TSTP Solution File: PUZ008-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : PUZ008-1 : 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 : n028.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 13:23:53 EDT 2023
% Result : Unsatisfiable 0.20s 0.44s
% Output : Proof 0.20s
% 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 : PUZ008-1 : 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
% 0.12/0.34 % Computer : n028.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 23:01:52 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.20/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.44 % SZS output start Proof
% 0.20/0.44 Take the following subset of the input axioms:
% 0.20/0.44 fof(extra_cannibal_meal_on_east_bank, axiom, ![X, Y, Z, W]: achievable(west(X, Y), Z, east(m(s(W)), c(s(s(W)))))).
% 0.20/0.44 fof(missionary_west_to_east, axiom, ![X2, Y2, Z2, W2]: (~achievable(west(m(s(X2)), c(Y2)), boatonwest, east(m(Z2), c(W2))) | achievable(west(m(X2), c(Y2)), boatoneast, east(m(s(Z2)), c(W2))))).
% 0.20/0.44 fof(prove_can_get_to_east_bank, negated_conjecture, ![X2]: ~achievable(west(m(n0), c(n0)), X2, east(m(s(s(s(n0)))), c(s(s(s(n0))))))).
% 0.20/0.44
% 0.20/0.44 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.20/0.44 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.20/0.44 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.20/0.44 fresh(y, y, x1...xn) = u
% 0.20/0.44 C => fresh(s, t, x1...xn) = v
% 0.20/0.44 where fresh is a fresh function symbol and x1..xn are the free
% 0.20/0.44 variables of u and v.
% 0.20/0.44 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.20/0.44 input problem has no model of domain size 1).
% 0.20/0.44
% 0.20/0.44 The encoding turns the above axioms into the following unit equations and goals:
% 0.20/0.44
% 0.20/0.44 Axiom 1 (missionary_west_to_east): fresh5(X, X, Y, Z, W, V) = true2.
% 0.20/0.44 Axiom 2 (extra_cannibal_meal_on_east_bank): achievable(west(X, Y), Z, east(m(s(W)), c(s(s(W))))) = true2.
% 0.20/0.44 Axiom 3 (missionary_west_to_east): fresh5(achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))), true2, X, Y, Z, W) = achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))).
% 0.20/0.44
% 0.20/0.44 Goal 1 (prove_can_get_to_east_bank): achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) = true2.
% 0.20/0.44 The goal is true when:
% 0.20/0.44 X = boatoneast
% 0.20/0.44
% 0.20/0.44 Proof:
% 0.20/0.44 achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0))))))
% 0.20/0.44 = { by axiom 3 (missionary_west_to_east) R->L }
% 0.20/0.44 fresh5(achievable(west(m(s(n0)), c(n0)), boatonwest, east(m(s(s(n0))), c(s(s(s(n0)))))), true2, n0, n0, s(s(n0)), s(s(s(n0))))
% 0.20/0.44 = { by axiom 2 (extra_cannibal_meal_on_east_bank) }
% 0.20/0.44 fresh5(true2, true2, n0, n0, s(s(n0)), s(s(s(n0))))
% 0.20/0.44 = { by axiom 1 (missionary_west_to_east) }
% 0.20/0.44 true2
% 0.20/0.44 % SZS output end Proof
% 0.20/0.44
% 0.20/0.44 RESULT: Unsatisfiable (the axioms are contradictory).
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