0.11/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.14 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.v1YHnIkoGd 0.15/0.36 % Computer : n019.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % DateTime : Thu Jul 2 08:24:56 EDT 2020 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 120 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.36 % Python version: Python 3.6.8 0.15/0.37 % Running in FO mode 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo7.sh for 25 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo8.sh for 20 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo5.sh for 20 95.96/96.42 % Warning: 95.96/96.42 % To remain in the chosen logic fragment, unification with booleans has been disabled. 95.96/96.42 % 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo11.sh for 20 95.96/96.42 % Warning: 95.96/96.42 % To remain in the chosen logic fragment, unification with booleans has been disabled. 95.96/96.42 % 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo11.lcnf.sh for 15 95.96/96.42 % Warning: 95.96/96.42 % To remain in the chosen logic fragment, unification with booleans has been disabled. 95.96/96.42 % 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo6.sh for 15 95.96/96.42 % Running /export/starexec/sandbox2/solver/bin/fo/fo13.sh for 15 95.96/96.42 % Solved by: fo/fo13.sh 95.96/96.42 To remain in the chosen logic fragment, unification with booleans has been disabled. 95.96/96.42 % done 1480 iterations in 1.174s 95.96/96.42 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 95.96/96.42 % SZS output start Refutation 95.96/96.42 tff(axiom_m9, axiom, 95.96/96.42 ((![X]: is_a_theorem(strict_implies(possibly(possibly(X)),possibly(X)))) <=> 95.96/96.42 axiom_m9)). 95.96/96.42 tff('0', plain, 95.96/96.42 ( axiom_m9 95.96/96.42 | ~ is_a_theorem( 95.96/96.42 strict_implies(possibly(possibly(sk_X_25)), possibly(sk_X_25)))), 95.96/96.42 inference('cnf', [status(esa)], [axiom_m9])). 95.96/96.42 tff(s1_0_m6s3m9b_axiom_m9, conjecture, (axiom_m9)). 95.96/96.42 tff(zf_stmt_0, negated_conjecture, (~axiom_m9)). 95.96/96.42 tff('1', plain, ~ axiom_m9, inference('cnf', [status(esa)], [zf_stmt_0])). 95.96/96.42 tff('2', plain, 95.96/96.42 ~ is_a_theorem( 95.96/96.42 strict_implies(possibly(possibly(sk_X_25)), possibly(sk_X_25))), 95.96/96.42 inference('clc', [status(thm)], ['0', '1'])). 95.96/96.42 tff(op_possibly, axiom, 95.96/96.42 (op_possibly => (![X]: (possibly(X) = not(necessarily(not(X))))))). 95.96/96.42 tff('3', plain, 95.96/96.42 ![X107]: (possibly(X107) = not(necessarily(not(X107))) | ~ op_possibly), 95.96/96.42 inference('cnf', [status(esa)], [op_possibly])). 95.96/96.42 tff(km5_op_possibly, axiom, (op_possibly)). 95.96/96.42 tff('4', plain, op_possibly, 95.96/96.42 inference('cnf', [status(esa)], [km5_op_possibly])). 95.96/96.42 tff('5', plain, ![X107]: possibly(X107) = not(necessarily(not(X107))), 95.96/96.42 inference('demod', [status(thm)], ['3', '4'])). 95.96/96.42 tff('6', plain, ![X107]: possibly(X107) = not(necessarily(not(X107))), 95.96/96.42 inference('demod', [status(thm)], ['3', '4'])). 