0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.14 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.Pd571bcWSq true 0.14/0.35 % Computer : n015.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 960 0.14/0.35 % WCLimit : 120 0.14/0.35 % DateTime : Tue Aug 9 05:34:41 EDT 2022 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 960 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in FO mode 0.39/0.72 % Total configuration time : 435 0.39/0.72 % Estimated wc time : 845 0.39/0.72 % Estimated cpu time (7 cpus) : 120.71428571428571 0.40/0.82 % /export/starexec/sandbox/solver/bin/fo/fo6_bce.sh running for 58s 0.40/0.82 % /export/starexec/sandbox/solver/bin/fo/fo1_av.sh running for 58s 0.40/0.82 % /export/starexec/sandbox/solver/bin/fo/fo13.sh running for 39s 0.40/0.82 % /export/starexec/sandbox/solver/bin/fo/fo7.sh running for 49s 0.40/0.83 % /export/starexec/sandbox/solver/bin/fo/fo3_bce.sh running for 58s 0.40/0.89 % /export/starexec/sandbox/solver/bin/fo/fo4.sh running for 39s 0.40/0.89 % /export/starexec/sandbox/solver/bin/fo/fo5.sh running for 39s 0.40/0.89 % /export/starexec/sandbox/solver/bin/fo/fo1_lcnf.sh running for 39s 0.40/0.90 % /export/starexec/sandbox/solver/bin/fo/fo17_bce.sh running for 39s 0.40/0.94 % /export/starexec/sandbox/solver/bin/fo/fo8.sh running for 39s 29.85/5.22 % Solved by fo/fo5.sh. 29.85/5.22 % done 2544 iterations in 4.239s 29.85/5.22 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 29.85/5.22 % SZS output start Refutation 29.85/5.22 thf(sk__20_type, type, sk__20: $i). 29.85/5.22 thf(axiom_m10_type, type, axiom_m10: $o). 29.85/5.22 thf(sk__93_type, type, sk__93: $i). 29.85/5.22 thf(necessitation_type, type, necessitation: $o). 29.85/5.22 thf(axiom_4_type, type, axiom_4: $o). 29.85/5.22 thf(necessarily_type, type, necessarily: $i > $i). 29.85/5.22 thf(op_implies_and_type, type, op_implies_and: $o). 29.85/5.22 thf(cn3_type, type, cn3: $o). 29.85/5.22 thf(modus_ponens_type, type, modus_ponens: $o). 29.85/5.22 thf(is_a_theorem_type, type, is_a_theorem: $i > $o). 29.85/5.22 thf(or_type, type, or: $i > $i > $i). 29.85/5.22 thf(and_type, type, and: $i > $i > $i). 29.85/5.22 thf(modus_tollens_type, type, modus_tollens: $o). 29.85/5.22 thf(substitution_of_equivalents_type, type, substitution_of_equivalents: $o). 29.85/5.22 thf(op_equiv_type, type, op_equiv: $o). 29.85/5.22 thf(axiom_B_type, type, axiom_B: $o). 29.85/5.22 thf(implies_2_type, type, implies_2: $o). 29.85/5.22 thf(strict_implies_type, type, strict_implies: $i > $i > $i). 29.85/5.22 thf(op_or_type, type, op_or: $o). 29.85/5.22 thf(and_3_type, type, and_3: $o). 29.85/5.22 thf(and_1_type, type, and_1: $o). 29.85/5.22 thf(equiv_type, type, equiv: $i > $i > $i). 29.85/5.22 thf(or_2_type, type, or_2: $o). 29.85/5.22 thf(possibly_type, type, possibly: $i > $i). 29.85/5.22 thf(op_strict_implies_type, type, op_strict_implies: $o). 29.85/5.22 thf(axiom_M_type, type, axiom_M: $o). 29.85/5.22 thf(or_1_type, type, or_1: $o). 29.85/5.22 thf(not_type, type, not: $i > $i). 29.85/5.22 thf(implies_type, type, implies: $i > $i > $i). 29.85/5.22 thf(op_possibly_type, type, op_possibly: $o). 29.85/5.22 thf(axiom_m10, axiom, 29.85/5.22 (( axiom_m10 ) <=> 29.85/5.22 ( ![X:$i]: 29.85/5.22 ( is_a_theorem @ 29.85/5.22 ( strict_implies @ 29.85/5.22 ( possibly @ X ) @ ( necessarily @ ( possibly @ X ) ) ) ) ))). 29.85/5.22 thf(zip_derived_cl129, plain, 29.85/5.22 (( (axiom_m10) 29.85/5.22 | ~ (is_a_theorem @ 29.85/5.22 (strict_implies @ (possibly @ sk__93) @ 29.85/5.22 (necessarily @ (possibly @ sk__93)))))), 29.85/5.22 inference('cnf', [status(esa)], [axiom_m10])). 29.85/5.22 thf(s1_0_m10_axiom_m10, conjecture, (axiom_m10)). 