0.09/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.12 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.KpfZKAbOsG 0.12/0.31 % Computer : n010.cluster.edu 0.12/0.31 % Model : x86_64 x86_64 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.31 % Memory : 8042.1875MB 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.31 % CPULimit : 960 0.12/0.31 % DateTime : Thu Jul 2 08:18:27 EDT 2020 0.12/0.31 % CPUTime : 0.12/0.31 % Running portfolio for 120 s 0.12/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.31 % Number of cores: 8 0.16/0.32 % Python version: Python 3.6.8 0.16/0.32 % Running in FO mode 50.38/50.73 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 50.38/50.73 % Running /export/starexec/sandbox2/solver/bin/fo/fo8.sh for 20 50.38/50.73 % Warning: 50.38/50.73 % To remain in the chosen logic fragment, unification with booleans has been disabled. 50.38/50.73 % 50.38/50.73 % Running /export/starexec/sandbox2/solver/bin/fo/fo5.sh for 20 50.38/50.73 % Solved by: fo/fo5.sh 50.38/50.73 To remain in the chosen logic fragment, unification with booleans has been disabled. 50.38/50.73 % done 2646 iterations in 5.504s 50.38/50.73 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 50.38/50.73 % SZS output start Refutation 50.38/50.73 tff(false_true_err_in_d, axiom, (d(err) & d(false) & d(true))). 50.38/50.73 tff('0', plain, d(false), 50.38/50.73 inference('cnf', [status(esa)], [false_true_err_in_d])). 50.38/50.73 tff(def_phi, axiom, 50.38/50.73 (![X]: (((phi(X) = err) & (~d(X))) | (d(X) & (phi(X) = X))))). 50.38/50.73 tff(zf_stmt_0, type, zip_tseitin_7 : ($i > $o)). 50.38/50.73 tff(zf_stmt_1, axiom, (zip_tseitin_7(X) => ((phi(X) = X) & d(X)))). 50.38/50.73 tff(zf_stmt_2, type, zip_tseitin_6 : ($i > $o)). 50.38/50.73 tff(zf_stmt_3, axiom, (zip_tseitin_6(X) => ((~d(X)) & (phi(X) = err)))). 50.38/50.73 tff(zf_stmt_4, axiom, (![X]: (zip_tseitin_7(X) | zip_tseitin_6(X)))). 50.38/50.73 tff('1', plain, ![X42]: ( zip_tseitin_7(X42) | zip_tseitin_6(X42)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_4])). 50.38/50.73 tff('2', plain, ![X41]: (phi(X41) = X41 | ~ zip_tseitin_7(X41)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_1])). 50.38/50.73 tff('3', plain, ![X0]: ( zip_tseitin_6(X0) | phi(X0) = X0), 50.38/50.73 inference('s_sup-', [status(thm)], ['1', '2'])). 50.38/50.73 tff('4', plain, ![X41]: (~ d(X41) | ~ zip_tseitin_6(X41)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_3])). 50.38/50.73 tff('5', plain, ![X0]: (phi(X0) = X0 | ~ d(X0)), 50.38/50.73 inference('s_sup-', [status(thm)], ['3', '4'])). 50.38/50.73 tff('6', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff(prop_false, axiom, (![X]: ((~bool(X)) <=> (prop(X) = false)))). 50.38/50.73 tff('7', plain, ![X17]: (prop(X17) = false | bool(X17)), 50.38/50.73 inference('cnf', [status(esa)], [prop_false])). 50.38/50.73 tff(lazy_impl_axiom1, axiom, 50.38/50.73 (![A,B]: ((~bool(A)) => (lazy_impl(A,B) = phi(A))))). 50.38/50.73 tff('8', plain, ![X9, X10]: ( bool(X9) | lazy_impl(X9, X10) = phi(X9)), 50.38/50.73 inference('cnf', [status(esa)], [lazy_impl_axiom1])). 50.38/50.73 tff(def_f7, axiom, (![P]: (lazy_impl(prop(P),P) = f7(P)))). 50.38/50.73 tff('9', plain, ![X54]: lazy_impl(prop(X54), X54) = f7(X54), 50.38/50.73 inference('cnf', [status(esa)], [def_f7])). 50.38/50.73 tff('10', plain, ![X0]: ( bool(prop(X0)) | phi(prop(X0)) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['8', '9'])). 50.38/50.73 tff(def_false2, axiom, 50.38/50.73 (?