95.96/96.42 tff('7', plain, ![X107]: possibly(X107) = not(necessarily(not(X107))), 95.96/96.42 inference('demod', [status(thm)], ['3', '4'])). 95.96/96.42 tff('8', plain, 95.96/96.42 ![X0]: possibly(necessarily(not(X0))) = not(necessarily(possibly(X0))), 95.96/96.42 inference('s_sup+', [status(thm)], ['6', '7'])). 95.96/96.42 tff(axiom_5, axiom, 95.96/96.42 ((![X]: is_a_theorem(implies(possibly(X),necessarily(possibly(X))))) <=> 95.96/96.42 axiom_5)). 95.96/96.42 tff('9', plain, 95.96/96.42 ![X101]: 95.96/96.42 ( is_a_theorem(implies(possibly(X101), necessarily(possibly(X101)))) 95.96/96.42 | ~ axiom_5), 95.96/96.42 inference('cnf', [status(esa)], [axiom_5])). 95.96/96.42 tff(km5_axiom_5, axiom, (axiom_5)). 95.96/96.42 tff('10', plain, axiom_5, inference('cnf', [status(esa)], [km5_axiom_5])). 95.96/96.42 tff('11', plain, 95.96/96.42 ![X101]: 95.96/96.42 is_a_theorem(implies(possibly(X101), necessarily(possibly(X101)))), 95.96/96.42 inference('demod', [status(thm)], ['9', '10'])). 95.96/96.42 tff(op_equiv, axiom, 95.96/96.42 (op_equiv => (![X,Y]: (and(implies(X,Y),implies(Y,X)) = equiv(X,Y))))). 95.96/96.42 tff('12', plain, 95.96/96.42 ![X57, X58]: 95.96/96.42 (and(implies(X57, X58), implies(X58, X57)) = equiv(X57, X58) 95.96/96.42 | ~ op_equiv), 95.96/96.42 inference('cnf', [status(esa)], [op_equiv])). 95.96/96.42 tff(hilbert_op_equiv, axiom, (op_equiv)). 95.96/96.42 tff('13', plain, op_equiv, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_op_equiv])). 95.96/96.42 tff('14', plain, 95.96/96.42 ![X57, X58]: and(implies(X57, X58), implies(X58, X57)) = equiv(X57, X58), 95.96/96.42 inference('demod', [status(thm)], ['12', '13'])). 95.96/96.42 tff(and_3, axiom, 95.96/96.42 ((![X,Y]: is_a_theorem(implies(X,implies(Y,and(X,Y))))) <=> and_3)). 95.96/96.42 tff('15', plain, 95.96/96.42 ![X6, X7]: 95.96/96.42 ( is_a_theorem(implies(X6, implies(X7, and(X6, X7)))) | ~ and_3), 95.96/96.42 inference('cnf', [status(esa)], [and_3])). 95.96/96.42 tff(hilbert_and_3, axiom, (and_3)). 95.96/96.42 tff('16', plain, and_3, inference('cnf', [status(esa)], [hilbert_and_3])). 95.96/96.42 tff('17', plain, 95.96/96.42 ![X6, X7]: is_a_theorem(implies(X6, implies(X7, and(X6, X7)))), 95.96/96.42 inference('demod', [status(thm)], ['15', '16'])). 95.96/96.42 tff(modus_ponens, axiom, 95.96/96.42 ((![X,Y]: 95.96/96.42 ((is_a_theorem(X) & is_a_theorem(implies(X,Y))) => is_a_theorem(Y))) <=> 95.96/96.42 modus_ponens)). 95.96/96.42 tff('18', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49) 95.96/96.42 | ~ modus_ponens), 95.96/96.42 inference('cnf', [status(esa)], [modus_ponens])). 95.96/96.42 tff(hilbert_modus_ponens, axiom, (modus_ponens)). 95.96/96.42 tff('19', plain, modus_ponens, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_modus_ponens])). 95.96/96.42 tff('20', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('21', plain, 95.96/96.42 ![X0, X1]: ( is_a_theorem(implies(X0, and(X1, X0))) | ~ is_a_theorem(X1)), 95.96/96.42 inference('s_sup-', [status(thm)], ['17', '20'])). 95.96/96.42 tff('22', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('23', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(X1) | is_a_theorem(and(X1, X0)) | ~ is_a_theorem(X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['21', '22'])). 