29.85/5.22 thf(zf_stmt_0, negated_conjecture, (~( axiom_m10 )), 29.85/5.22 inference('cnf.neg', [status(esa)], [s1_0_m10_axiom_m10])). 29.85/5.22 thf(zip_derived_cl140, plain, (~ (axiom_m10)), 29.85/5.22 inference('cnf', [status(esa)], [zf_stmt_0])). 29.85/5.22 thf(zip_derived_cl227, plain, 29.85/5.22 (~ (is_a_theorem @ 29.85/5.22 (strict_implies @ (possibly @ sk__93) @ 29.85/5.22 (necessarily @ (possibly @ sk__93))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl129, zip_derived_cl140])). 29.85/5.22 thf(and_3, axiom, 29.85/5.22 (( and_3 ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( is_a_theorem @ ( implies @ X @ ( implies @ Y @ ( and @ X @ Y ) ) ) ) ))). 29.85/5.22 thf(zip_derived_cl8, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ X0 @ (implies @ X1 @ (and @ X0 @ X1)))) 29.85/5.22 | ~ (and_3))), 29.85/5.22 inference('cnf', [status(esa)], [and_3])). 29.85/5.22 thf(hilbert_and_3, axiom, (and_3)). 29.85/5.22 thf(zip_derived_cl68, plain, ( (and_3)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_and_3])). 29.85/5.22 thf(zip_derived_cl247, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (is_a_theorem @ (implies @ X0 @ (implies @ X1 @ (and @ X0 @ X1))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl68])). 29.85/5.22 thf(implies_2, axiom, 29.85/5.22 (( ![X:$i,Y:$i]: 29.85/5.22 ( is_a_theorem @ 29.85/5.22 ( implies @ 29.85/5.22 ( implies @ X @ ( implies @ X @ Y ) ) @ ( implies @ X @ Y ) ) ) ) <=> 29.85/5.22 ( implies_2 ))). 29.85/5.22 thf(zip_derived_cl36, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ 29.85/5.22 (implies @ (implies @ X0 @ (implies @ X0 @ X1)) @ 29.85/5.22 (implies @ X0 @ X1))) 29.85/5.22 | ~ (implies_2))), 29.85/5.22 inference('cnf', [status(esa)], [implies_2])). 29.85/5.22 thf(hilbert_implies_2, axiom, (implies_2)). 29.85/5.22 thf(zip_derived_cl61, plain, ( (implies_2)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_implies_2])). 29.85/5.22 thf(zip_derived_cl341, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (implies @ (implies @ X0 @ (implies @ X0 @ X1)) @ 29.85/5.22 (implies @ X0 @ X1)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl61])). 29.85/5.22 thf(modus_ponens, axiom, 29.85/5.22 (( modus_ponens ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( ( is_a_theorem @ X ) & ( is_a_theorem @ ( implies @ X @ Y ) ) ) => 29.85/5.22 ( is_a_theorem @ Y ) ) ))). 29.85/5.22 thf(zip_derived_cl47, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ X0) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ X1) 29.85/5.22 | ~ (modus_ponens))), 29.85/5.22 inference('cnf', [status(esa)], [modus_ponens])). 29.85/5.22 thf(hilbert_modus_ponens, axiom, (modus_ponens)). 29.85/5.22 thf(zip_derived_cl69, plain, ( (modus_ponens)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_modus_ponens])). 29.85/5.22 thf(zip_derived_cl160, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ X0) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl69])). 29.85/5.22 thf(zip_derived_cl342, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (implies @ X1 @ (implies @ X1 @ X0))) 29.85/5.22 | (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl341, zip_derived_cl160])). 29.85/5.22 thf(zip_derived_cl662, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (implies @ X0 @ (and @ X0 @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl342])). 29.85/5.22 thf(op_equiv, axiom, 29.85/5.22 (( op_equiv ) => 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( equiv @ X @ Y ) = 29.85/5.22 ( and @ ( implies @ X @ Y ) @ ( implies @ Y @ X ) ) ) ))). 29.85/5.22 thf(zip_derived_cl57, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (((equiv @ X0 @ X1) 29.85/5.22 = (and @ (implies @ X0 @ X1) @ (implies @ X1 @ X0))) 29.85/5.22 | ~ (op_equiv))), 29.85/5.22 inference('cnf', [status(esa)], [op_equiv])). 