%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : PUZ008-3 : TPTP v9.0.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 : Sat Jun 21 05:23:08 AM UTC 2025
% Result : Unsatisfiable 2.28s 2.48s
% Output : Proof 2.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ008-3 : TPTP v9.0.0. Released v1.2.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n005.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 : Fri Jun 20 02:39:20 EDT 2025
% 0.12/0.33 % CPUTime :
% 2.28/2.48 % SZS status Unsatisfiable
% 2.28/2.48 % SZS output start Proof
% 2.28/2.48 tff(achievable_type, type, (
% 2.28/2.48 achievable: ( $i * $i * $i ) > $o)).
% 2.28/2.48 tff(east_type, type, (
% 2.28/2.48 east: ( $i * $i ) > $i)).
% 2.28/2.48 tff(c_type, type, (
% 2.28/2.48 c: $i > $i)).
% 2.28/2.48 tff(s_type, type, (
% 2.28/2.48 s: $i > $i)).
% 2.28/2.48 tff(n0_type, type, (
% 2.28/2.48 n0: $i)).
% 2.28/2.48 tff(m_type, type, (
% 2.28/2.48 m: $i > $i)).
% 2.28/2.48 tff(boatonwest_type, type, (
% 2.28/2.48 boatonwest: $i)).
% 2.28/2.48 tff(west_type, type, (
% 2.28/2.48 west: ( $i * $i ) > $i)).
% 2.28/2.48 tff(boatoneast_type, type, (
% 2.28/2.48 boatoneast: $i)).
% 2.28/2.48 tff(safe_type, type, (
% 2.28/2.48 safe: ( $i * $i ) > $o)).
% 2.28/2.48 tff(greater_or_equal_type, type, (
% 2.28/2.48 greater_or_equal: ( $i * $i ) > $o)).
% 2.28/2.48 tff(1,assumption,(achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0))))))), introduced(assumption)).
% 2.28/2.48 tff(2,plain,
% 2.28/2.48 (^[X: $i] : refl((~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0))))))) <=> (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0))))))))),
% 2.28/2.48 inference(bind,[status(th)],[])).
% 2.28/2.48 tff(3,plain,
% 2.28/2.48 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0))))))) <=> ![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(quant_intro,[status(thm)],[2])).
% 2.28/2.48 tff(4,plain,
% 2.28/2.48 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0))))))) <=> ![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(5,axiom,(![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_can_get_to_east_bank')).
% 2.28/2.48 tff(6,plain,
% 2.28/2.48 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[5, 4])).
% 2.28/2.48 tff(7,plain,(
% 2.28/2.48 ![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(skolemize,[status(sab)],[6])).
% 2.28/2.48 tff(8,plain,
% 2.28/2.48 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[7, 3])).
% 2.28/2.48 tff(9,plain,
% 2.28/2.48 ((~![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))) | (~achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(10,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[9, 8, 1])).
% 2.28/2.48 tff(11,plain,(~achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0))))))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(12,assumption,(~greater_or_equal(n0, n0)), introduced(assumption)).
% 2.28/2.48 tff(13,plain,
% 2.28/2.48 (^[X: $i] : refl(greater_or_equal(X, n0) <=> greater_or_equal(X, n0))),
% 2.28/2.48 inference(bind,[status(th)],[])).
% 2.28/2.48 tff(14,plain,
% 2.28/2.48 (![X: $i] : greater_or_equal(X, n0) <=> ![X: $i] : greater_or_equal(X, n0)),
% 2.28/2.48 inference(quant_intro,[status(thm)],[13])).
% 2.28/2.48 tff(15,plain,
% 2.28/2.48 (![X: $i] : greater_or_equal(X, n0) <=> ![X: $i] : greater_or_equal(X, n0)),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(16,axiom,(![X: $i] : greater_or_equal(X, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','great_eq_base')).
% 2.28/2.48 tff(17,plain,
% 2.28/2.48 (![X: $i] : greater_or_equal(X, n0)),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[16, 15])).
% 2.28/2.48 tff(18,plain,(
% 2.28/2.48 ![X: $i] : greater_or_equal(X, n0)),
% 2.28/2.48 inference(skolemize,[status(sab)],[17])).
% 2.28/2.48 tff(19,plain,
% 2.28/2.48 (![X: $i] : greater_or_equal(X, n0)),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[18, 14])).
% 2.28/2.48 tff(20,plain,
% 2.28/2.48 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(n0, n0)),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(21,plain,
% 2.28/2.48 ($false),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[20, 19, 12])).
% 2.28/2.48 tff(22,plain,(greater_or_equal(n0, n0)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.48 tff(23,plain,
% 2.28/2.48 (^[Y: $i, X: $i] : refl(((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y))) <=> ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y))))),
% 2.28/2.48 inference(bind,[status(th)],[])).
