0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.TIhkBWNOm8 true 0.14/0.34 % Computer : n003.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1200 0.14/0.34 % WCLimit : 120 0.14/0.34 % DateTime : Tue Jul 13 11:49:54 EDT 2021 0.14/0.34 % CPUTime : 0.14/0.34 % Running portfolio for 120 s 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.35 % Running in FO mode 0.57/0.67 % Total configuration time : 435 0.57/0.67 % Estimated wc time : 845 0.57/0.67 % Estimated cpu time (7 cpus) : 120.71428571428571 0.62/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo3_bce.sh running for 58s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo6_bce.sh running for 58s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/fo/fo1_av.sh running for 58s 0.63/0.81 % /export/starexec/sandbox2/solver/bin/fo/fo13.sh running for 39s 0.63/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo7.sh running for 49s 0.63/0.82 % /export/starexec/sandbox2/solver/bin/fo/fo5.sh running for 39s 0.63/0.86 % /export/starexec/sandbox2/solver/bin/fo/fo4.sh running for 39s 272.65/40.11 % /export/starexec/sandbox2/solver/bin/fo/fo1_lcnf.sh running for 39s 273.06/40.21 % /export/starexec/sandbox2/solver/bin/fo/fo17_bce.sh running for 39s 273.06/40.22 % /export/starexec/sandbox2/solver/bin/fo/fo8.sh running for 39s 343.96/50.58 % /export/starexec/sandbox2/solver/bin/fo/fo2.sh running for 29s 403.74/59.16 % /export/starexec/sandbox2/solver/bin/fo/fo14.sh running for 39s 403.99/59.28 % /export/starexec/sandbox2/solver/bin/fo/fo20.sh running for 39s 404.15/59.32 % /export/starexec/sandbox2/solver/bin/fo/fo19.sh running for 39s 518.81/75.81 % Solved by fo/fo1_lcnf.sh. 518.81/75.81 % done 15551 iterations in 35.528s 518.81/75.81 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 518.81/75.81 % SZS output start Refutation 518.81/75.81 thf(g_true_type, type, g_true: $i > $i > $o). 518.81/75.81 thf(g_false_type, type, g_false: $i > $i > $o). 518.81/75.81 thf('#form7_type', type, '#form7': $o). 518.81/75.81 thf('#form12_type', type, '#form12': $i > $i > $o). 518.81/75.81 thf('#sk5_type', type, '#sk5': $i > $i). 518.81/75.81 thf(g_true_only_type, type, g_true_only: $i > $i > $o). 518.81/75.81 thf('#sk4_type', type, '#sk4': $i). 518.81/75.81 thf('#sk9_type', type, '#sk9': $i > $i). 518.81/75.81 thf('#sk11_type', type, '#sk11': $i > $i > $i). 518.81/75.81 thf('#sk3_type', type, '#sk3': $i). 518.81/75.81 thf('#form13_type', type, '#form13': $i > $i > $o). 518.81/75.81 thf(g_false_only_type, type, g_false_only: $i > $i > $o). 518.81/75.81 thf('#sk10_type', type, '#sk10': $i > $i). 518.81/75.81 thf('#form6_type', type, '#form6': $i > $o). 518.81/75.81 thf('#sk2_type', type, '#sk2': $i > $i). 518.81/75.81 thf('#form8_type', type, '#form8': $o). 518.81/75.81 thf('#sk1_type', type, '#sk1': $i). 518.81/75.81 thf(g_both_type, type, g_both: $i > $i > $o). 518.81/75.81 thf(false_only_g, axiom, 518.81/75.81 (![X_2:$i,X_1:$i]: 518.81/75.81 ( ( ( ~( g_true @ X_2 @ X_1 ) ) & ( g_false @ X_2 @ X_1 ) ) <=> 518.81/75.82 ( g_false_only @ X_2 @ X_1 ) ))). 