TSTP Solution File: PUZ008-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 : Sun Sep 18 14:10:48 EDT 2022
% Result : Unsatisfiable 0.15s 0.36s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : PUZ008-3 : TPTP v8.1.0. Released v1.2.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.10/0.30 % Computer : n015.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Fri Sep 2 18:27:54 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.30 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.15/0.30 Usage: tptp [options] [-file:]file
% 0.15/0.30 -h, -? prints this message.
% 0.15/0.30 -smt2 print SMT-LIB2 benchmark.
% 0.15/0.30 -m, -model generate model.
% 0.15/0.30 -p, -proof generate proof.
% 0.15/0.30 -c, -core generate unsat core of named formulas.
% 0.15/0.30 -st, -statistics display statistics.
% 0.15/0.30 -t:timeout set timeout (in second).
% 0.15/0.30 -smt2status display status in smt2 format instead of SZS.
% 0.15/0.30 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.15/0.30 -<param>:<value> configuration parameter and value.
% 0.15/0.30 -o:<output-file> file to place output in.
% 0.15/0.36 % SZS status Unsatisfiable
% 0.15/0.36 % SZS output start Proof
% 0.15/0.36 tff(safe_type, type, (
% 0.15/0.36 safe: ( $i * $i ) > $o)).
% 0.15/0.36 tff(s_type, type, (
% 0.15/0.36 s: $i > $i)).
% 0.15/0.36 tff(n0_type, type, (
% 0.15/0.36 n0: $i)).
% 0.15/0.36 tff(greater_or_equal_type, type, (
% 0.15/0.36 greater_or_equal: ( $i * $i ) > $o)).
% 0.15/0.36 tff(achievable_type, type, (
% 0.15/0.36 achievable: ( $i * $i * $i ) > $o)).
% 0.15/0.36 tff(east_type, type, (
% 0.15/0.36 east: ( $i * $i ) > $i)).
% 0.15/0.36 tff(c_type, type, (
% 0.15/0.36 c: $i > $i)).
% 0.15/0.36 tff(m_type, type, (
% 0.15/0.36 m: $i > $i)).
% 0.15/0.36 tff(boatoneast_type, type, (
% 0.15/0.36 boatoneast: $i)).
% 0.15/0.36 tff(west_type, type, (
% 0.15/0.36 west: ( $i * $i ) > $i)).
% 0.15/0.36 tff(boatonwest_type, type, (
% 0.15/0.36 boatonwest: $i)).
% 0.15/0.36 tff(1,assumption,(~safe(s(s(s(n0))), s(s(s(n0))))), introduced(assumption)).
% 0.15/0.36 tff(2,assumption,(~greater_or_equal(s(s(s(n0))), s(s(s(n0))))), introduced(assumption)).
% 0.15/0.36 tff(3,assumption,(~greater_or_equal(s(s(n0)), s(s(n0)))), introduced(assumption)).
% 0.15/0.36 tff(4,assumption,(~greater_or_equal(s(n0), s(n0))), introduced(assumption)).
% 0.15/0.36 tff(5,assumption,(~greater_or_equal(n0, n0)), introduced(assumption)).
% 0.15/0.36 tff(6,plain,
% 0.15/0.36 (^[X: $i] : refl(greater_or_equal(X, n0) <=> greater_or_equal(X, n0))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(7,plain,
% 0.15/0.36 (![X: $i] : greater_or_equal(X, n0) <=> ![X: $i] : greater_or_equal(X, n0)),
% 0.15/0.36 inference(quant_intro,[status(thm)],[6])).
% 0.15/0.36 tff(8,plain,
% 0.15/0.36 (![X: $i] : greater_or_equal(X, n0) <=> ![X: $i] : greater_or_equal(X, n0)),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(9,axiom,(![X: $i] : greater_or_equal(X, n0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','great_eq_base')).
% 0.15/0.36 tff(10,plain,
% 0.15/0.36 (![X: $i] : greater_or_equal(X, n0)),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[9, 8])).
% 0.15/0.36 tff(11,plain,(
% 0.15/0.36 ![X: $i] : greater_or_equal(X, n0)),
% 0.15/0.36 inference(skolemize,[status(sab)],[10])).
% 0.15/0.36 tff(12,plain,
% 0.15/0.36 (![X: $i] : greater_or_equal(X, n0)),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[11, 7])).
