0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.HpGMzUa6a9 0.11/0.32 % Computer : n024.cluster.edu 0.11/0.32 % Model : x86_64 x86_64 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.32 % Memory : 8042.1875MB 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.32 % CPULimit : 960 0.11/0.32 % DateTime : Thu Jul 2 08:38:41 EDT 2020 0.11/0.32 % CPUTime : 0.11/0.32 % Running portfolio for 120 s 0.11/0.32 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.33 % Number of cores: 8 0.11/0.33 % Python version: Python 3.6.8 0.11/0.33 % Running in FO mode 16.38/16.61 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 16.38/16.61 % Solved by: fo/fo7.sh 16.38/16.61 To remain in the chosen logic fragment, unification with booleans has been disabled. 16.38/16.61 % done 12339 iterations in 16.166s 16.38/16.61 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 16.38/16.61 % SZS output start Refutation 16.38/16.61 tff(less_or_equal, axiom, 16.38/16.61 (![X,Y]: (less_or_equal(X,Y) <=> ((X = Y) | less(X,Y))))). 16.38/16.61 tff('0', plain, ![X79, X81]: ( less_or_equal(X79, X81) | X79 != X81), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('1', plain, ![X81]: less_or_equal(X81, X81), 16.38/16.61 inference('simplify', [status(thm)], ['0'])). 16.38/16.61 tff(less5, axiom, (![X]: (less_or_equal(X,n4) <=> less(X,n5)))). 16.38/16.61 tff('2', plain, ![X90]: ( less(X90, n5) | ~ less_or_equal(X90, n4)), 16.38/16.61 inference('cnf', [status(esa)], [less5])). 16.38/16.61 tff('3', plain, less(n4, n5), inference('sup-', [status(thm)], ['1', '2'])). 16.38/16.61 tff(less_property, axiom, 16.38/16.61 (![X,Y]: (((Y != X) & (~less(Y,X))) <=> less(X,Y)))). 16.38/16.61 tff('4', plain, ![X102, X104]: (~ less(X104, X102) | ~ less(X102, X104)), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff('5', plain, ~ less(n5, n4), inference('sup-', [status(thm)], ['3', '4'])). 16.38/16.61 tff(plus3_3, axiom, (plus(n3,n3) = n6)). 16.38/16.61 tff('6', plain, plus(n3, n3) = n6, inference('cnf', [status(esa)], [plus3_3])). 16.38/16.61 tff('7', plain, 16.38/16.61 ![X102, X103]: ( less(X102, X103) | less(X103, X102) | X103 = X102), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff(less2, axiom, (![X]: (less_or_equal(X,n1) <=> less(X,n2)))). 16.38/16.61 tff('8', plain, ![X106]: ( less_or_equal(X106, n1) | ~ less(X106, n2)), 16.38/16.61 inference('cnf', [status(esa)], [less2])). 16.38/16.61 tff('9', plain, ![X0]: (n2 = X0 | less(n2, X0) | less_or_equal(X0, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['7', '8'])). 16.38/16.61 tff('10', plain, 16.38/16.61 ![X79, X80]: ( less(X79, X80) | X79 = X80 | ~ less_or_equal(X79, X80)), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('11', plain, ![X0]: ( less(n2, X0) | n2 = X0 | X0 = n1 | less(X0, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['9', '10'])). 16.38/16.61 tff(less1, axiom, (![X]: (less(X,n1) <=> less_or_equal(X,n0)))). 16.38/16.61 tff('12', plain, ![X94]: ( less_or_equal(X94, n0) | ~ less(X94, n1)), 16.38/16.61 inference('cnf', [status(esa)], [less1])). 16.38/16.61 tff('13', plain, 16.38/16.61 ![X0]: (X0 = n1 | n2 = X0 | less(n2, X0) | less_or_equal(X0, n0)), 16.38/16.61 inference('sup-', [status(thm)], ['11', '12'])). 16.38/16.61 tff('14', plain, 16.38/16.61 ![X79, X80]: ( less(X79, X80) | X79 = X80 | ~ less_or_equal(X79, X80)), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('15', plain, 16.38/16.61 ![X0]: ( less(n2, X0) | n2 = X0 | X0 = n1 | X0 = n0 | less(X0, n0)), 16.38/16.61 inference('sup-', [status(thm)], ['13', '14'])). 16.38/16.61 tff(less0, axiom, (~(?[X]: less(X,n0)))). 16.38/16.61 tff('16', plain, ![X101]: ~ less(X101, n0), 16.38/16.61 inference('cnf', [status(esa)], [less0])). 16.38/16.61 tff('17', plain, ![X0]: (X0 = n0 | X0 = n1 | n2 = X0 | less(n2, X0)), 16.38/16.61 inference('sup-', [status(thm)], ['15', '16'])). 16.38/16.61 tff(initiates_all_defn, axiom, 16.38/16.61 (![Event,Fluent,Time]: 16.38/16.61 (initiates(Event,Fluent,Time) <=> 16.38/16.61 (((Fluent = spilling) & (Event = overflow)) | 16.38/16.61 ((tapOn = Event) & (filling = Fluent)) | 16.38/16.61 (?[Height]: 16.38/16.61 ((waterLevel(Height) = Fluent) & (tapOff = Event) & 16.38/16.61 holdsAt(waterLevel(Height),Time))) | 16.38/16.61 (?[Height]: 16.38/16.61 (holdsAt(waterLevel(Height),Time) & 16.38/16.61 (waterLevel(Height) = Fluent) & (Event = overflow))))))). 16.38/16.61 tff(zf_stmt_0, axiom, 16.38/16.61 (zip_tseitin_1(Fluent,Event) <=> ((filling = Fluent) & (tapOn = Event)))). 16.38/16.61 tff('18', plain, 16.38/16.61 ![X53, X54]: ( zip_tseitin_1(X54, X53) | tapOn != X53 | filling != X54), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_0])). 16.38/16.61 tff('19', plain, zip_tseitin_1(filling, tapOn), 16.38/16.61 inference('simplify', [status(thm)], ['18'])). 16.38/16.61 tff(zf_stmt_1, type, zip_tseitin_3 : ($i * $i * $i * $i) > $o). 16.38/16.61 tff(zf_stmt_2, axiom, 16.38/16.61 (zip_tseitin_3(Height,Time,Fluent,Event) <=> 16.38/16.61 ((Event = overflow) & (waterLevel(Height) = Fluent) & 16.38/16.61 holdsAt(waterLevel(Height),Time)))). 