518.81/75.82 thf(zip_derived_cl4, plain, 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((((~) @ (g_true @ Y0 @ Y1))) & (g_false @ 518.81/75.82 Y0 @ Y1))) <=> 518.81/75.82 (g_false_only @ Y0 @ Y1)))))))))), 518.81/75.82 inference('cnf', [status(esa)], [false_only_g])). 518.81/75.82 thf(zip_derived_cl295, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((((((~) @ (g_true @ X2 @ Y0))) & (g_false @ X2 @ Y0))) <=> 518.81/75.82 (g_false_only @ X2 @ Y0))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 518.81/75.82 thf(zip_derived_cl296, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (((((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) <=> 518.81/75.82 (g_false_only @ X2 @ X4)))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl295])). 518.81/75.82 thf(zip_derived_cl297, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 = (g_false_only @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl296])). 518.81/75.82 thf(zip_derived_cl298, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 | ~ (g_false_only @ X2 @ X4))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl297])). 518.81/75.82 thf(zip_derived_cl1610, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_false @ X2 @ X4) | ~ (g_false_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl298])). 518.81/75.82 thf(exhaustion_g, axiom, 518.81/75.82 (![X_2:$i,X_1:$i]: 518.81/75.82 ( ( g_false_only @ X_2 @ X_1 ) | ( g_both @ X_2 @ X_1 ) | 518.81/75.82 ( g_true_only @ X_2 @ X_1 ) ))). 518.81/75.82 thf(zip_derived_cl3, plain, 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((g_false_only @ Y0 @ Y1) | 518.81/75.82 (g_both @ Y0 @ Y1) | (g_true_only @ Y0 @ Y1)))))))))), 518.81/75.82 inference('cnf', [status(esa)], [exhaustion_g])). 518.81/75.82 thf(zip_derived_cl5, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((g_false_only @ X2 @ Y0) | (g_both @ X2 @ Y0) | 518.81/75.82 (g_true_only @ X2 @ Y0))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 518.81/75.82 thf(zip_derived_cl6, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (((g_false_only @ X2 @ X4) | (g_both @ X2 @ X4) | 518.81/75.82 (g_true_only @ X2 @ X4)))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl1620, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_false @ X1 @ X0) | (g_both @ X1 @ X0) | (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup+', [status(thm)], [zip_derived_cl1610, zip_derived_cl7])). 518.81/75.82 thf(both_g, axiom, 518.81/75.82 (![X_2:$i,X_1:$i]: 518.81/75.82 ( ( ( g_true @ X_2 @ X_1 ) & ( g_false @ X_2 @ X_1 ) ) <=> 518.81/75.82 ( g_both @ X_2 @ X_1 ) ))). 518.81/75.82 thf(zip_derived_cl1, plain, 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_true @ Y0 @ Y1) & (g_false @ Y0 @ Y1))) <=> 518.81/75.82 (g_both @ Y0 @ Y1)))))))))), 518.81/75.82 inference('cnf', [status(esa)], [both_g])). 518.81/75.82 thf(zip_derived_cl8, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((((g_true @ X2 @ Y0) & (g_false @ X2 @ Y0))) <=> 518.81/75.82 (g_both @ X2 @ Y0))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 518.81/75.82 thf(zip_derived_cl9, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) <=> (g_both @ X2 @ X4)))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 518.81/75.82 thf(zip_derived_cl10, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.82 thf(zip_derived_cl11, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) | ~ (g_both @ X2 @ X4))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl10])). 