0.11/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.2igLxcM7d5 0.13/0.33 % Computer : n005.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 960 0.13/0.33 % DateTime : Thu Jul 2 07:32:36 EDT 2020 0.13/0.33 % CPUTime : 0.13/0.33 % Running portfolio for 120 s 0.13/0.33 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % Running in FO mode 6.29/3.49 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 6.29/3.49 % Solved by: fo/fo7.sh 6.29/3.49 To remain in the chosen logic fragment, unification with booleans has been disabled. 6.29/3.49 % done 2654 iterations in 3.041s 6.29/3.49 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 6.29/3.49 % SZS output start Refutation 6.29/3.49 tff(goals, conjecture, 6.29/3.49 (![X0]: 6.29/3.49 (composition(complement(composition(X0,top)),top) = 6.29/3.49 complement(composition(X0,top))))). 6.29/3.49 tff(zf_stmt_0, negated_conjecture, 6.29/3.49 (~ 6.29/3.49 (![X0]: 6.29/3.49 (composition(complement(composition(X0,top)),top) = 6.29/3.49 complement(composition(X0,top)))))). 6.29/3.49 tff('0', plain, 6.29/3.49 composition(complement(composition(sk_X0, top)), top) 6.29/3.49 != complement(composition(sk_X0, top)), 6.29/3.49 inference('cnf', [status(esa)], [zf_stmt_0])). 6.29/3.49 tff(def_top, axiom, (![X0]: (join(X0,complement(X0)) = top))). 6.29/3.49 tff('1', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff(composition_identity, axiom, (![X0]: (X0 = composition(X0,one)))). 6.29/3.49 tff('2', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff(converse_idempotence, axiom, (![X0]: (X0 = converse(converse(X0))))). 6.29/3.49 tff('3', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff(converse_multiplicativity, axiom, 6.29/3.49 (![X0,X1]: 6.29/3.49 (converse(composition(X0,X1)) = composition(converse(X1),converse(X0))))). 6.29/3.49 tff('4', plain, 6.29/3.49 ![X2, X3]: 6.29/3.49 converse(composition(X3, X2)) = composition(converse(X2), converse(X3)), 6.29/3.49 inference('cnf', [status(esa)], [converse_multiplicativity])). 6.29/3.49 tff('5', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(converse(X0), X1)) = composition(converse(X1), X0), 6.29/3.49 inference('sup+', [status(thm)], ['3', '4'])). 6.29/3.49 tff('6', plain, 6.29/3.49 ![X0]: converse(converse(X0)) = composition(converse(one), X0), 6.29/3.49 inference('sup+', [status(thm)], ['2', '5'])). 6.29/3.49 tff('7', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('8', plain, ![X0]: X0 = composition(converse(one), X0), 6.29/3.49 inference('demod', [status(thm)], ['6', '7'])). 6.29/3.49 tff('9', plain, ![X0]: X0 = composition(converse(one), X0), 6.29/3.49 inference('demod', [status(thm)], ['6', '7'])). 6.29/3.49 tff('10', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff('11', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('12', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff(converse_cancellativity, axiom, 6.29/3.49 (![X0,X1]: 6.29/3.49 (complement(X1) = 6.29/3.49 join(composition(converse(X0),complement(composition(X0,X1))), 6.29/3.49 complement(X1))))). 6.29/3.49 tff('13', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(composition(converse(X0), complement(composition(X0, X1))), 6.29/3.49 complement(X1)), 6.29/3.49 inference('cnf', [status(esa)], [converse_cancellativity])). 6.29/3.49 tff(maddux1_join_commutativity, axiom, 6.29/3.49 (![X0,X1]: (join(X0,X1) = join(X1,X0)))). 6.29/3.49 tff('14', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('15', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('16', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(X0) 6.29/3.49 = join(complement(X0), composition(converse(one), complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['12', '15'])). 6.29/3.49 tff('17', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('18', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff('19', plain, 6.29/3.49 ![X0]: complement(X0) = join(complement(X0), complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['16', '17', '18'])). 6.29/3.49 tff(maddux3_a_kind_of_de_Morgan, axiom, 6.29/3.49 (![X0,X1]: 6.29/3.49 (join(complement(join(complement(X0),complement(X1))), 6.29/3.49 complement(join(complement(X0),X1))) = 6.29/3.49 X0))). 6.29/3.49 tff('20', plain, 6.29/3.49 ![X4, X5]: 6.29/3.49 join(complement(join(complement(X4), complement(X5))), 6.29/3.49 complement(join(complement(X4), X5))) 6.29/3.49 = X4, 6.29/3.49 inference('cnf', [status(esa)], [maddux3_a_kind_of_de_Morgan])). 6.29/3.49 tff(maddux4_definiton_of_meet, axiom, 6.29/3.49 (![X0,X1]: (complement(join(complement(X0),complement(X1))) = meet(X0,X1)))). 6.29/3.49 tff('21', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('22', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('23', plain, 6.29/3.49 ![X0]: join(meet(X0, complement(X0)), complement(complement(X0))) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['19', '22'])). 6.29/3.49 tff(def_zero, axiom, (![X0]: (zero = meet(X0,complement(X0))))). 6.29/3.49 tff('24', plain, ![X22]: zero = meet(X22, complement(X22)), 6.29/3.49 inference('cnf', [status(esa)], [def_zero])). 6.29/3.49 tff('25', plain, ![X0]: join(zero, complement(complement(X0))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['23', '24'])). 6.29/3.49 tff('26', plain, ![X0]: join(zero, complement(complement(X0))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['23', '24'])). 6.29/3.49 tff('27', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('28', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('29', plain, ![X0]: complement(top) = meet(X0, complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['27', '28'])). 6.29/3.49 tff('30', plain, ![X22]: zero = meet(X22, complement(X22)), 6.29/3.49 inference('cnf', [status(esa)], [def_zero])). 6.29/3.49 tff('31', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('32', plain, 6.29/3.49 ![X0]: complement(X0) = join(complement(X0), complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['16', '17', '18'])). 6.29/3.49 tff('33', plain, complement(top) = join(zero, complement(top)), 6.29/3.49 inference('sup+', [status(thm)], ['31', '32'])). 6.29/3.49 tff('34', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('35', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('36', plain, zero = join(zero, zero), 6.29/3.49 inference('demod', [status(thm)], ['33', '34', '35'])). 