% 0.15/0.36 tff(13,plain,
% 0.15/0.36 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(n0, n0)),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(14,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[13, 12, 5])).
% 0.15/0.36 tff(15,plain,(greater_or_equal(n0, n0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(16,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(17,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[16])).
% 0.15/0.36 tff(18,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(19,plain,
% 0.15/0.36 (^[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))))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(20,plain,
% 0.15/0.36 (![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)))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[19])).
% 0.15/0.36 tff(21,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')).
% 0.15/0.36 tff(22,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.15/0.36 tff(23,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[22, 18])).
% 0.15/0.36 tff(24,plain,(
% 0.15/0.36 ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 0.15/0.36 inference(skolemize,[status(sab)],[23])).
% 0.15/0.36 tff(25,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[24, 17])).
% 0.15/0.36 tff(26,plain,
% 0.15/0.36 (((~![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)))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(27,plain,
% 0.15/0.36 ((~![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)))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(28,plain,
% 0.15/0.36 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(n0, n0)) | greater_or_equal(s(n0), s(n0))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.15/0.36 tff(29,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[28, 25, 15, 4])).
% 0.15/0.36 tff(30,plain,(greater_or_equal(s(n0), s(n0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(31,plain,
% 0.15/0.36 (((~![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))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(32,plain,
% 0.15/0.36 ((~![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))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(33,plain,
% 0.15/0.36 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), s(n0))) | greater_or_equal(s(s(n0)), s(s(n0)))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[32, 31])).
% 0.15/0.36 tff(34,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[33, 25, 30, 3])).
% 0.15/0.36 tff(35,plain,(greater_or_equal(s(s(n0)), s(s(n0)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(36,plain,
% 0.15/0.36 (((~![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)))))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(37,plain,
% 0.15/0.36 ((~![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)))))),
% 0.15/0.36 inference(quant_inst,[status(thm)],[])).
% 0.15/0.36 tff(38,plain,
% 0.15/0.36 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(s(n0)))) | greater_or_equal(s(s(s(n0))), s(s(s(n0))))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.15/0.36 tff(39,plain,
% 0.15/0.36 ($false),
% 0.15/0.36 inference(unit_resolution,[status(thm)],[38, 25, 35, 2])).
% 0.15/0.36 tff(40,plain,(greater_or_equal(s(s(s(n0))), s(s(s(n0))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.36 tff(41,plain,
% 0.15/0.36 (^[Y: $i, X: $i] : refl(((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ((~greater_or_equal(X, Y)) | safe(X, Y)))),
% 0.15/0.36 inference(bind,[status(th)],[])).
% 0.15/0.36 tff(42,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 0.15/0.36 inference(quant_intro,[status(thm)],[41])).
% 0.15/0.36 tff(43,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y)) <=> ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 0.15/0.36 inference(rewrite,[status(thm)],[])).
% 0.15/0.36 tff(44,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')).
% 0.15/0.36 tff(45,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[44, 43])).
% 0.15/0.36 tff(46,plain,(
% 0.15/0.36 ![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 0.15/0.36 inference(skolemize,[status(sab)],[45])).
% 0.15/0.36 tff(47,plain,
% 0.15/0.36 (![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))),
% 0.15/0.36 inference(modus_ponens,[status(thm)],[46, 42])).
% 0.15/0.36 tff(48,plain,
% 0.15/0.36 (((~![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)))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(49,plain,
% 0.15/0.37 ((~![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)))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(50,plain,
% 0.15/0.37 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(s(s(n0))), s(s(s(n0))))) | safe(s(s(s(n0))), s(s(s(n0))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[49, 48])).
% 0.15/0.37 tff(51,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[50, 47, 40, 1])).
% 0.15/0.37 tff(52,plain,(safe(s(s(s(n0))), s(s(s(n0))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(53,assumption,(achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0))))))), introduced(assumption)).
% 0.15/0.37 tff(54,plain,
% 0.15/0.37 (^[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))))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(55,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[54])).
% 0.15/0.37 tff(56,plain,
% 0.15/0.37 (![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)))))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(57,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')).
% 0.15/0.37 tff(58,plain,
% 0.15/0.37 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[57, 56])).
% 0.15/0.37 tff(59,plain,(
% 0.15/0.37 ![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 0.15/0.37 inference(skolemize,[status(sab)],[58])).
% 0.15/0.37 tff(60,plain,
% 0.15/0.37 (![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[59, 55])).