16.38/16.61 tff(zf_stmt_3, type, zip_tseitin_2 : ($i * $i * $i * $i) > $o). 16.38/16.61 tff(zf_stmt_4, axiom, 16.38/16.61 (zip_tseitin_2(Height,Time,Fluent,Event) <=> 16.38/16.61 (holdsAt(waterLevel(Height),Time) & (tapOff = Event) & 16.38/16.61 (waterLevel(Height) = Fluent)))). 16.38/16.61 tff(zf_stmt_5, type, zip_tseitin_1 : ($i * $i) > $o). 16.38/16.61 tff(zf_stmt_6, type, zip_tseitin_0 : ($i * $i) > $o). 16.38/16.61 tff(zf_stmt_7, axiom, 16.38/16.61 (zip_tseitin_0(Fluent,Event) <=> ((Event = overflow) & (Fluent = spilling)))). 16.38/16.61 tff(zf_stmt_8, axiom, 16.38/16.61 (![Event,Fluent,Time]: 16.38/16.61 (initiates(Event,Fluent,Time) <=> 16.38/16.61 ((?[Height]: zip_tseitin_3(Height,Time,Fluent,Event)) | 16.38/16.61 (?[Height]: zip_tseitin_2(Height,Time,Fluent,Event)) | 16.38/16.61 zip_tseitin_1(Fluent,Event) | zip_tseitin_0(Fluent,Event))))). 16.38/16.61 tff('20', plain, 16.38/16.61 ![X58, X59, X61]: ( initiates(X59, X58, X61) | ~ zip_tseitin_1(X58, X59)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_8])). 16.38/16.61 tff('21', plain, ![X0]: initiates(tapOn, filling, X0), 16.38/16.61 inference('sup-', [status(thm)], ['19', '20'])). 16.38/16.61 tff(waterLevel_0, axiom, (holdsAt(waterLevel(n0),n0))). 16.38/16.61 tff('22', plain, holdsAt(waterLevel(n0), n0), 16.38/16.61 inference('cnf', [status(esa)], [waterLevel_0])). 16.38/16.61 tff(change_of_waterLevel, axiom, 16.38/16.61 (![Height1,Time,Height2,Offset]: 16.38/16.61 (((Height2 = plus(Height1,Offset)) & holdsAt(waterLevel(Height1),Time)) => 16.38/16.61 trajectory(filling,Time,waterLevel(Height2),Offset)))). 16.38/16.61 tff('23', plain, 16.38/16.61 ![X48, X49, X50, X51]: 16.38/16.61 (~ holdsAt(waterLevel(X48), X49) 16.38/16.61 | X51 != plus(X48, X50) 16.38/16.61 | trajectory(filling, X49, waterLevel(X51), X50)), 16.38/16.61 inference('cnf', [status(esa)], [change_of_waterLevel])). 16.38/16.61 tff('24', plain, 16.38/16.61 ![X48, X49, X50]: 16.38/16.61 ( trajectory(filling, X49, waterLevel(plus(X48, X50)), X50) 16.38/16.61 | ~ holdsAt(waterLevel(X48), X49)), 16.38/16.61 inference('simplify', [status(thm)], ['23'])). 16.38/16.61 tff('25', plain, 16.38/16.61 ![X0]: trajectory(filling, n0, waterLevel(plus(n0, X0)), X0), 16.38/16.61 inference('sup-', [status(thm)], ['22', '24'])). 16.38/16.61 tff('26', plain, ![X81]: less_or_equal(X81, X81), 16.38/16.61 inference('simplify', [status(thm)], ['0'])). 16.38/16.61 tff('27', plain, ![X95]: ( less(X95, n1) | ~ less_or_equal(X95, n0)), 16.38/16.61 inference('cnf', [status(esa)], [less1])). 16.38/16.61 tff('28', plain, less(n0, n1), 16.38/16.61 inference('sup-', [status(thm)], ['26', '27'])). 16.38/16.61 tff('29', plain, ![X79, X81]: ( less_or_equal(X79, X81) | ~ less(X79, X81)), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('30', plain, less_or_equal(n0, n1), 16.38/16.61 inference('sup-', [status(thm)], ['28', '29'])). 16.38/16.61 tff('31', plain, ![X105]: ( less(X105, n2) | ~ less_or_equal(X105, n1)), 16.38/16.61 inference('cnf', [status(esa)], [less2])). 16.38/16.61 tff('32', plain, less(n0, n2), 16.38/16.61 inference('sup-', [status(thm)], ['30', '31'])). 16.38/16.61 tff(change_holding, axiom, 16.38/16.61 (![Event,Time,Fluent,Fluent2,Offset]: 16.38/16.61 ((initiates(Event,Fluent,Time) & 16.38/16.61 trajectory(Fluent,Time,Fluent2,Offset) & less(n0,Offset) & 16.38/16.61 happens(Event,Time) & (~stoppedIn(Time,Fluent,plus(Time,Offset)))) => 16.38/16.61 holdsAt(Fluent2,plus(Time,Offset))))). 16.38/16.61 tff('33', plain, 16.38/16.61 ![X33, X34, X35, X36, X37]: 16.38/16.61 (~ happens(X33, X34) 16.38/16.61 | ~ initiates(X33, X35, X34) 16.38/16.61 | ~ trajectory(X35, X34, X36, X37) 16.38/16.61 | ~ less(n0, X37) 16.38/16.61 | stoppedIn(X34, X35, plus(X34, X37)) 16.38/16.61 | holdsAt(X36, plus(X34, X37))), 16.38/16.61 inference('cnf', [status(esa)], [change_holding])). 16.38/16.61 tff('34', plain, 16.38/16.61 ![X0, X1, X2, X3]: 16.38/16.61 ( holdsAt(X1, plus(X0, n2)) 16.38/16.61 | stoppedIn(X0, X2, plus(X0, n2)) 16.38/16.61 | ~ trajectory(X2, X0, X1, n2) 16.38/16.61 | ~ initiates(X3, X2, X0) 16.38/16.61 | ~ happens(X3, X0)), 16.38/16.61 inference('sup-', [status(thm)], ['32', '33'])). 16.38/16.61 tff('35', plain, 16.38/16.61 ![X0]: 16.38/16.61 (~ happens(X0, n0) 16.38/16.61 | ~ initiates(X0, filling, n0) 16.38/16.61 | stoppedIn(n0, filling, plus(n0, n2)) 16.38/16.61 | holdsAt(waterLevel(plus(n0, n2)), plus(n0, n2))), 16.38/16.61 inference('sup-', [status(thm)], ['25', '34'])). 16.38/16.61 tff(symmetry_of_plus, axiom, (![X,Y]: (plus(X,Y) = plus(Y,X)))). 16.38/16.61 tff('36', plain, ![X98, X99]: plus(X99, X98) = plus(X98, X99), 16.38/16.61 inference('cnf', [status(esa)], [symmetry_of_plus])). 16.38/16.61 tff(plus0_2, axiom, (n2 = plus(n0,n2))). 16.38/16.61 tff('37', plain, n2 = plus(n0, n2), 16.38/16.61 inference('cnf', [status(esa)], [plus0_2])). 16.38/16.61 tff('38', plain, ![X98, X99]: plus(X99, X98) = plus(X98, X99), 16.38/16.61 inference('cnf', [status(esa)], [symmetry_of_plus])). 16.38/16.61 tff('39', plain, n2 = plus(n2, n0), 16.38/16.61 inference('demod', [status(thm)], ['37', '38'])). 