6.29/3.49 tff(maddux2_join_associativity, axiom, 6.29/3.49 (![X0,X1,X2]: (join(X0,join(X1,X2)) = join(join(X0,X1),X2)))). 6.29/3.49 tff('37', plain, 6.29/3.49 ![X18, X19, X20]: join(X18, join(X19, X20)) = join(join(X18, X19), X20), 6.29/3.49 inference('cnf', [status(esa)], [maddux2_join_associativity])). 6.29/3.49 tff('38', plain, ![X0]: join(zero, join(zero, X0)) = join(zero, X0), 6.29/3.49 inference('sup+', [status(thm)], ['36', '37'])). 6.29/3.49 tff('39', plain, 6.29/3.49 ![X0]: join(zero, X0) = join(zero, complement(complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['26', '38'])). 6.29/3.49 tff('40', plain, ![X0]: join(zero, complement(complement(X0))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['23', '24'])). 6.29/3.49 tff('41', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('42', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('43', plain, 6.29/3.49 ![X0]: complement(X0) = join(complement(X0), complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['16', '17', '18'])). 6.29/3.49 tff('44', plain, 6.29/3.49 ![X0]: complement(complement(X0)) = join(complement(complement(X0)), X0), 6.29/3.49 inference('sup+', [status(thm)], ['42', '43'])). 6.29/3.49 tff('45', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('46', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('47', plain, ![X0]: X0 = join(X0, X0), 6.29/3.49 inference('demod', [status(thm)], ['44', '45', '46'])). 6.29/3.49 tff('48', plain, 6.29/3.49 ![X18, X19, X20]: join(X18, join(X19, X20)) = join(join(X18, X19), X20), 6.29/3.49 inference('cnf', [status(esa)], [maddux2_join_associativity])). 6.29/3.49 tff('49', plain, ![X0, X1]: join(X0, join(X0, X1)) = join(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['47', '48'])). 6.29/3.49 tff('50', plain, ![X0]: join(X0, top) = join(X0, complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['1', '49'])). 6.29/3.49 tff('51', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('52', plain, ![X0]: join(X0, top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['50', '51'])). 6.29/3.49 tff('53', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff(converse_additivity, axiom, 6.29/3.49 (![X0,X1]: (converse(join(X0,X1)) = join(converse(X0),converse(X1))))). 6.29/3.49 tff('54', plain, 6.29/3.49 ![X23, X24]: 6.29/3.49 converse(join(X23, X24)) = join(converse(X23), converse(X24)), 6.29/3.49 inference('cnf', [status(esa)], [converse_additivity])). 6.29/3.49 tff('55', plain, 6.29/3.49 ![X0, X1]: converse(join(converse(X0), X1)) = join(X0, converse(X1)), 6.29/3.49 inference('sup+', [status(thm)], ['53', '54'])). 6.29/3.49 tff('56', plain, ![X0]: converse(top) = join(X0, converse(top)), 6.29/3.49 inference('sup+', [status(thm)], ['52', '55'])). 6.29/3.49 tff('57', plain, ![X0]: join(X0, top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['50', '51'])). 6.29/3.49 tff('58', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('59', plain, ![X0]: join(top, X0) = top, 6.29/3.49 inference('sup+', [status(thm)], ['57', '58'])). 6.29/3.49 tff('60', plain, converse(top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['56', '59'])). 6.29/3.49 tff('61', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('62', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('63', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(top) 6.29/3.49 = join(zero, 6.29/3.49 composition(converse(X0), complement(composition(X0, top)))), 6.29/3.49 inference('sup+', [status(thm)], ['61', '62'])). 6.29/3.49 tff('64', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('65', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = join(zero, 6.29/3.49 composition(converse(X0), complement(composition(X0, top)))), 6.29/3.49 inference('demod', [status(thm)], ['63', '64'])). 6.29/3.49 tff('66', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('67', plain, 6.29/3.49 ![X0]: zero = composition(converse(X0), complement(composition(X0, top))), 6.29/3.49 inference('demod', [status(thm)], ['65', '66'])). 6.29/3.49 tff('68', plain, zero = composition(top, complement(composition(top, top))), 6.29/3.49 inference('sup+', [status(thm)], ['60', '67'])). 6.29/3.49 tff(composition_distributivity, axiom, 6.29/3.49 (![X0,X1,X2]: 6.29/3.49 (composition(join(X0,X1),X2) = 6.29/3.49 join(composition(X0,X2),composition(X1,X2))))). 6.29/3.49 tff('69', plain, 6.29/3.49 ![X7, X8, X9]: 6.29/3.49 composition(join(X7, X9), X8) 6.29/3.49 = join(composition(X7, X8), composition(X9, X8)), 6.29/3.49 inference('cnf', [status(esa)], [composition_distributivity])). 6.29/3.49 tff('70', plain, 6.29/3.49 ![X0]: 6.29/3.49 composition(join(top, X0), complement(composition(top, top))) 6.29/3.49 = join(zero, composition(X0, complement(composition(top, top)))), 6.29/3.49 inference('sup+', [status(thm)], ['68', '69'])). 6.29/3.49 tff('71', plain, ![X0]: join(top, X0) = top, 6.29/3.49 inference('sup+', [status(thm)], ['57', '58'])). 6.29/3.49 tff('72', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('73', plain, 6.29/3.49 ![X0]: 6.29/3.49 composition(top, complement(composition(top, top))) 6.29/3.49 = composition(X0, complement(composition(top, top))), 6.29/3.49 inference('demod', [status(thm)], ['70', '71', '72'])). 6.29/3.49 tff('74', plain, zero = composition(top, complement(composition(top, top))), 6.29/3.49 inference('sup+', [status(thm)], ['60', '67'])). 6.29/3.49 tff('75', plain, 6.29/3.49 ![X0]: zero = composition(X0, complement(composition(top, top))), 6.29/3.49 inference('demod', [status(thm)], ['73', '74'])). 6.29/3.49 tff('76', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff('77', plain, complement(composition(top, top)) = zero, 6.29/3.49 inference('sup+', [status(thm)], ['75', '76'])). 6.29/3.49 tff('78', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('79', plain, join(composition(top, top), zero) = top, 6.29/3.49 inference('sup+', [status(thm)], ['77', '78'])). 6.29/3.49 tff('80', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('81', plain, ![X0]: join(zero, join(zero, X0)) = join(zero, X0), 6.29/3.49 inference('sup+', [status(thm)], ['36', '37'])). 6.29/3.49 tff('82', plain, ![X0]: join(zero, join(X0, zero)) = join(zero, X0), 6.29/3.49 inference('sup+', [status(thm)], ['80', '81'])). 