% 0.15/0.37 tff(61,plain,
% 0.15/0.37 ((~![X: $i] : (~achievable(west(m(n0), c(n0)), X, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))) | (~achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(62,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[61, 60, 53])).
% 0.15/0.37 tff(63,plain,(~achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0))))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(64,assumption,(~safe(n0, s(s(s(n0))))), introduced(assumption)).
% 0.15/0.37 tff(65,plain,
% 0.15/0.37 (^[X: $i] : refl(safe(n0, X) <=> safe(n0, X))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(66,plain,
% 0.15/0.37 (![X: $i] : safe(n0, X) <=> ![X: $i] : safe(n0, X)),
% 0.15/0.37 inference(quant_intro,[status(thm)],[65])).
% 0.15/0.37 tff(67,plain,
% 0.15/0.37 (![X: $i] : safe(n0, X) <=> ![X: $i] : safe(n0, X)),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(68,axiom,(![X: $i] : safe(n0, X)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','no_missionaries_is_safe')).
% 0.15/0.37 tff(69,plain,
% 0.15/0.37 (![X: $i] : safe(n0, X)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[68, 67])).
% 0.15/0.37 tff(70,plain,(
% 0.15/0.37 ![X: $i] : safe(n0, X)),
% 0.15/0.37 inference(skolemize,[status(sab)],[69])).
% 0.15/0.37 tff(71,plain,
% 0.15/0.37 (![X: $i] : safe(n0, X)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.15/0.37 tff(72,plain,
% 0.15/0.37 ((~![X: $i] : safe(n0, X)) | safe(n0, s(s(s(n0))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(73,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[72, 71, 64])).
% 0.15/0.37 tff(74,plain,(safe(n0, s(s(s(n0))))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(75,assumption,(~greater_or_equal(s(s(s(n0))), n0)), introduced(assumption)).
% 0.15/0.37 tff(76,plain,
% 0.15/0.37 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(s(s(n0))), n0)),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(77,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[76, 12, 75])).
% 0.15/0.37 tff(78,plain,(greater_or_equal(s(s(s(n0))), n0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(79,plain,
% 0.15/0.37 (((~![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))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(80,plain,
% 0.15/0.37 ((~![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))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(81,plain,
% 0.15/0.37 ((~![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)),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.15/0.37 tff(82,plain,
% 0.15/0.37 (safe(s(s(s(n0))), n0)),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[81, 47, 78])).
% 0.15/0.37 tff(83,assumption,(~greater_or_equal(s(s(s(n0))), s(s(n0)))), introduced(assumption)).
% 0.15/0.37 tff(84,assumption,(~greater_or_equal(s(s(n0)), s(n0))), introduced(assumption)).
% 0.15/0.37 tff(85,assumption,(~greater_or_equal(s(n0), n0)), introduced(assumption)).
% 0.15/0.37 tff(86,plain,
% 0.15/0.37 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(n0), n0)),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(87,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[86, 12, 85])).
% 0.15/0.37 tff(88,plain,(greater_or_equal(s(n0), n0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(89,plain,
% 0.15/0.37 (((~![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)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(90,plain,
% 0.15/0.37 ((~![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)))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(91,plain,
% 0.15/0.37 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(n0), n0)) | greater_or_equal(s(s(n0)), s(n0))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.15/0.37 tff(92,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[91, 25, 88, 84])).
% 0.15/0.37 tff(93,plain,(greater_or_equal(s(s(n0)), s(n0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(94,plain,
% 0.15/0.37 (((~![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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(95,plain,
% 0.15/0.37 ((~![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))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(96,plain,
% 0.15/0.37 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), s(n0))) | greater_or_equal(s(s(s(n0))), s(s(n0)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[95, 94])).
% 0.15/0.37 tff(97,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[96, 25, 93, 83])).
% 0.15/0.37 tff(98,plain,(greater_or_equal(s(s(s(n0))), s(s(n0)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(99,plain,
% 0.15/0.37 (((~![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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(100,plain,
% 0.15/0.37 ((~![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))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(101,plain,
% 0.15/0.37 ((~![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)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.15/0.37 tff(102,plain,
% 0.15/0.37 (safe(s(s(s(n0))), s(s(n0)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[101, 47, 98])).
% 0.15/0.37 tff(103,assumption,(~safe(n0, s(n0))), introduced(assumption)).
