TSTP Solution File: PUZ008-2 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : PUZ008-2 : 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 : n013.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 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ008-2 : 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
% 0.13/0.34 % Computer : n013.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 : Sat Aug 26 21:52:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.44 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.19/0.44
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44
% 0.19/0.45 % SZS output start Proof
% 0.19/0.45 Take the following subset of the input axioms:
% 0.19/0.45 fof(bcc_mmmc_to_x_bmmmccc, axiom, ~banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatonwest) | banks(west(m(n0), c(n0)), east(m(n3), c(n3)), boatoneast)).
% 0.19/0.45 fof(bccc_mmm_to_c_bmmmcc, axiom, ~banks(west(m(n0), c(n3)), east(m(n3), c(n0)), boatonwest) | banks(west(m(n0), c(n1)), east(m(n3), c(n2)), boatoneast)).
% 0.19/0.45 fof(bmmcc_mc_to_cc_bmmmc, axiom, ~banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatonwest) | banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatoneast)).
% 0.19/0.45 fof(bmmmc_cc_to_mc_bmmcc, axiom, ~banks(west(m(n3), c(n1)), east(m(n0), c(n2)), boatonwest) | banks(west(m(n1), c(n1)), east(m(n2), c(n2)), boatoneast)).
% 0.19/0.45 fof(bmmmcc_c_to_mmm_bccc, axiom, ~banks(west(m(n3), c(n2)), east(m(n0), c(n1)), boatonwest) | banks(west(m(n3), c(n0)), east(m(n0), c(n3)), boatoneast)).
% 0.19/0.45 fof(bmmmccc_x_to_mmcc_bmc, axiom, ~banks(west(m(n3), c(n3)), east(m(n0), c(n0)), boatonwest) | banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatoneast)).
% 0.19/0.45 fof(c_bmmmcc_to_bcc_mmmc, axiom, ~banks(west(m(n0), c(n1)), east(m(n3), c(n2)), boatoneast) | banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatonwest)).
% 0.19/0.45 fof(cc_bmmmc_to_bccc_mmm, axiom, ~banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatoneast) | banks(west(m(n0), c(n3)), east(m(n3), c(n0)), boatonwest)).
% 0.19/0.45 fof(mc_bmmcc_to_bmmcc_mc, axiom, ~banks(west(m(n1), c(n1)), east(m(n2), c(n2)), boatoneast) | banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatonwest)).
% 0.19/0.45 fof(mmcc_bmc_to_bmmmcc_c, axiom, ~banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatoneast) | banks(west(m(n3), c(n2)), east(m(n0), c(n1)), boatonwest)).
% 0.19/0.45 fof(mmm_bccc_to_bmmmc_cc, axiom, ~banks(west(m(n3), c(n0)), east(m(n0), c(n3)), boatoneast) | banks(west(m(n3), c(n1)), east(m(n0), c(n2)), boatonwest)).
% 0.19/0.45 fof(prove_can_get_across, negated_conjecture, ~banks(west(m(n0), c(n0)), east(m(n3), c(n3)), boatoneast)).
% 0.19/0.45 fof(starting_configuration, hypothesis, banks(west(m(n3), c(n3)), east(m(n0), c(n0)), boatonwest)).
% 0.19/0.45
% 0.19/0.45 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.19/0.45 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.19/0.45 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.19/0.45 fresh(y, y, x1...xn) = u
% 0.19/0.45 C => fresh(s, t, x1...xn) = v
% 0.19/0.45 where fresh is a fresh function symbol and x1..xn are the free
% 0.19/0.45 variables of u and v.
% 0.19/0.45 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.19/0.45 input problem has no model of domain size 1).
% 0.19/0.45
% 0.19/0.45 The encoding turns the above axioms into the following unit equations and goals:
% 0.19/0.45
% 0.19/0.45 Axiom 1 (bcc_mmmc_to_x_bmmmccc): fresh28(X, X) = true.
% 0.19/0.45 Axiom 2 (bccc_mmm_to_c_bmmmcc): fresh27(X, X) = true.
% 0.19/0.45 Axiom 3 (bmmcc_mc_to_cc_bmmmc): fresh23(X, X) = true.
