TSTP Solution File: PUZ047+1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ047+1 : TPTP v8.1.2. Released v2.5.0.
% 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 : n023.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 13:24:04 EDT 2023
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : PUZ047+1 : TPTP v8.1.2. Released v2.5.0.
% 0.03/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 22:52:41 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.43 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.43
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43
% 0.19/0.44 % SZS output start Proof
% 0.19/0.44 Take the following subset of the input axioms:
% 0.19/0.47 fof(thm100, conjecture, (p(south, south, south, south, start) & (![T]: (p(south, north, south, north, T) => p(north, north, south, north, go_alone(T))) & (![T1]: (p(north, north, south, north, T1) => p(south, north, south, north, go_alone(T1))) & (![T2]: (p(south, south, north, south, T2) => p(north, south, north, south, go_alone(T2))) & (![T3]: (p(north, south, north, south, T3) => p(south, south, north, south, go_alone(T3))) & (![T4]: (p(south, south, south, north, T4) => p(north, north, south, north, take_wolf(T4))) & (![T5]: (p(north, north, south, north, T5) => p(south, south, south, north, take_wolf(T5))) & (![T6]: (p(south, south, north, south, T6) => p(north, north, north, south, take_wolf(T6))) & (![T7]: (p(north, north, north, south, T7) => p(south, south, north, south, take_wolf(T7))) & (![X, Y, U]: (p(south, X, south, Y, U) => p(north, X, north, Y, take_goat(U))) & (![X1, Y1, V]: (p(north, X1, north, Y1, V) => p(south, X1, south, Y1, take_goat(V))) & (![T8]: (p(south, north, south, south, T8) => p(north, north, south, north, take_cabbage(T8))) & (![T9]: (p(north, north, south, north, T9) => p(south, north, south, south, take_cabbage(T9))) & (![U1]: (p(south, south, north, south, U1) => p(north, south, north, north, take_cabbage(U1))) & ![V1]: (p(north, south, north, north, V1) => p(south, south, north, south, take_cabbage(V1))))))))))))))))) => ?[Z]: p(north, north, north, north, Z)).
% 0.19/0.47
% 0.19/0.47 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.47 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.47 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.47 fresh(y, y, x1...xn) = u
% 0.19/0.47 C => fresh(s, t, x1...xn) = v
% 0.19/0.47 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.47 variables of u and v.
% 0.19/0.47 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.47 input problem has no model of domain size 1).
% 0.19/0.47
% 0.19/0.47 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.47
% 0.19/0.47 Axiom 1 (thm100_9): fresh(X, X, Y) = true2.
% 0.19/0.47 Axiom 2 (thm100_11): fresh12(X, X, Y) = true2.
% 0.19/0.47 Axiom 3 (thm100_4): fresh6(X, X, Y) = true2.
% 0.19/0.47 Axiom 4 (thm100_6): fresh4(X, X, Y) = true2.
% 0.19/0.47 Axiom 5 (thm100): p(south, south, south, south, start) = true2.
% 0.19/0.47 Axiom 6 (thm100_1): fresh13(X, X, Y, Z, W) = true2.
% 0.19/0.47 Axiom 7 (thm100_8): fresh2(X, X, Y, Z, W) = true2.
% 0.19/0.47 Axiom 8 (thm100_9): fresh(p(north, south, north, south, X), true2, X) = p(south, south, north, south, go_alone(X)).
% 0.19/0.47 Axiom 9 (thm100_11): fresh12(p(north, north, south, north, X), true2, X) = p(south, north, south, north, go_alone(X)).
% 0.19/0.47 Axiom 10 (thm100_4): fresh6(p(south, south, north, south, X), true2, X) = p(north, north, north, south, take_wolf(X)).
% 0.19/0.47 Axiom 11 (thm100_6): fresh4(p(south, north, south, south, X), true2, X) = p(north, north, south, north, take_cabbage(X)).
% 0.19/0.47 Axiom 12 (thm100_1): fresh13(p(south, X, south, Y, Z), true2, X, Y, Z) = p(north, X, north, Y, take_goat(Z)).
% 0.19/0.47 Axiom 13 (thm100_8): fresh2(p(north, X, north, Y, Z), true2, X, Y, Z) = p(south, X, south, Y, take_goat(Z)).
% 0.19/0.47
% 0.19/0.47 Goal 1 (thm100_15): p(north, north, north, north, X) = true2.
% 0.19/0.47 The goal is true when:
% 0.19/0.47 X = take_goat(go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47
% 0.19/0.47 Proof:
% 0.19/0.47 p(north, north, north, north, take_goat(go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start))))))))
% 0.19/0.47 = { by axiom 12 (thm100_1) R->L }
% 0.19/0.47 fresh13(p(south, north, south, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start))))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 9 (thm100_11) R->L }
% 0.19/0.47 fresh13(fresh12(p(north, north, south, north, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 11 (thm100_6) R->L }
% 0.19/0.47 fresh13(fresh12(fresh4(p(south, north, south, south, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 13 (thm100_8) R->L }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(p(north, north, north, south, take_wolf(go_alone(take_goat(start)))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 10 (thm100_4) R->L }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(p(south, south, north, south, go_alone(take_goat(start))), true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 8 (thm100_9) R->L }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(fresh(p(north, south, north, south, take_goat(start)), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 12 (thm100_1) R->L }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(fresh(fresh13(p(south, south, south, south, start), true2, south, south, start), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 5 (thm100) }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(fresh(fresh13(true2, true2, south, south, start), true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 6 (thm100_1) }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(fresh(true2, true2, take_goat(start)), true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 1 (thm100_9) }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(fresh6(true2, true2, go_alone(take_goat(start))), true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 3 (thm100_4) }
% 0.19/0.47 fresh13(fresh12(fresh4(fresh2(true2, true2, north, south, take_wolf(go_alone(take_goat(start)))), true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 7 (thm100_8) }
% 0.19/0.47 fresh13(fresh12(fresh4(true2, true2, take_goat(take_wolf(go_alone(take_goat(start))))), true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 4 (thm100_6) }
% 0.19/0.47 fresh13(fresh12(true2, true2, take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))), true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 2 (thm100_11) }
% 0.19/0.47 fresh13(true2, true2, north, north, go_alone(take_cabbage(take_goat(take_wolf(go_alone(take_goat(start)))))))
% 0.19/0.47 = { by axiom 6 (thm100_1) }
% 0.19/0.47 true2
% 0.19/0.47 % SZS output end Proof
% 0.19/0.47
% 0.19/0.47 RESULT: Theorem (the conjecture is true).
%------------------------------------------------------------------------------