6.29/3.49 tff('83', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('84', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('85', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('86', plain, composition(top, top) = top, 6.29/3.49 inference('demod', [status(thm)], ['79', '85'])). 6.29/3.49 tff(composition_associativity, axiom, 6.29/3.49 (![X0,X1,X2]: 6.29/3.49 (composition(composition(X0,X1),X2) = composition(X0,composition(X1,X2))))). 6.29/3.49 tff('87', plain, 6.29/3.49 ![X15, X16, X17]: 6.29/3.49 composition(composition(X15, X16), X17) 6.29/3.49 = composition(X15, composition(X16, X17)), 6.29/3.49 inference('cnf', [status(esa)], [composition_associativity])). 6.29/3.49 tff('88', plain, 6.29/3.49 ![X0]: composition(top, X0) = composition(top, composition(top, X0)), 6.29/3.49 inference('sup+', [status(thm)], ['86', '87'])). 6.29/3.49 tff('89', plain, converse(top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['56', '59'])). 6.29/3.49 tff('90', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('91', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(X0) 6.29/3.49 = join(complement(X0), 6.29/3.49 composition(top, complement(composition(top, X0)))), 6.29/3.49 inference('sup+', [status(thm)], ['89', '90'])). 6.29/3.49 tff('92', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('93', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('94', plain, 6.29/3.49 ![X18, X19, X20]: join(X18, join(X19, X20)) = join(join(X18, X19), X20), 6.29/3.49 inference('cnf', [status(esa)], [maddux2_join_associativity])). 6.29/3.49 tff('95', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('96', plain, 6.29/3.49 ![X0, X1, X2]: join(X0, join(X2, X1)) = join(X2, join(X1, X0)), 6.29/3.49 inference('sup+', [status(thm)], ['94', '95'])). 6.29/3.49 tff('97', plain, 6.29/3.49 ![X0, X1]: join(X0, top) = join(X1, join(complement(X1), X0)), 6.29/3.49 inference('sup+', [status(thm)], ['93', '96'])). 6.29/3.49 tff('98', plain, ![X0]: join(X0, top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['50', '51'])). 6.29/3.49 tff('99', plain, ![X0, X1]: top = join(X1, join(complement(X1), X0)), 6.29/3.49 inference('demod', [status(thm)], ['97', '98'])). 6.29/3.49 tff('100', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('101', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 join(meet(X0, join(complement(complement(X0)), X1)), complement(top)) 6.29/3.49 = X0, 6.29/3.49 inference('sup+', [status(thm)], ['99', '100'])). 6.29/3.49 tff('102', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('103', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('104', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('105', plain, ![X0, X1]: meet(X0, join(X0, X1)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['101', '102', '103', '104'])). 6.29/3.49 tff('106', plain, ![X0, X1]: meet(X0, join(X1, X0)) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['92', '105'])). 6.29/3.49 tff('107', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('108', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('109', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(complement(X1), complement(X0))) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['107', '108'])). 6.29/3.49 tff('110', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('111', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('112', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('113', plain, 6.29/3.49 ![X18, X19, X20]: join(X18, join(X19, X20)) = join(join(X18, X19), X20), 6.29/3.49 inference('cnf', [status(esa)], [maddux2_join_associativity])). 6.29/3.49 tff('114', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 join(meet(X0, X2), join(complement(join(complement(X0), X2)), X1)) 6.29/3.49 = join(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['112', '113'])). 6.29/3.49 tff('115', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('116', plain, ![X0, X1]: top = join(X1, join(complement(X1), X0)), 6.29/3.49 inference('demod', [status(thm)], ['97', '98'])). 6.29/3.49 tff('117', plain, ![X0, X1]: top = join(X0, join(X1, complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['115', '116'])). 6.29/3.49 tff('118', plain, ![X0, X1]: top = join(X1, complement(meet(X1, X0))), 6.29/3.49 inference('sup+', [status(thm)], ['114', '117'])). 6.29/3.49 tff('119', plain, ![X0, X1]: top = join(X0, complement(meet(X1, X0))), 6.29/3.49 inference('sup+', [status(thm)], ['111', '118'])). 6.29/3.49 tff('120', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('121', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(complement(X1), complement(X0))) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['107', '108'])). 6.29/3.49 tff('122', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(X0, complement(X1))) = meet(X1, complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['120', '121'])). 6.29/3.49 tff('123', plain, 6.29/3.49 ![X0, X1]: complement(top) = meet(meet(X1, X0), complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['119', '122'])). 6.29/3.49 tff('124', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('125', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('126', plain, ![X0, X1]: zero = meet(complement(X0), meet(X1, X0)), 6.29/3.49 inference('demod', [status(thm)], ['123', '124', '125'])). 6.29/3.49 tff('127', plain, ![X0, X1]: zero = meet(complement(join(X1, X0)), X0), 6.29/3.49 inference('sup+', [status(thm)], ['106', '126'])). 6.29/3.49 tff('128', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('129', plain, ![X0, X1]: zero = meet(X0, complement(join(X1, X0))), 6.29/3.49 inference('demod', [status(thm)], ['127', '128'])). 6.29/3.49 tff('130', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = meet(composition(top, complement(composition(top, X0))), 6.29/3.49 complement(complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['91', '129'])). 6.29/3.49 tff('131', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('132', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('133', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero = meet(X0, composition(top, complement(composition(top, X0)))), 6.29/3.49 inference('demod', [status(thm)], ['130', '131', '132'])). 