% 0.15/0.37 tff(104,plain,
% 0.15/0.37 ((~![X: $i] : safe(n0, X)) | safe(n0, s(n0))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(105,plain,
% 0.15/0.37 ($false),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[104, 71, 103])).
% 0.15/0.37 tff(106,plain,(safe(n0, s(n0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.37 tff(107,plain,
% 0.15/0.37 (((~![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)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(108,plain,
% 0.15/0.37 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0)))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(109,plain,
% 0.15/0.37 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(s(n0), s(n0))) | safe(s(n0), s(n0))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.15/0.37 tff(110,plain,
% 0.15/0.37 (safe(s(n0), s(n0))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[109, 47, 30])).
% 0.15/0.37 tff(111,plain,
% 0.15/0.37 (((~![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))))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(112,plain,
% 0.15/0.37 ((~![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))))),
% 0.15/0.37 inference(quant_inst,[status(thm)],[])).
% 0.15/0.37 tff(113,plain,
% 0.15/0.37 ((~![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)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.15/0.37 tff(114,plain,
% 0.15/0.37 (safe(s(s(n0)), s(s(n0)))),
% 0.15/0.37 inference(unit_resolution,[status(thm)],[113, 47, 35])).
% 0.15/0.37 tff(115,plain,
% 0.15/0.37 (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)))),
% 0.15/0.37 inference(rewrite,[status(thm)],[])).
% 0.15/0.37 tff(116,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')).
% 0.15/0.37 tff(117,plain,
% 0.15/0.37 (achievable(west(m(s(s(s(n0)))), c(s(s(s(n0))))), boatonwest, east(m(n0), c(n0)))),
% 0.15/0.37 inference(modus_ponens,[status(thm)],[116, 115])).
% 0.15/0.37 tff(118,plain,
% 0.15/0.37 (^[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))))))),
% 0.15/0.37 inference(bind,[status(th)],[])).
% 0.15/0.37 tff(119,plain,
% 0.15/0.37 (![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)))))),
% 0.15/0.37 inference(quant_intro,[status(thm)],[118])).
% 0.15/0.37 tff(120,plain,
% 0.15/0.37 (![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)))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(121,plain,
% 0.15/0.38 (^[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)))))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(122,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[121])).
% 0.15/0.38 tff(123,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')).
% 0.15/0.38 tff(124,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[123, 122])).
% 0.15/0.38 tff(125,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[124, 120])).
% 0.15/0.38 tff(126,plain,(
% 0.15/0.38 ![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)))))),
% 0.15/0.38 inference(skolemize,[status(sab)],[125])).
% 0.15/0.38 tff(127,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[126, 119])).
% 0.15/0.38 tff(128,plain,
% 0.15/0.38 (((~![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(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)))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(129,plain,
% 0.15/0.38 ((~![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)))))),
% 0.15/0.38 inference(quant_inst,[status(thm)],[])).
% 0.15/0.38 tff(130,plain,
% 0.15/0.38 ((~![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))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[129, 128])).
% 0.15/0.38 tff(131,plain,
% 0.15/0.38 ((~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)))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[130, 127, 117])).
% 0.15/0.38 tff(132,plain,
% 0.15/0.38 (achievable(west(m(s(s(n0))), c(s(s(n0)))), boatoneast, east(m(s(n0)), c(s(n0))))),
% 0.15/0.38 inference(unit_resolution,[status(thm)],[131, 114, 110])).
% 0.15/0.38 tff(133,plain,
% 0.15/0.38 (^[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))))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(134,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[133])).
% 0.15/0.38 tff(135,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(rewrite,[status(thm)],[])).
% 0.15/0.38 tff(136,plain,
% 0.15/0.38 (^[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)))))))),
% 0.15/0.38 inference(bind,[status(th)],[])).
% 0.15/0.38 tff(137,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(quant_intro,[status(thm)],[136])).
% 0.15/0.38 tff(138,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')).
% 0.15/0.38 tff(139,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[138, 137])).
% 0.15/0.38 tff(140,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[139, 135])).
% 0.15/0.38 tff(141,plain,(
% 0.15/0.38 ![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)))))),
% 0.15/0.38 inference(skolemize,[status(sab)],[140])).
% 0.15/0.38 tff(142,plain,
% 0.15/0.38 (![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)))))),
% 0.15/0.38 inference(modus_ponens,[status(thm)],[141, 134])).