16.38/16.61 tff('40', plain, ![X98, X99]: plus(X99, X98) = plus(X98, X99), 16.38/16.61 inference('cnf', [status(esa)], [symmetry_of_plus])). 16.38/16.61 tff('41', plain, n2 = plus(n2, n0), 16.38/16.61 inference('demod', [status(thm)], ['37', '38'])). 16.38/16.61 tff('42', plain, ![X98, X99]: plus(X99, X98) = plus(X98, X99), 16.38/16.61 inference('cnf', [status(esa)], [symmetry_of_plus])). 16.38/16.61 tff('43', plain, n2 = plus(n2, n0), 16.38/16.61 inference('demod', [status(thm)], ['37', '38'])). 16.38/16.61 tff('44', plain, 16.38/16.61 ![X0]: 16.38/16.61 (~ happens(X0, n0) 16.38/16.61 | ~ initiates(X0, filling, n0) 16.38/16.61 | stoppedIn(n0, filling, n2) 16.38/16.61 | holdsAt(waterLevel(n2), n2)), 16.38/16.61 inference('demod', [status(thm)], 16.38/16.61 ['35', '36', '39', '40', '41', '42', '43'])). 16.38/16.61 tff('45', plain, 16.38/16.61 ( holdsAt(waterLevel(n2), n2) 16.38/16.61 | stoppedIn(n0, filling, n2) 16.38/16.61 | ~ happens(tapOn, n0)), 16.38/16.61 inference('sup-', [status(thm)], ['21', '44'])). 16.38/16.61 tff(happens_all_defn, axiom, 16.38/16.61 (![Event,Time]: 16.38/16.61 (happens(Event,Time) <=> 16.38/16.61 ((holdsAt(waterLevel(n3),Time) & (Event = overflow) & 16.38/16.61 holdsAt(filling,Time)) | 16.38/16.61 ((Time = n0) & (Event = tapOn)))))). 16.38/16.61 tff(zf_stmt_9, axiom, 16.38/16.61 (zip_tseitin_5(Time,Event) <=> ((Event = tapOn) & (Time = n0)))). 16.38/16.61 tff('46', plain, 16.38/16.61 ![X68, X69]: ( zip_tseitin_5(X68, X69) | X68 != n0 | X69 != tapOn), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_9])). 16.38/16.61 tff('47', plain, zip_tseitin_5(n0, tapOn), 16.38/16.61 inference('simplify', [status(thm)], ['46'])). 16.38/16.61 tff(zf_stmt_10, type, zip_tseitin_5 : ($i * $i) > $o). 16.38/16.61 tff(zf_stmt_11, type, zip_tseitin_4 : ($i * $i) > $o). 16.38/16.61 tff(zf_stmt_12, axiom, 16.38/16.61 (zip_tseitin_4(Time,Event) <=> 16.38/16.61 (holdsAt(filling,Time) & (Event = overflow) & holdsAt(waterLevel(n3),Time)))). 16.38/16.61 tff(zf_stmt_13, axiom, 16.38/16.61 (![Event,Time]: 16.38/16.61 (happens(Event,Time) <=> 16.38/16.61 (zip_tseitin_5(Time,Event) | zip_tseitin_4(Time,Event))))). 16.38/16.61 tff('48', plain, 16.38/16.61 ![X71, X72]: ( happens(X71, X72) | ~ zip_tseitin_5(X72, X71)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_13])). 16.38/16.61 tff('49', plain, happens(tapOn, n0), 16.38/16.61 inference('sup-', [status(thm)], ['47', '48'])). 16.38/16.61 tff('50', plain, 16.38/16.61 ( holdsAt(waterLevel(n2), n2) | stoppedIn(n0, filling, n2)), 16.38/16.61 inference('demod', [status(thm)], ['45', '49'])). 16.38/16.61 tff(waterlevel_not_3, conjecture, (~holdsAt(waterLevel(n3),n2))). 16.38/16.61 tff(zf_stmt_14, negated_conjecture, (holdsAt(waterLevel(n3),n2))). 16.38/16.61 tff('51', plain, holdsAt(waterLevel(n3), n2), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_14])). 16.38/16.61 tff(same_waterLevel, axiom, 16.38/16.61 (![Time,Height1,Height2]: 16.38/16.61 ((holdsAt(waterLevel(Height2),Time) & holdsAt(waterLevel(Height1),Time)) => 16.38/16.61 (Height2 = Height1)))). 16.38/16.61 tff('52', plain, 16.38/16.61 ![X45, X46, X47]: 16.38/16.61 (~ holdsAt(waterLevel(X45), X46) 16.38/16.61 | ~ holdsAt(waterLevel(X47), X46) 16.38/16.61 | X47 = X45), 16.38/16.61 inference('cnf', [status(esa)], [same_waterLevel])). 16.38/16.61 tff('53', plain, ![X0]: (X0 = n3 | ~ holdsAt(waterLevel(X0), n2)), 16.38/16.61 inference('sup-', [status(thm)], ['51', '52'])). 16.38/16.61 tff('54', plain, ( stoppedIn(n0, filling, n2) | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['50', '53'])). 16.38/16.61 tff(stoppedin_defn, axiom, 16.38/16.61 (![Time1,Fluent,Time2]: 16.38/16.61 ((?[Event,Time]: 16.38/16.61 (happens(Event,Time) & less(Time,Time2) & 16.38/16.61 terminates(Event,Fluent,Time) & less(Time1,Time))) <=> 16.38/16.61 stoppedIn(Time1,Fluent,Time2)))). 16.38/16.61 tff('55', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( less(sk_Time_1(X30, X26, X25), X30) | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('56', plain, (n2 = n3 | less(sk_Time_1(n2, filling, n0), n2)), 16.38/16.61 inference('sup-', [status(thm)], ['54', '55'])). 16.38/16.61 tff('57', plain, ![X102, X104]: (~ less(X104, X102) | ~ less(X102, X104)), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff('58', plain, (n2 = n3 | ~ less(n2, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['56', '57'])). 16.38/16.61 tff('59', plain, 16.38/16.61 (n2 = sk_Time_1(n2, filling, n0) 16.38/16.61 | sk_Time_1(n2, filling, n0) = n1 16.38/16.61 | sk_Time_1(n2, filling, n0) = n0 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['17', '58'])). 16.38/16.61 tff('60', plain, ( stoppedIn(n0, filling, n2) | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['50', '53'])). 16.38/16.61 tff('61', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( terminates(sk_Event_2(X30, X26, X25), X26, sk_Time_1(X30, X26, X25)) 16.38/16.61 | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('62', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | terminates(sk_Event_2(n2, filling, n0), filling, 16.38/16.61 sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['60', '61'])). 