95.96/96.42 tff('24', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(implies(X1, X0)) 95.96/96.42 | is_a_theorem(equiv(X1, X0)) 95.96/96.42 | ~ is_a_theorem(implies(X0, X1))), 95.96/96.42 inference('s_sup+', [status(thm)], ['14', '23'])). 95.96/96.42 tff('25', plain, 95.96/96.42 ![X0]: 95.96/96.42 ( is_a_theorem(equiv(possibly(X0), necessarily(possibly(X0)))) 95.96/96.42 | ~ is_a_theorem(implies(necessarily(possibly(X0)), possibly(X0)))), 95.96/96.42 inference('s_sup-', [status(thm)], ['11', '24'])). 95.96/96.42 tff(axiom_M, axiom, 95.96/96.42 ((![X]: is_a_theorem(implies(necessarily(X),X))) <=> axiom_M)). 95.96/96.42 tff('26', plain, 95.96/96.42 ![X70]: ( is_a_theorem(implies(necessarily(X70), X70)) | ~ axiom_M), 95.96/96.42 inference('cnf', [status(esa)], [axiom_M])). 95.96/96.42 tff(km5_axiom_M, axiom, (axiom_M)). 95.96/96.42 tff('27', plain, axiom_M, inference('cnf', [status(esa)], [km5_axiom_M])). 95.96/96.42 tff('28', plain, ![X70]: is_a_theorem(implies(necessarily(X70), X70)), 95.96/96.42 inference('demod', [status(thm)], ['26', '27'])). 95.96/96.42 tff('29', plain, 95.96/96.42 ![X0]: is_a_theorem(equiv(possibly(X0), necessarily(possibly(X0)))), 95.96/96.42 inference('demod', [status(thm)], ['25', '28'])). 95.96/96.42 tff(substitution_of_equivalents, axiom, 95.96/96.42 ((![X,Y]: (is_a_theorem(equiv(X,Y)) => (X = Y))) <=> 95.96/96.42 substitution_of_equivalents)). 95.96/96.42 tff('30', plain, 95.96/96.42 ![X21, X22]: 95.96/96.42 (~ is_a_theorem(equiv(X21, X22)) 95.96/96.42 | X21 = X22 95.96/96.42 | ~ substitution_of_equivalents), 95.96/96.42 inference('cnf', [status(esa)], [substitution_of_equivalents])). 95.96/96.42 tff(substitution_of_equivalents, axiom, (substitution_of_equivalents)). 95.96/96.42 tff('31', plain, substitution_of_equivalents, 95.96/96.42 inference('cnf', [status(esa)], [substitution_of_equivalents])). 95.96/96.42 tff('32', plain, ![X21, X22]: (~ is_a_theorem(equiv(X21, X22)) | X21 = X22), 95.96/96.42 inference('demod', [status(thm)], ['30', '31'])). 95.96/96.42 tff('33', plain, ![X0]: possibly(X0) = necessarily(possibly(X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['29', '32'])). 95.96/96.42 tff('34', plain, ![X0]: possibly(necessarily(not(X0))) = not(possibly(X0)), 95.96/96.42 inference('demod', [status(thm)], ['8', '33'])). 95.96/96.42 tff('35', plain, 95.96/96.42 ![X0]: 95.96/96.42 possibly(necessarily(possibly(X0))) 95.96/96.42 = not(possibly(necessarily(not(X0)))), 95.96/96.42 inference('s_sup+', [status(thm)], ['5', '34'])). 95.96/96.42 tff('36', plain, ![X0]: possibly(X0) = necessarily(possibly(X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['29', '32'])). 95.96/96.42 tff('37', plain, ![X0]: possibly(necessarily(not(X0))) = not(possibly(X0)), 95.96/96.42 inference('demod', [status(thm)], ['8', '33'])). 95.96/96.42 tff('38', plain, ![X0]: possibly(possibly(X0)) = not(not(possibly(X0))), 95.96/96.42 inference('demod', [status(thm)], ['35', '36', '37'])). 95.96/96.42 tff('39', plain, 95.96/96.42 ![X6, X7]: is_a_theorem(implies(X6, implies(X7, and(X6, X7)))), 95.96/96.42 inference('demod', [status(thm)], ['15', '16'])). 