% 0.15/0.38 tff(143,plain,
% 0.15/0.38 (((~![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))) | (~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))))) | 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(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))) | (~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))))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(144,plain,
% 0.15/0.39 (((~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(n0, 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))))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(145,plain,
% 0.15/0.39 (((~![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(n0, 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))))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[144])).
% 0.15/0.39 tff(146,plain,
% 0.15/0.39 (((~![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(n0, 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))))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0)))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[145, 143])).
% 0.15/0.39 tff(147,plain,
% 0.15/0.39 ((~![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))))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(148,plain,
% 0.15/0.39 ((~![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))) | (~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))))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[147, 146])).
% 0.15/0.39 tff(149,plain,
% 0.15/0.39 ((~safe(n0, s(n0))) | (~safe(s(s(s(n0))), s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[148, 142, 132])).
% 0.15/0.39 tff(150,plain,
% 0.15/0.39 ((~safe(s(s(s(n0))), s(s(n0)))) | achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[149, 106])).
% 0.15/0.39 tff(151,plain,
% 0.15/0.39 (achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(s(n0))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[150, 102])).
% 0.15/0.39 tff(152,plain,
% 0.15/0.39 (^[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))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(153,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[152])).
% 0.15/0.39 tff(154,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(155,plain,
% 0.15/0.39 (^[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)))))))),
% 0.15/0.39 inference(bind,[status(th)],[])).
% 0.15/0.39 tff(156,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(quant_intro,[status(thm)],[155])).
% 0.15/0.39 tff(157,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')).
% 0.15/0.39 tff(158,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.15/0.39 tff(159,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[158, 154])).
% 0.15/0.39 tff(160,plain,(
% 0.15/0.39 ![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)))))),
% 0.15/0.39 inference(skolemize,[status(sab)],[159])).
% 0.15/0.39 tff(161,plain,
% 0.15/0.39 (![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)))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[160, 153])).
% 0.15/0.39 tff(162,plain,
% 0.15/0.39 (((~![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)))))) | ((~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(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)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(s(n0))))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(163,plain,
% 0.15/0.39 (((~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)))))) <=> ((~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(s(n0))))))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(164,plain,
% 0.15/0.39 (((~![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)))))) | ((~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(s(n0)))))))),
% 0.15/0.39 inference(monotonicity,[status(thm)],[163])).
% 0.15/0.39 tff(165,plain,
% 0.15/0.39 (((~![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)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(s(n0))))))),
% 0.15/0.39 inference(transitivity,[status(thm)],[164, 162])).
% 0.15/0.39 tff(166,plain,
% 0.15/0.39 ((~![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))))))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(167,plain,
% 0.15/0.39 ((~![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)))))) | (~achievable(west(m(s(s(s(n0)))), c(s(s(n0)))), boatonwest, east(m(n0), c(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)))))) | (~safe(n0, s(s(s(n0)))))),
% 0.15/0.39 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.15/0.39 tff(168,plain,
% 0.15/0.39 ((~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)))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[167, 161, 151])).
% 0.15/0.39 tff(169,plain,
% 0.15/0.39 (achievable(west(m(s(s(s(n0)))), c(n0)), boatoneast, east(m(n0), c(s(s(s(n0))))))),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[168, 82, 74])).
% 0.15/0.39 tff(170,assumption,(~safe(n0, s(s(n0)))), introduced(assumption)).
% 0.15/0.39 tff(171,plain,
% 0.15/0.39 ((~![X: $i] : safe(n0, X)) | safe(n0, s(s(n0)))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(172,plain,
% 0.15/0.39 ($false),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[171, 71, 170])).
% 0.15/0.39 tff(173,plain,(safe(n0, s(s(n0)))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.39 tff(174,assumption,(~greater_or_equal(s(s(s(n0))), s(n0))), introduced(assumption)).
% 0.15/0.39 tff(175,assumption,(~greater_or_equal(s(s(n0)), n0)), introduced(assumption)).
% 0.15/0.39 tff(176,plain,
% 0.15/0.39 ((~![X: $i] : greater_or_equal(X, n0)) | greater_or_equal(s(s(n0)), n0)),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(177,plain,
% 0.15/0.39 ($false),
% 0.15/0.39 inference(unit_resolution,[status(thm)],[176, 12, 175])).
% 0.15/0.39 tff(178,plain,(greater_or_equal(s(s(n0)), n0)), inference(lemma,lemma(discharge,[]))).