16.38/16.61 tff(terminates_all_defn, axiom, 16.38/16.61 (![Event,Fluent,Time]: 16.38/16.61 (terminates(Event,Fluent,Time) <=> 16.38/16.61 (((filling = Fluent) & (tapOff = Event)) | 16.38/16.61 ((Fluent = filling) & (Event = overflow)))))). 16.38/16.61 tff('63', plain, 16.38/16.61 ![X64, X65, X66]: 16.38/16.61 (X65 = overflow | tapOff = X65 | ~ terminates(X65, X64, X66)), 16.38/16.61 inference('cnf', [status(esa)], [terminates_all_defn])). 16.38/16.61 tff('64', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | sk_Event_2(n2, filling, n0) = overflow), 16.38/16.61 inference('sup-', [status(thm)], ['62', '63'])). 16.38/16.61 tff('65', plain, ( stoppedIn(n0, filling, n2) | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['50', '53'])). 16.38/16.61 tff('66', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( happens(sk_Event_2(X30, X26, X25), sk_Time_1(X30, X26, X25)) 16.38/16.61 | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('67', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | happens(sk_Event_2(n2, filling, n0), sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['65', '66'])). 16.38/16.61 tff('68', plain, 16.38/16.61 ( happens(overflow, sk_Time_1(n2, filling, n0)) 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['64', '67'])). 16.38/16.61 tff('69', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | happens(overflow, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('simplify', [status(thm)], ['68'])). 16.38/16.61 tff('70', plain, 16.38/16.61 ( happens(overflow, n1) 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Time_1(n2, filling, n0) = n0 16.38/16.61 | n2 = sk_Time_1(n2, filling, n0) 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['59', '69'])). 16.38/16.61 tff('71', plain, 16.38/16.61 (tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = sk_Time_1(n2, filling, n0) 16.38/16.61 | sk_Time_1(n2, filling, n0) = n0 16.38/16.61 | n2 = n3 16.38/16.61 | happens(overflow, n1)), 16.38/16.61 inference('simplify', [status(thm)], ['70'])). 16.38/16.61 tff('72', plain, ( stoppedIn(n0, filling, n2) | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['50', '53'])). 16.38/16.61 tff('73', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( less(X25, sk_Time_1(X30, X26, X25)) | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('74', plain, (n2 = n3 | less(n0, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['72', '73'])). 16.38/16.61 tff('75', plain, 16.38/16.61 ( less(n0, n0) 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | n2 = n3 16.38/16.61 | n2 = sk_Time_1(n2, filling, n0) 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['71', '74'])). 16.38/16.61 tff('76', plain, 16.38/16.61 (tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = sk_Time_1(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | less(n0, n0)), 16.38/16.61 inference('simplify', [status(thm)], ['75'])). 16.38/16.61 tff('77', plain, (n2 = n3 | less(sk_Time_1(n2, filling, n0), n2)), 16.38/16.61 inference('sup-', [status(thm)], ['54', '55'])). 16.38/16.61 tff('78', plain, ![X106]: ( less_or_equal(X106, n1) | ~ less(X106, n2)), 16.38/16.61 inference('cnf', [status(esa)], [less2])). 16.38/16.61 tff('79', plain, (n2 = n3 | less_or_equal(sk_Time_1(n2, filling, n0), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['77', '78'])). 16.38/16.61 tff('80', plain, 16.38/16.61 ![X79, X80]: ( less(X79, X80) | X79 = X80 | ~ less_or_equal(X79, X80)), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('81', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | sk_Time_1(n2, filling, n0) = n1 16.38/16.61 | less(sk_Time_1(n2, filling, n0), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['79', '80'])). 16.38/16.61 tff('82', plain, ![X102, X104]: (~ less(X104, X102) | ~ less(X102, X104)), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff('83', plain, 16.38/16.61 (sk_Time_1(n2, filling, n0) = n1 16.38/16.61 | n2 = n3 16.38/16.61 | ~ less(n1, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['81', '82'])). 16.38/16.61 tff('84', plain, 16.38/16.61 (~ less(n1, n2) 16.38/16.61 | less(n0, n0) 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Time_1(n2, filling, n0) = n1), 16.38/16.61 inference('sup-', [status(thm)], ['76', '83'])). 16.38/16.61 tff('85', plain, ![X81]: less_or_equal(X81, X81), 16.38/16.61 inference('simplify', [status(thm)], ['0'])). 16.38/16.61 tff('86', plain, ![X105]: ( less(X105, n2) | ~ less_or_equal(X105, n1)), 16.38/16.61 inference('cnf', [status(esa)], [less2])). 16.38/16.61 tff('87', plain, less(n1, n2), 16.38/16.61 inference('sup-', [status(thm)], ['85', '86'])). 16.38/16.61 tff('88', plain, 16.38/16.61 ( less(n0, n0) 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Time_1(n2, filling, n0) = n1), 16.38/16.61 inference('demod', [status(thm)], ['84', '87'])). 16.38/16.61 tff('89', plain, 16.38/16.61 (sk_Time_1(n2, filling, n0) = n1 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | less(n0, n0)), 16.38/16.61 inference('simplify', [status(thm)], ['88'])). 