29.85/5.22 thf(hilbert_op_equiv, axiom, (op_equiv)). 29.85/5.22 thf(zip_derived_cl75, plain, ( (op_equiv)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_op_equiv])). 29.85/5.22 thf(zip_derived_cl344, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ((equiv @ X0 @ X1) = (and @ (implies @ X0 @ X1) @ (implies @ X1 @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl57, zip_derived_cl75])). 29.85/5.22 thf(zip_derived_cl247, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (is_a_theorem @ (implies @ X0 @ (implies @ X1 @ (and @ X0 @ X1))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl8, zip_derived_cl68])). 29.85/5.22 thf(zip_derived_cl160, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ X0) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl69])). 29.85/5.22 thf(zip_derived_cl248, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ X1) 29.85/5.22 | (is_a_theorem @ (implies @ X0 @ (and @ X1 @ X0))))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl160])). 29.85/5.22 thf(zip_derived_cl160, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ X0) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl69])). 29.85/5.22 thf(zip_derived_cl1567, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ X1) 29.85/5.22 | ~ (is_a_theorem @ X0) 29.85/5.22 | (is_a_theorem @ (and @ X1 @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl248, zip_derived_cl160])). 29.85/5.22 thf(zip_derived_cl1596, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (equiv @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X0 @ X1)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl1567])). 29.85/5.22 thf(zip_derived_cl2781, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (~ (is_a_theorem @ (implies @ (and @ X0 @ X0) @ X0)) 29.85/5.22 | (is_a_theorem @ (equiv @ (and @ X0 @ X0) @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl662, zip_derived_cl1596])). 29.85/5.22 thf(and_1, axiom, 29.85/5.22 (( and_1 ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: ( is_a_theorem @ ( implies @ ( and @ X @ Y ) @ X ) ) ))). 29.85/5.22 thf(zip_derived_cl0, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ (and @ X0 @ X1) @ X0)) | ~ (and_1))), 29.85/5.22 inference('cnf', [status(esa)], [and_1])). 29.85/5.22 thf(hilbert_and_1, axiom, (and_1)). 29.85/5.22 thf(zip_derived_cl74, plain, ( (and_1)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_and_1])). 29.85/5.22 thf(zip_derived_cl147, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: (is_a_theorem @ (implies @ (and @ X0 @ X1) @ X0))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl0, zip_derived_cl74])). 29.85/5.22 thf(zip_derived_cl2822, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (equiv @ (and @ X0 @ X0) @ X0))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl2781, zip_derived_cl147])). 29.85/5.22 thf(substitution_of_equivalents, axiom, 29.85/5.22 (( substitution_of_equivalents ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( is_a_theorem @ ( equiv @ X @ Y ) ) => ( ( Y ) = ( X ) ) ) ))). 29.85/5.22 thf(zip_derived_cl24, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (equiv @ X0 @ X1)) 29.85/5.22 | ((X1) = (X0)) 29.85/5.22 | ~ (substitution_of_equivalents))), 29.85/5.22 inference('cnf', [status(esa)], [substitution_of_equivalents])). 29.85/5.22 thf(substitution_of_equivalents, axiom, (substitution_of_equivalents)). 29.85/5.22 thf(zip_derived_cl77, plain, ( (substitution_of_equivalents)), 29.85/5.22 inference('cnf', [status(esa)], [substitution_of_equivalents])). 29.85/5.22 thf(zip_derived_cl157, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (equiv @ X0 @ X1)) | ((X1) = (X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl77])). 