518.81/75.82 thf(zip_derived_cl18, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_false @ X2 @ X4) | ~ (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 518.81/75.82 thf(zip_derived_cl1889, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.82 thf(true_only_g, axiom, 518.81/75.82 (![X_2:$i,X_1:$i]: 518.81/75.82 ( ( g_true_only @ X_2 @ X_1 ) <=> 518.81/75.82 ( ( ~( g_false @ X_2 @ X_1 ) ) & ( g_true @ X_2 @ X_1 ) ) ))). 518.81/75.82 thf(zip_derived_cl2, plain, 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((g_true_only @ Y0 @ Y1) <=> 518.81/75.82 (((((~) @ (g_false @ Y0 @ Y1))) & (g_true @ 518.81/75.82 Y0 @ Y1)))))))))))), 518.81/75.82 inference('cnf', [status(esa)], [true_only_g])). 518.81/75.82 thf(zip_derived_cl274, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((g_true_only @ X2 @ Y0) <=> 518.81/75.82 (((((~) @ (g_false @ X2 @ Y0))) & (g_true @ X2 @ Y0))))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2])). 518.81/75.82 thf(zip_derived_cl275, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (((g_true_only @ X2 @ X4) <=> 518.81/75.82 (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4)))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl274])). 518.81/75.82 thf(zip_derived_cl276, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((g_true_only @ X2 @ X4) 518.81/75.82 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl275])). 518.81/75.82 thf(zip_derived_cl278, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X2 @ X4) 518.81/75.82 | (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl276])). 518.81/75.82 thf(zip_derived_cl1541, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_true @ X2 @ X4) | ~ (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 518.81/75.82 thf(zip_derived_cl1891, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.82 thf(zip_derived_cl297, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 = (g_false_only @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl296])). 518.81/75.82 thf(zip_derived_cl300, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | ((((((~) @ ($false))) & (g_false @ X2 @ X4))) 518.81/75.82 = (g_false_only @ X2 @ X4)))), 518.81/75.82 inference('bool_hoist', [status(thm)], [zip_derived_cl297])). 518.81/75.82 thf(zip_derived_cl301, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(nc4, conjecture, 518.81/75.82 (( ?[B:$i]: 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[C:$i]: 518.81/75.82 ( ( ( g_false_only @ C @ A ) & 518.81/75.82 ( ( g_both @ C @ B ) | ( g_false_only @ C @ B ) ) ) | 518.81/75.82 ( ( g_both @ C @ A ) & 518.81/75.82 ( ( g_false_only @ C @ B ) | ( g_true_only @ C @ B ) ) ) | 518.81/75.82 ( ( ( g_true_only @ C @ B ) | ( g_both @ C @ B ) ) & 518.81/75.82 ( g_true_only @ C @ A ) ) ) ) ) ) | 518.81/75.82 ( ( ~( ?