95.96/96.42 tff(implies_2, axiom, 95.96/96.42 (implies_2 <=> 95.96/96.42 (![X,Y]: is_a_theorem(implies(implies(X,implies(X,Y)),implies(X,Y)))))). 95.96/96.42 tff('40', plain, 95.96/96.42 ![X50, X51]: 95.96/96.42 ( is_a_theorem( 95.96/96.42 implies(implies(X50, implies(X50, X51)), implies(X50, X51))) 95.96/96.42 | ~ implies_2), 95.96/96.42 inference('cnf', [status(esa)], [implies_2])). 95.96/96.42 tff(hilbert_implies_2, axiom, (implies_2)). 95.96/96.42 tff('41', plain, implies_2, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_implies_2])). 95.96/96.42 tff('42', plain, 95.96/96.42 ![X50, X51]: 95.96/96.42 is_a_theorem( 95.96/96.42 implies(implies(X50, implies(X50, X51)), implies(X50, X51))), 95.96/96.42 inference('demod', [status(thm)], ['40', '41'])). 95.96/96.42 tff('43', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('44', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 ( is_a_theorem(implies(X1, X0)) 95.96/96.42 | ~ is_a_theorem(implies(X1, implies(X1, X0)))), 95.96/96.42 inference('s_sup-', [status(thm)], ['42', '43'])). 95.96/96.42 tff('45', plain, ![X0]: is_a_theorem(implies(X0, and(X0, X0))), 95.96/96.42 inference('s_sup-', [status(thm)], ['39', '44'])). 95.96/96.42 tff('46', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(implies(X1, X0)) 95.96/96.42 | is_a_theorem(equiv(X1, X0)) 95.96/96.42 | ~ is_a_theorem(implies(X0, X1))), 95.96/96.42 inference('s_sup+', [status(thm)], ['14', '23'])). 95.96/96.42 tff('47', plain, 95.96/96.42 ![X0]: 95.96/96.42 ( is_a_theorem(equiv(X0, and(X0, X0))) 95.96/96.42 | ~ is_a_theorem(implies(and(X0, X0), X0))), 95.96/96.42 inference('s_sup-', [status(thm)], ['45', '46'])). 95.96/96.42 tff(and_2, axiom, (and_2 <=> (![X,Y]: is_a_theorem(implies(and(X,Y),Y))))). 95.96/96.42 tff('48', plain, 95.96/96.42 ![X36, X37]: ( is_a_theorem(implies(and(X36, X37), X37)) | ~ and_2), 95.96/96.42 inference('cnf', [status(esa)], [and_2])). 95.96/96.42 tff(hilbert_and_2, axiom, (and_2)). 95.96/96.42 tff('49', plain, and_2, inference('cnf', [status(esa)], [hilbert_and_2])). 95.96/96.42 tff('50', plain, ![X36, X37]: is_a_theorem(implies(and(X36, X37), X37)), 95.96/96.42 inference('demod', [status(thm)], ['48', '49'])). 95.96/96.42 tff('51', plain, ![X0]: is_a_theorem(equiv(X0, and(X0, X0))), 95.96/96.42 inference('demod', [status(thm)], ['47', '50'])). 95.96/96.42 tff('52', plain, ![X21, X22]: (~ is_a_theorem(equiv(X21, X22)) | X21 = X22), 95.96/96.42 inference('demod', [status(thm)], ['30', '31'])). 95.96/96.42 tff('53', plain, ![X0]: X0 = and(X0, X0), 95.96/96.42 inference('s_sup-', [status(thm)], ['51', '52'])). 95.96/96.42 tff(op_implies_and, axiom, 95.96/96.42 (op_implies_and => (![X,Y]: (not(and(X,not(Y))) = implies(X,Y))))). 95.96/96.42 tff('54', plain, 95.96/96.42 ![X61, X62]: 95.96/96.42 (not(and(X61, not(X62))) = implies(X61, X62) | ~ op_implies_and), 95.96/96.42 inference('cnf', [status(esa)], [op_implies_and])). 95.96/96.42 tff(hilbert_op_implies_and, axiom, (op_implies_and)). 95.96/96.42 tff('55', plain, op_implies_and, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_op_implies_and])). 