[P]: ((false2 = phi(f7(P))) & (~(?[P1]: forallprefers(f7(P1),f7(P))))))). 50.38/50.73 tff('11', plain, false2 = phi(f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('12', plain, ( bool(prop(sk_P)) | false2 = phi(phi(prop(sk_P)))), 50.38/50.73 inference('s_sup+', [status(thm)], ['10', '11'])). 50.38/50.73 tff('13', plain, 50.38/50.73 (false2 = phi(phi(prop(sk_P)))) <= ((false2 = phi(phi(prop(sk_P))))), 50.38/50.73 inference('split', [status(esa)], ['12'])). 50.38/50.73 tff('14', plain, 50.38/50.73 (( bool(sk_P) | false2 = phi(phi(false)))) 50.38/50.73 <= ((false2 = phi(phi(prop(sk_P))))), 50.38/50.73 inference('s_sup+', [status(thm)], ['7', '13'])). 50.38/50.73 tff('15', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff('16', plain, 50.38/50.73 (( bool(sk_P) | false2 = phi(false))) 50.38/50.73 <= ((false2 = phi(phi(prop(sk_P))))), 50.38/50.73 inference('demod', [status(thm)], ['14', '15'])). 50.38/50.73 tff('17', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff(prop_true, axiom, (![X]: (bool(X) <=> (true = prop(X))))). 50.38/50.73 tff('18', plain, ![X76]: (true = prop(X76) | ~ bool(X76)), 50.38/50.73 inference('cnf', [status(esa)], [prop_true])). 50.38/50.73 tff('19', plain, ![X54]: lazy_impl(prop(X54), X54) = f7(X54), 50.38/50.73 inference('cnf', [status(esa)], [def_f7])). 50.38/50.73 tff('20', plain, ![X0]: (~ bool(X0) | lazy_impl(true, X0) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['18', '19'])). 50.38/50.73 tff(lazy_impl_axiom3, axiom, (![B]: (phi(B) = lazy_impl(true,B)))). 50.38/50.73 tff('21', plain, ![X1]: phi(X1) = lazy_impl(true, X1), 50.38/50.73 inference('cnf', [status(esa)], [lazy_impl_axiom3])). 50.38/50.73 tff('22', plain, ![X0]: (~ bool(X0) | phi(X0) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['20', '21'])). 50.38/50.73 tff(def_forallprefers, axiom, 50.38/50.73 (![X,Y]: 50.38/50.73 (forallprefers(X,Y) <=> 50.38/50.73 ((bool(Y) & (~bool(X)) & d(X) & d(Y)) | ((X = false) & (Y = true)) | 50.38/50.73 (d(Y) & (~d(X))))))). 50.38/50.73 tff(zf_stmt_5, axiom, 50.38/50.73 (zip_tseitin_3(Y,X) <=> (d(Y) & d(X) & (~bool(X)) & bool(Y)))). 50.38/50.73 tff('23', plain, 50.38/50.73 ![X36, X37]: 50.38/50.73 ( zip_tseitin_3(X36, X37) 50.38/50.73 | ~ bool(X36) 50.38/50.73 | bool(X37) 50.38/50.73 | ~ d(X37) 50.38/50.73 | ~ d(X36)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_5])). 50.38/50.73 tff(zf_stmt_6, type, zip_tseitin_5 : ($i * $i) > $o). 50.38/50.73 tff(zf_stmt_7, axiom, (zip_tseitin_5(Y,X) <=> ((~d(X)) & d(Y)))). 50.38/50.73 tff(zf_stmt_8, type, zip_tseitin_4 : ($i * $i) > $o). 50.38/50.73 tff(zf_stmt_9, axiom, (zip_tseitin_4(Y,X) <=> ((Y = true) & (X = false)))). 50.38/50.73 tff(zf_stmt_10, type, zip_tseitin_3 : ($i * $i) > $o). 50.38/50.73 tff(zf_stmt_11, axiom, 50.38/50.73 (![X,Y]: 50.38/50.73 (forallprefers(X,Y) <=> 50.38/50.73 (zip_tseitin_5(Y,X) | zip_tseitin_4(Y,X) | zip_tseitin_3(Y,X))))). 50.38/50.73 tff('24', plain, 50.38/50.73 ![X39, X40]: ( forallprefers(X39, X40) | ~ zip_tseitin_3(X40, X39)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_11])). 50.38/50.73 tff('25', plain, 50.38/50.73 ![X0, X1]: 50.38/50.73 (~ d(X1) | ~ d(X0) | bool(X0) | ~ bool(X1) | forallprefers(X0, X1)), 50.38/50.73 inference('s_sup-', [status(thm)], ['23', '24'])). 50.38/50.73 tff('26', plain, ![X0]: ( bool(prop(X0)) | phi(prop(X0)) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['8', '9'])). 