[A:$i]: 518.81/75.82 ( ![B:$i]: 518.81/75.82 ( ( ( g_false_only @ B @ B ) & ( g_false_only @ B @ A ) ) | 518.81/75.82 ( ( g_true_only @ B @ A ) & ( g_true_only @ B @ B ) ) ) ) ) ) & 518.81/75.82 ( ~( ?[B:$i]: 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[C:$i]: 518.81/75.82 ( ( ( ( g_false_only @ C @ B ) | ( g_true_only @ C @ B ) ) & 518.81/75.82 ( g_both @ C @ A ) ) | 518.81/75.82 ( ( ( g_both @ C @ B ) | ( g_false_only @ C @ B ) ) & 518.81/75.82 ( g_false_only @ C @ A ) ) | 518.81/75.82 ( ( g_true_only @ C @ A ) & 518.81/75.82 ( ( g_both @ C @ B ) | ( g_true_only @ C @ B ) ) ) ) ) ) ) ) & 518.81/75.82 ( ?[B:$i]: 518.81/75.82 ( ( ~( ?[A:$i]: 518.81/75.82 ( ![C:$i]: 518.81/75.82 ( ( ( g_true_only @ C @ A ) & ( g_false_only @ C @ B ) ) | 518.81/75.82 ( ( g_false_only @ C @ A ) & ( g_true_only @ C @ B ) ) ) ) ) ) & 518.81/75.82 ( ?[A:$i]: 518.81/75.82 ( ( ?[C:$i]: ( ( g_both @ C @ A ) & ( g_both @ C @ B ) ) ) & 518.81/75.82 ( ~( ?[C:$i]: 518.81/75.82 ( ( ( g_false_only @ C @ A ) & 518.81/75.82 ( ( g_false_only @ C @ B ) | ( g_both @ C @ B ) ) ) | 518.81/75.82 ( ( g_both @ C @ A ) & 518.81/75.82 ( ( g_true_only @ C @ B ) | ( g_false_only @ C @ B ) ) ) | 518.81/75.82 ( ( g_true_only @ C @ A ) & 518.81/75.82 ( ( g_true_only @ C @ B ) | ( g_both @ C @ B ) ) ) ) ) ) ) ) ) ) & 518.81/75.82 ( ?[A:$i]: 518.81/75.82 ( ( ?[B:$i]: ( ( g_both @ B @ B ) & ( g_both @ B @ A ) ) ) & 518.81/75.82 ( ~( ?[B:$i]: 518.81/75.82 ( ( ( ( g_false_only @ B @ B ) | ( g_both @ B @ B ) ) & 518.81/75.82 ( g_true_only @ B @ A ) ) | 518.81/75.82 ( ( g_false_only @ B @ A ) & 518.81/75.82 ( ( g_true_only @ B @ B ) | ( g_both @ B @ B ) ) ) | 518.81/75.82 ( ( g_both @ B @ A ) & 518.81/75.82 ( ( g_false_only @ B @ B ) | ( g_true_only @ B @ B ) ) ) ) ) ) ) ) ) | 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[B:$i]: 518.81/75.82 ( ( ( g_both @ B @ A ) & 518.81/75.82 ( ( g_false_only @ B @ B ) | ( g_true_only @ B @ B ) ) ) | 518.81/75.82 ( ( g_false_only @ B @ A ) & 518.81/75.82 ( ( g_both @ B @ B ) | ( g_true_only @ B @ B ) ) ) | 518.81/75.82 ( ( ( g_false_only @ B @ B ) | ( g_both @ B @ B ) ) & 518.81/75.82 ( g_true_only @ B @ A ) ) ) ) ))). 518.81/75.82 thf(zf_stmt_0, negated_conjecture, 518.81/75.82 (~( ( ?[B:$i]: 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[C:$i]: 518.81/75.82 ( ( ( g_false_only @ C @ A ) & 518.81/75.82 ( ( g_both @ C @ B ) | ( g_false_only @ C @ B ) ) ) | 518.81/75.82 ( ( g_both @ C @ A ) & 518.81/75.82 ( ( g_false_only @ C @ B ) | ( g_true_only @ C @ B ) ) ) | 518.81/75.82 ( ( ( g_true_only @ C @ B ) | ( g_both @ C @ B ) ) & 518.81/75.82 ( g_true_only @ C @ A ) ) ) ) ) ) | 518.81/75.82 ( ( ~( ?[A:$i]: 518.81/75.82 ( ![B:$i]: 518.81/75.82 ( ( ( g_false_only @ B @ B ) & ( g_false_only @ B @ A ) ) | 518.81/75.82 ( ( g_true_only @ B @ A ) & ( g_true_only @ B @ B ) ) ) ) ) ) & 518.81/75.82 ( ~( ?[B:$i]: 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[C:$i]: 518.81/75.82 ( ( ( ( g_false_only @ C @ B ) | ( g_true_only @ C @ B ) ) & 518.81/75.82 ( g_both @ C @ A ) ) | 518.81/75.82 ( ( ( g_both @ C @ B ) | ( g_false_only @ C @ B ) ) & 518.81/75.82 ( g_false_only @ C @ A ) ) | 518.81/75.82 ( ( g_true_only @ C @ A ) & 518.81/75.82 ( ( g_both @ C @ B ) | ( g_true_only @ C @ B ) ) ) ) ) ) ) ) & 518.81/75.82 ( ?