6.29/3.49 tff('134', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff(modular_law_2, axiom, 6.29/3.49 (![X0,X1,X2]: 6.29/3.49 (join(meet(composition(X0,X1),X2), 6.29/3.49 meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)) = 6.29/3.49 meet(composition(meet(X0,composition(X2,converse(X1))),X1),X2)))). 6.29/3.49 tff('135', plain, 6.29/3.49 ![X25, X26, X27]: 6.29/3.49 join(meet(composition(X25, X27), X26), 6.29/3.49 meet(composition(meet(X25, composition(X26, converse(X27))), X27), 6.29/3.49 X26)) 6.29/3.49 = meet(composition(meet(X25, composition(X26, converse(X27))), X27), 6.29/3.49 X26), 6.29/3.49 inference('cnf', [status(esa)], [modular_law_2])). 6.29/3.49 tff('136', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 join(meet(composition(X2, converse(X0)), X1), 6.29/3.49 meet(composition(meet(X2, composition(X1, X0)), converse(X0)), X1)) 6.29/3.49 = meet( 6.29/3.49 composition(meet(X2, composition(X1, converse(converse(X0)))), 6.29/3.49 converse(X0)), X1), 6.29/3.49 inference('sup+', [status(thm)], ['134', '135'])). 6.29/3.49 tff('137', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('138', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 join(meet(composition(X2, converse(X0)), X1), 6.29/3.49 meet(composition(meet(X2, composition(X1, X0)), converse(X0)), X1)) 6.29/3.49 = meet(composition(meet(X2, composition(X1, X0)), converse(X0)), X1), 6.29/3.49 inference('demod', [status(thm)], ['136', '137'])). 6.29/3.49 tff('139', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('140', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('141', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 join(meet(composition(X2, converse(X0)), X1), 6.29/3.49 meet(X1, composition(meet(X2, composition(X1, X0)), converse(X0)))) 6.29/3.49 = meet(X1, composition(meet(X2, composition(X1, X0)), converse(X0))), 6.29/3.49 inference('demod', [status(thm)], ['138', '139', '140'])). 6.29/3.49 tff('142', plain, 6.29/3.49 ![X0]: 6.29/3.49 join( 6.29/3.49 meet(composition(X0, converse(complement(composition(top, X0)))), 6.29/3.49 top), 6.29/3.49 meet(top, 6.29/3.49 composition(zero, converse(complement(composition(top, X0)))))) 6.29/3.49 = meet(top, 6.29/3.49 composition( 6.29/3.49 meet(X0, composition(top, complement(composition(top, X0)))), 6.29/3.49 converse(complement(composition(top, X0))))), 6.29/3.49 inference('sup+', [status(thm)], ['133', '141'])). 6.29/3.49 tff('143', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('144', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('145', plain, 6.29/3.49 ![X0]: complement(join(zero, complement(X0))) = meet(top, X0), 6.29/3.49 inference('sup+', [status(thm)], ['143', '144'])). 6.29/3.49 tff('146', plain, 6.29/3.49 ![X0]: complement(X0) = join(complement(X0), complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['16', '17', '18'])). 6.29/3.49 tff('147', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('148', plain, ![X0]: complement(complement(X0)) = meet(X0, X0), 6.29/3.49 inference('sup+', [status(thm)], ['146', '147'])). 6.29/3.49 tff('149', plain, 6.29/3.49 ![X0]: complement(join(zero, complement(X0))) = meet(top, X0), 6.29/3.49 inference('sup+', [status(thm)], ['143', '144'])). 6.29/3.49 tff('150', plain, 6.29/3.49 ![X0]: complement(join(zero, meet(X0, X0))) = meet(top, complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['148', '149'])). 6.29/3.49 tff('151', plain, ![X22]: zero = meet(X22, complement(X22)), 6.29/3.49 inference('cnf', [status(esa)], [def_zero])). 6.29/3.49 tff('152', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('153', plain, 6.29/3.49 ![X0]: join(zero, complement(join(complement(X0), complement(X0)))) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['151', '152'])). 6.29/3.49 tff('154', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('155', plain, ![X0]: join(zero, meet(X0, X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['153', '154'])). 6.29/3.49 tff('156', plain, ![X0]: complement(X0) = meet(top, complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['150', '155'])). 6.29/3.49 tff('157', plain, 6.29/3.49 ![X0]: complement(join(zero, complement(X0))) = meet(top, meet(top, X0)), 6.29/3.49 inference('sup+', [status(thm)], ['145', '156'])). 6.29/3.49 tff('158', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('159', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('160', plain, 6.29/3.49 ![X0]: complement(join(complement(X0), zero)) = meet(X0, top), 6.29/3.49 inference('sup+', [status(thm)], ['158', '159'])). 6.29/3.49 tff('161', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('162', plain, 6.29/3.49 ![X0]: complement(join(zero, complement(X0))) = meet(X0, top), 6.29/3.49 inference('demod', [status(thm)], ['160', '161'])). 6.29/3.49 tff('163', plain, ![X0]: meet(X0, top) = meet(top, meet(top, X0)), 6.29/3.49 inference('demod', [status(thm)], ['157', '162'])). 6.29/3.49 tff('164', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('165', plain, ![X0]: complement(X0) = meet(top, complement(X0)), 6.29/3.49 inference('demod', [status(thm)], ['150', '155'])). 6.29/3.49 tff('166', plain, ![X0]: complement(complement(X0)) = meet(top, X0), 6.29/3.49 inference('sup+', [status(thm)], ['164', '165'])). 6.29/3.49 tff('167', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('168', plain, ![X0]: X0 = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['166', '167'])). 6.29/3.49 tff('169', plain, ![X0]: meet(X0, top) = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['163', '168'])). 6.29/3.49 tff('170', plain, ![X0]: X0 = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['166', '167'])). 6.29/3.49 tff('171', plain, ![X0]: meet(X0, top) = X0, 6.29/3.49 inference('demod', [status(thm)], ['169', '170'])). 6.29/3.49 tff('172', plain, 6.29/3.49 ![X15, X16, X17]: 6.29/3.49 composition(composition(X15, X16), X17) 6.29/3.49 = composition(X15, composition(X16, X17)), 6.29/3.49 inference('cnf', [status(esa)], [composition_associativity])). 6.29/3.49 tff('173', plain, 6.29/3.49 ![X0]: zero = composition(X0, complement(composition(top, top))), 6.29/3.49 inference('demod', [status(thm)], ['73', '74'])). 