50.38/50.73 tff('27', plain, false2 = phi(f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('28', plain, ![X0]: ( zip_tseitin_6(X0) | phi(X0) = X0), 50.38/50.73 inference('s_sup-', [status(thm)], ['1', '2'])). 50.38/50.73 tff('29', plain, ![X41]: (phi(X41) = err | ~ zip_tseitin_6(X41)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_3])). 50.38/50.73 tff('30', plain, ![X0]: (phi(X0) = X0 | phi(X0) = err), 50.38/50.73 inference('s_sup-', [status(thm)], ['28', '29'])). 50.38/50.73 tff('31', plain, (false2 = f7(sk_P) | false2 = err), 50.38/50.73 inference('s_sup+', [status(thm)], ['27', '30'])). 50.38/50.73 tff('32', plain, (false2 = f7(sk_P)) <= ((false2 = f7(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['31'])). 50.38/50.73 tff('33', plain, 50.38/50.73 (( bool(prop(sk_P)) | false2 = phi(prop(sk_P)))) <= ((false2 = f7(sk_P))), 50.38/50.73 inference('s_sup+', [status(thm)], ['26', '32'])). 50.38/50.73 tff('34', plain, ( bool(prop(sk_P))) <= (( bool(prop(sk_P)))), 50.38/50.73 inference('split', [status(esa)], ['33'])). 50.38/50.73 tff(def_bool, axiom, (![X]: (((false = X) | (X = true)) <=> bool(X)))). 50.38/50.73 tff('35', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('36', plain, 50.38/50.73 ((prop(sk_P) = true | false = prop(sk_P))) <= (( bool(prop(sk_P)))), 50.38/50.73 inference('s_sup-', [status(thm)], ['34', '35'])). 50.38/50.73 tff('37', plain, (false = prop(sk_P)) <= ((false = prop(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['36'])). 50.38/50.73 tff('38', plain, ![X54]: lazy_impl(prop(X54), X54) = f7(X54), 50.38/50.73 inference('cnf', [status(esa)], [def_f7])). 50.38/50.73 tff('39', plain, 50.38/50.73 (lazy_impl(false, sk_P) = f7(sk_P)) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup+', [status(thm)], ['37', '38'])). 50.38/50.73 tff(lazy_impl_axiom2, axiom, (![B]: (true = lazy_impl(false,B)))). 50.38/50.73 tff('40', plain, ![X43]: true = lazy_impl(false, X43), 50.38/50.73 inference('cnf', [status(esa)], [lazy_impl_axiom2])). 50.38/50.73 tff('41', plain, (true = f7(sk_P)) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['39', '40'])). 50.38/50.73 tff('42', plain, ![X25]: ~ forallprefers(f7(X25), f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('43', plain, 50.38/50.73 (![X0]: ~ forallprefers(f7(X0), true)) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['41', '42'])). 50.38/50.73 tff('44', plain, 50.38/50.73 (![X0]: (~ bool(true) | bool(f7(X0)) | ~ d(f7(X0)) | ~ d(true))) 50.38/50.73 <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['25', '43'])). 50.38/50.73 tff('45', plain, ![X69]: ( bool(X69) | X69 != true), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('46', plain, bool(true), inference('simplify', [status(thm)], ['45'])). 50.38/50.73 tff('47', plain, d(true), 50.38/50.73 inference('cnf', [status(esa)], [false_true_err_in_d])). 50.38/50.73 tff('48', plain, 50.38/50.73 (![X0]: ( bool(f7(X0)) | ~ d(f7(X0)))) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['44', '46', '47'])). 50.38/50.73 tff('49', plain, 50.38/50.73 ![X36, X37]: ( zip_tseitin_5(X36, X37) | ~ d(X36) | d(X37)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_7])). 50.38/50.73 tff('50', plain, 50.38/50.73 ![X39, X40]: ( forallprefers(X39, X40) | ~ zip_tseitin_5(X40, X39)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_11])). 50.38/50.73 tff('51', plain, ![X0, X1]: ( d(X0) | ~ d(X1) | forallprefers(X0, X1)), 50.38/50.73 inference('s_sup-', [status(thm)], ['49', '50'])). 50.38/50.73 tff('52', plain, 50.38/50.73 (![X0]: ~ forallprefers(f7(X0), true)) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['41', '42'])). 