% 2.28/2.48 tff(24,plain,
% 2.28/2.48 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y))) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(quant_intro,[status(thm)],[23])).
% 2.28/2.48 tff(25,plain,
% 2.28/2.48 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y))) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(26,plain,
% 2.28/2.48 (^[Y: $i, X: $i] : rewrite((greater_or_equal(s(X), s(Y)) | (~greater_or_equal(X, Y))) <=> ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y))))),
% 2.28/2.48 inference(bind,[status(th)],[])).
% 2.28/2.48 tff(27,plain,
% 2.28/2.48 (![Y: $i, X: $i] : (greater_or_equal(s(X), s(Y)) | (~greater_or_equal(X, Y))) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(quant_intro,[status(thm)],[26])).
% 2.28/2.48 tff(28,axiom,(![Y: $i, X: $i] : (greater_or_equal(s(X), s(Y)) | (~greater_or_equal(X, Y)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','great_eq_recursive')).
% 2.28/2.48 tff(29,plain,
% 2.28/2.48 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[28, 27])).
% 2.28/2.48 tff(30,plain,
% 2.28/2.48 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[29, 25])).
% 2.28/2.48 tff(31,plain,(
% 2.28/2.48 ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(skolemize,[status(sab)],[30])).
% 2.28/2.48 tff(32,plain,
% 2.28/2.48 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[31, 24])).
% 2.28/2.48 tff(33,plain,
% 2.28/2.48 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0)))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0)))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(34,plain,
% 2.28/2.48 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0)))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(35,plain,
% 2.28/2.48 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[34, 33])).
% 2.28/2.48 tff(36,plain,
% 2.28/2.48 ((~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[35, 32])).
% 2.28/2.48 tff(37,plain,
% 2.28/2.48 (greater_or_equal(s(n0), s(n0))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[36, 22])).
% 2.28/2.48 tff(38,plain,
% 2.28/2.48 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0))))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(39,plain,
% 2.28/2.48 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0))))),
% 2.28/2.48 inference(quant_inst,[status(thm)],[])).
% 2.28/2.48 tff(40,plain,
% 2.28/2.48 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0)))),
% 2.28/2.48 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.28/2.48 tff(41,plain,
% 2.28/2.48 ((~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0)))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[40, 32])).
% 2.28/2.48 tff(42,plain,
% 2.28/2.48 (greater_or_equal(s(s(n0)), s(s(n0)))),
% 2.28/2.48 inference(unit_resolution,[status(thm)],[41, 37])).
% 2.28/2.48 tff(43,plain,
% 2.28/2.48 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0)))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0)))))),
% 2.28/2.48 inference(rewrite,[status(thm)],[])).
% 2.28/2.48 tff(44,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0)))))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(45,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[44, 43])).
% 2.28/2.49 tff(46,plain,
% 2.28/2.49 ((~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[45, 32])).
% 2.28/2.49 tff(47,plain,
% 2.28/2.49 (greater_or_equal(s(s(s(n0))), s(s(s(n0))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[46, 42])).
% 2.28/2.49 tff(48,plain,
% 2.28/2.49 (^[Y: $i, X: $i] : refl(((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ((~greater_or_equal(X, Y)) | safe(X, Y)))),
% 2.28/2.49 inference(bind,[status(th)],[])).
% 2.28/2.49 tff(49,plain,
% 2.28/2.49 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 2.28/2.49 inference(quant_intro,[status(thm)],[48])).
% 2.28/2.49 tff(50,plain,
% 2.28/2.49 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(51,axiom,(![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','same_or_more_missionaries_is_safe')).
% 2.28/2.49 tff(52,plain,
% 2.28/2.49 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[51, 50])).
% 2.28/2.49 tff(53,plain,(
% 2.28/2.49 ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 2.28/2.49 inference(skolemize,[status(sab)],[52])).
% 2.28/2.49 tff(54,plain,
% 2.28/2.49 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[53, 49])).
% 2.28/2.49 tff(55,plain,
% 2.28/2.49 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(s(s(n0))))) | safe(s(s(s(n0))), s(s(s(n0)))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(s(s(n0))))) | safe(s(s(s(n0))), s(s(s(n0)))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(56,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(s(s(n0))))) | safe(s(s(s(n0))), s(s(s(n0)))))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(57,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(s(s(n0))))) | safe(s(s(s(n0))), s(s(s(n0))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[56, 55])).
% 2.28/2.49 tff(58,plain,
% 2.28/2.49 (safe(s(s(s(n0))), s(s(s(n0))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[57, 54, 47])).
% 2.28/2.49 tff(59,plain,
% 2.28/2.49 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(n0, n0)) | safe(n0, n0))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(n0, n0)) | safe(n0, n0))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(60,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(n0, n0)) | safe(n0, n0))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(61,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(n0, n0)) | safe(n0, n0)),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[60, 59])).