16.38/16.61 tff('90', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | happens(overflow, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('simplify', [status(thm)], ['68'])). 16.38/16.61 tff('91', plain, 16.38/16.61 ( happens(overflow, n1) 16.38/16.61 | less(n0, n0) 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | n2 = n3 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['89', '90'])). 16.38/16.61 tff('92', plain, 16.38/16.61 (tapOff = sk_Event_2(n2, filling, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | less(n0, n0) 16.38/16.61 | happens(overflow, n1)), 16.38/16.61 inference('simplify', [status(thm)], ['91'])). 16.38/16.61 tff('93', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | happens(sk_Event_2(n2, filling, n0), sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['65', '66'])). 16.38/16.61 tff('94', plain, 16.38/16.61 ![X70, X71]: 16.38/16.61 ( zip_tseitin_4(X70, X71) 16.38/16.61 | zip_tseitin_5(X70, X71) 16.38/16.61 | ~ happens(X71, X70)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_13])). 16.38/16.61 tff('95', plain, 16.38/16.61 (n2 = n3 16.38/16.61 | zip_tseitin_5(sk_Time_1(n2, filling, n0), 16.38/16.61 sk_Event_2(n2, filling, n0)) 16.38/16.61 | zip_tseitin_4(sk_Time_1(n2, filling, n0), 16.38/16.61 sk_Event_2(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['93', '94'])). 16.38/16.61 tff('96', plain, ![X68, X69]: (X69 = overflow | ~ zip_tseitin_4(X68, X69)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_12])). 16.38/16.61 tff('97', plain, 16.38/16.61 ( zip_tseitin_5(sk_Time_1(n2, filling, n0), sk_Event_2(n2, filling, n0)) 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Event_2(n2, filling, n0) = overflow), 16.38/16.61 inference('sup-', [status(thm)], ['95', '96'])). 16.38/16.61 tff('98', plain, ![X68, X69]: (X68 = n0 | ~ zip_tseitin_5(X68, X69)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_9])). 16.38/16.61 tff('99', plain, 16.38/16.61 (sk_Event_2(n2, filling, n0) = overflow 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Time_1(n2, filling, n0) = n0), 16.38/16.61 inference('sup-', [status(thm)], ['97', '98'])). 16.38/16.61 tff('100', plain, (n2 = n3 | less(n0, sk_Time_1(n2, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['72', '73'])). 16.38/16.61 tff('101', plain, 16.38/16.61 ( less(n0, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Event_2(n2, filling, n0) = overflow 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['99', '100'])). 16.38/16.61 tff('102', plain, 16.38/16.61 (sk_Event_2(n2, filling, n0) = overflow | n2 = n3 | less(n0, n0)), 16.38/16.61 inference('simplify', [status(thm)], ['101'])). 16.38/16.61 tff('103', plain, ![X102, X104]: (X104 != X102 | ~ less(X102, X104)), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff('104', plain, ![X102]: ~ less(X102, X102), 16.38/16.61 inference('simplify', [status(thm)], ['103'])). 16.38/16.61 tff('105', plain, (n2 = n3 | sk_Event_2(n2, filling, n0) = overflow), 16.38/16.61 inference('clc', [status(thm)], ['102', '104'])). 16.38/16.61 tff('106', plain, 16.38/16.61 (tapOff = overflow 16.38/16.61 | happens(overflow, n1) 16.38/16.61 | less(n0, n0) 16.38/16.61 | n2 = n3 16.38/16.61 | n2 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['92', '105'])). 16.38/16.61 tff('107', plain, 16.38/16.61 (n2 = n3 | less(n0, n0) | happens(overflow, n1) | tapOff = overflow), 16.38/16.61 inference('simplify', [status(thm)], ['106'])). 16.38/16.61 tff(tapOff_not_overflow, axiom, (overflow != tapOff)). 16.38/16.61 tff('108', plain, overflow != tapOff, 16.38/16.61 inference('cnf', [status(esa)], [tapOff_not_overflow])). 16.38/16.61 tff('109', plain, (n2 = n3 | less(n0, n0) | happens(overflow, n1)), 16.38/16.61 inference('simplify_reflect-', [status(thm)], ['107', '108'])). 16.38/16.61 tff('110', plain, ![X102]: ~ less(X102, X102), 16.38/16.61 inference('simplify', [status(thm)], ['103'])). 16.38/16.61 tff('111', plain, ( happens(overflow, n1) | n2 = n3), 16.38/16.61 inference('clc', [status(thm)], ['109', '110'])). 16.38/16.61 tff('112', plain, ![X0]: initiates(tapOn, filling, X0), 16.38/16.61 inference('sup-', [status(thm)], ['19', '20'])). 16.38/16.61 tff('113', plain, 16.38/16.61 ![X0]: trajectory(filling, n0, waterLevel(plus(n0, X0)), X0), 16.38/16.61 inference('sup-', [status(thm)], ['22', '24'])). 16.38/16.61 tff('114', plain, less(n0, n1), 16.38/16.61 inference('sup-', [status(thm)], ['26', '27'])). 16.38/16.61 tff('115', plain, 16.38/16.61 ![X33, X34, X35, X36, X37]: 16.38/16.61 (~ happens(X33, X34) 16.38/16.61 | ~ initiates(X33, X35, X34) 16.38/16.61 | ~ trajectory(X35, X34, X36, X37) 16.38/16.61 | ~ less(n0, X37) 16.38/16.61 | stoppedIn(X34, X35, plus(X34, X37)) 16.38/16.61 | holdsAt(X36, plus(X34, X37))), 16.38/16.61 inference('cnf', [status(esa)], [change_holding])). 16.38/16.61 tff('116', plain, 16.38/16.61 ![X0, X1, X2, X3]: 16.38/16.61 ( holdsAt(X1, plus(X0, n1)) 16.38/16.61 | stoppedIn(X0, X2, plus(X0, n1)) 16.38/16.61 | ~ trajectory(X2, X0, X1, n1) 16.38/16.61 | ~ initiates(X3, X2, X0) 16.38/16.61 | ~ happens(X3, X0)), 16.38/16.61 inference('sup-', [status(thm)], ['114', '115'])). 