50.38/50.73 tff('53', plain, (![X0]: (~ d(true) | d(f7(X0)))) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['51', '52'])). 50.38/50.73 tff('54', plain, d(true), 50.38/50.73 inference('cnf', [status(esa)], [false_true_err_in_d])). 50.38/50.73 tff('55', plain, (![X0]: d(f7(X0))) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['53', '54'])). 50.38/50.73 tff('56', plain, (![X0]: bool(f7(X0))) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['48', '55'])). 50.38/50.73 tff('57', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('58', plain, 50.38/50.73 (![X0]: (f7(X0) = true | false = f7(X0))) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['56', '57'])). 50.38/50.73 tff('59', plain, ![X25]: ~ forallprefers(f7(X25), f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('60', plain, 50.38/50.73 (![X0]: (f7(X0) = true | ~ forallprefers(false, f7(sk_P)))) 50.38/50.73 <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['58', '59'])). 50.38/50.73 tff('61', plain, (true = f7(sk_P)) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['39', '40'])). 50.38/50.73 tff('62', plain, 50.38/50.73 ![X36, X37]: ( zip_tseitin_4(X36, X37) | X37 != false | X36 != true), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_9])). 50.38/50.73 tff('63', plain, zip_tseitin_4(true, false), 50.38/50.73 inference('simplify', [status(thm)], ['62'])). 50.38/50.73 tff('64', plain, 50.38/50.73 ![X39, X40]: ( forallprefers(X39, X40) | ~ zip_tseitin_4(X40, X39)), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_11])). 50.38/50.73 tff('65', plain, forallprefers(false, true), 50.38/50.73 inference('s_sup-', [status(thm)], ['63', '64'])). 50.38/50.73 tff('66', plain, (![X0]: f7(X0) = true) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['60', '61', '65'])). 50.38/50.73 tff('67', plain, 50.38/50.73 (![X0]: (~ bool(X0) | phi(X0) = true)) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup+', [status(thm)], ['22', '66'])). 50.38/50.73 tff('68', plain, ((~ bool(false) | false = true)) <= ((false = prop(sk_P))), 50.38/50.73 inference('s_sup+', [status(thm)], ['17', '67'])). 50.38/50.73 tff('69', plain, ![X69]: ( bool(X69) | false != X69), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('70', plain, bool(false), inference('simplify', [status(thm)], ['69'])). 50.38/50.73 tff('71', plain, (false = true) <= ((false = prop(sk_P))), 50.38/50.73 inference('demod', [status(thm)], ['68', '70'])). 50.38/50.73 tff(distinct_false_true_err, axiom, 50.38/50.73 ((false != err) & (err != true) & (false != true))). 50.38/50.73 tff('72', plain, false != true, 50.38/50.73 inference('cnf', [status(esa)], [distinct_false_true_err])). 50.38/50.73 tff('73', plain, ~ (false = prop(sk_P)), 50.38/50.73 inference('simplify_reflect-', [status(thm)], ['71', '72'])). 50.38/50.73 tff('74', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff('75', plain, ![X0]: (~ bool(X0) | phi(X0) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['20', '21'])). 50.38/50.73 tff('76', plain, (false2 = phi(prop(sk_P))) <= ((false2 = phi(prop(sk_P)))), 50.38/50.73 inference('split', [status(esa)], ['33'])). 50.38/50.73 tff('77', plain, ![X0]: (phi(X0) = X0 | phi(X0) = err), 50.38/50.73 inference('s_sup-', [status(thm)], ['28', '29'])). 50.38/50.73 tff('78', plain, 50.38/50.73 ((false2 = prop(sk_P) | false2 = err)) <= ((false2 = phi(prop(sk_P)))), 50.38/50.73 inference('s_sup+', [status(thm)], ['76', '77'])). 