% 2.28/2.49 tff(62,plain,
% 2.28/2.49 (safe(n0, n0)),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[61, 54, 22])).
% 2.28/2.49 tff(63,plain,
% 2.28/2.49 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))))),
% 2.28/2.49 inference(bind,[status(th)],[])).
% 2.28/2.49 tff(64,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(quant_intro,[status(thm)],[63])).
% 2.28/2.49 tff(65,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(66,plain,
% 2.28/2.49 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) <=> ((~safe(X, Y)) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) <=> (((~safe(X, Y)) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) | (~safe(s(Z), s(W)))))), rewrite((((~safe(X, Y)) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) | (~safe(s(Z), s(W)))) <=> ((~safe(X, Y)) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) <=> ((~safe(X, Y)) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))))), (((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) <=> (((~safe(X, Y)) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))), rewrite((((~safe(X, Y)) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))), (((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))))),
% 2.28/2.49 inference(bind,[status(th)],[])).
% 2.28/2.49 tff(67,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(quant_intro,[status(thm)],[66])).
% 2.28/2.49 tff(68,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(Z), s(W)))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','missionary_and_cannibal_west_to_east')).
% 2.28/2.49 tff(69,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[68, 67])).
% 2.28/2.49 tff(70,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[69, 65])).
% 2.28/2.49 tff(71,plain,(
% 2.28/2.49 ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(skolemize,[status(sab)],[70])).
% 2.28/2.49 tff(72,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[71, 64])).
% 2.28/2.49 tff(73,plain,
% 2.28/2.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(74,plain,
% 2.28/2.49 (((~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))))) <=> ((~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(75,plain,
% 2.28/2.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))))))),
% 2.28/2.49 inference(monotonicity,[status(thm)],[74])).
% 2.28/2.49 tff(76,plain,
% 2.28/2.49 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.49 inference(transitivity,[status(thm)],[75, 73])).
% 2.28/2.49 tff(77,plain,
% 2.28/2.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(78,plain,
% 2.28/2.49 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[77, 76])).
% 2.28/2.49 tff(79,plain,
% 2.28/2.49 ((~safe(s(s(s(n0))), s(s(s(n0))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[78, 72])).
% 2.28/2.49 tff(80,plain,
% 2.28/2.49 (achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[79, 62, 58])).
% 2.28/2.49 tff(81,plain,
% 2.28/2.49 (~achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0)))))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[80, 11])).
% 2.28/2.49 tff(82,plain,
% 2.28/2.49 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(n0)), s(s(n0)))) | safe(s(s(n0)), s(s(n0))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(n0)), s(s(n0)))) | safe(s(s(n0)), s(s(n0))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(83,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(n0)), s(s(n0)))) | safe(s(s(n0)), s(s(n0))))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(84,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(n0)), s(s(n0)))) | safe(s(s(n0)), s(s(n0)))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[83, 82])).
% 2.28/2.49 tff(85,plain,
% 2.28/2.49 (safe(s(s(n0)), s(s(n0)))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[84, 54, 42])).
% 2.28/2.49 tff(86,plain,
% 2.28/2.49 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0)))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0)))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(87,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0)))),
% 2.28/2.49 inference(quant_inst,[status(thm)],[])).
% 2.28/2.49 tff(88,plain,
% 2.28/2.49 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[87, 86])).
% 2.28/2.49 tff(89,plain,
% 2.28/2.49 (safe(s(n0), s(n0))),
% 2.28/2.49 inference(unit_resolution,[status(thm)],[88, 54, 37])).
% 2.28/2.49 tff(90,plain,
% 2.28/2.49 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))))),
% 2.28/2.49 inference(bind,[status(th)],[])).
% 2.28/2.49 tff(91,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.49 inference(quant_intro,[status(thm)],[90])).
% 2.28/2.49 tff(92,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.49 inference(rewrite,[status(thm)],[])).
% 2.28/2.49 tff(93,plain,
% 2.28/2.49 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) <=> ((~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) <=> (((~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) | (~safe(Z, W))))), rewrite((((~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W)))) <=> (((~safe(Z, W)) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W)))))), rewrite((((~safe(Z, W)) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W))))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W)))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W)))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))))),
% 2.28/2.49 inference(bind,[status(th)],[])).
% 2.28/2.49 tff(94,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W)))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.49 inference(quant_intro,[status(thm)],[93])).
% 2.28/2.49 tff(95,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))) | (~safe(s(X), Y))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','missionary_east_to_west')).
% 2.28/2.49 tff(96,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[95, 94])).
% 2.28/2.49 tff(97,plain,
% 2.28/2.49 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.49 inference(modus_ponens,[status(thm)],[96, 92])).
% 2.28/2.49 tff(98,plain,(
% 2.28/2.49 ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.50 inference(skolemize,[status(sab)],[97])).