29.85/5.22 thf(zip_derived_cl2892, plain, (![X0 : $i]: ((X0) = (and @ X0 @ X0))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl2822, zip_derived_cl157])). 29.85/5.22 thf(op_or, axiom, 29.85/5.22 (( op_or ) => 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( not @ ( and @ ( not @ X ) @ ( not @ Y ) ) ) = ( or @ X @ Y ) ) ))). 29.85/5.22 thf(zip_derived_cl58, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (((not @ (and @ (not @ X0) @ (not @ X1))) = (or @ X0 @ X1)) 29.85/5.22 | ~ (op_or))), 29.85/5.22 inference('cnf', [status(esa)], [op_or])). 29.85/5.22 thf(hilbert_op_or, axiom, (op_or)). 29.85/5.22 thf(zip_derived_cl66, plain, ( (op_or)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_op_or])). 29.85/5.22 thf(zip_derived_cl315, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ((not @ (and @ (not @ X0) @ (not @ X1))) = (or @ X0 @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl66])). 29.85/5.22 thf(zip_derived_cl2935, plain, 29.85/5.22 (![X0 : $i]: ((not @ (not @ X0)) = (or @ X0 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl2892, zip_derived_cl315])). 29.85/5.22 thf(cn3, axiom, 29.85/5.22 (( cn3 ) <=> 29.85/5.22 ( ![P:$i]: 29.85/5.22 ( is_a_theorem @ ( implies @ ( implies @ ( not @ P ) @ P ) @ P ) ) ))). 29.85/5.22 thf(zip_derived_cl18, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ (implies @ (not @ X0) @ X0) @ X0)) 29.85/5.22 | ~ (cn3))), 29.85/5.22 inference('cnf', [status(esa)], [cn3])). 29.85/5.22 thf(zip_derived_cl315, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ((not @ (and @ (not @ X0) @ (not @ X1))) = (or @ X0 @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl58, zip_derived_cl66])). 29.85/5.22 thf(op_implies_and, axiom, 29.85/5.22 (( op_implies_and ) => 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( implies @ X @ Y ) = ( not @ ( and @ X @ ( not @ Y ) ) ) ) ))). 29.85/5.22 thf(zip_derived_cl55, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (((implies @ X0 @ X1) = (not @ (and @ X0 @ (not @ X1)))) 29.85/5.22 | ~ (op_implies_and))), 29.85/5.22 inference('cnf', [status(esa)], [op_implies_and])). 29.85/5.22 thf(hilbert_op_implies_and, axiom, (op_implies_and)). 29.85/5.22 thf(zip_derived_cl67, plain, ( (op_implies_and)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_op_implies_and])). 29.85/5.22 thf(zip_derived_cl232, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ((implies @ X0 @ X1) = (not @ (and @ X0 @ (not @ X1))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl55, zip_derived_cl67])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(zip_derived_cl352, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ (or @ X0 @ X0) @ X0)) | ~ (cn3))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl18, zip_derived_cl328])). 29.85/5.22 thf(zip_derived_cl19, plain, 29.85/5.22 (( (cn3) 29.85/5.22 | ~ (is_a_theorem @ 29.85/5.22 (implies @ (implies @ (not @ sk__20) @ sk__20) @ sk__20)))), 29.85/5.22 inference('cnf', [status(esa)], [cn3])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(zip_derived_cl353, plain, 29.85/5.22 (( (cn3) | ~ (is_a_theorem @ (implies @ (or @ sk__20 @ sk__20) @ sk__20)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl19, zip_derived_cl328])). 29.85/5.22 thf(zip_derived_cl2935, plain, 29.85/5.22 (![X0 : $i]: ((not @ (not @ X0)) = (or @ X0 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl2892, zip_derived_cl315])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(zip_derived_cl3829, plain, 29.85/5.22 (( (cn3) | ~ (is_a_theorem @ (or @ (not @ sk__20) @ sk__20)))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl353, zip_derived_cl2935, zip_derived_cl328])). 