TSTP Solution File: CSR048+1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : CSR048+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 : n019.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 21:41:21 EDT 2023
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : CSR048+1 : TPTP v8.1.2. Released v3.4.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.36 % Computer : n019.cluster.edu
% 0.19/0.36 % Model : x86_64 x86_64
% 0.19/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36 % Memory : 8042.1875MB
% 0.19/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36 % CPULimit : 300
% 0.19/0.36 % WCLimit : 300
% 0.19/0.36 % DateTime : Mon Aug 28 10:26:28 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.47 Command-line arguments: --flip-ordering --lhs-weight 1 --depth-weight 60 --distributivity-heuristic
% 0.22/0.47
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47
% 0.22/0.47 % SZS output start Proof
% 0.22/0.47 Take the following subset of the input axioms:
% 0.22/0.47 fof(just1, axiom, genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member1_mt)).
% 0.22/0.47 fof(just2, axiom, mtvisible(c_tptpgeo_member1_mt) => borderson(c_georegion_l4_x45_y9, c_georegion_l4_x45_y10)).
% 0.22/0.47 fof(just3, axiom, ![OBJ, COL1, COL2]: ~(isa(OBJ, COL1) & (isa(OBJ, COL2) & disjointwith(COL1, COL2)))).
% 0.22/0.47 fof(just30, axiom, ![X]: ~borderson(X, X)).
% 0.22/0.47 fof(just31, axiom, ![SPECMT, GENLMT]: ((mtvisible(SPECMT) & genlmt(SPECMT, GENLMT)) => mtvisible(GENLMT))).
% 0.22/0.47 fof(query48, conjecture, ?[ARG2]: (mtvisible(c_tptpgeo_spindlecollectormt) => borderson(c_georegion_l4_x45_y9, ARG2))).
% 0.22/0.47
% 0.22/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.22/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.22/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.22/0.47 fresh(y, y, x1...xn) = u
% 0.22/0.47 C => fresh(s, t, x1...xn) = v
% 0.22/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.22/0.47 variables of u and v.
% 0.22/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.22/0.47 input problem has no model of domain size 1).
% 0.22/0.47
% 0.22/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.22/0.47
% 0.22/0.47 Axiom 1 (query48): mtvisible(c_tptpgeo_spindlecollectormt) = true2.
% 0.22/0.47 Axiom 2 (just1): genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member1_mt) = true2.
% 0.22/0.47 Axiom 3 (just2): fresh30(X, X) = true2.
% 0.22/0.47 Axiom 4 (just2): fresh30(mtvisible(c_tptpgeo_member1_mt), true2) = borderson(c_georegion_l4_x45_y9, c_georegion_l4_x45_y10).
% 0.22/0.47 Axiom 5 (just31): fresh17(X, X, Y) = true2.
% 0.22/0.47 Axiom 6 (just31): fresh18(X, X, Y, Z) = mtvisible(Z).
% 0.22/0.47 Axiom 7 (just31): fresh18(mtvisible(X), true2, X, Y) = fresh17(genlmt(X, Y), true2, Y).
% 0.22/0.47
% 0.22/0.47 Goal 1 (query48_1): borderson(c_georegion_l4_x45_y9, X) = true2.
% 0.22/0.47 The goal is true when:
% 0.22/0.47 X = c_georegion_l4_x45_y10
% 0.22/0.47
% 0.22/0.47 Proof:
% 0.22/0.47 borderson(c_georegion_l4_x45_y9, c_georegion_l4_x45_y10)
% 0.22/0.47 = { by axiom 4 (just2) R->L }
% 0.22/0.47 fresh30(mtvisible(c_tptpgeo_member1_mt), true2)
% 0.22/0.47 = { by axiom 6 (just31) R->L }
% 0.22/0.47 fresh30(fresh18(true2, true2, c_tptpgeo_spindlecollectormt, c_tptpgeo_member1_mt), true2)
% 0.22/0.47 = { by axiom 1 (query48) R->L }
% 0.22/0.47 fresh30(fresh18(mtvisible(c_tptpgeo_spindlecollectormt), true2, c_tptpgeo_spindlecollectormt, c_tptpgeo_member1_mt), true2)
% 0.22/0.47 = { by axiom 7 (just31) }
% 0.22/0.47 fresh30(fresh17(genlmt(c_tptpgeo_spindlecollectormt, c_tptpgeo_member1_mt), true2, c_tptpgeo_member1_mt), true2)
% 0.22/0.47 = { by axiom 2 (just1) }
% 0.22/0.47 fresh30(fresh17(true2, true2, c_tptpgeo_member1_mt), true2)
% 0.22/0.47 = { by axiom 5 (just31) }
% 0.22/0.47 fresh30(true2, true2)
% 0.22/0.47 = { by axiom 3 (just2) }
% 0.22/0.47 true2
% 0.22/0.47 % SZS output end Proof
% 0.22/0.47
% 0.22/0.47 RESULT: Theorem (the conjecture is true).
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