% 2.28/2.50 tff(99,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[98, 91])).
% 2.28/2.50 tff(100,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(101,plain,
% 2.28/2.50 (((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))))) <=> ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(102,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))))))),
% 2.28/2.50 inference(monotonicity,[status(thm)],[101])).
% 2.28/2.50 tff(103,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))),
% 2.28/2.50 inference(transitivity,[status(thm)],[102, 100])).
% 2.28/2.50 tff(104,plain,
% 2.28/2.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(105,plain,
% 2.28/2.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(n0)), c(s(n0))), boatonwest, east(m(s(s(n0))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[104, 103])).
% 2.28/2.50 tff(106,plain,
% 2.28/2.50 (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[105, 99, 89, 85, 81])).
% 2.28/2.50 tff(107,assumption,(~safe(n0, s(n0))), introduced(assumption)).
% 2.28/2.50 tff(108,plain,
% 2.28/2.50 (^[X: $i] : refl(safe(n0, X) <=> safe(n0, X))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(109,plain,
% 2.28/2.50 (![X: $i] : safe(n0, X) <=> ![X: $i] : safe(n0, X)),
% 2.28/2.50 inference(quant_intro,[status(thm)],[108])).
% 2.28/2.50 tff(110,plain,
% 2.28/2.50 (![X: $i] : safe(n0, X) <=> ![X: $i] : safe(n0, X)),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(111,axiom,(![X: $i] : safe(n0, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_missionaries_is_safe')).
% 2.28/2.50 tff(112,plain,
% 2.28/2.50 (![X: $i] : safe(n0, X)),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[111, 110])).
% 2.28/2.50 tff(113,plain,(
% 2.28/2.50 ![X: $i] : safe(n0, X)),
% 2.28/2.50 inference(skolemize,[status(sab)],[112])).
% 2.28/2.50 tff(114,plain,
% 2.28/2.50 (![X: $i] : safe(n0, X)),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[113, 109])).
% 2.28/2.50 tff(115,plain,
% 2.28/2.50 ((~![X: $i] : safe(n0, X)) | safe(n0, s(n0))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(116,plain,
% 2.28/2.50 ($false),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[115, 114, 107])).
% 2.28/2.50 tff(117,plain,(safe(n0, s(n0))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.50 tff(118,assumption,(~greater_or_equal(s(n0), n0)), introduced(assumption)).
% 2.28/2.50 tff(119,plain,
% 2.28/2.50 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(n0), n0)),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(120,plain,
% 2.28/2.50 ($false),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[119, 19, 118])).
% 2.28/2.50 tff(121,plain,(greater_or_equal(s(n0), n0)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.50 tff(122,plain,
% 2.28/2.50 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0)))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0)))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(123,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0)))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(124,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[123, 122])).
% 2.28/2.50 tff(125,plain,
% 2.28/2.50 ((~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[124, 32])).
% 2.28/2.50 tff(126,plain,
% 2.28/2.50 (greater_or_equal(s(s(n0)), s(n0))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[125, 121])).
% 2.28/2.50 tff(127,plain,
% 2.28/2.50 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(128,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0))))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(129,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0)))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[128, 127])).
% 2.28/2.50 tff(130,plain,
% 2.28/2.50 ((~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0)))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[129, 32])).
% 2.28/2.50 tff(131,plain,
% 2.28/2.50 (greater_or_equal(s(s(s(n0))), s(s(n0)))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[130, 126])).
% 2.28/2.50 tff(132,plain,
% 2.28/2.50 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(s(n0)))) | safe(s(s(s(n0))), s(s(n0))))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(s(n0)))) | safe(s(s(s(n0))), s(s(n0))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(133,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(s(n0)))) | safe(s(s(s(n0))), s(s(n0))))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(134,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(s(n0)))) | safe(s(s(s(n0))), s(s(n0)))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[133, 132])).
% 2.28/2.50 tff(135,plain,
% 2.28/2.50 (safe(s(s(s(n0))), s(s(n0)))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[134, 54, 131])).
% 2.28/2.50 tff(136,plain,
% 2.28/2.50 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(137,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(quant_intro,[status(thm)],[136])).
% 2.28/2.50 tff(138,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(139,plain,
% 2.28/2.50 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) <=> ((~safe(X, Y)) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) <=> (((~safe(X, Y)) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) | (~safe(Z, s(s(W))))))), rewrite((((~safe(X, Y)) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) | (~safe(Z, s(s(W))))) <=> ((~safe(X, Y)) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) <=> ((~safe(X, Y)) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))))), (((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W)))))) <=> (((~safe(X, Y)) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W)))))))), rewrite((((~safe(X, Y)) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W)))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))), (((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W)))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(140,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W)))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(quant_intro,[status(thm)],[139])).
% 2.28/2.50 tff(141,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(Z, s(s(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','two_cannibals_west_to_east')).