29.85/5.22 thf(zip_derived_cl2935, plain, 29.85/5.22 (![X0 : $i]: ((not @ (not @ X0)) = (or @ X0 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl2892, zip_derived_cl315])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(or_2, axiom, 29.85/5.22 (( or_2 ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: ( is_a_theorem @ ( implies @ Y @ ( or @ X @ Y ) ) ) ))). 29.85/5.22 thf(zip_derived_cl31, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ X0 @ (or @ X1 @ X0))) | ~ (or_2))), 29.85/5.22 inference('cnf', [status(esa)], [or_2])). 29.85/5.22 thf(hilbert_or_2, axiom, (or_2)). 29.85/5.22 thf(zip_derived_cl70, plain, ( (or_2)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_or_2])). 29.85/5.22 thf(zip_derived_cl190, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: (is_a_theorem @ (implies @ X0 @ (or @ X1 @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl31, zip_derived_cl70])). 29.85/5.22 thf(zip_derived_cl381, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (is_a_theorem @ (or @ X0 @ (or @ X1 @ (not @ X0))))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl328, zip_derived_cl190])). 29.85/5.22 thf(zip_derived_cl3856, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (or @ X0 @ (not @ (not @ (not @ X0)))))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl2935, zip_derived_cl381])). 29.85/5.22 thf(modus_tollens, axiom, 29.85/5.22 (( modus_tollens ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( is_a_theorem @ 29.85/5.22 ( implies @ 29.85/5.22 ( implies @ ( not @ Y ) @ ( not @ X ) ) @ ( implies @ X @ Y ) ) ) ))). 29.85/5.22 thf(zip_derived_cl2, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ 29.85/5.22 (implies @ (implies @ (not @ X0) @ (not @ X1)) @ 29.85/5.22 (implies @ X1 @ X0))) 29.85/5.22 | ~ (modus_tollens))), 29.85/5.22 inference('cnf', [status(esa)], [modus_tollens])). 29.85/5.22 thf(hilbert_modus_tollens, axiom, (modus_tollens)). 29.85/5.22 thf(zip_derived_cl73, plain, ( (modus_tollens)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_modus_tollens])). 29.85/5.22 thf(zip_derived_cl156, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (implies @ (implies @ (not @ X0) @ (not @ X1)) @ (implies @ X1 @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl2, zip_derived_cl73])). 29.85/5.22 thf(zip_derived_cl160, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ X0) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ X1))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl47, zip_derived_cl69])). 29.85/5.22 thf(zip_derived_cl161, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (implies @ (not @ X0) @ (not @ X1))) 29.85/5.22 | (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl156, zip_derived_cl160])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(zip_derived_cl357, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (or @ X0 @ (not @ X1))) 29.85/5.22 | (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl161, zip_derived_cl328])). 29.85/5.22 thf(zip_derived_cl14947, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (implies @ (not @ (not @ X0)) @ X0))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl3856, zip_derived_cl357])). 29.85/5.22 thf(zip_derived_cl328, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: ((implies @ (not @ X1) @ X0) = (or @ X1 @ X0))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl315, zip_derived_cl232])). 29.85/5.22 thf(zip_derived_cl15001, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (or @ (not @ X0) @ X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl14947, zip_derived_cl328])). 29.85/5.22 thf(zip_derived_cl15091, plain, ( (cn3)), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl3829, zip_derived_cl15001])). 