95.96/96.42 tff('56', plain, ![X61, X62]: not(and(X61, not(X62))) = implies(X61, X62), 95.96/96.42 inference('demod', [status(thm)], ['54', '55'])). 95.96/96.42 tff('57', plain, ![X0]: not(not(X0)) = implies(not(X0), X0), 95.96/96.42 inference('s_sup+', [status(thm)], ['53', '56'])). 95.96/96.42 tff(op_or, axiom, (op_or => (![X,Y]: (or(X,Y) = not(and(not(X),not(Y))))))). 95.96/96.42 tff('58', plain, 95.96/96.42 ![X59, X60]: (or(X59, X60) = not(and(not(X59), not(X60))) | ~ op_or), 95.96/96.42 inference('cnf', [status(esa)], [op_or])). 95.96/96.42 tff('59', plain, ![X61, X62]: not(and(X61, not(X62))) = implies(X61, X62), 95.96/96.42 inference('demod', [status(thm)], ['54', '55'])). 95.96/96.42 tff(hilbert_op_or, axiom, (op_or)). 95.96/96.42 tff('60', plain, op_or, inference('cnf', [status(esa)], [hilbert_op_or])). 95.96/96.42 tff('61', plain, ![X59, X60]: or(X59, X60) = implies(not(X59), X60), 95.96/96.42 inference('demod', [status(thm)], ['58', '59', '60'])). 95.96/96.42 tff('62', plain, ![X0]: not(not(X0)) = or(X0, X0), 95.96/96.42 inference('demod', [status(thm)], ['57', '61'])). 95.96/96.42 tff('63', plain, 95.96/96.42 ![X0]: possibly(possibly(X0)) = or(possibly(X0), possibly(X0)), 95.96/96.42 inference('s_sup+', [status(thm)], ['38', '62'])). 95.96/96.42 tff('64', plain, ![X0]: not(not(X0)) = or(X0, X0), 95.96/96.42 inference('demod', [status(thm)], ['57', '61'])). 95.96/96.42 tff('65', plain, ![X0]: not(not(X0)) = or(X0, X0), 95.96/96.42 inference('demod', [status(thm)], ['57', '61'])). 95.96/96.42 tff('66', plain, ![X59, X60]: or(X59, X60) = implies(not(X59), X60), 95.96/96.42 inference('demod', [status(thm)], ['58', '59', '60'])). 95.96/96.42 tff(or_2, axiom, ((![X,Y]: is_a_theorem(implies(Y,or(X,Y)))) <=> or_2)). 95.96/96.42 tff('67', plain, 95.96/96.42 ![X2, X3]: ( is_a_theorem(implies(X2, or(X3, X2))) | ~ or_2), 95.96/96.42 inference('cnf', [status(esa)], [or_2])). 95.96/96.42 tff(hilbert_or_2, axiom, (or_2)). 95.96/96.42 tff('68', plain, or_2, inference('cnf', [status(esa)], [hilbert_or_2])). 95.96/96.42 tff('69', plain, ![X2, X3]: is_a_theorem(implies(X2, or(X3, X2))), 95.96/96.42 inference('demod', [status(thm)], ['67', '68'])). 95.96/96.42 tff('70', plain, ![X0, X1]: is_a_theorem(or(X0, or(X1, not(X0)))), 95.96/96.42 inference('s_sup+', [status(thm)], ['66', '69'])). 95.96/96.42 tff('71', plain, ![X0]: is_a_theorem(or(X0, not(not(not(X0))))), 95.96/96.42 inference('s_sup+', [status(thm)], ['65', '70'])). 95.96/96.42 tff('72', plain, ![X59, X60]: or(X59, X60) = implies(not(X59), X60), 95.96/96.42 inference('demod', [status(thm)], ['58', '59', '60'])). 95.96/96.42 tff(modus_tollens, axiom, 95.96/96.42 ((![X,Y]: is_a_theorem(implies(implies(not(Y),not(X)),implies(X,Y)))) <=> 95.96/96.42 modus_tollens)). 95.96/96.42 tff('73', plain, 95.96/96.42 ![X12, X13]: 95.96/96.42 ( is_a_theorem(implies(implies(not(X12), not(X13)), implies(X13, X12))) 95.96/96.42 | ~ modus_tollens), 95.96/96.42 inference('cnf', [status(esa)], [modus_tollens])). 95.96/96.42 tff('74', plain, ![X59, X60]: or(X59, X60) = implies(not(X59), X60), 95.96/96.42 inference('demod', [status(thm)], ['58', '59', '60'])). 