% 0.15/0.39 tff(179,plain,
% 0.15/0.39 (((~![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)))),
% 0.15/0.39 inference(rewrite,[status(thm)],[])).
% 0.15/0.39 tff(180,plain,
% 0.15/0.39 ((~![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)))),
% 0.15/0.39 inference(quant_inst,[status(thm)],[])).
% 0.15/0.39 tff(181,plain,
% 0.15/0.39 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | greater_or_equal(s(X), s(Y)))) | (~greater_or_equal(s(s(n0)), n0)) | greater_or_equal(s(s(s(n0))), s(n0))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.15/0.40 tff(182,plain,
% 0.15/0.40 ($false),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[181, 25, 178, 174])).
% 0.15/0.40 tff(183,plain,(greater_or_equal(s(s(s(n0))), s(n0))), inference(lemma,lemma(discharge,[]))).
% 0.15/0.40 tff(184,plain,
% 0.15/0.40 (((~![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)))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(185,plain,
% 0.15/0.40 ((~![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)))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(186,plain,
% 0.15/0.40 ((~![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))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.15/0.40 tff(187,plain,
% 0.15/0.40 (safe(s(s(s(n0))), s(n0))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[186, 47, 183])).
% 0.15/0.40 tff(188,plain,
% 0.15/0.40 (^[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)))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(189,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[188])).
% 0.15/0.40 tff(190,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(191,plain,
% 0.15/0.40 (^[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))))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(192,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[191])).
% 0.15/0.40 tff(193,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')).
% 0.15/0.40 tff(194,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[193, 192])).
% 0.15/0.40 tff(195,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.15/0.40 tff(196,plain,(
% 0.15/0.40 ![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))))))),
% 0.15/0.40 inference(skolemize,[status(sab)],[195])).
% 0.15/0.40 tff(197,plain,
% 0.15/0.40 (![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))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[196, 189])).
% 0.15/0.40 tff(198,plain,
% 0.15/0.40 (((~![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))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(199,plain,
% 0.15/0.40 ((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))))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(200,plain,
% 0.15/0.40 (((~![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)))))))))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[199])).
% 0.15/0.40 tff(201,plain,
% 0.15/0.40 (((~![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))))))))),
% 0.15/0.40 inference(transitivity,[status(thm)],[200, 198])).
% 0.15/0.40 tff(202,plain,
% 0.15/0.40 ((~![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))))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(203,plain,
% 0.15/0.40 ((~![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)))))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.15/0.40 tff(204,plain,
% 0.15/0.40 (achievable(west(m(s(s(s(n0)))), c(s(n0))), boatonwest, east(m(n0), c(s(s(n0)))))),
% 0.15/0.40 inference(unit_resolution,[status(thm)],[203, 197, 187, 173, 169])).
% 0.15/0.40 tff(205,plain,
% 0.15/0.40 (^[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))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(206,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[205])).
% 0.15/0.40 tff(207,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(208,plain,
% 0.15/0.40 (^[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)))))))),
% 0.15/0.40 inference(bind,[status(th)],[])).
% 0.15/0.40 tff(209,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(quant_intro,[status(thm)],[208])).
% 0.15/0.40 tff(210,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')).
% 0.15/0.40 tff(211,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.15/0.40 tff(212,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.15/0.40 tff(213,plain,(
% 0.15/0.40 ![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)))))),
% 0.15/0.40 inference(skolemize,[status(sab)],[212])).
% 0.15/0.40 tff(214,plain,
% 0.15/0.40 (![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)))))),
% 0.15/0.40 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.15/0.40 tff(215,plain,
% 0.15/0.40 (((~![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(n0)), s(s(n0)))) | (~safe(s(n0), 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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(216,plain,
% 0.15/0.40 (((~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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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))))))),
% 0.15/0.40 inference(rewrite,[status(thm)],[])).
% 0.15/0.40 tff(217,plain,
% 0.15/0.40 (((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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)))))))),
% 0.15/0.40 inference(monotonicity,[status(thm)],[216])).
% 0.15/0.40 tff(218,plain,
% 0.15/0.40 (((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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))))))),
% 0.15/0.40 inference(transitivity,[status(thm)],[217, 215])).
% 0.15/0.40 tff(219,plain,
% 0.15/0.40 ((~![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)))))))),
% 0.15/0.40 inference(quant_inst,[status(thm)],[])).