16.38/16.61 tff('117', plain, 16.38/16.61 ![X0]: 16.38/16.61 (~ happens(X0, n0) 16.38/16.61 | ~ initiates(X0, filling, n0) 16.38/16.61 | stoppedIn(n0, filling, plus(n0, n1)) 16.38/16.61 | holdsAt(waterLevel(plus(n0, n1)), plus(n0, n1))), 16.38/16.61 inference('sup-', [status(thm)], ['113', '116'])). 16.38/16.61 tff(plus0_1, axiom, (plus(n0,n1) = n1)). 16.38/16.61 tff('118', plain, plus(n0, n1) = n1, 16.38/16.61 inference('cnf', [status(esa)], [plus0_1])). 16.38/16.61 tff('119', plain, plus(n0, n1) = n1, 16.38/16.61 inference('cnf', [status(esa)], [plus0_1])). 16.38/16.61 tff('120', plain, plus(n0, n1) = n1, 16.38/16.61 inference('cnf', [status(esa)], [plus0_1])). 16.38/16.61 tff('121', plain, 16.38/16.61 ![X0]: 16.38/16.61 (~ happens(X0, n0) 16.38/16.61 | ~ initiates(X0, filling, n0) 16.38/16.61 | stoppedIn(n0, filling, n1) 16.38/16.61 | holdsAt(waterLevel(n1), n1)), 16.38/16.61 inference('demod', [status(thm)], ['117', '118', '119', '120'])). 16.38/16.61 tff('122', plain, 16.38/16.61 ( holdsAt(waterLevel(n1), n1) 16.38/16.61 | stoppedIn(n0, filling, n1) 16.38/16.61 | ~ happens(tapOn, n0)), 16.38/16.61 inference('sup-', [status(thm)], ['112', '121'])). 16.38/16.61 tff('123', plain, happens(tapOn, n0), 16.38/16.61 inference('sup-', [status(thm)], ['47', '48'])). 16.38/16.61 tff('124', plain, 16.38/16.61 ( holdsAt(waterLevel(n1), n1) | stoppedIn(n0, filling, n1)), 16.38/16.61 inference('demod', [status(thm)], ['122', '123'])). 16.38/16.61 tff('125', plain, 16.38/16.61 ![X53, X54, X56, X57]: 16.38/16.61 ( zip_tseitin_3(X57, X56, X54, X53) 16.38/16.61 | ~ holdsAt(waterLevel(X57), X56) 16.38/16.61 | waterLevel(X57) != X54 16.38/16.61 | X53 != overflow), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_2])). 16.38/16.61 tff('126', plain, 16.38/16.61 ![X56, X57]: 16.38/16.61 (~ holdsAt(waterLevel(X57), X56) 16.38/16.61 | zip_tseitin_3(X57, X56, waterLevel(X57), overflow)), 16.38/16.61 inference('simplify', [status(thm)], ['125'])). 16.38/16.61 tff('127', plain, 16.38/16.61 ( stoppedIn(n0, filling, n1) 16.38/16.61 | zip_tseitin_3(n1, n1, waterLevel(n1), overflow)), 16.38/16.61 inference('sup-', [status(thm)], ['124', '126'])). 16.38/16.61 tff('128', plain, 16.38/16.61 ![X58, X59, X61, X62]: 16.38/16.61 ( initiates(X59, X58, X61) | ~ zip_tseitin_3(X62, X61, X58, X59)), 16.38/16.61 inference('cnf', [status(esa)], [zf_stmt_8])). 16.38/16.61 tff('129', plain, 16.38/16.61 ( stoppedIn(n0, filling, n1) | initiates(overflow, waterLevel(n1), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['127', '128'])). 16.38/16.61 tff('130', plain, happens(tapOn, n0), 16.38/16.61 inference('sup-', [status(thm)], ['47', '48'])). 16.38/16.61 tff(releases_all_defn, axiom, 16.38/16.61 (![Event,Fluent,Time]: 16.38/16.61 (releases(Event,Fluent,Time) <=> 16.38/16.61 (?[Height]: ((Fluent = waterLevel(Height)) & (Event = tapOn)))))). 16.38/16.61 tff('131', plain, 16.38/16.61 ![X73, X74, X76, X77]: 16.38/16.61 ( releases(X73, X74, X76) | X74 != waterLevel(X77) | X73 != tapOn), 16.38/16.61 inference('cnf', [status(esa)], [releases_all_defn])). 16.38/16.61 tff('132', plain, ![X76, X77]: releases(tapOn, waterLevel(X77), X76), 16.38/16.61 inference('simplify', [status(thm)], ['131'])). 16.38/16.61 tff(happens_releases, axiom, 16.38/16.61 (![Event,Time,Fluent]: 16.38/16.61 ((releases(Event,Fluent,Time) & happens(Event,Time)) => 16.38/16.61 releasedAt(Fluent,plus(Time,n1))))). 16.38/16.61 tff('133', plain, 16.38/16.61 ![X22, X23, X24]: 16.38/16.61 (~ happens(X22, X23) 16.38/16.61 | ~ releases(X22, X24, X23) 16.38/16.61 | releasedAt(X24, plus(X23, n1))), 16.38/16.61 inference('cnf', [status(esa)], [happens_releases])). 16.38/16.61 tff('134', plain, 16.38/16.61 ![X0, X1]: 16.38/16.61 ( releasedAt(waterLevel(X1), plus(X0, n1)) | ~ happens(tapOn, X0)), 16.38/16.61 inference('sup-', [status(thm)], ['132', '133'])). 16.38/16.61 tff('135', plain, ![X0]: releasedAt(waterLevel(X0), plus(n0, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['130', '134'])). 16.38/16.61 tff('136', plain, plus(n0, n1) = n1, 16.38/16.61 inference('cnf', [status(esa)], [plus0_1])). 16.38/16.61 tff('137', plain, ![X0]: releasedAt(waterLevel(X0), n1), 16.38/16.61 inference('demod', [status(thm)], ['135', '136'])). 16.38/16.61 tff(keep_released, axiom, 16.38/16.61 (![Fluent,Time]: 16.38/16.61 ((releasedAt(Fluent,Time) & 16.38/16.61 (~ 16.38/16.61 (?[Event]: 16.38/16.61 ((initiates(Event,Fluent,Time) | terminates(Event,Fluent,Time)) & 16.38/16.61 happens(Event,Time))))) => 16.38/16.61 releasedAt(Fluent,plus(Time,n1))))). 16.38/16.61 tff('138', plain, 16.38/16.61 ![X38, X39]: 16.38/16.61 ( releasedAt(X38, plus(X39, n1)) 16.38/16.61 | terminates(sk_Event_4(X39, X38), X38, X39) 16.38/16.61 | initiates(sk_Event_4(X39, X38), X38, X39) 16.38/16.61 | ~ releasedAt(X38, X39)), 16.38/16.61 inference('cnf', [status(esa)], [keep_released])). 