% 2.28/2.50 tff(142,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[141, 140])).
% 2.28/2.50 tff(143,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[142, 138])).
% 2.28/2.50 tff(144,plain,(
% 2.28/2.50 ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(skolemize,[status(sab)],[143])).
% 2.28/2.50 tff(145,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[144, 137])).
% 2.28/2.50 tff(146,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(147,plain,
% 2.28/2.50 (((~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))) <=> ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(148,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))))),
% 2.28/2.50 inference(monotonicity,[status(thm)],[147])).
% 2.28/2.50 tff(149,plain,
% 2.28/2.50 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))),
% 2.28/2.50 inference(transitivity,[status(thm)],[148, 146])).
% 2.28/2.50 tff(150,plain,
% 2.28/2.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(151,plain,
% 2.28/2.50 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[150, 149])).
% 2.28/2.50 tff(152,plain,
% 2.28/2.50 (~achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[151, 145, 135, 117, 106])).
% 2.28/2.50 tff(153,assumption,(~greater_or_equal(s(s(s(n0))), n0)), introduced(assumption)).
% 2.28/2.50 tff(154,plain,
% 2.28/2.50 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(s(s(n0))), n0)),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(155,plain,
% 2.28/2.50 ($false),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[154, 19, 153])).
% 2.28/2.50 tff(156,plain,(greater_or_equal(s(s(s(n0))), n0)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.50 tff(157,plain,
% 2.28/2.50 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), n0)) | safe(s(s(s(n0))), n0))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), n0)) | safe(s(s(s(n0))), n0))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(158,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), n0)) | safe(s(s(s(n0))), n0))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(159,plain,
% 2.28/2.50 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), n0)) | safe(s(s(s(n0))), n0)),
% 2.28/2.50 inference(modus_ponens,[status(thm)],[158, 157])).
% 2.28/2.50 tff(160,plain,
% 2.28/2.50 (safe(s(s(s(n0))), n0)),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[159, 54, 156])).
% 2.28/2.50 tff(161,assumption,(~safe(n0, s(s(s(n0))))), introduced(assumption)).
% 2.28/2.50 tff(162,plain,
% 2.28/2.50 ((~![X: $i] : safe(n0, X)) | safe(n0, s(s(s(n0))))),
% 2.28/2.50 inference(quant_inst,[status(thm)],[])).
% 2.28/2.50 tff(163,plain,
% 2.28/2.50 ($false),
% 2.28/2.50 inference(unit_resolution,[status(thm)],[162, 114, 161])).
% 2.28/2.50 tff(164,plain,(safe(n0, s(s(s(n0))))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.50 tff(165,plain,
% 2.28/2.50 (^[W: $i, Z: $i, Y: $i, X: $i] : refl((achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) <=> (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(166,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.50 inference(quant_intro,[status(thm)],[165])).
% 2.28/2.50 tff(167,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.50 inference(rewrite,[status(thm)],[])).
% 2.28/2.50 tff(168,plain,
% 2.28/2.50 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) <=> ((~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) <=> (((~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) | (~safe(Z, W))))), rewrite((((~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> (((~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W)))))), rewrite((((~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W)))))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))))),
% 2.28/2.50 inference(bind,[status(th)],[])).
% 2.28/2.50 tff(169,plain,
% 2.28/2.50 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.51 inference(quant_intro,[status(thm)],[168])).
% 2.28/2.51 tff(170,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))) | (~safe(X, s(Y)))) | (~safe(Z, W))) | achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','cannibal_east_to_west')).
% 2.28/2.51 tff(171,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[170, 169])).
% 2.28/2.51 tff(172,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[171, 167])).
% 2.28/2.51 tff(173,plain,(
% 2.28/2.51 ![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.51 inference(skolemize,[status(sab)],[172])).
% 2.28/2.51 tff(174,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[173, 166])).
% 2.28/2.51 tff(175,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(176,plain,
% 2.28/2.51 ((achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~safe(s(s(s(n0))), n0)) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))) <=> ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(177,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~safe(s(s(s(n0))), n0)) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))))),
% 2.28/2.51 inference(monotonicity,[status(thm)],[176])).
% 2.28/2.51 tff(178,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~safe(s(s(s(n0))), n0)) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))),
% 2.28/2.51 inference(transitivity,[status(thm)],[177, 175])).
% 2.28/2.51 tff(179,plain,
% 2.28/2.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~safe(s(s(s(n0))), n0)) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(180,plain,
% 2.28/2.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[179, 178])).
% 2.28/2.51 tff(181,plain,
% 2.28/2.51 ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[180, 174])).
% 2.28/2.51 tff(182,plain,
% 2.28/2.51 ((~safe(s(s(s(n0))), n0)) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[181, 164])).