29.85/5.22 thf(zip_derived_cl15137, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (implies @ (or @ X0 @ X0) @ X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl352, zip_derived_cl15091])). 29.85/5.22 thf(zip_derived_cl1596, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (equiv @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X0 @ X1)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl1567])). 29.85/5.22 thf(zip_derived_cl15392, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (~ (is_a_theorem @ (implies @ X0 @ (or @ X0 @ X0))) 29.85/5.22 | (is_a_theorem @ (equiv @ X0 @ (or @ X0 @ X0))))), 29.85/5.22 inference('sup-', [status(thm)], 29.85/5.22 [zip_derived_cl15137, zip_derived_cl1596])). 29.85/5.22 thf(or_1, axiom, 29.85/5.22 (( or_1 ) <=> 29.85/5.22 ( ![X:$i,Y:$i]: ( is_a_theorem @ ( implies @ X @ ( or @ X @ Y ) ) ) ))). 29.85/5.22 thf(zip_derived_cl16, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ X0 @ (or @ X0 @ X1))) | ~ (or_1))), 29.85/5.22 inference('cnf', [status(esa)], [or_1])). 29.85/5.22 thf(hilbert_or_1, axiom, (or_1)). 29.85/5.22 thf(zip_derived_cl64, plain, ( (or_1)), 29.85/5.22 inference('cnf', [status(esa)], [hilbert_or_1])). 29.85/5.22 thf(zip_derived_cl188, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: (is_a_theorem @ (implies @ X0 @ (or @ X0 @ X1)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl16, zip_derived_cl64])). 29.85/5.22 thf(zip_derived_cl15425, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (equiv @ X0 @ (or @ X0 @ X0)))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl15392, zip_derived_cl188])). 29.85/5.22 thf(zip_derived_cl157, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (equiv @ X0 @ X1)) | ((X1) = (X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl77])). 29.85/5.22 thf(zip_derived_cl15609, plain, (![X0 : $i]: ((or @ X0 @ X0) = (X0))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl15425, zip_derived_cl157])). 29.85/5.22 thf(zip_derived_cl15714, plain, (![X0 : $i]: ((not @ (not @ X0)) = (X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl2935, zip_derived_cl15609])). 29.85/5.22 thf(axiom_4, axiom, 29.85/5.22 (( axiom_4 ) <=> 29.85/5.22 ( ![X:$i]: 29.85/5.22 ( is_a_theorem @ 29.85/5.22 ( implies @ 29.85/5.22 ( necessarily @ X ) @ ( necessarily @ ( necessarily @ X ) ) ) ) ))). 29.85/5.22 thf(zip_derived_cl93, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ( (is_a_theorem @ 29.85/5.22 (implies @ (necessarily @ X0) @ (necessarily @ (necessarily @ X0)))) 29.85/5.22 | ~ (axiom_4))), 29.85/5.22 inference('cnf', [status(esa)], [axiom_4])). 29.85/5.22 thf(km4b_axiom_4, axiom, (axiom_4)). 29.85/5.22 thf(zip_derived_cl135, plain, ( (axiom_4)), 29.85/5.22 inference('cnf', [status(esa)], [km4b_axiom_4])). 29.85/5.22 thf(zip_derived_cl270, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (implies @ (necessarily @ X0) @ (necessarily @ (necessarily @ X0))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl93, zip_derived_cl135])). 29.85/5.22 thf(zip_derived_cl1596, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (equiv @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X0 @ X1)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl344, zip_derived_cl1567])). 29.85/5.22 thf(zip_derived_cl2810, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (~ (is_a_theorem @ 29.85/5.22 (implies @ (necessarily @ (necessarily @ X0)) @ (necessarily @ X0))) 29.85/5.22 | (is_a_theorem @ 29.85/5.22 (equiv @ (necessarily @ (necessarily @ X0)) @ (necessarily @ X0))))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl270, zip_derived_cl1596])). 29.85/5.22 thf(axiom_M, axiom, 29.85/5.22 (( axiom_M ) <=> 29.85/5.22 ( ![X:$i]: ( is_a_theorem @ ( implies @ ( necessarily @ X ) @ X ) ) ))). 