6.29/3.49 tff('174', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 zero 6.29/3.49 = composition(X1, composition(X0, complement(composition(top, top)))), 6.29/3.49 inference('sup+', [status(thm)], ['172', '173'])). 6.29/3.49 tff('175', plain, 6.29/3.49 ![X0]: zero = composition(X0, complement(composition(top, top))), 6.29/3.49 inference('demod', [status(thm)], ['73', '74'])). 6.29/3.49 tff('176', plain, ![X1]: zero = composition(X1, zero), 6.29/3.49 inference('demod', [status(thm)], ['174', '175'])). 6.29/3.49 tff('177', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(converse(X0), X1)) = composition(converse(X1), X0), 6.29/3.49 inference('sup+', [status(thm)], ['3', '4'])). 6.29/3.49 tff('178', plain, ![X0]: converse(zero) = composition(converse(zero), X0), 6.29/3.49 inference('sup+', [status(thm)], ['176', '177'])). 6.29/3.49 tff('179', plain, 6.29/3.49 ![X0]: zero = composition(X0, complement(composition(top, top))), 6.29/3.49 inference('demod', [status(thm)], ['73', '74'])). 6.29/3.49 tff('180', plain, 6.29/3.49 ![X0]: zero = composition(converse(X0), complement(composition(X0, top))), 6.29/3.49 inference('demod', [status(thm)], ['65', '66'])). 6.29/3.49 tff('181', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(converse(X0), X1)) = composition(converse(X1), X0), 6.29/3.49 inference('sup+', [status(thm)], ['3', '4'])). 6.29/3.49 tff('182', plain, 6.29/3.49 ![X0]: 6.29/3.49 converse(zero) 6.29/3.49 = composition(converse(complement(composition(X0, top))), X0), 6.29/3.49 inference('sup+', [status(thm)], ['180', '181'])). 6.29/3.49 tff('183', plain, converse(zero) = zero, 6.29/3.49 inference('sup+', [status(thm)], ['179', '182'])). 6.29/3.49 tff('184', plain, converse(zero) = zero, 6.29/3.49 inference('sup+', [status(thm)], ['179', '182'])). 6.29/3.49 tff('185', plain, ![X0]: zero = composition(zero, X0), 6.29/3.49 inference('demod', [status(thm)], ['178', '183', '184'])). 6.29/3.49 tff('186', plain, ![X0]: X0 = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['166', '167'])). 6.29/3.49 tff('187', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('188', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero = meet(X0, composition(top, complement(composition(top, X0)))), 6.29/3.49 inference('demod', [status(thm)], ['130', '131', '132'])). 6.29/3.49 tff('189', plain, ![X0]: zero = composition(zero, X0), 6.29/3.49 inference('demod', [status(thm)], ['178', '183', '184'])). 6.29/3.49 tff('190', plain, ![X0]: X0 = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['166', '167'])). 6.29/3.49 tff('191', plain, 6.29/3.49 ![X0]: composition(X0, converse(complement(composition(top, X0)))) = zero, 6.29/3.49 inference('demod', [status(thm)], 6.29/3.49 ['142', '171', '185', '186', '187', '188', '189', '190'])). 6.29/3.49 tff('192', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('193', plain, 6.29/3.49 ![X2, X3]: 6.29/3.49 converse(composition(X3, X2)) = composition(converse(X2), converse(X3)), 6.29/3.49 inference('cnf', [status(esa)], [converse_multiplicativity])). 6.29/3.49 tff('194', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(X1, converse(X0))) = composition(X0, converse(X1)), 6.29/3.49 inference('sup+', [status(thm)], ['192', '193'])). 6.29/3.49 tff('195', plain, 6.29/3.49 ![X0]: 6.29/3.49 converse(zero) 6.29/3.49 = composition(complement(composition(top, X0)), converse(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['191', '194'])). 6.29/3.49 tff('196', plain, converse(zero) = zero, 6.29/3.49 inference('sup+', [status(thm)], ['179', '182'])). 6.29/3.49 tff('197', plain, 6.29/3.49 ![X0]: zero = composition(complement(composition(top, X0)), converse(X0)), 6.29/3.49 inference('demod', [status(thm)], ['195', '196'])). 6.29/3.49 tff('198', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = composition(complement(composition(top, X0)), 6.29/3.49 converse(composition(top, X0))), 6.29/3.49 inference('sup+', [status(thm)], ['88', '197'])). 6.29/3.49 tff('199', plain, converse(top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['56', '59'])). 6.29/3.49 tff('200', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(converse(X0), X1)) = composition(converse(X1), X0), 6.29/3.49 inference('sup+', [status(thm)], ['3', '4'])). 6.29/3.49 tff('201', plain, 6.29/3.49 ![X0]: converse(composition(top, X0)) = composition(converse(X0), top), 6.29/3.49 inference('sup+', [status(thm)], ['199', '200'])). 6.29/3.49 tff('202', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = composition(complement(composition(top, X0)), 6.29/3.49 composition(converse(X0), top)), 6.29/3.49 inference('demod', [status(thm)], ['198', '201'])). 6.29/3.49 tff('203', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 converse(composition(X1, converse(X0))) = composition(X0, converse(X1)), 6.29/3.49 inference('sup+', [status(thm)], ['192', '193'])). 6.29/3.49 tff('204', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('205', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 complement(X2) 6.29/3.49 = join(complement(X2), 6.29/3.49 composition(composition(X1, converse(X0)), 6.29/3.49 complement(composition(composition(X0, converse(X1)), X2)))), 6.29/3.49 inference('sup+', [status(thm)], ['203', '204'])). 6.29/3.49 tff('206', plain, 6.29/3.49 ![X15, X16, X17]: 6.29/3.49 composition(composition(X15, X16), X17) 6.29/3.49 = composition(X15, composition(X16, X17)), 6.29/3.49 inference('cnf', [status(esa)], [composition_associativity])). 6.29/3.49 tff('207', plain, 6.29/3.49 ![X15, X16, X17]: 6.29/3.49 composition(composition(X15, X16), X17) 6.29/3.49 = composition(X15, composition(X16, X17)), 6.29/3.49 inference('cnf', [status(esa)], [composition_associativity])). 6.29/3.49 tff('208', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 complement(X2) 6.29/3.49 = join(complement(X2), 6.29/3.49 composition(X1, 6.29/3.49 composition(converse(X0), 6.29/3.49 complement(composition(X0, composition(converse(X1), X2)))))), 6.29/3.49 inference('demod', [status(thm)], ['205', '206', '207'])). 6.29/3.49 tff('209', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(top) 6.29/3.49 = join(complement(top), 6.29/3.49 composition(X0, 6.29/3.49 composition(converse(complement(composition(top, X0))), 6.29/3.49 complement(zero)))), 6.29/3.49 inference('sup+', [status(thm)], ['202', '208'])). 