% 2.28/2.51 tff(183,plain,
% 2.28/2.51 (achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))) | (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[182, 160])).
% 2.28/2.51 tff(184,plain,
% 2.28/2.51 (~achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[183, 152])).
% 2.28/2.51 tff(185,assumption,(~safe(n0, s(s(n0)))), introduced(assumption)).
% 2.28/2.51 tff(186,plain,
% 2.28/2.51 ((~![X: $i] : safe(n0, X)) | safe(n0, s(s(n0)))),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(187,plain,
% 2.28/2.51 ($false),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[186, 114, 185])).
% 2.28/2.51 tff(188,plain,(safe(n0, s(s(n0)))), inference(lemma,lemma(discharge,[]))).
% 2.28/2.51 tff(189,assumption,(~greater_or_equal(s(s(n0)), n0)), introduced(assumption)).
% 2.28/2.51 tff(190,plain,
% 2.28/2.51 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(s(n0)), n0)),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(191,plain,
% 2.28/2.51 ($false),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[190, 19, 189])).
% 2.28/2.51 tff(192,plain,(greater_or_equal(s(s(n0)), n0)), inference(lemma,lemma(discharge,[]))).
% 2.28/2.51 tff(193,plain,
% 2.28/2.51 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0)))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0)))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(194,plain,
% 2.28/2.51 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | ((~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0)))),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(195,plain,
% 2.28/2.51 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[194, 193])).
% 2.28/2.51 tff(196,plain,
% 2.28/2.51 ((~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[195, 32])).
% 2.28/2.51 tff(197,plain,
% 2.28/2.51 (greater_or_equal(s(s(s(n0))), s(n0))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[196, 192])).
% 2.28/2.51 tff(198,plain,
% 2.28/2.51 (((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(n0))) | safe(s(s(s(n0))), s(n0)))) <=> ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(n0))) | safe(s(s(s(n0))), s(n0)))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(199,plain,
% 2.28/2.51 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(s(s(n0))), s(n0))) | safe(s(s(s(n0))), s(n0)))),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(200,plain,
% 2.28/2.51 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(n0))) | safe(s(s(s(n0))), s(n0))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[199, 198])).
% 2.28/2.51 tff(201,plain,
% 2.28/2.51 (safe(s(s(s(n0))), s(n0))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[200, 54, 197])).
% 2.28/2.51 tff(202,plain,
% 2.28/2.51 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))))),
% 2.28/2.51 inference(bind,[status(th)],[])).
% 2.28/2.51 tff(203,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(quant_intro,[status(thm)],[202])).
% 2.28/2.51 tff(204,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(205,plain,
% 2.28/2.51 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) <=> ((~safe(X, Y)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) <=> (((~safe(X, Y)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) | (~safe(s(s(Z)), W))))), rewrite((((~safe(X, Y)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) | (~safe(s(s(Z)), W))) <=> ((~safe(X, Y)) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))), ((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) <=> ((~safe(X, Y)) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))))), (((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W)))) <=> (((~safe(X, Y)) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W)))))), rewrite((((~safe(X, Y)) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W))))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W)))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))), (((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W)))) <=> ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))))),
% 2.28/2.51 inference(bind,[status(th)],[])).
% 2.28/2.51 tff(206,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W)))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(quant_intro,[status(thm)],[205])).
% 2.28/2.51 tff(207,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))) | (~safe(X, Y))) | (~safe(s(s(Z)), W))) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','two_missionaries_west_to_east')).
% 2.28/2.51 tff(208,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[207, 206])).
% 2.28/2.51 tff(209,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[208, 204])).
% 2.28/2.51 tff(210,plain,(
% 2.28/2.51 ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(skolemize,[status(sab)],[209])).
% 2.28/2.51 tff(211,plain,
% 2.28/2.51 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[210, 203])).
% 2.28/2.51 tff(212,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(213,plain,
% 2.28/2.51 (((~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))))) <=> ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(214,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))))))),
% 2.28/2.51 inference(monotonicity,[status(thm)],[213])).
% 2.28/2.51 tff(215,plain,
% 2.28/2.51 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.51 inference(transitivity,[status(thm)],[214, 212])).
% 2.28/2.51 tff(216,plain,
% 2.28/2.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.51 inference(quant_inst,[status(thm)],[])).
% 2.28/2.51 tff(217,plain,
% 2.28/2.51 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[216, 215])).
% 2.28/2.51 tff(218,plain,
% 2.28/2.51 (achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[217, 211, 201, 188])).
% 2.28/2.51 tff(219,plain,
% 2.28/2.51 (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))),
% 2.28/2.51 inference(unit_resolution,[status(thm)],[218, 184])).
% 2.28/2.51 tff(220,plain,
% 2.28/2.51 (achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0))) <=> achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))),
% 2.28/2.51 inference(rewrite,[status(thm)],[])).