50.38/50.73 tff('79', plain, (false2 = prop(sk_P)) <= ((false2 = prop(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['78'])). 50.38/50.73 tff('80', plain, ![X77]: ( bool(X77) | true != prop(X77)), 50.38/50.73 inference('cnf', [status(esa)], [prop_true])). 50.38/50.73 tff('81', plain, (( bool(sk_P) | true != false2)) <= ((false2 = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['79', '80'])). 50.38/50.73 tff('82', plain, ( bool(sk_P)) <= (( bool(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['81'])). 50.38/50.73 tff('83', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('84', plain, ((sk_P = true | false = sk_P)) <= (( bool(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['82', '83'])). 50.38/50.73 tff('85', plain, (false = sk_P) <= ((false = sk_P)), 50.38/50.73 inference('split', [status(esa)], ['84'])). 50.38/50.73 tff('86', plain, false2 = phi(f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('87', plain, (false2 = phi(f7(false))) <= ((false = sk_P)), 50.38/50.73 inference('s_sup+', [status(thm)], ['85', '86'])). 50.38/50.73 tff('88', plain, 50.38/50.73 ((~ bool(false) | false2 = phi(phi(false)))) <= ((false = sk_P)), 50.38/50.73 inference('s_sup+', [status(thm)], ['75', '87'])). 50.38/50.73 tff('89', plain, bool(false), inference('simplify', [status(thm)], ['69'])). 50.38/50.73 tff('90', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff('91', plain, (false2 = phi(false)) <= ((false = sk_P)), 50.38/50.73 inference('demod', [status(thm)], ['88', '89', '90'])). 50.38/50.73 tff('92', plain, (false2 = false) <= ((false = sk_P)), 50.38/50.73 inference('s_sup+', [status(thm)], ['74', '91'])). 50.38/50.73 tff('93', plain, (false2 = prop(sk_P)) <= ((false2 = prop(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['78'])). 50.38/50.73 tff('94', plain, ![X18]: (~ bool(X18) | prop(X18) != false), 50.38/50.73 inference('cnf', [status(esa)], [prop_false])). 50.38/50.73 tff('95', plain, 50.38/50.73 ((~ bool(sk_P) | false2 != false)) <= ((false2 = prop(sk_P))), 50.38/50.73 inference('s_sup-', [status(thm)], ['93', '94'])). 50.38/50.73 tff('96', plain, (false2 != false) <= (~ (false = false2)), 50.38/50.73 inference('split', [status(esa)], ['95'])). 50.38/50.73 tff(impl_axiom3, axiom, (![B]: (bool(B) => (true = impl(false,B))))). 50.38/50.73 tff('97', plain, ![X19]: (true = impl(false, X19) | ~ bool(X19)), 50.38/50.73 inference('cnf', [status(esa)], [impl_axiom3])). 50.38/50.73 tff(impl_axiom2, axiom, 50.38/50.73 (![A,B]: (((~bool(B)) & bool(A)) => (impl(A,B) = phi(B))))). 50.38/50.73 tff('98', plain, 50.38/50.73 ![X23, X24]: (~ bool(X23) | bool(X24) | impl(X23, X24) = phi(X24)), 50.38/50.73 inference('cnf', [status(esa)], [impl_axiom2])). 50.38/50.73 tff(def_not2, axiom, (![P]: (impl(P,false2) = not2(P)))). 50.38/50.73 tff('99', plain, ![X68]: impl(X68, false2) = not2(X68), 50.38/50.73 inference('cnf', [status(esa)], [def_not2])). 50.38/50.73 tff('100', plain, 50.38/50.73 ![X0]: ( bool(false2) | ~ bool(X0) | phi(false2) = not2(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['98', '99'])). 50.38/50.73 tff('101', plain, ( bool(false2)) <= (( bool(false2))), 50.38/50.73 inference('split', [status(esa)], ['100'])). 50.38/50.73 tff('102', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('103', plain, ((false2 = true | false = false2)) <= (( bool(false2))), 50.38/50.73 inference('s_sup-', [status(thm)], ['101', '102'])). 