6.29/3.49 tff('210', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('211', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('212', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('213', plain, 6.29/3.49 ![X0, X1]: converse(join(converse(X0), X1)) = join(X0, converse(X1)), 6.29/3.49 inference('sup+', [status(thm)], ['53', '54'])). 6.29/3.49 tff('214', plain, 6.29/3.49 ![X0]: converse(top) = join(X0, converse(complement(converse(X0)))), 6.29/3.49 inference('sup+', [status(thm)], ['212', '213'])). 6.29/3.49 tff('215', plain, converse(top) = top, 6.29/3.49 inference('sup+', [status(thm)], ['56', '59'])). 6.29/3.49 tff('216', plain, ![X0]: top = join(X0, converse(complement(converse(X0)))), 6.29/3.49 inference('demod', [status(thm)], ['214', '215'])). 6.29/3.49 tff('217', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('218', plain, 6.29/3.49 ![X0]: 6.29/3.49 join(meet(X0, converse(complement(converse(complement(X0))))), 6.29/3.49 complement(top)) 6.29/3.49 = X0, 6.29/3.49 inference('sup+', [status(thm)], ['216', '217'])). 6.29/3.49 tff('219', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('220', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('221', plain, 6.29/3.49 ![X0]: meet(X0, converse(complement(converse(complement(X0))))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['218', '219', '220'])). 6.29/3.49 tff('222', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(complement(X1), complement(X0))) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['107', '108'])). 6.29/3.49 tff('223', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('224', plain, 6.29/3.49 ![X0, X1]: join(meet(X0, complement(X1)), meet(X1, X0)) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['222', '223'])). 6.29/3.49 tff('225', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('226', plain, 6.29/3.49 ![X0, X1]: join(meet(X1, X0), meet(X0, complement(X1))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['224', '225'])). 6.29/3.49 tff('227', plain, 6.29/3.49 ![X0]: 6.29/3.49 join(X0, 6.29/3.49 meet(converse(complement(converse(complement(X0)))), complement(X0))) 6.29/3.49 = converse(complement(converse(complement(X0)))), 6.29/3.49 inference('sup+', [status(thm)], ['221', '226'])). 6.29/3.49 tff('228', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('229', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('230', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff('231', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('232', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(one) 6.29/3.49 = join(complement(one), composition(converse(X0), complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['230', '231'])). 6.29/3.49 tff('233', plain, ![X0, X1]: zero = meet(X0, complement(join(X1, X0))), 6.29/3.49 inference('demod', [status(thm)], ['127', '128'])). 6.29/3.49 tff('234', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = meet(composition(converse(X0), complement(X0)), 6.29/3.49 complement(complement(one))), 6.29/3.49 inference('sup+', [status(thm)], ['232', '233'])). 6.29/3.49 tff('235', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('236', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('237', plain, 6.29/3.49 ![X0]: zero = meet(one, composition(converse(X0), complement(X0))), 6.29/3.49 inference('demod', [status(thm)], ['234', '235', '236'])). 6.29/3.49 tff('238', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff(dedekind_law, axiom, 6.29/3.49 (![X0,X1,X2]: 6.29/3.49 (composition(meet(X0,composition(X2,converse(X1))), 6.29/3.49 meet(X1,composition(converse(X0),X2))) = 6.29/3.49 join(meet(composition(X0,X1),X2), 6.29/3.49 composition(meet(X0,composition(X2,converse(X1))), 6.29/3.49 meet(X1,composition(converse(X0),X2))))))). 6.29/3.49 tff('239', plain, 6.29/3.49 ![X28, X29, X30]: 6.29/3.49 composition(meet(X28, composition(X30, converse(X29))), 6.29/3.49 meet(X29, composition(converse(X28), X30))) 6.29/3.49 = join(meet(composition(X28, X29), X30), 6.29/3.49 composition(meet(X28, composition(X30, converse(X29))), 6.29/3.49 meet(X29, composition(converse(X28), X30)))), 6.29/3.49 inference('cnf', [status(esa)], [dedekind_law])). 6.29/3.49 tff('240', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 composition(meet(X2, composition(X1, converse(converse(X0)))), 6.29/3.49 meet(converse(X0), composition(converse(X2), X1))) 6.29/3.49 = join(meet(composition(X2, converse(X0)), X1), 6.29/3.49 composition(meet(X2, composition(X1, X0)), 6.29/3.49 meet(converse(X0), composition(converse(X2), X1)))), 6.29/3.49 inference('sup+', [status(thm)], ['238', '239'])). 6.29/3.49 tff('241', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('242', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 composition(meet(X2, composition(X1, X0)), 6.29/3.49 meet(converse(X0), composition(converse(X2), X1))) 6.29/3.49 = join(meet(composition(X2, converse(X0)), X1), 6.29/3.49 composition(meet(X2, composition(X1, X0)), 6.29/3.49 meet(converse(X0), composition(converse(X2), X1)))), 6.29/3.49 inference('demod', [status(thm)], ['240', '241'])). 6.29/3.49 tff('243', plain, 6.29/3.49 ![X0]: 6.29/3.49 composition(meet(one, composition(converse(X0), complement(X0))), 6.29/3.49 meet(converse(complement(X0)), 6.29/3.49 composition(converse(one), converse(X0)))) 6.29/3.49 = join( 6.29/3.49 meet(composition(one, converse(complement(X0))), converse(X0)), 6.29/3.49 composition(zero, 6.29/3.49 meet(converse(complement(X0)), 6.29/3.49 composition(converse(one), converse(X0))))), 6.29/3.49 inference('sup+', [status(thm)], ['237', '242'])). 6.29/3.49 tff('244', plain, 6.29/3.49 ![X0]: zero = meet(one, composition(converse(X0), complement(X0))), 6.29/3.49 inference('demod', [status(thm)], ['234', '235', '236'])). 6.29/3.49 tff('245', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('246', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff('247', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('248', plain, ![X0]: zero = composition(zero, X0), 6.29/3.49 inference('demod', [status(thm)], ['178', '183', '184'])). 6.29/3.49 tff('249', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff('250', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('251', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('252', plain, ![X0]: X0 = composition(one, X0), 6.29/3.49 inference('demod', [status(thm)], ['8', '11'])). 