95.96/96.42 tff(hilbert_modus_tollens, axiom, (modus_tollens)). 95.96/96.42 tff('75', plain, modus_tollens, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_modus_tollens])). 95.96/96.42 tff('76', plain, 95.96/96.42 ![X12, X13]: is_a_theorem(implies(or(X12, not(X13)), implies(X13, X12))), 95.96/96.42 inference('demod', [status(thm)], ['73', '74', '75'])). 95.96/96.42 tff('77', plain, 95.96/96.42 ![X0, X1]: is_a_theorem(implies(or(X0, not(not(X1))), or(X1, X0))), 95.96/96.42 inference('s_sup+', [status(thm)], ['72', '76'])). 95.96/96.42 tff('78', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('79', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 ( is_a_theorem(or(X1, X0)) | ~ is_a_theorem(or(X0, not(not(X1))))), 95.96/96.42 inference('s_sup-', [status(thm)], ['77', '78'])). 95.96/96.42 tff('80', plain, ![X0]: is_a_theorem(or(not(X0), X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['71', '79'])). 95.96/96.42 tff('81', plain, ![X59, X60]: or(X59, X60) = implies(not(X59), X60), 95.96/96.42 inference('demod', [status(thm)], ['58', '59', '60'])). 95.96/96.42 tff(op_strict_implies, axiom, 95.96/96.42 (op_strict_implies => 95.96/96.42 (![X,Y]: (necessarily(implies(X,Y)) = strict_implies(X,Y))))). 95.96/96.42 tff('82', plain, 95.96/96.42 ![X105, X106]: 95.96/96.42 (necessarily(implies(X105, X106)) = strict_implies(X105, X106) 95.96/96.42 | ~ op_strict_implies), 95.96/96.42 inference('cnf', [status(esa)], [op_strict_implies])). 95.96/96.42 tff(s1_0_op_strict_implies, axiom, (op_strict_implies)). 95.96/96.42 tff('83', plain, op_strict_implies, 95.96/96.42 inference('cnf', [status(esa)], [s1_0_op_strict_implies])). 95.96/96.42 tff('84', plain, 95.96/96.42 ![X105, X106]: 95.96/96.42 necessarily(implies(X105, X106)) = strict_implies(X105, X106), 95.96/96.42 inference('demod', [status(thm)], ['82', '83'])). 95.96/96.42 tff('85', plain, 95.96/96.42 ![X0, X1]: necessarily(or(X1, X0)) = strict_implies(not(X1), X0), 95.96/96.42 inference('s_sup+', [status(thm)], ['81', '84'])). 95.96/96.42 tff(necessitation, axiom, 95.96/96.42 (necessitation <=> 95.96/96.42 (![X]: (is_a_theorem(X) => is_a_theorem(necessarily(X)))))). 95.96/96.42 tff('86', plain, 95.96/96.42 ![X83]: 95.96/96.42 (~ is_a_theorem(X83) 95.96/96.42 | is_a_theorem(necessarily(X83)) 95.96/96.42 | ~ necessitation), 95.96/96.42 inference('cnf', [status(esa)], [necessitation])). 95.96/96.42 tff(km5_necessitation, axiom, (necessitation)). 95.96/96.42 tff('87', plain, necessitation, 95.96/96.42 inference('cnf', [status(esa)], [km5_necessitation])). 95.96/96.42 tff('88', plain, 95.96/96.42 ![X83]: (~ is_a_theorem(X83) | is_a_theorem(necessarily(X83))), 95.96/96.42 inference('demod', [status(thm)], ['86', '87'])). 95.96/96.42 tff('89', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(or(X1, X0)) 95.96/96.42 | is_a_theorem(strict_implies(not(X1), X0))), 95.96/96.42 inference('s_sup+', [status(thm)], ['85', '88'])). 95.96/96.42 tff('90', plain, ![X0]: is_a_theorem(strict_implies(not(not(X0)), X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['80', '89'])). 95.96/96.42 tff('91', plain, ![X0]: is_a_theorem(strict_implies(or(X0, X0), X0)), 95.96/96.42 inference('s_sup+', [status(thm)], ['64', '90'])). 