% 0.19/0.45 Axiom 4 (bmmmc_cc_to_mc_bmmcc): fresh21(X, X) = true.
% 0.19/0.45 Axiom 5 (bmmmcc_c_to_mmm_bccc): fresh18(X, X) = true.
% 0.19/0.45 Axiom 6 (bmmmccc_x_to_mmcc_bmc): fresh16(X, X) = true.
% 0.19/0.45 Axiom 7 (c_bmmmcc_to_bcc_mmmc): fresh14(X, X) = true.
% 0.19/0.45 Axiom 8 (cc_bmmmc_to_bccc_mmm): fresh11(X, X) = true.
% 0.19/0.45 Axiom 9 (mc_bmmcc_to_bmmcc_mc): fresh9(X, X) = true.
% 0.19/0.45 Axiom 10 (mmcc_bmc_to_bmmmcc_c): fresh7(X, X) = true.
% 0.19/0.45 Axiom 11 (mmm_bccc_to_bmmmc_cc): fresh5(X, X) = true.
% 0.19/0.45 Axiom 12 (starting_configuration): banks(west(m(n3), c(n3)), east(m(n0), c(n0)), boatonwest) = true.
% 0.19/0.45 Axiom 13 (bcc_mmmc_to_x_bmmmccc): fresh28(banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatonwest), true) = banks(west(m(n0), c(n0)), east(m(n3), c(n3)), boatoneast).
% 0.19/0.45 Axiom 14 (bccc_mmm_to_c_bmmmcc): fresh27(banks(west(m(n0), c(n3)), east(m(n3), c(n0)), boatonwest), true) = banks(west(m(n0), c(n1)), east(m(n3), c(n2)), boatoneast).
% 0.19/0.45 Axiom 15 (bmmcc_mc_to_cc_bmmmc): fresh23(banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatonwest), true) = banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatoneast).
% 0.19/0.45 Axiom 16 (bmmmc_cc_to_mc_bmmcc): fresh21(banks(west(m(n3), c(n1)), east(m(n0), c(n2)), boatonwest), true) = banks(west(m(n1), c(n1)), east(m(n2), c(n2)), boatoneast).
% 0.19/0.45 Axiom 17 (bmmmcc_c_to_mmm_bccc): fresh18(banks(west(m(n3), c(n2)), east(m(n0), c(n1)), boatonwest), true) = banks(west(m(n3), c(n0)), east(m(n0), c(n3)), boatoneast).
% 0.19/0.45 Axiom 18 (bmmmccc_x_to_mmcc_bmc): fresh16(banks(west(m(n3), c(n3)), east(m(n0), c(n0)), boatonwest), true) = banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatoneast).
% 0.19/0.45 Axiom 19 (c_bmmmcc_to_bcc_mmmc): fresh14(banks(west(m(n0), c(n1)), east(m(n3), c(n2)), boatoneast), true) = banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatonwest).
% 0.19/0.45 Axiom 20 (cc_bmmmc_to_bccc_mmm): fresh11(banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatoneast), true) = banks(west(m(n0), c(n3)), east(m(n3), c(n0)), boatonwest).
% 0.19/0.45 Axiom 21 (mc_bmmcc_to_bmmcc_mc): fresh9(banks(west(m(n1), c(n1)), east(m(n2), c(n2)), boatoneast), true) = banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatonwest).
% 0.19/0.45 Axiom 22 (mmcc_bmc_to_bmmmcc_c): fresh7(banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatoneast), true) = banks(west(m(n3), c(n2)), east(m(n0), c(n1)), boatonwest).
% 0.19/0.45 Axiom 23 (mmm_bccc_to_bmmmc_cc): fresh5(banks(west(m(n3), c(n0)), east(m(n0), c(n3)), boatoneast), true) = banks(west(m(n3), c(n1)), east(m(n0), c(n2)), boatonwest).
% 0.19/0.45
% 0.19/0.45 Goal 1 (prove_can_get_across): banks(west(m(n0), c(n0)), east(m(n3), c(n3)), boatoneast) = true.