6.29/3.49 tff('253', plain, ![X0, X1]: meet(X1, X0) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['109', '110'])). 6.29/3.49 tff('254', plain, ![X0]: zero = composition(zero, X0), 6.29/3.49 inference('demod', [status(thm)], ['178', '183', '184'])). 6.29/3.49 tff('255', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('256', plain, ![X0]: zero = meet(converse(X0), converse(complement(X0))), 6.29/3.49 inference('demod', [status(thm)], 6.29/3.49 ['243', '244', '245', '246', '247', '248', '249', '250', 6.29/3.49 '251', '252', '253', '254', '255'])). 6.29/3.49 tff('257', plain, ![X0]: zero = meet(X0, converse(complement(converse(X0)))), 6.29/3.49 inference('sup+', [status(thm)], ['229', '256'])). 6.29/3.49 tff('258', plain, 6.29/3.49 ![X0]: join(X0, zero) = converse(complement(converse(complement(X0)))), 6.29/3.49 inference('demod', [status(thm)], ['227', '228', '257'])). 6.29/3.49 tff('259', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('260', plain, ![X0]: X0 = converse(complement(converse(complement(X0)))), 6.29/3.49 inference('demod', [status(thm)], ['258', '259'])). 6.29/3.49 tff('261', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('262', plain, ![X0]: complement(converse(complement(X0))) = converse(X0), 6.29/3.49 inference('sup+', [status(thm)], ['260', '261'])). 6.29/3.49 tff('263', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('264', plain, ![X0]: complement(converse(X0)) = converse(complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['262', '263'])). 6.29/3.49 tff('265', plain, 6.29/3.49 ![X0]: converse(composition(top, X0)) = composition(converse(X0), top), 6.29/3.49 inference('sup+', [status(thm)], ['199', '200'])). 6.29/3.49 tff('266', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('267', plain, ![X6]: join(X6, complement(X6)) = top, 6.29/3.49 inference('cnf', [status(esa)], [def_top])). 6.29/3.49 tff('268', plain, complement(zero) = top, 6.29/3.49 inference('sup+', [status(thm)], ['266', '267'])). 6.29/3.49 tff('269', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('270', plain, 6.29/3.49 ![X0]: 6.29/3.49 zero 6.29/3.49 = composition(X0, 6.29/3.49 composition(complement(composition(converse(X0), top)), top)), 6.29/3.49 inference('demod', [status(thm)], 6.29/3.49 ['209', '210', '211', '264', '265', '268', '269'])). 6.29/3.49 tff('271', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('272', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(converse(X0), complement(composition(X0, X1)))), 6.29/3.49 inference('demod', [status(thm)], ['13', '14'])). 6.29/3.49 tff('273', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(X1) 6.29/3.49 = join(complement(X1), 6.29/3.49 composition(X0, complement(composition(converse(X0), X1)))), 6.29/3.49 inference('sup+', [status(thm)], ['271', '272'])). 6.29/3.49 tff('274', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement( 6.29/3.49 composition(complement(composition(converse(converse(X0)), top)), 6.29/3.49 top)) 6.29/3.49 = join( 6.29/3.49 complement( 6.29/3.49 composition( 6.29/3.49 complement(composition(converse(converse(X0)), top)), top)), 6.29/3.49 composition(X0, complement(zero))), 6.29/3.49 inference('sup+', [status(thm)], ['270', '273'])). 6.29/3.49 tff('275', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('276', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('277', plain, complement(zero) = top, 6.29/3.49 inference('sup+', [status(thm)], ['266', '267'])). 6.29/3.49 tff('278', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('279', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('280', plain, 6.29/3.49 ![X0]: zero = composition(converse(X0), complement(composition(X0, top))), 6.29/3.49 inference('demod', [status(thm)], ['65', '66'])). 6.29/3.49 tff('281', plain, 6.29/3.49 ![X0]: zero = composition(X0, complement(composition(converse(X0), top))), 6.29/3.49 inference('sup+', [status(thm)], ['279', '280'])). 6.29/3.49 tff('282', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff('283', plain, 6.29/3.49 ![X28, X29, X30]: 6.29/3.49 composition(meet(X28, composition(X30, converse(X29))), 6.29/3.49 meet(X29, composition(converse(X28), X30))) 6.29/3.49 = join(meet(composition(X28, X29), X30), 6.29/3.49 composition(meet(X28, composition(X30, converse(X29))), 6.29/3.49 meet(X29, composition(converse(X28), X30)))), 6.29/3.49 inference('cnf', [status(esa)], [dedekind_law])). 6.29/3.49 tff('284', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 composition(meet(X0, composition(X1, converse(one))), 6.29/3.49 meet(one, composition(converse(X0), X1))) 6.29/3.49 = join(meet(X0, X1), 6.29/3.49 composition(meet(X0, composition(X1, converse(one))), 6.29/3.49 meet(one, composition(converse(X0), X1)))), 6.29/3.49 inference('sup+', [status(thm)], ['282', '283'])). 6.29/3.49 tff('285', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('286', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff('287', plain, converse(one) = one, 6.29/3.49 inference('sup+', [status(thm)], ['9', '10'])). 6.29/3.49 tff('288', plain, ![X21]: X21 = composition(X21, one), 6.29/3.49 inference('cnf', [status(esa)], [composition_identity])). 6.29/3.49 tff('289', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 composition(meet(X0, X1), meet(one, composition(converse(X0), X1))) 6.29/3.49 = join(meet(X0, X1), 6.29/3.49 composition(meet(X0, X1), 6.29/3.49 meet(one, composition(converse(X0), X1)))), 6.29/3.49 inference('demod', [status(thm)], ['284', '285', '286', '287', '288'])). 6.29/3.49 tff('290', plain, 6.29/3.49 ![X0]: 6.29/3.49 composition( 6.29/3.49 meet(X0, complement(composition(converse(converse(X0)), top))), 6.29/3.49 meet(one, 6.29/3.49 composition(converse(X0), 6.29/3.49 complement(composition(converse(converse(X0)), top))))) 6.29/3.49 = join( 6.29/3.49 meet(X0, complement(composition(converse(converse(X0)), top))), 6.29/3.49 composition( 6.29/3.49 meet(X0, complement(composition(converse(converse(X0)), top))), 6.29/3.49 meet(one, zero))), 6.29/3.49 inference('sup+', [status(thm)], ['281', '289'])). 