TSTP Solution File: PLA001-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PLA001-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n022.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 : Thu Aug 31 13:03:12 EDT 2023
% Result : Unsatisfiable 169.42s 22.21s
% Output : Proof 169.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PLA001-1 : TPTP v8.1.2. Released v1.0.0.
% 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 : n022.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 : Sun Aug 27 05:43:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 169.42/22.21 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 169.42/22.21
% 169.42/22.21 % SZS status Unsatisfiable
% 169.42/22.21
% 169.42/22.22 % SZS output start Proof
% 169.42/22.22 Take the following subset of the input axioms:
% 169.42/22.22 fof(buy_in_city, axiom, ![Loaves, Time, Situation, City]: (~at(City, Loaves, Time, Situation) | at(City, s(Loaves), s(Time), buy(Situation)))).
% 169.42/22.22 fof(drive1, axiom, ![FromCity, ToCity, Time2, Situation2, Loaves2]: (~at(FromCity, Loaves2, Time2, Situation2) | (~next_to(FromCity, ToCity) | at(ToCity, Loaves2, s(s(Time2)), drive(ToCity, Situation2))))).
% 169.42/22.22 fof(initial, hypothesis, at(cheyenne, none, start, initial_situation)).
% 169.42/22.22 fof(map10, hypothesis, next_to(omaha, desMoines)).
% 169.42/22.22 fof(map6, hypothesis, next_to(cheyenne, northPlatte)).
% 169.42/22.22 fof(map7, hypothesis, next_to(northPlatte, grandIsland)).
% 169.42/22.22 fof(map8, hypothesis, next_to(grandIsland, lincoln)).
% 169.42/22.22 fof(map9, hypothesis, next_to(lincoln, omaha)).
% 169.42/22.22 fof(prove_you_gat_get_there_with_bread, negated_conjecture, ![Time2, Situation2]: ~at(desMoines, s(none), Time2, Situation2)).
% 169.42/22.22
% 169.42/22.22 Now clausify the problem and encode Horn clauses using encoding 3 of
% 169.42/22.22 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 169.42/22.22 We repeatedly replace C & s=t => u=v by the two clauses:
% 169.42/22.22 fresh(y, y, x1...xn) = u
% 169.42/22.22 C => fresh(s, t, x1...xn) = v
% 169.42/22.22 where fresh is a fresh function symbol and x1..xn are the free
% 169.42/22.22 variables of u and v.
% 169.42/22.22 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 169.42/22.22 input problem has no model of domain size 1).
% 169.42/22.22
% 169.42/22.22 The encoding turns the above axioms into the following unit equations and goals:
% 169.42/22.22
% 169.42/22.22 Axiom 1 (map6): next_to(cheyenne, northPlatte) = true2.
% 169.42/22.22 Axiom 2 (map7): next_to(northPlatte, grandIsland) = true2.
% 169.42/22.22 Axiom 3 (map8): next_to(grandIsland, lincoln) = true2.
% 169.42/22.22 Axiom 4 (map9): next_to(lincoln, omaha) = true2.
% 169.42/22.22 Axiom 5 (map10): next_to(omaha, desMoines) = true2.
% 169.42/22.22 Axiom 6 (initial): at(cheyenne, none, start, initial_situation) = true2.
% 169.42/22.22 Axiom 7 (buy_in_city): fresh5(X, X, Y, Z, W, V) = true2.
% 169.42/22.22 Axiom 8 (drive1): fresh4(X, X, Y, Z, W, V) = true2.
% 169.42/22.22 Axiom 9 (drive1): fresh6(X, X, Y, Z, W, V, U) = at(U, Z, s(s(W)), drive(U, V)).
% 169.42/22.22 Axiom 10 (buy_in_city): fresh5(at(X, Y, Z, W), true2, X, Y, Z, W) = at(X, s(Y), s(Z), buy(W)).
% 169.42/22.22 Axiom 11 (drive1): fresh6(next_to(X, Y), true2, X, Z, W, V, Y) = fresh4(at(X, Z, W, V), true2, Z, W, V, Y).
% 169.42/22.22
% 169.42/22.22 Goal 1 (prove_you_gat_get_there_with_bread): at(desMoines, s(none), X, Y) = true2.
% 169.42/22.22 The goal is true when:
% 169.42/22.22 X = s(s(s(s(s(s(s(s(s(s(s(start)))))))))))
% 169.42/22.22 Y = buy(drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.22
% 169.42/22.22 Proof:
% 169.42/22.23 at(desMoines, s(none), s(s(s(s(s(s(s(s(s(s(s(start))))))))))), buy(drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))))))
% 169.42/22.23 = { by axiom 10 (buy_in_city) R->L }
% 169.42/22.23 fresh5(at(desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))))), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 9 (drive1) R->L }
% 169.42/22.23 fresh5(fresh6(true2, true2, omaha, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 5 (map10) R->L }
% 169.42/22.23 fresh5(fresh6(next_to(omaha, desMoines), true2, omaha, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 11 (drive1) }
% 169.42/22.23 fresh5(fresh4(at(omaha, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 9 (drive1) R->L }
% 169.42/22.23 fresh5(fresh4(fresh6(true2, true2, lincoln, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 4 (map9) R->L }
% 169.42/22.23 fresh5(fresh4(fresh6(next_to(lincoln, omaha), true2, lincoln, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 11 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(at(lincoln, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 9 (drive1) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh6(true2, true2, grandIsland, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 3 (map8) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh6(next_to(grandIsland, lincoln), true2, grandIsland, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 11 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(at(grandIsland, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation))), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 9 (drive1) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh6(true2, true2, northPlatte, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 2 (map7) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh6(next_to(northPlatte, grandIsland), true2, northPlatte, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 11 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(at(northPlatte, none, s(s(start)), drive(northPlatte, initial_situation)), true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 9 (drive1) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(fresh6(true2, true2, cheyenne, none, start, initial_situation, northPlatte), true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 1 (map6) R->L }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(fresh6(next_to(cheyenne, northPlatte), true2, cheyenne, none, start, initial_situation, northPlatte), true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 11 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(fresh4(at(cheyenne, none, start, initial_situation), true2, none, start, initial_situation, northPlatte), true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 6 (initial) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(fresh4(true2, true2, none, start, initial_situation, northPlatte), true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 8 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(fresh4(true2, true2, none, s(s(start)), drive(northPlatte, initial_situation), grandIsland), true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 8 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(fresh4(true2, true2, none, s(s(s(s(start)))), drive(grandIsland, drive(northPlatte, initial_situation)), lincoln), true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 8 (drive1) }
% 169.42/22.23 fresh5(fresh4(fresh4(true2, true2, none, s(s(s(s(s(s(start)))))), drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))), omaha), true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 8 (drive1) }
% 169.42/22.23 fresh5(fresh4(true2, true2, none, s(s(s(s(s(s(s(s(start)))))))), drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation)))), desMoines), true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 8 (drive1) }
% 169.42/22.23 fresh5(true2, true2, desMoines, none, s(s(s(s(s(s(s(s(s(s(start)))))))))), drive(desMoines, drive(omaha, drive(lincoln, drive(grandIsland, drive(northPlatte, initial_situation))))))
% 169.42/22.23 = { by axiom 7 (buy_in_city) }
% 169.42/22.23 true2
% 169.42/22.23 % SZS output end Proof
% 169.42/22.23
% 169.42/22.23 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------