50.38/50.73 tff('104', plain, (false = false2) <= ((false = false2)), 50.38/50.73 inference('split', [status(esa)], ['103'])). 50.38/50.73 tff('105', plain, ![X68]: impl(X68, false2) = not2(X68), 50.38/50.73 inference('cnf', [status(esa)], [def_not2])). 50.38/50.73 tff('106', plain, (![X0]: impl(X0, false) = not2(X0)) <= ((false = false2)), 50.38/50.73 inference('s_sup+', [status(thm)], ['104', '105'])). 50.38/50.73 tff('107', plain, 50.38/50.73 ((~ bool(false) | true = not2(false))) <= ((false = false2)), 50.38/50.73 inference('s_sup+', [status(thm)], ['97', '106'])). 50.38/50.73 tff('108', plain, bool(false), inference('simplify', [status(thm)], ['69'])). 50.38/50.73 tff('109', plain, (true = not2(false)) <= ((false = false2)), 50.38/50.73 inference('demod', [status(thm)], ['107', '108'])). 50.38/50.73 tff(impl_axiom1, axiom, (![A,B]: ((~bool(A)) => (phi(A) = impl(A,B))))). 50.38/50.73 tff('110', plain, ![X55, X56]: ( bool(X55) | phi(X55) = impl(X55, X56)), 50.38/50.73 inference('cnf', [status(esa)], [impl_axiom1])). 50.38/50.73 tff('111', plain, ![X68]: impl(X68, false2) = not2(X68), 50.38/50.73 inference('cnf', [status(esa)], [def_not2])). 50.38/50.73 tff('112', plain, ![X0]: ( bool(X0) | phi(X0) = not2(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['110', '111'])). 50.38/50.73 tff(not1_not2, conjecture, (![P]: (not2(P) = not1(P)))). 50.38/50.73 tff(zf_stmt_12, negated_conjecture, (~(![P]: (not2(P) = not1(P))))). 50.38/50.73 tff('113', plain, not2(sk_P_1) != not1(sk_P_1), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_12])). 50.38/50.73 tff('114', plain, ( bool(sk_P_1) | phi(sk_P_1) != not1(sk_P_1)), 50.38/50.73 inference('s_sup-', [status(thm)], ['112', '113'])). 50.38/50.73 tff(not1_axiom1, axiom, (![A]: ((~bool(A)) => (not1(A) = phi(A))))). 50.38/50.73 tff('115', plain, ![X6]: (not1(X6) = phi(X6) | bool(X6)), 50.38/50.73 inference('cnf', [status(esa)], [not1_axiom1])). 50.38/50.73 tff('116', plain, bool(sk_P_1), 50.38/50.73 inference('clc', [status(thm)], ['114', '115'])). 50.38/50.73 tff('117', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('118', plain, (sk_P_1 = true | false = sk_P_1), 50.38/50.73 inference('s_sup-', [status(thm)], ['116', '117'])). 50.38/50.73 tff('119', plain, (false = sk_P_1) <= ((false = sk_P_1)), 50.38/50.73 inference('split', [status(esa)], ['118'])). 50.38/50.73 tff('120', plain, not2(sk_P_1) != not1(sk_P_1), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_12])). 50.38/50.73 tff('121', plain, (not2(false) != not1(false)) <= ((false = sk_P_1)), 50.38/50.73 inference('s_sup-', [status(thm)], ['119', '120'])). 50.38/50.73 tff(not1_axiom2, axiom, (not1(false) = true)). 50.38/50.73 tff('122', plain, not1(false) = true, 50.38/50.73 inference('cnf', [status(esa)], [not1_axiom2])). 50.38/50.73 tff('123', plain, (not2(false) != true) <= ((false = sk_P_1)), 50.38/50.73 inference('demod', [status(thm)], ['121', '122'])). 50.38/50.73 tff('124', plain, (true != true) <= ((false = sk_P_1) & (false = false2)), 50.38/50.73 inference('s_sup-', [status(thm)], ['109', '123'])). 50.38/50.73 tff('125', plain, ~ (false = false2) | ~ (false = sk_P_1), 50.38/50.73 inference('simplify', [status(thm)], ['124'])). 50.38/50.73 tff(impl_axiom4, axiom, (![B]: (bool(B) => (impl(true,B) = B)))). 50.38/50.73 tff('126', plain, ![X5]: (impl(true, X5) = X5 | ~ bool(X5)), 50.38/50.73 inference('cnf', [status(esa)], [impl_axiom4])). 50.38/50.73 tff('127', plain, (![X0]: impl(X0, false) = not2(X0)) <= ((false = false2)), 50.38/50.73 inference('s_sup+', [status(thm)], ['104', '105'])). 