16.38/16.61 tff('139', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( initiates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | terminates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | releasedAt(waterLevel(X0), plus(n1, n1))), 16.38/16.61 inference('sup-', [status(thm)], ['137', '138'])). 16.38/16.61 tff(plus1_1, axiom, (plus(n1,n1) = n2)). 16.38/16.61 tff('140', plain, plus(n1, n1) = n2, 16.38/16.61 inference('cnf', [status(esa)], [plus1_1])). 16.38/16.61 tff('141', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( initiates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | terminates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | releasedAt(waterLevel(X0), n2)), 16.38/16.61 inference('demod', [status(thm)], ['139', '140'])). 16.38/16.61 tff('142', plain, 16.38/16.61 ![X64, X65, X66]: 16.38/16.61 (X64 = filling | filling = X64 | ~ terminates(X65, X64, X66)), 16.38/16.61 inference('cnf', [status(esa)], [terminates_all_defn])). 16.38/16.61 tff('143', plain, 16.38/16.61 ![X64, X65, X66]: (~ terminates(X65, X64, X66) | X64 = filling), 16.38/16.61 inference('simplify', [status(thm)], ['142'])). 16.38/16.61 tff('144', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( releasedAt(waterLevel(X0), n2) 16.38/16.61 | initiates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | waterLevel(X0) = filling), 16.38/16.61 inference('sup-', [status(thm)], ['141', '143'])). 16.38/16.61 tff(filling_not_waterLevel, axiom, (![X]: (filling != waterLevel(X)))). 16.38/16.61 tff('145', plain, ![X78]: filling != waterLevel(X78), 16.38/16.61 inference('cnf', [status(esa)], [filling_not_waterLevel])). 16.38/16.61 tff('146', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( initiates(sk_Event_4(n1, waterLevel(X0)), waterLevel(X0), n1) 16.38/16.61 | releasedAt(waterLevel(X0), n2)), 16.38/16.61 inference('clc', [status(thm)], ['144', '145'])). 16.38/16.61 tff(happens_holds, axiom, 16.38/16.61 (![Event,Time,Fluent]: 16.38/16.61 ((initiates(Event,Fluent,Time) & happens(Event,Time)) => 16.38/16.61 holdsAt(Fluent,plus(Time,n1))))). 16.38/16.61 tff('147', plain, 16.38/16.61 ![X8, X9, X10]: 16.38/16.61 (~ happens(X8, X9) 16.38/16.61 | ~ initiates(X8, X10, X9) 16.38/16.61 | holdsAt(X10, plus(X9, n1))), 16.38/16.61 inference('cnf', [status(esa)], [happens_holds])). 16.38/16.61 tff('148', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( releasedAt(waterLevel(X0), n2) 16.38/16.61 | holdsAt(waterLevel(X0), plus(n1, n1)) 16.38/16.61 | ~ happens(sk_Event_4(n1, waterLevel(X0)), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['146', '147'])). 16.38/16.61 tff('149', plain, plus(n1, n1) = n2, 16.38/16.61 inference('cnf', [status(esa)], [plus1_1])). 16.38/16.61 tff('150', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( releasedAt(waterLevel(X0), n2) 16.38/16.61 | holdsAt(waterLevel(X0), n2) 16.38/16.61 | ~ happens(sk_Event_4(n1, waterLevel(X0)), n1)), 16.38/16.61 inference('demod', [status(thm)], ['148', '149'])). 16.38/16.61 tff('151', plain, ![X0]: releasedAt(waterLevel(X0), n1), 16.38/16.61 inference('demod', [status(thm)], ['135', '136'])). 16.38/16.61 tff('152', plain, 16.38/16.61 ![X38, X39]: 16.38/16.61 ( releasedAt(X38, plus(X39, n1)) 16.38/16.61 | happens(sk_Event_4(X39, X38), X39) 16.38/16.61 | ~ releasedAt(X38, X39)), 16.38/16.61 inference('cnf', [status(esa)], [keep_released])). 16.38/16.61 tff('153', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( happens(sk_Event_4(n1, waterLevel(X0)), n1) 16.38/16.61 | releasedAt(waterLevel(X0), plus(n1, n1))), 16.38/16.61 inference('sup-', [status(thm)], ['151', '152'])). 16.38/16.61 tff('154', plain, plus(n1, n1) = n2, 16.38/16.61 inference('cnf', [status(esa)], [plus1_1])). 16.38/16.61 tff('155', plain, 16.38/16.61 ![X0]: 16.38/16.61 ( happens(sk_Event_4(n1, waterLevel(X0)), n1) 16.38/16.61 | releasedAt(waterLevel(X0), n2)), 16.38/16.61 inference('demod', [status(thm)], ['153', '154'])). 16.38/16.61 tff('156', plain, 16.38/16.61 ![X0]: ( holdsAt(waterLevel(X0), n2) | releasedAt(waterLevel(X0), n2)), 16.38/16.61 inference('clc', [status(thm)], ['150', '155'])). 16.38/16.61 tff('157', plain, ![X0]: (X0 = n3 | ~ holdsAt(waterLevel(X0), n2)), 16.38/16.61 inference('sup-', [status(thm)], ['51', '52'])). 16.38/16.61 tff('158', plain, ![X0]: ( releasedAt(waterLevel(X0), n2) | X0 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['156', '157'])). 16.38/16.61 tff('159', plain, plus(n1, n1) = n2, 16.38/16.61 inference('cnf', [status(esa)], [plus1_1])). 16.38/16.61 tff(happens_not_released, axiom, 16.38/16.61 (![Event,Time,Fluent]: 16.38/16.61 (((terminates(Event,Fluent,Time) | initiates(Event,Fluent,Time)) & 16.38/16.61 happens(Event,Time)) => 16.38/16.61 (~releasedAt(Fluent,plus(Time,n1)))))). 16.38/16.61 tff('160', plain, 16.38/16.61 ![X19, X20, X21]: 16.38/16.61 (~ happens(X19, X20) 16.38/16.61 | ~ initiates(X19, X21, X20) 16.38/16.61 | ~ releasedAt(X21, plus(X20, n1))), 16.38/16.61 inference('cnf', [status(esa)], [happens_not_released])). 16.38/16.61 tff('161', plain, 16.38/16.61 ![X0, X1]: 16.38/16.61 (~ releasedAt(X0, n2) | ~ initiates(X1, X0, n1) | ~ happens(X1, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['159', '160'])). 