29.85/5.22 thf(zip_derived_cl120, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ (necessarily @ X0) @ X0)) | ~ (axiom_M))), 29.85/5.22 inference('cnf', [status(esa)], [axiom_M])). 29.85/5.22 thf(km4b_axiom_M, axiom, (axiom_M)). 29.85/5.22 thf(zip_derived_cl137, plain, ( (axiom_M)), 29.85/5.22 inference('cnf', [status(esa)], [km4b_axiom_M])). 29.85/5.22 thf(zip_derived_cl162, plain, 29.85/5.22 (![X0 : $i]: (is_a_theorem @ (implies @ (necessarily @ X0) @ X0))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl120, zip_derived_cl137])). 29.85/5.22 thf(zip_derived_cl2826, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (equiv @ (necessarily @ (necessarily @ X0)) @ (necessarily @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl2810, zip_derived_cl162])). 29.85/5.22 thf(zip_derived_cl157, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (~ (is_a_theorem @ (equiv @ X0 @ X1)) | ((X1) = (X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl24, zip_derived_cl77])). 29.85/5.22 thf(zip_derived_cl9411, plain, 29.85/5.22 (![X0 : $i]: ((necessarily @ X0) = (necessarily @ (necessarily @ X0)))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl2826, zip_derived_cl157])). 29.85/5.22 thf(zip_derived_cl15714, plain, (![X0 : $i]: ((not @ (not @ X0)) = (X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl2935, zip_derived_cl15609])). 29.85/5.22 thf(op_possibly, axiom, 29.85/5.22 (( op_possibly ) => 29.85/5.22 ( ![X:$i]: ( ( possibly @ X ) = ( not @ ( necessarily @ ( not @ X ) ) ) ) ))). 29.85/5.22 thf(zip_derived_cl130, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (((possibly @ X0) = (not @ (necessarily @ (not @ X0)))) 29.85/5.22 | ~ (op_possibly))), 29.85/5.22 inference('cnf', [status(esa)], [op_possibly])). 29.85/5.22 thf(km4b_op_possibly, axiom, (op_possibly)). 29.85/5.22 thf(zip_derived_cl136, plain, ( (op_possibly)), 29.85/5.22 inference('cnf', [status(esa)], [km4b_op_possibly])). 29.85/5.22 thf(zip_derived_cl166, plain, 29.85/5.22 (![X0 : $i]: ((possibly @ X0) = (not @ (necessarily @ (not @ X0))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl130, zip_derived_cl136])). 29.85/5.22 thf(zip_derived_cl15809, plain, 29.85/5.22 (![X0 : $i]: ((possibly @ (not @ X0)) = (not @ (necessarily @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl15714, zip_derived_cl166])). 29.85/5.22 thf(zip_derived_cl16229, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ((possibly @ (not @ (necessarily @ X0))) = (not @ (necessarily @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], 29.85/5.22 [zip_derived_cl9411, zip_derived_cl15809])). 29.85/5.22 thf(zip_derived_cl15809, plain, 29.85/5.22 (![X0 : $i]: ((possibly @ (not @ X0)) = (not @ (necessarily @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl15714, zip_derived_cl166])). 29.85/5.22 thf(zip_derived_cl15809, plain, 29.85/5.22 (![X0 : $i]: ((possibly @ (not @ X0)) = (not @ (necessarily @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl15714, zip_derived_cl166])). 29.85/5.22 thf(zip_derived_cl16231, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ((possibly @ (possibly @ (not @ X0))) = (possibly @ (not @ X0)))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl16229, zip_derived_cl15809, zip_derived_cl15809])). 29.85/5.22 thf(zip_derived_cl17450, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ((possibly @ (possibly @ X0)) = (possibly @ (not @ (not @ X0))))), 29.85/5.22 inference('sup+', [status(thm)], 29.85/5.22 [zip_derived_cl15714, zip_derived_cl16231])). 29.85/5.22 thf(zip_derived_cl15714, plain, (![X0 : $i]: ((not @ (not @ X0)) = (X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl2935, zip_derived_cl15609])). 29.85/5.22 thf(zip_derived_cl17457, plain, 29.85/5.22 (![X0 : $i]: ((possibly @ (possibly @ X0)) = (possibly @ X0))), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl17450, zip_derived_cl15714])). 