% 2.28/2.51 tff(221,axiom,(achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','start_on_west_bank')).
% 2.28/2.51 tff(222,plain,
% 2.28/2.51 (achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))),
% 2.28/2.51 inference(modus_ponens,[status(thm)],[221, 220])).
% 2.28/2.52 tff(223,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(224,plain,
% 2.28/2.52 (((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0))))) <=> ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(225,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.52 inference(monotonicity,[status(thm)],[224])).
% 2.28/2.52 tff(226,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.52 inference(transitivity,[status(thm)],[225, 223])).
% 2.28/2.52 tff(227,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))) | (~safe(s(n0), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))))),
% 2.28/2.52 inference(quant_inst,[status(thm)],[])).
% 2.28/2.52 tff(228,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))) | (~safe(s(Z), s(W))) | (~achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))),
% 2.28/2.52 inference(modus_ponens,[status(thm)],[227, 226])).
% 2.28/2.52 tff(229,plain,
% 2.28/2.52 (achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[228, 72, 222, 89, 85])).
% 2.28/2.52 tff(230,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(231,plain,
% 2.28/2.52 (((~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))) <=> ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(232,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))))),
% 2.28/2.52 inference(monotonicity,[status(thm)],[231])).
% 2.28/2.52 tff(233,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.52 inference(transitivity,[status(thm)],[232, 230])).
% 2.28/2.52 tff(234,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | ((~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))))),
% 2.28/2.52 inference(quant_inst,[status(thm)],[])).
% 2.28/2.52 tff(235,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(Y)), boatonwest, east(m(Z), c(W))) | (~safe(s(X), Y)) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(W)))))) | (~safe(s(s(s(n0))), s(s(n0)))) | (~safe(n0, s(n0))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))) | (~achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0)))))),
% 2.28/2.52 inference(modus_ponens,[status(thm)],[234, 233])).
% 2.28/2.52 tff(236,plain,
% 2.28/2.52 (achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[235, 99, 135, 117, 229])).
% 2.28/2.52 tff(237,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(238,plain,
% 2.28/2.52 (((~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))) <=> ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(239,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))))),
% 2.28/2.52 inference(monotonicity,[status(thm)],[238])).
% 2.28/2.52 tff(240,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))),
% 2.28/2.52 inference(transitivity,[status(thm)],[239, 237])).
% 2.28/2.52 tff(241,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~safe(n0, s(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))),
% 2.28/2.52 inference(quant_inst,[status(thm)],[])).
% 2.28/2.52 tff(242,plain,
% 2.28/2.52 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 2.28/2.52 inference(modus_ponens,[status(thm)],[241, 240])).
% 2.28/2.52 tff(243,plain,
% 2.28/2.52 ((~safe(n0, s(s(s(n0))))) | (~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[242, 145])).
% 2.28/2.52 tff(244,plain,
% 2.28/2.52 ((~safe(s(s(s(n0))), n0)) | achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[243, 164])).
% 2.28/2.52 tff(245,plain,
% 2.28/2.52 (achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[244, 160])).
% 2.28/2.52 tff(246,plain,
% 2.28/2.52 (achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))),
% 2.28/2.52 inference(unit_resolution,[status(thm)],[245, 236])).
% 2.28/2.52 tff(247,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(248,plain,
% 2.28/2.52 ((achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~safe(n0, s(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))))) <=> ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))),
% 2.28/2.52 inference(rewrite,[status(thm)],[])).
% 2.28/2.52 tff(249,plain,
% 2.28/2.52 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~safe(n0, s(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | ((~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))))))),
% 2.28/2.53 inference(monotonicity,[status(thm)],[248])).
% 2.28/2.53 tff(250,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~safe(n0, s(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))),
% 2.28/2.53 inference(transitivity,[status(thm)],[249, 247])).
% 2.28/2.53 tff(251,plain,
% 2.28/2.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~safe(n0, s(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))))),
% 2.28/2.53 inference(quant_inst,[status(thm)],[])).
% 2.28/2.53 tff(252,plain,
% 2.28/2.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : (achievable(west(m(X), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(Z, W)) | (~safe(X, s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(W))))))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))))),
% 2.28/2.53 inference(modus_ponens,[status(thm)],[251, 250])).
% 2.28/2.53 tff(253,plain,
% 2.28/2.53 (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))) | (~achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0)))))))),
% 2.28/2.53 inference(unit_resolution,[status(thm)],[252, 174, 201, 188])).
% 2.28/2.53 tff(254,plain,
% 2.28/2.53 (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))),
% 2.28/2.53 inference(unit_resolution,[status(thm)],[253, 246])).
% 2.28/2.53 tff(255,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.53 inference(rewrite,[status(thm)],[])).
% 2.28/2.53 tff(256,plain,
% 2.28/2.53 (((~safe(s(n0), s(n0))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0))))))) <=> ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.53 inference(rewrite,[status(thm)],[])).