95.96/96.42 tff('92', plain, 95.96/96.42 ![X105, X106]: 95.96/96.42 necessarily(implies(X105, X106)) = strict_implies(X105, X106), 95.96/96.42 inference('demod', [status(thm)], ['82', '83'])). 95.96/96.42 tff('93', plain, ![X70]: is_a_theorem(implies(necessarily(X70), X70)), 95.96/96.42 inference('demod', [status(thm)], ['26', '27'])). 95.96/96.42 tff('94', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('95', plain, 95.96/96.42 ![X0]: ( is_a_theorem(X0) | ~ is_a_theorem(necessarily(X0))), 95.96/96.42 inference('s_sup-', [status(thm)], ['93', '94'])). 95.96/96.42 tff('96', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 ( is_a_theorem(implies(X1, X0)) 95.96/96.42 | ~ is_a_theorem(strict_implies(X1, X0))), 95.96/96.42 inference('s_sup-', [status(thm)], ['92', '95'])). 95.96/96.42 tff('97', plain, ![X0]: is_a_theorem(implies(or(X0, X0), X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['91', '96'])). 95.96/96.42 tff('98', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(implies(X1, X0)) 95.96/96.42 | is_a_theorem(equiv(X1, X0)) 95.96/96.42 | ~ is_a_theorem(implies(X0, X1))), 95.96/96.42 inference('s_sup+', [status(thm)], ['14', '23'])). 95.96/96.42 tff('99', plain, 95.96/96.42 ![X0]: 95.96/96.42 ( is_a_theorem(equiv(or(X0, X0), X0)) 95.96/96.42 | ~ is_a_theorem(implies(X0, or(X0, X0)))), 95.96/96.42 inference('s_sup-', [status(thm)], ['97', '98'])). 95.96/96.42 tff('100', plain, ![X2, X3]: is_a_theorem(implies(X2, or(X3, X2))), 95.96/96.42 inference('demod', [status(thm)], ['67', '68'])). 95.96/96.42 tff('101', plain, ![X0]: is_a_theorem(equiv(or(X0, X0), X0)), 95.96/96.42 inference('demod', [status(thm)], ['99', '100'])). 95.96/96.42 tff('102', plain, ![X21, X22]: (~ is_a_theorem(equiv(X21, X22)) | X21 = X22), 95.96/96.42 inference('demod', [status(thm)], ['30', '31'])). 95.96/96.42 tff('103', plain, ![X0]: or(X0, X0) = X0, 95.96/96.42 inference('s_sup-', [status(thm)], ['101', '102'])). 95.96/96.42 tff('104', plain, ![X0]: possibly(possibly(X0)) = possibly(X0), 95.96/96.42 inference('demod', [status(thm)], ['63', '103'])). 95.96/96.42 tff('105', plain, ![X0]: X0 = and(X0, X0), 95.96/96.42 inference('s_sup-', [status(thm)], ['51', '52'])). 95.96/96.42 tff(op_strict_equiv, axiom, 95.96/96.42 (op_strict_equiv => 95.96/96.42 (![X,Y]: 95.96/96.42 (and(strict_implies(X,Y),strict_implies(Y,X)) = strict_equiv(X,Y))))). 95.96/96.42 tff('106', plain, 95.96/96.42 ![X108, X109]: 95.96/96.42 (and(strict_implies(X108, X109), strict_implies(X109, X108)) 95.96/96.42 = strict_equiv(X108, X109) 95.96/96.42 | ~ op_strict_equiv), 95.96/96.42 inference('cnf', [status(esa)], [op_strict_equiv])). 95.96/96.42 tff(s1_0_op_strict_equiv, axiom, (op_strict_equiv)). 95.96/96.42 tff('107', plain, op_strict_equiv, 95.96/96.42 inference('cnf', [status(esa)], [s1_0_op_strict_equiv])). 95.96/96.42 tff('108', plain, 95.96/96.42 ![X108, X109]: 95.96/96.42 and(strict_implies(X108, X109), strict_implies(X109, X108)) 95.96/96.42 = strict_equiv(X108, X109), 95.96/96.42 inference('demod', [status(thm)], ['106', '107'])). 