16.38/16.61 tff('162', plain, 16.38/16.61 ![X0, X1]: 16.38/16.61 (X0 = n3 | ~ happens(X1, n1) | ~ initiates(X1, waterLevel(X0), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['158', '161'])). 16.38/16.61 tff('163', plain, 16.38/16.61 ( stoppedIn(n0, filling, n1) | ~ happens(overflow, n1) | n1 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['129', '162'])). 16.38/16.61 tff('164', plain, (n2 = n3 | n1 = n3 | stoppedIn(n0, filling, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['111', '163'])). 16.38/16.61 tff('165', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( less(sk_Time_1(X30, X26, X25), X30) | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('166', plain, 16.38/16.61 (n1 = n3 | n2 = n3 | less(sk_Time_1(n1, filling, n0), n1)), 16.38/16.61 inference('sup-', [status(thm)], ['164', '165'])). 16.38/16.61 tff('167', plain, ![X94]: ( less_or_equal(X94, n0) | ~ less(X94, n1)), 16.38/16.61 inference('cnf', [status(esa)], [less1])). 16.38/16.61 tff('168', plain, 16.38/16.61 (n2 = n3 | n1 = n3 | less_or_equal(sk_Time_1(n1, filling, n0), n0)), 16.38/16.61 inference('sup-', [status(thm)], ['166', '167'])). 16.38/16.61 tff('169', plain, 16.38/16.61 ![X79, X80]: ( less(X79, X80) | X79 = X80 | ~ less_or_equal(X79, X80)), 16.38/16.61 inference('cnf', [status(esa)], [less_or_equal])). 16.38/16.61 tff('170', plain, 16.38/16.61 (n1 = n3 16.38/16.61 | n2 = n3 16.38/16.61 | sk_Time_1(n1, filling, n0) = n0 16.38/16.61 | less(sk_Time_1(n1, filling, n0), n0)), 16.38/16.61 inference('sup-', [status(thm)], ['168', '169'])). 16.38/16.61 tff('171', plain, ![X101]: ~ less(X101, n0), 16.38/16.61 inference('cnf', [status(esa)], [less0])). 16.38/16.61 tff('172', plain, (sk_Time_1(n1, filling, n0) = n0 | n2 = n3 | n1 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['170', '171'])). 16.38/16.61 tff('173', plain, (n2 = n3 | n1 = n3 | stoppedIn(n0, filling, n1)), 16.38/16.61 inference('sup-', [status(thm)], ['111', '163'])). 16.38/16.61 tff('174', plain, 16.38/16.61 ![X25, X26, X30]: 16.38/16.61 ( less(X25, sk_Time_1(X30, X26, X25)) | ~ stoppedIn(X25, X26, X30)), 16.38/16.61 inference('cnf', [status(esa)], [stoppedin_defn])). 16.38/16.61 tff('175', plain, 16.38/16.61 (n1 = n3 | n2 = n3 | less(n0, sk_Time_1(n1, filling, n0))), 16.38/16.61 inference('sup-', [status(thm)], ['173', '174'])). 16.38/16.61 tff('176', plain, ( less(n0, n0) | n1 = n3 | n2 = n3 | n2 = n3 | n1 = n3), 16.38/16.61 inference('sup+', [status(thm)], ['172', '175'])). 16.38/16.61 tff('177', plain, (n2 = n3 | n1 = n3 | less(n0, n0)), 16.38/16.61 inference('simplify', [status(thm)], ['176'])). 16.38/16.61 tff('178', plain, ![X102]: ~ less(X102, X102), 16.38/16.61 inference('simplify', [status(thm)], ['103'])). 16.38/16.61 tff('179', plain, (n1 = n3 | n2 = n3), 16.38/16.61 inference('clc', [status(thm)], ['177', '178'])). 16.38/16.61 tff('180', plain, less(n1, n2), 16.38/16.61 inference('sup-', [status(thm)], ['85', '86'])). 16.38/16.61 tff('181', plain, ![X102, X104]: (~ less(X104, X102) | ~ less(X102, X104)), 16.38/16.61 inference('cnf', [status(esa)], [less_property])). 16.38/16.61 tff('182', plain, ~ less(n2, n1), 16.38/16.61 inference('sup-', [status(thm)], ['180', '181'])). 16.38/16.61 tff('183', plain, (~ less(n2, n3) | n2 = n3), 16.38/16.61 inference('sup-', [status(thm)], ['179', '182'])). 16.38/16.61 tff('184', plain, ![X81]: less_or_equal(X81, X81), 16.38/16.61 inference('simplify', [status(thm)], ['0'])). 16.38/16.61 tff(less3, axiom, (![X]: (less_or_equal(X,n2) <=> less(X,n3)))). 16.38/16.61 tff('185', plain, ![X96]: ( less(X96, n3) | ~ less_or_equal(X96, n2)), 16.38/16.61 inference('cnf', [status(esa)], [less3])). 16.38/16.61 tff('186', plain, less(n2, n3), 16.38/16.61 inference('sup-', [status(thm)], ['184', '185'])). 16.38/16.61 tff('187', plain, n2 = n3, inference('demod', [status(thm)], ['183', '186'])). 16.38/16.61 tff('188', plain, n2 = n3, inference('demod', [status(thm)], ['183', '186'])). 16.38/16.61 tff('189', plain, plus(n2, n2) = n6, 16.38/16.61 inference('demod', [status(thm)], ['6', '187', '188'])). 16.38/16.61 tff(plus2_2, axiom, (plus(n2,n2) = n4)). 16.38/16.61 tff('190', plain, plus(n2, n2) = n4, 16.38/16.61 inference('cnf', [status(esa)], [plus2_2])). 16.38/16.61 tff('191', plain, n6 = n4, inference('sup+', [status(thm)], ['189', '190'])). 16.38/16.61 tff('192', plain, ![X81]: less_or_equal(X81, X81), 16.38/16.61 inference('simplify', [status(thm)], ['0'])). 16.38/16.61 tff(less6, axiom, (![X]: (less(X,n6) <=> less_or_equal(X,n5)))). 16.38/16.61 tff('193', plain, ![X83]: ( less(X83, n6) | ~ less_or_equal(X83, n5)), 16.38/16.61 inference('cnf', [status(esa)], [less6])). 16.38/16.61 tff('194', plain, less(n5, n6), 16.38/16.61 inference('sup-', [status(thm)], ['192', '193'])). 16.38/16.61 tff('195', plain, $false, 16.38/16.61 inference('demod', [status(thm)], ['5', '191', '194'])). 16.38/16.61 16.38/16.61 % SZS output end Refutation 16.38/16.61 16.38/16.62 % Zipperpin 1.5 exiting 16.38/16.62 EOF