29.85/5.22 thf(axiom_B, axiom, 29.85/5.22 (( ![X:$i]: 29.85/5.22 ( is_a_theorem @ ( implies @ X @ ( necessarily @ ( possibly @ X ) ) ) ) ) <=> 29.85/5.22 ( axiom_B ))). 29.85/5.22 thf(zip_derived_cl81, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 ( (is_a_theorem @ (implies @ X0 @ (necessarily @ (possibly @ X0)))) 29.85/5.22 | ~ (axiom_B))), 29.85/5.22 inference('cnf', [status(esa)], [axiom_B])). 29.85/5.22 thf(km4b_axiom_B, axiom, (axiom_B)). 29.85/5.22 thf(zip_derived_cl134, plain, ( (axiom_B)), 29.85/5.22 inference('cnf', [status(esa)], [km4b_axiom_B])). 29.85/5.22 thf(zip_derived_cl198, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (is_a_theorem @ (implies @ X0 @ (necessarily @ (possibly @ X0))))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl81, zip_derived_cl134])). 29.85/5.22 thf(op_strict_implies, axiom, 29.85/5.22 (( op_strict_implies ) => 29.85/5.22 ( ![X:$i,Y:$i]: 29.85/5.22 ( ( strict_implies @ X @ Y ) = ( necessarily @ ( implies @ X @ Y ) ) ) ))). 29.85/5.22 thf(zip_derived_cl133, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 (((strict_implies @ X0 @ X1) = (necessarily @ (implies @ X0 @ X1))) 29.85/5.22 | ~ (op_strict_implies))), 29.85/5.22 inference('cnf', [status(esa)], [op_strict_implies])). 29.85/5.22 thf(s1_0_op_strict_implies, axiom, (op_strict_implies)). 29.85/5.22 thf(zip_derived_cl145, plain, ( (op_strict_implies)), 29.85/5.22 inference('cnf', [status(esa)], [s1_0_op_strict_implies])). 29.85/5.22 thf(zip_derived_cl203, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ((strict_implies @ X0 @ X1) = (necessarily @ (implies @ X0 @ X1)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl133, zip_derived_cl145])). 29.85/5.22 thf(necessitation, axiom, 29.85/5.22 (( ![X:$i]: 29.85/5.22 ( ( is_a_theorem @ X ) => ( is_a_theorem @ ( necessarily @ X ) ) ) ) <=> 29.85/5.22 ( necessitation ))). 29.85/5.22 thf(zip_derived_cl107, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (~ (is_a_theorem @ X0) 29.85/5.22 | (is_a_theorem @ (necessarily @ X0)) 29.85/5.22 | ~ (necessitation))), 29.85/5.22 inference('cnf', [status(esa)], [necessitation])). 29.85/5.22 thf(km4b_necessitation, axiom, (necessitation)). 29.85/5.22 thf(zip_derived_cl138, plain, ( (necessitation)), 29.85/5.22 inference('cnf', [status(esa)], [km4b_necessitation])). 29.85/5.22 thf(zip_derived_cl158, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (~ (is_a_theorem @ X0) | (is_a_theorem @ (necessarily @ X0)))), 29.85/5.22 inference('demod', [status(thm)], [zip_derived_cl107, zip_derived_cl138])). 29.85/5.22 thf(zip_derived_cl204, plain, 29.85/5.22 (![X0 : $i, X1 : $i]: 29.85/5.22 ( (is_a_theorem @ (strict_implies @ X1 @ X0)) 29.85/5.22 | ~ (is_a_theorem @ (implies @ X1 @ X0)))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl203, zip_derived_cl158])). 29.85/5.22 thf(zip_derived_cl222, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (strict_implies @ X0 @ (necessarily @ (possibly @ X0))))), 29.85/5.22 inference('sup-', [status(thm)], [zip_derived_cl198, zip_derived_cl204])). 29.85/5.22 thf(zip_derived_cl17556, plain, 29.85/5.22 (![X0 : $i]: 29.85/5.22 (is_a_theorem @ 29.85/5.22 (strict_implies @ (possibly @ X0) @ (necessarily @ (possibly @ X0))))), 29.85/5.22 inference('sup+', [status(thm)], [zip_derived_cl17457, zip_derived_cl222])). 29.85/5.22 thf(zip_derived_cl26482, plain, ($false), 29.85/5.22 inference('demod', [status(thm)], 29.85/5.22 [zip_derived_cl227, zip_derived_cl17556])). 29.85/5.22 29.85/5.22 % SZS output end Refutation 29.85/5.22 29.85/5.22 29.85/5.22 % Terminating... 30.83/5.33 % Runner terminated. 30.83/5.34 % Zipperpin 1.5 exiting 30.83/5.35 EOF