6.29/3.49 tff('291', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('292', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('293', plain, 6.29/3.49 ![X0]: zero = composition(converse(X0), complement(composition(X0, top))), 6.29/3.49 inference('demod', [status(thm)], ['65', '66'])). 6.29/3.49 tff('294', plain, complement(zero) = top, 6.29/3.49 inference('sup+', [status(thm)], ['266', '267'])). 6.29/3.49 tff('295', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(complement(X1), complement(X0))) = meet(X0, X1), 6.29/3.49 inference('sup+', [status(thm)], ['107', '108'])). 6.29/3.49 tff('296', plain, 6.29/3.49 ![X0]: complement(join(top, complement(X0))) = meet(X0, zero), 6.29/3.49 inference('sup+', [status(thm)], ['294', '295'])). 6.29/3.49 tff('297', plain, ![X0]: join(top, X0) = top, 6.29/3.49 inference('sup+', [status(thm)], ['57', '58'])). 6.29/3.49 tff('298', plain, ![X0]: complement(top) = meet(X0, zero), 6.29/3.49 inference('demod', [status(thm)], ['296', '297'])). 6.29/3.49 tff('299', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('300', plain, ![X0]: zero = meet(X0, zero), 6.29/3.49 inference('demod', [status(thm)], ['298', '299'])). 6.29/3.49 tff('301', plain, ![X1]: zero = composition(X1, zero), 6.29/3.49 inference('demod', [status(thm)], ['174', '175'])). 6.29/3.49 tff('302', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('303', plain, ![X14]: X14 = converse(converse(X14)), 6.29/3.49 inference('cnf', [status(esa)], [converse_idempotence])). 6.29/3.49 tff('304', plain, ![X0]: zero = meet(X0, zero), 6.29/3.49 inference('demod', [status(thm)], ['298', '299'])). 6.29/3.49 tff('305', plain, ![X1]: zero = composition(X1, zero), 6.29/3.49 inference('demod', [status(thm)], ['174', '175'])). 6.29/3.49 tff('306', plain, ![X0]: join(X0, zero) = X0, 6.29/3.49 inference('demod', [status(thm)], ['82', '83', '84'])). 6.29/3.49 tff('307', plain, ![X0]: zero = meet(X0, complement(composition(X0, top))), 6.29/3.49 inference('demod', [status(thm)], 6.29/3.49 ['290', '291', '292', '293', '300', '301', '302', '303', 6.29/3.49 '304', '305', '306'])). 6.29/3.49 tff('308', plain, ![X12, X13]: join(X13, X12) = join(X12, X13), 6.29/3.49 inference('cnf', [status(esa)], [maddux1_join_commutativity])). 6.29/3.49 tff('309', plain, 6.29/3.49 ![X4, X5]: join(meet(X4, X5), complement(join(complement(X4), X5))) = X4, 6.29/3.49 inference('demod', [status(thm)], ['20', '21'])). 6.29/3.49 tff('310', plain, 6.29/3.49 ![X0, X1]: join(meet(X0, X1), complement(join(X1, complement(X0)))) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['308', '309'])). 6.29/3.49 tff('311', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 complement(join(X0, complement(X1))) = meet(X1, complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['120', '121'])). 6.29/3.49 tff('312', plain, 6.29/3.49 ![X0, X1]: join(meet(X0, X1), meet(X0, complement(X1))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['310', '311'])). 6.29/3.49 tff('313', plain, 6.29/3.49 ![X0]: 6.29/3.49 join(zero, meet(X0, complement(complement(composition(X0, top))))) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['307', '312'])). 6.29/3.49 tff('314', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('315', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('316', plain, ![X0]: meet(X0, composition(X0, top)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['313', '314', '315'])). 6.29/3.49 tff('317', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('318', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('319', plain, 6.29/3.49 ![X10, X11]: 6.29/3.49 complement(join(complement(X10), complement(X11))) = meet(X10, X11), 6.29/3.49 inference('cnf', [status(esa)], [maddux4_definiton_of_meet])). 6.29/3.49 tff('320', plain, 6.29/3.49 ![X0, X1, X2]: 6.29/3.49 complement(join(complement(X2), meet(X1, X0))) 6.29/3.49 = meet(X2, join(complement(X1), complement(X0))), 6.29/3.49 inference('sup+', [status(thm)], ['318', '319'])). 6.29/3.49 tff('321', plain, ![X0]: X0 = meet(top, X0), 6.29/3.49 inference('demod', [status(thm)], ['166', '167'])). 6.29/3.49 tff('322', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 join(complement(X1), complement(X0)) 6.29/3.49 = complement(join(complement(top), meet(X1, X0))), 6.29/3.49 inference('sup+', [status(thm)], ['320', '321'])). 6.29/3.49 tff('323', plain, zero = complement(top), 6.29/3.49 inference('sup+', [status(thm)], ['29', '30'])). 6.29/3.49 tff('324', plain, ![X0]: join(zero, X0) = X0, 6.29/3.49 inference('sup+', [status(thm)], ['39', '40'])). 6.29/3.49 tff('325', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 join(complement(X1), complement(X0)) = complement(meet(X1, X0)), 6.29/3.49 inference('demod', [status(thm)], ['322', '323', '324'])). 6.29/3.49 tff('326', plain, 6.29/3.49 ![X0, X1]: 6.29/3.49 join(X0, complement(X1)) = complement(meet(complement(X0), X1)), 6.29/3.49 inference('sup+', [status(thm)], ['317', '325'])). 6.29/3.49 tff('327', plain, 6.29/3.49 ![X0]: 6.29/3.49 join(X0, complement(composition(complement(X0), top))) 6.29/3.49 = complement(complement(X0)), 6.29/3.49 inference('sup+', [status(thm)], ['316', '326'])). 6.29/3.49 tff('328', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('329', plain, 6.29/3.49 ![X0]: join(X0, complement(composition(complement(X0), top))) = X0, 6.29/3.49 inference('demod', [status(thm)], ['327', '328'])). 6.29/3.49 tff('330', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(composition(complement(composition(X0, top)), top)) 6.29/3.49 = composition(X0, top), 6.29/3.49 inference('demod', [status(thm)], 6.29/3.49 ['274', '275', '276', '277', '278', '329'])). 6.29/3.49 tff('331', plain, ![X0]: complement(complement(X0)) = X0, 6.29/3.49 inference('demod', [status(thm)], ['25', '41'])). 6.29/3.49 tff('332', plain, 6.29/3.49 ![X0]: 6.29/3.49 complement(composition(X0, top)) 6.29/3.49 = composition(complement(composition(X0, top)), top), 6.29/3.49 inference('sup+', [status(thm)], ['330', '331'])). 6.29/3.49 tff('333', plain, 6.29/3.49 complement(composition(sk_X0, top)) 6.29/3.49 != complement(composition(sk_X0, top)), 6.29/3.49 inference('demod', [status(thm)], ['0', '332'])). 6.29/3.49 tff('334', plain, $false, inference('simplify', [status(thm)], ['333'])). 6.29/3.49 6.29/3.49 % SZS output end Refutation 6.29/3.49 6.30/3.50 % Zipperpin 1.5 exiting 6.30/3.50 EOF