% 2.28/2.53 tff(257,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.53 inference(monotonicity,[status(thm)],[256])).
% 2.28/2.53 tff(258,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.53 inference(transitivity,[status(thm)],[257, 255])).
% 2.28/2.53 tff(259,plain,
% 2.28/2.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))))),
% 2.28/2.53 inference(quant_inst,[status(thm)],[])).
% 2.28/2.53 tff(260,plain,
% 2.28/2.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(s(s(Z))), c(W))) | (~safe(s(s(Z)), W)) | (~achievable(west(m(s(s(X))), c(Y)), boatonwest, east(m(Z), c(W)))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))),
% 2.28/2.53 inference(modus_ponens,[status(thm)],[259, 258])).
% 2.28/2.53 tff(261,plain,
% 2.28/2.53 ((~achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))) | achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))),
% 2.28/2.53 inference(unit_resolution,[status(thm)],[260, 211, 89, 85])).
% 2.28/2.53 tff(262,plain,
% 2.28/2.53 (achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))),
% 2.28/2.53 inference(unit_resolution,[status(thm)],[261, 254])).
% 2.28/2.53 tff(263,plain,
% 2.28/2.53 (^[W: $i, Z: $i, Y: $i, X: $i] : refl(((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))))),
% 2.28/2.53 inference(bind,[status(th)],[])).
% 2.28/2.53 tff(264,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(quant_intro,[status(thm)],[263])).
% 2.28/2.53 tff(265,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(rewrite,[status(thm)],[])).
% 2.28/2.53 tff(266,plain,
% 2.28/2.53 (^[W: $i, Z: $i, Y: $i, X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) <=> ((~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) <=> (((~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) | (~safe(Z, W))))), rewrite((((~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))), ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) <=> ((~safe(Z, W)) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> (((~safe(Z, W)) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))))), rewrite((((~safe(Z, W)) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W)))))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))), (((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))))),
% 2.28/2.53 inference(bind,[status(th)],[])).
% 2.28/2.53 tff(267,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W)))) <=> ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(quant_intro,[status(thm)],[266])).
% 2.28/2.53 tff(268,axiom,(![W: $i, Z: $i, Y: $i, X: $i] : ((((~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))) | (~safe(s(X), s(Y)))) | (~safe(Z, W))) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','missionary_and_cannibal_east_to_west')).
% 2.28/2.53 tff(269,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(modus_ponens,[status(thm)],[268, 267])).
% 2.28/2.53 tff(270,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(modus_ponens,[status(thm)],[269, 265])).
% 2.28/2.53 tff(271,plain,(
% 2.28/2.53 ![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(skolemize,[status(sab)],[270])).
% 2.28/2.53 tff(272,plain,
% 2.28/2.53 (![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))),
% 2.28/2.53 inference(modus_ponens,[status(thm)],[271, 264])).
% 2.28/2.53 tff(273,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.53 inference(rewrite,[status(thm)],[])).
% 2.28/2.53 tff(274,plain,
% 2.28/2.53 (((~safe(s(n0), s(n0))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))) <=> ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.53 inference(rewrite,[status(thm)],[])).
% 2.28/2.53 tff(275,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | ((~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))))),
% 2.28/2.53 inference(monotonicity,[status(thm)],[274])).
% 2.28/2.53 tff(276,plain,
% 2.28/2.53 (((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))) <=> ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.53 inference(transitivity,[status(thm)],[275, 273])).
% 2.28/2.53 tff(277,plain,
% 2.28/2.53 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | ((~safe(s(n0), s(n0))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~safe(s(s(n0)), s(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))))),
% 2.28/2.54 inference(quant_inst,[status(thm)],[])).
% 2.28/2.54 tff(278,plain,
% 2.28/2.54 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(Z, W)) | achievable(west(m(s(X)), c(s(Y))), boatonwest, east(m(Z), c(W))) | (~safe(s(X), s(Y))) | (~achievable(west(m(X), c(Y)), boatoneast, east(m(s(Z)), c(s(W))))))) | (~safe(s(n0), s(n0))) | (~safe(s(s(n0)), s(s(n0)))) | achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.54 inference(modus_ponens,[status(thm)],[277, 276])).
% 2.28/2.54 tff(279,plain,
% 2.28/2.54 (achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0)))) | (~achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0))))))),
% 2.28/2.54 inference(unit_resolution,[status(thm)],[278, 272, 89, 85])).
% 2.28/2.54 tff(280,plain,
% 2.28/2.54 ($false),
% 2.28/2.54 inference(unit_resolution,[status(thm)],[279, 262, 219])).
% 2.28/2.54 % SZS output end Proof
% 2.28/2.54 % E exiting
%------------------------------------------------------------------------------