% 0.15/0.40 tff(220,plain,
% 0.15/0.40 ((~![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(n0)), s(s(n0)))) | (~safe(s(n0), 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)))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.15/0.41 tff(221,plain,
% 0.15/0.41 (achievable(west(m(s(n0)), c(s(n0))), boatoneast, east(m(s(s(n0))), c(s(s(n0)))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[220, 214, 114, 110, 204])).
% 0.15/0.41 tff(222,plain,
% 0.15/0.41 (^[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)))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(223,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[222])).
% 0.15/0.41 tff(224,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(225,plain,
% 0.15/0.41 (^[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))))))))),
% 0.15/0.41 inference(bind,[status(th)],[])).
% 0.15/0.41 tff(226,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(quant_intro,[status(thm)],[225])).
% 0.15/0.41 tff(227,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')).
% 0.15/0.41 tff(228,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.15/0.41 tff(229,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.15/0.41 tff(230,plain,(
% 0.15/0.41 ![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))))))),
% 0.15/0.41 inference(skolemize,[status(sab)],[229])).
% 0.15/0.41 tff(231,plain,
% 0.15/0.41 (![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))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.15/0.41 tff(232,plain,
% 0.15/0.41 (((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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)))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(233,plain,
% 0.15/0.41 (((~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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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)))))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(234,plain,
% 0.15/0.41 (((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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))))))))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[233])).
% 0.15/0.41 tff(235,plain,
% 0.15/0.41 (((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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)))))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[234, 232])).
% 0.15/0.41 tff(236,plain,
% 0.15/0.41 ((~![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)))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(237,plain,
% 0.15/0.41 ((~![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(s(n0)), s(s(n0)))) | (~safe(s(n0), 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))))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.15/0.41 tff(238,plain,
% 0.15/0.41 (achievable(west(m(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[237, 231, 114, 110, 221])).
% 0.15/0.41 tff(239,plain,
% 0.15/0.41 (((~![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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(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] : ((~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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(240,plain,
% 0.15/0.41 (((~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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(241,plain,
% 0.15/0.41 (((~![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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))))),
% 0.15/0.41 inference(monotonicity,[status(thm)],[240])).
% 0.15/0.41 tff(242,plain,
% 0.15/0.41 (((~![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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.41 inference(transitivity,[status(thm)],[241, 239])).
% 0.15/0.41 tff(243,plain,
% 0.15/0.41 ((~![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))))))),
% 0.15/0.41 inference(quant_inst,[status(thm)],[])).
% 0.15/0.41 tff(244,plain,
% 0.15/0.41 ((~![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(s(s(n0))), c(s(s(n0)))), boatonwest, east(m(s(n0)), c(s(n0))))) | achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))),
% 0.15/0.41 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.15/0.41 tff(245,plain,
% 0.15/0.41 (achievable(west(m(n0), c(s(s(n0)))), boatoneast, east(m(s(s(s(n0)))), c(s(n0))))),
% 0.15/0.41 inference(unit_resolution,[status(thm)],[244, 214, 187, 173, 238])).
% 0.15/0.41 tff(246,plain,
% 0.15/0.41 (((~![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))), 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))))) | 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] : (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))), 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))))) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(247,plain,
% 0.15/0.41 ((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(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))))) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))),
% 0.15/0.41 inference(rewrite,[status(thm)],[])).
% 0.15/0.41 tff(248,plain,
% 0.15/0.41 (((~![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(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))))) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[247])).
% 0.15/0.42 tff(249,plain,
% 0.15/0.42 (((~![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(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))))) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[248, 246])).
% 0.15/0.42 tff(250,plain,
% 0.15/0.42 ((~![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))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(251,plain,
% 0.15/0.42 ((~![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))), 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))))) | achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[250, 249])).
% 0.15/0.42 tff(252,plain,
% 0.15/0.42 (achievable(west(m(n0), c(s(s(s(n0))))), boatonwest, east(m(s(s(s(n0)))), c(n0)))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[251, 197, 82, 74, 245])).
% 0.15/0.42 tff(253,plain,
% 0.15/0.42 (((~![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))) | (~safe(s(s(s(n0))), s(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(n0, s(n0))) | (~safe(s(s(s(n0))), s(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)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(254,plain,
% 0.15/0.42 (((~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(n0, s(n0))) | (~safe(s(s(s(n0))), s(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)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(255,plain,
% 0.15/0.42 (((~![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(n0, s(n0))) | (~safe(s(s(s(n0))), s(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))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[254])).