50.38/50.73 tff('128', plain, 50.38/50.73 ((~ bool(false) | false = not2(true))) <= ((false = false2)), 50.38/50.73 inference('s_sup+', [status(thm)], ['126', '127'])). 50.38/50.73 tff('129', plain, bool(false), inference('simplify', [status(thm)], ['69'])). 50.38/50.73 tff('130', plain, (false = not2(true)) <= ((false = false2)), 50.38/50.73 inference('demod', [status(thm)], ['128', '129'])). 50.38/50.73 tff('131', plain, (sk_P_1 = true) <= ((sk_P_1 = true)), 50.38/50.73 inference('split', [status(esa)], ['118'])). 50.38/50.73 tff('132', plain, not2(sk_P_1) != not1(sk_P_1), 50.38/50.73 inference('cnf', [status(esa)], [zf_stmt_12])). 50.38/50.73 tff('133', plain, (not2(true) != not1(true)) <= ((sk_P_1 = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['131', '132'])). 50.38/50.73 tff(not1_axiom3, axiom, (false = not1(true))). 50.38/50.73 tff('134', plain, false = not1(true), 50.38/50.73 inference('cnf', [status(esa)], [not1_axiom3])). 50.38/50.73 tff('135', plain, (not2(true) != false) <= ((sk_P_1 = true)), 50.38/50.73 inference('demod', [status(thm)], ['133', '134'])). 50.38/50.73 tff('136', plain, (false != false) <= ((sk_P_1 = true) & (false = false2)), 50.38/50.73 inference('s_sup-', [status(thm)], ['130', '135'])). 50.38/50.73 tff('137', plain, ~ (sk_P_1 = true) | ~ (false = false2), 50.38/50.73 inference('simplify', [status(thm)], ['136'])). 50.38/50.73 tff('138', plain, (false = sk_P_1) | (sk_P_1 = true), 50.38/50.73 inference('split', [status(esa)], ['118'])). 50.38/50.73 tff('139', plain, ~ (false = false2), 50.38/50.73 inference('sat_resolution*', [status(thm)], ['125', '137', '138'])). 50.38/50.73 tff('140', plain, false2 != false, 50.38/50.73 inference('simpl_trail', [status(thm)], ['96', '139'])). 50.38/50.73 tff('141', plain, ~ (false = sk_P), 50.38/50.73 inference('simplify_reflect-', [status(thm)], ['92', '140'])). 50.38/50.73 tff('142', plain, phi(false) = false, 50.38/50.73 inference('s_sup-', [status(thm)], ['0', '5'])). 50.38/50.73 tff('143', plain, ![X0]: (~ bool(X0) | phi(X0) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['20', '21'])). 50.38/50.73 tff('144', plain, ![X0]: (~ bool(X0) | phi(X0) = f7(X0)), 50.38/50.73 inference('s_sup+', [status(thm)], ['20', '21'])). 50.38/50.73 tff('145', plain, (sk_P = true) <= ((sk_P = true)), 50.38/50.73 inference('split', [status(esa)], ['84'])). 50.38/50.73 tff('146', plain, ![X25]: ~ forallprefers(f7(X25), f7(sk_P)), 50.38/50.73 inference('cnf', [status(esa)], [def_false2])). 50.38/50.73 tff('147', plain, 50.38/50.73 (![X0]: ~ forallprefers(f7(X0), f7(true))) <= ((sk_P = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['145', '146'])). 50.38/50.73 tff('148', plain, 50.38/50.73 (![X0]: (~ bool(true) | ~ forallprefers(f7(X0), phi(true)))) 50.38/50.73 <= ((sk_P = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['144', '147'])). 50.38/50.73 tff('149', plain, bool(true), inference('simplify', [status(thm)], ['45'])). 50.38/50.73 tff('150', plain, d(true), 50.38/50.73 inference('cnf', [status(esa)], [false_true_err_in_d])). 50.38/50.73 tff('151', plain, ![X0]: (phi(X0) = X0 | ~ d(X0)), 50.38/50.73 inference('s_sup-', [status(thm)], ['3', '4'])). 50.38/50.73 tff('152', plain, phi(true) = true, 50.38/50.73 inference('s_sup-', [status(thm)], ['150', '151'])). 50.38/50.73 tff('153', plain, (![X0]: ~ forallprefers(f7(X0), true)) <= ((sk_P = true)), 50.38/50.73 inference('demod', [status(thm)], ['148', '149', '152'])). 