46 fof(just9, axiom, genlmt(c_tptp_member3717_mt, c_tptp_spindleheadmt)).
% 0.19/0.46 fof(query56, conjecture, ?[QUANTITY]: (mtvisible(c_tptp_member3717_mt) => tptpofobject(c_tptpartsupplies, QUANTITY))).
% 0.19/0.46
% 0.19/0.46 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.46 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.46 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.46 fresh(y, y, x1...xn) = u
% 0.19/0.46 C => fresh(s, t, x1...xn) = v
% 0.19/0.46 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.46 variables of u and v.
% 0.19/0.46 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.46 input problem has no model of domain size 1).
% 0.19/0.46
% 0.19/0.46 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.46
% 0.19/0.46 Axiom 1 (just8): genlmt(c_tptp_spindleheadmt, c_cyclistsmt) = true2.
% 0.19/0.46 Axiom 2 (just9): genlmt(c_tptp_member3717_mt, c_tptp_spindleheadmt) = true2.
% 0.19/0.46 Axiom 3 (query56): mtvisible(c_tptp_member3717_mt) = true2.
% 0.19/0.46 Axiom 4 (just12): fresh64(X, X) = true2.
% 0.19/0.46 Axiom 5 (just10): fresh67(X, X, Y) = true2.
% 0.19/0.46 Axiom 6 (just10): fresh66(X, X, Y) = tptpofobject(Y, f_tptpquantityfn_14(n_232)).
% 0.19/0.46 Axiom 7 (just12): fresh64(mtvisible(c_cyclistsmt), true2) = artsupplies(c_tptpartsupplies).
% 0.19/0.46 Axiom 8 (just2): fresh55(X, X, Y) = true2.
% 0.19/0.46 Axiom 9 (just47): fresh25(X, X, Y) = true2.
% 0.19/0.46 Axiom 10 (just10): fresh66(mtvisible(c_tptp_spindleheadmt), true2, X) = fresh67(supplies(X), true2, X).
% 0.19/0.46 Axiom 11 (just2): fresh55(artsupplies(X), true2, X) = supplies(X).
% 0.19/0.46 Axiom 12 (just47): fresh26(X, X, Y, Z) = mtvisible(Z).
% 0.19/0.46 Axiom 13 (just47): fresh26(mtvisible(X), true2, X, Y) = fresh25(genlmt(X, Y), true2, Y).
% 0.19/0.46
% 0.19/0.46 Lemma 14: mtvisible(c_tptp_spindleheadmt) = true2.
% 0.19/0.46 Proof:
% 0.19/0.46 mtvisible(c_tptp_spindleheadmt)
% 0.19/0.46 = { by axiom 12 (just47) R->L }
% 0.19/0.46 fresh26(true2, true2, c_tptp_member3717_mt, c_tptp_spindleheadmt)
% 0.19/0.46 = { by axiom 3 (query56) R->L }
% 0.19/0.46 fresh26(mtvisible(c_tptp_member3717_mt), true2, c_tptp_member3717_mt, c_tptp_spindleheadmt)
% 0.19/0.46 = { by axiom 13 (just47) }
% 0.19/0.46 fresh25(genlmt(c_tptp_member3717_mt, c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt)
% 0.19/0.46 = { by axiom 2 (just9) }
% 0.19/0.46 fresh25(true2, true2, c_tptp_spindleheadmt)
% 0.19/0.46 = { by axiom 9 (just47) }
% 0.19/0.46 true2
% 0.19/0.46
% 0.19/0.46 Goal 1 (query56_1): tptpofobject(c_tptpartsupplies, X) = true2.
% 0.19/0.46 The goal is true when:
% 0.19/0.46 X = f_tptpquantityfn_14(n_232)
% 0.19/0.46
% 0.19/0.46 Proof:
% 0.19/0.46 tptpofobject(c_tptpartsupplies, f_tptpquantityfn_14(n_232))
% 0.19/0.46 = { by axiom 6 (just10) R->L }
% 0.19/0.46 fresh66(true2, true2, c_tptpartsupplies)
% 0.19/0.46 = { by lemma 14 R->L }
% 0.19/0.46 fresh66(mtvisible(c_tptp_spindleheadmt), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 10 (just10) }
% 0.19/0.46 fresh67(supplies(c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 11 (just2) R->L }
% 0.19/0.46 fresh67(fresh55(artsupplies(c_tptpartsupplies), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 7 (just12) R->L }
% 0.19/0.46 fresh67(fresh55(fresh64(mtvisible(c_cyclistsmt), true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 12 (just47) R->L }
% 0.19/0.46 fresh67(fresh55(fresh64(fresh26(true2, true2, c_tptp_spindleheadmt, c_cyclistsmt), true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by lemma 14 R->L }
% 0.19/0.46 fresh67(fresh55(fresh64(fresh26(mtvisible(c_tptp_spindleheadmt), true2, c_tptp_spindleheadmt, c_cyclistsmt), true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 13 (just47) }
% 0.19/0.46 fresh67(fresh55(fresh64(fresh25(genlmt(c_tptp_spindleheadmt, c_cyclistsmt), true2, c_cyclistsmt), true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 1 (just8) }
% 0.19/0.46 fresh67(fresh55(fresh64(fresh25(true2, true2, c_cyclistsmt), true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 9 (just47) }
% 0.19/0.46 fresh67(fresh55(fresh64(true2, true2), true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 4 (just12) }
% 0.19/0.46 fresh67(fresh55(true2, true2, c_tptpartsupplies), true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 8 (just2) }
% 0.19/0.46 fresh67(true2, true2, c_tptpartsupplies)
% 0.19/0.46 = { by axiom 5 (just10) }
% 0.19/0.46 true2
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Theorem (the conjecture is true).
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