% 0.15/0.42 tff(256,plain,
% 0.15/0.42 (((~![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(n0, s(n0))) | (~safe(s(s(s(n0))), s(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)))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[255, 253])).
% 0.15/0.42 tff(257,plain,
% 0.15/0.42 ((~![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)))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(258,plain,
% 0.15/0.42 ((~![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))) | (~safe(s(s(s(n0))), s(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))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[257, 256])).
% 0.15/0.42 tff(259,plain,
% 0.15/0.42 (achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[258, 161, 106, 102, 252])).
% 0.15/0.42 tff(260,plain,
% 0.15/0.42 (((~![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(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))) | achievable(west(m(n0), c(s(s(n0)))), boatonwest, 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(s(s(s(n0))), s(n0))) | (~safe(n0, s(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(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(261,plain,
% 0.15/0.42 ((achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(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(n0))) | (~safe(n0, s(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(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(262,plain,
% 0.15/0.42 (((~![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(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, 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] : (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(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))) | achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0))))))),
% 0.15/0.42 inference(monotonicity,[status(thm)],[261])).
% 0.15/0.42 tff(263,plain,
% 0.15/0.42 (((~![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(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, 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] : (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(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))) | achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.42 inference(transitivity,[status(thm)],[262, 260])).
% 0.15/0.42 tff(264,plain,
% 0.15/0.42 ((~![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(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))) | (~safe(s(s(s(n0))), s(n0))) | (~safe(n0, s(s(n0)))) | (~achievable(west(m(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(265,plain,
% 0.15/0.42 ((~![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(n0), c(s(n0))), boatoneast, east(m(s(s(s(n0)))), c(s(s(n0)))))) | achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0))))),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[264, 263])).
% 0.15/0.42 tff(266,plain,
% 0.15/0.42 (achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0))))),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[265, 197, 187, 173, 259])).
% 0.15/0.42 tff(267,plain,
% 0.15/0.42 (((~![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))),
% 0.15/0.42 inference(rewrite,[status(thm)],[])).
% 0.15/0.42 tff(268,plain,
% 0.15/0.42 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | ((~greater_or_equal(n0, n0)) | safe(n0, n0))),
% 0.15/0.42 inference(quant_inst,[status(thm)],[])).
% 0.15/0.42 tff(269,plain,
% 0.15/0.42 ((~![Y: $i, X: $i] : ((~greater_or_equal(X, Y)) | safe(X, Y))) | (~greater_or_equal(n0, n0)) | safe(n0, n0)),
% 0.15/0.42 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.15/0.42 tff(270,plain,
% 0.15/0.42 (safe(n0, n0)),
% 0.15/0.42 inference(unit_resolution,[status(thm)],[269, 47, 15])).
% 0.15/0.42 tff(271,plain,
% 0.15/0.42 (((~![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, 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(n0), c(s(s(n0)))), boatonwest, east(m(s(s(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(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, 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(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0))))))),
% 0.15/0.43 inference(rewrite,[status(thm)],[])).
% 0.15/0.43 tff(272,plain,
% 0.15/0.43 ((~![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, 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(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0))))))),
% 0.15/0.43 inference(quant_inst,[status(thm)],[])).
% 0.15/0.43 tff(273,plain,
% 0.15/0.43 ((~![W: $i, Z: $i, Y: $i, X: $i] : ((~safe(X, Y)) | achievable(west(m(X), c(Y)), boatoneast, east(m(Z), c(s(s(W))))) | (~safe(Z, s(s(W)))) | (~achievable(west(m(X), c(s(s(Y)))), boatonwest, east(m(Z), c(W)))))) | (~safe(n0, n0)) | achievable(west(m(n0), c(n0)), boatoneast, east(m(s(s(s(n0)))), c(s(s(s(n0)))))) | (~safe(s(s(s(n0))), s(s(s(n0))))) | (~achievable(west(m(n0), c(s(s(n0)))), boatonwest, east(m(s(s(s(n0)))), c(s(n0)))))),
% 0.15/0.43 inference(modus_ponens,[status(thm)],[272, 271])).
% 0.15/0.43 tff(274,plain,
% 0.15/0.43 ($false),
% 0.15/0.43 inference(unit_resolution,[status(thm)],[273, 161, 270, 266, 63, 52])).
% 0.15/0.43 % SZS output end Proof
%------------------------------------------------------------------------------