50.38/50.73 tff('154', plain, 50.38/50.73 (![X0]: (~ bool(X0) | ~ forallprefers(phi(X0), true))) <= ((sk_P = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['143', '153'])). 50.38/50.73 tff('155', plain, 50.38/50.73 ((~ bool(false) | ~ forallprefers(false, true))) <= ((sk_P = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['142', '154'])). 50.38/50.73 tff('156', plain, bool(false), inference('simplify', [status(thm)], ['69'])). 50.38/50.73 tff('157', plain, forallprefers(false, true), 50.38/50.73 inference('s_sup-', [status(thm)], ['63', '64'])). 50.38/50.73 tff('158', plain, ~ (sk_P = true), 50.38/50.73 inference('demod', [status(thm)], ['155', '156', '157'])). 50.38/50.73 tff('159', plain, ![X17]: (prop(X17) = false | bool(X17)), 50.38/50.73 inference('cnf', [status(esa)], [prop_false])). 50.38/50.73 tff('160', plain, (prop(sk_P) = true) <= ((prop(sk_P) = true)), 50.38/50.73 inference('split', [status(esa)], ['36'])). 50.38/50.73 tff('161', plain, (( bool(sk_P) | false = true)) <= ((prop(sk_P) = true)), 50.38/50.73 inference('s_sup+', [status(thm)], ['159', '160'])). 50.38/50.73 tff('162', plain, false != true, 50.38/50.73 inference('cnf', [status(esa)], [distinct_false_true_err])). 50.38/50.73 tff('163', plain, ( bool(sk_P)) <= ((prop(sk_P) = true)), 50.38/50.73 inference('simplify_reflect-', [status(thm)], ['161', '162'])). 50.38/50.73 tff('164', plain, ![X70]: (X70 = true | false = X70 | ~ bool(X70)), 50.38/50.73 inference('cnf', [status(esa)], [def_bool])). 50.38/50.73 tff('165', plain, ((sk_P = true | false = sk_P)) <= ((prop(sk_P) = true)), 50.38/50.73 inference('s_sup-', [status(thm)], ['163', '164'])). 50.38/50.73 tff('166', plain, ~ (prop(sk_P) = true) | (sk_P = true) | (false = sk_P), 50.38/50.73 inference('split', [status(esa)], ['165'])). 50.38/50.73 tff('167', plain, 50.38/50.73 ~ ( bool(prop(sk_P))) | (prop(sk_P) = true) | (false = prop(sk_P)), 50.38/50.73 inference('split', [status(esa)], ['36'])). 50.38/50.73 tff('168', plain, (false2 = phi(phi(prop(sk_P)))) | ( bool(prop(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['12'])). 50.38/50.73 tff('169', plain, (false2 = phi(phi(prop(sk_P)))), 50.38/50.73 inference('sat_resolution*', [status(thm)], 50.38/50.73 ['73', '141', '158', '166', '167', '168'])). 50.38/50.73 tff('170', plain, ( bool(sk_P) | false2 = phi(false)), 50.38/50.73 inference('simpl_trail', [status(thm)], ['16', '169'])). 50.38/50.73 tff('171', plain, (~ bool(sk_P)) <= (~ ( bool(sk_P))), 50.38/50.73 inference('split', [status(esa)], ['95'])). 50.38/50.73 tff('172', plain, ~ ( bool(sk_P)) | (sk_P = true) | (false = sk_P), 50.38/50.73 inference('split', [status(esa)], ['84'])). 50.38/50.73 tff('173', plain, ~ ( bool(sk_P)), 50.38/50.73 inference('sat_resolution*', [status(thm)], ['141', '158', '172'])). 50.38/50.73 tff('174', plain, ~ bool(sk_P), 50.38/50.73 inference('simpl_trail', [status(thm)], ['171', '173'])). 50.38/50.73 tff('175', plain, false2 = phi(false), 50.38/50.73 inference('clc', [status(thm)], ['170', '174'])). 50.38/50.73 tff('176', plain, false2 = false, 50.38/50.73 inference('s_sup+', [status(thm)], ['6', '175'])). 50.38/50.73 tff('177', plain, false2 != false, 50.38/50.73 inference('simpl_trail', [status(thm)], ['96', '139'])). 50.38/50.73 tff('178', plain, $false, 50.38/50.73 inference('simplify_reflect-', [status(thm)], ['176', '177'])). 50.38/50.73 50.38/50.73 % SZS output end Refutation 50.38/50.73 50.38/50.74 % Zipperpin 1.5 exiting 50.38/50.74 EOF