95.96/96.42 tff('109', plain, ![X0]: strict_implies(X0, X0) = strict_equiv(X0, X0), 95.96/96.42 inference('s_sup+', [status(thm)], ['105', '108'])). 95.96/96.42 tff('110', plain, 95.96/96.42 ![X108, X109]: 95.96/96.42 and(strict_implies(X108, X109), strict_implies(X109, X108)) 95.96/96.42 = strict_equiv(X108, X109), 95.96/96.42 inference('demod', [status(thm)], ['106', '107'])). 95.96/96.42 tff('111', plain, ![X0]: is_a_theorem(implies(X0, and(X0, X0))), 95.96/96.42 inference('s_sup-', [status(thm)], ['39', '44'])). 95.96/96.42 tff('112', plain, 95.96/96.42 ![X48, X49]: 95.96/96.42 ( is_a_theorem(X48) 95.96/96.42 | ~ is_a_theorem(implies(X49, X48)) 95.96/96.42 | ~ is_a_theorem(X49)), 95.96/96.42 inference('demod', [status(thm)], ['18', '19'])). 95.96/96.42 tff('113', plain, ![X0]: ( is_a_theorem(and(X0, X0)) | ~ is_a_theorem(X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['111', '112'])). 95.96/96.42 tff('114', plain, 95.96/96.42 ![X0]: 95.96/96.42 ( is_a_theorem(strict_equiv(X0, X0)) 95.96/96.42 | ~ is_a_theorem(strict_implies(X0, X0))), 95.96/96.42 inference('s_sup+', [status(thm)], ['110', '113'])). 95.96/96.42 tff(implies_1, axiom, 95.96/96.42 (implies_1 <=> (![X,Y]: is_a_theorem(implies(X,implies(Y,X)))))). 95.96/96.42 tff('115', plain, 95.96/96.42 ![X19, X20]: 95.96/96.42 ( is_a_theorem(implies(X19, implies(X20, X19))) | ~ implies_1), 95.96/96.42 inference('cnf', [status(esa)], [implies_1])). 95.96/96.42 tff(hilbert_implies_1, axiom, (implies_1)). 95.96/96.42 tff('116', plain, implies_1, 95.96/96.42 inference('cnf', [status(esa)], [hilbert_implies_1])). 95.96/96.42 tff('117', plain, 95.96/96.42 ![X19, X20]: is_a_theorem(implies(X19, implies(X20, X19))), 95.96/96.42 inference('demod', [status(thm)], ['115', '116'])). 95.96/96.42 tff('118', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 ( is_a_theorem(implies(X1, X0)) 95.96/96.42 | ~ is_a_theorem(implies(X1, implies(X1, X0)))), 95.96/96.42 inference('s_sup-', [status(thm)], ['42', '43'])). 95.96/96.42 tff('119', plain, ![X0]: is_a_theorem(implies(X0, X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['117', '118'])). 95.96/96.42 tff('120', plain, 95.96/96.42 ![X105, X106]: 95.96/96.42 necessarily(implies(X105, X106)) = strict_implies(X105, X106), 95.96/96.42 inference('demod', [status(thm)], ['82', '83'])). 95.96/96.42 tff('121', plain, 95.96/96.42 ![X83]: (~ is_a_theorem(X83) | is_a_theorem(necessarily(X83))), 95.96/96.42 inference('demod', [status(thm)], ['86', '87'])). 95.96/96.42 tff('122', plain, 95.96/96.42 ![X0, X1]: 95.96/96.42 (~ is_a_theorem(implies(X1, X0)) 95.96/96.42 | is_a_theorem(strict_implies(X1, X0))), 95.96/96.42 inference('s_sup+', [status(thm)], ['120', '121'])). 95.96/96.42 tff('123', plain, ![X0]: is_a_theorem(strict_implies(X0, X0)), 95.96/96.42 inference('s_sup-', [status(thm)], ['119', '122'])). 95.96/96.42 tff('124', plain, ![X0]: is_a_theorem(strict_equiv(X0, X0)), 95.96/96.42 inference('demod', [status(thm)], ['114', '123'])). 95.96/96.42 tff('125', plain, $false, 95.96/96.42 inference('demod', [status(thm)], ['2', '104', '109', '124'])). 95.96/96.42 95.96/96.42 % SZS output end Refutation 95.96/96.42 96.01/96.42 % Zipperpin 1.5 exiting 96.01/96.43 EOF