% 0.19/0.45 Proof:
% 0.19/0.45 banks(west(m(n0), c(n0)), east(m(n3), c(n3)), boatoneast)
% 0.19/0.45 = { by axiom 13 (bcc_mmmc_to_x_bmmmccc) R->L }
% 0.19/0.45 fresh28(banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatonwest), true)
% 0.19/0.45 = { by axiom 19 (c_bmmmcc_to_bcc_mmmc) R->L }
% 0.19/0.45 fresh28(fresh14(banks(west(m(n0), c(n1)), east(m(n3), c(n2)), boatoneast), true), true)
% 0.19/0.45 = { by axiom 14 (bccc_mmm_to_c_bmmmcc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(banks(west(m(n0), c(n3)), east(m(n3), c(n0)), boatonwest), true), true), true)
% 0.19/0.45 = { by axiom 20 (cc_bmmmc_to_bccc_mmm) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(banks(west(m(n0), c(n2)), east(m(n3), c(n1)), boatoneast), true), true), true), true)
% 0.19/0.45 = { by axiom 15 (bmmcc_mc_to_cc_bmmmc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatonwest), true), true), true), true), true)
% 0.19/0.45 = { by axiom 21 (mc_bmmcc_to_bmmcc_mc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(banks(west(m(n1), c(n1)), east(m(n2), c(n2)), boatoneast), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 16 (bmmmc_cc_to_mc_bmmcc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(banks(west(m(n3), c(n1)), east(m(n0), c(n2)), boatonwest), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 23 (mmm_bccc_to_bmmmc_cc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(banks(west(m(n3), c(n0)), east(m(n0), c(n3)), boatoneast), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 17 (bmmmcc_c_to_mmm_bccc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(banks(west(m(n3), c(n2)), east(m(n0), c(n1)), boatonwest), true), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 22 (mmcc_bmc_to_bmmmcc_c) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(fresh7(banks(west(m(n2), c(n2)), east(m(n1), c(n1)), boatoneast), true), true), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 18 (bmmmccc_x_to_mmcc_bmc) R->L }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(fresh7(fresh16(banks(west(m(n3), c(n3)), east(m(n0), c(n0)), boatonwest), true), true), true), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 12 (starting_configuration) }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(fresh7(fresh16(true, true), true), true), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 6 (bmmmccc_x_to_mmcc_bmc) }
% 0.19/0.45 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(fresh7(true, true), true), true), true), true), true), true), true), true), true)
% 0.19/0.45 = { by axiom 10 (mmcc_bmc_to_bmmmcc_c) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(fresh18(true, true), true), true), true), true), true), true), true), true)
% 0.19/0.46 = { by axiom 5 (bmmmcc_c_to_mmm_bccc) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(fresh5(true, true), true), true), true), true), true), true), true)
% 0.19/0.46 = { by axiom 11 (mmm_bccc_to_bmmmc_cc) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(fresh21(true, true), true), true), true), true), true), true)
% 0.19/0.46 = { by axiom 4 (bmmmc_cc_to_mc_bmmcc) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(fresh23(fresh9(true, true), true), true), true), true), true)
% 0.19/0.46 = { by axiom 9 (mc_bmmcc_to_bmmcc_mc) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(fresh23(true, true), true), true), true), true)
% 0.19/0.46 = { by axiom 3 (bmmcc_mc_to_cc_bmmmc) }
% 0.19/0.46 fresh28(fresh14(fresh27(fresh11(true, true), true), true), true)
% 0.19/0.46 = { by axiom 8 (cc_bmmmc_to_bccc_mmm) }
% 0.19/0.46 fresh28(fresh14(fresh27(true, true), true), true)
% 0.19/0.46 = { by axiom 2 (bccc_mmm_to_c_bmmmcc) }
% 0.19/0.46 fresh28(fresh14(true, true), true)
% 0.19/0.46 = { by axiom 7 (c_bmmmcc_to_bcc_mmmc) }
% 0.19/0.46 fresh28(true, true)
% 0.19/0.46 = { by axiom 1 (bcc_mmmc_to_x_bmmmccc) }
% 0.19/0.46 true
% 0.19/0.46 % SZS output end Proof
% 0.19/0.46
% 0.19/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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