[B:$i]: 518.81/75.82 ( ( ~( ?[A:$i]: 518.81/75.82 ( ![C:$i]: 518.81/75.82 ( ( ( g_true_only @ C @ A ) & ( g_false_only @ C @ B ) ) | 518.81/75.82 ( ( g_false_only @ C @ A ) & ( g_true_only @ C @ B ) ) ) ) ) ) & 518.81/75.82 ( ?[A:$i]: 518.81/75.82 ( ( ?[C:$i]: ( ( g_both @ C @ A ) & ( g_both @ C @ B ) ) ) & 518.81/75.82 ( ~( ?[C:$i]: 518.81/75.82 ( ( ( g_false_only @ C @ A ) & 518.81/75.82 ( ( g_false_only @ C @ B ) | ( g_both @ C @ B ) ) ) | 518.81/75.82 ( ( g_both @ C @ A ) & 518.81/75.82 ( ( g_true_only @ C @ B ) | ( g_false_only @ C @ B ) ) ) | 518.81/75.82 ( ( g_true_only @ C @ A ) & 518.81/75.82 ( ( g_true_only @ C @ B ) | ( g_both @ C @ B ) ) ) ) ) ) ) ) ) ) & 518.81/75.82 ( ?[A:$i]: 518.81/75.82 ( ( ?[B:$i]: ( ( g_both @ B @ B ) & ( g_both @ B @ A ) ) ) & 518.81/75.82 ( ~( ?[B:$i]: 518.81/75.82 ( ( ( ( g_false_only @ B @ B ) | ( g_both @ B @ B ) ) & 518.81/75.82 ( g_true_only @ B @ A ) ) | 518.81/75.82 ( ( g_false_only @ B @ A ) & 518.81/75.82 ( ( g_true_only @ B @ B ) | ( g_both @ B @ B ) ) ) | 518.81/75.82 ( ( g_both @ B @ A ) & 518.81/75.82 ( ( g_false_only @ B @ B ) | ( g_true_only @ B @ B ) ) ) ) ) ) ) ) ) | 518.81/75.82 ( ![A:$i]: 518.81/75.82 ( ?[B:$i]: 518.81/75.82 ( ( ( g_both @ B @ A ) & 518.81/75.82 ( ( g_false_only @ B @ B ) | ( g_true_only @ B @ B ) ) ) | 518.81/75.82 ( ( g_false_only @ B @ A ) & 518.81/75.82 ( ( g_both @ B @ B ) | ( g_true_only @ B @ B ) ) ) | 518.81/75.82 ( ( ( g_false_only @ B @ B ) | ( g_both @ B @ B ) ) & 518.81/75.82 ( g_true_only @ B @ A ) ) ) ) ) )), 518.81/75.82 inference('cnf.neg', [status(esa)], [nc4])). 518.81/75.82 thf(zip_derived_cl0, plain, 518.81/75.82 (~ (((((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (((g_false_only @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0))))) | 518.81/75.82 (((((g_true_only @ Y2 @ Y0) | 518.81/75.82 (g_both @ Y2 @ Y0))) & 518.81/75.82 (g_true_only @ Y2 @ Y1)))))))))))))) | 518.81/75.82 (((((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y1) & 518.81/75.82 (g_false_only @ Y1 @ Y0))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ 518.81/75.82 Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y0) | 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0)))))))))))))))))) & 518.81/75.82 (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) & 518.81/75.82 (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))))) | 518.81/75.82 (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_both @ Y1 @ Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))) | 518.81/75.82 (((((g_false_only @ Y1 @ Y1) | (g_both @ 518.81/75.82 Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0)))))))))))))), 518.81/75.82 inference('cnf', [status(esa)], [zf_stmt_0])). 518.81/75.82 thf(zip_derived_cl21, plain, 518.81/75.82 (~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (((g_false_only @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0))))) | 518.81/75.82 (((((g_true_only @ Y2 @ Y0) | 518.81/75.82 (g_both @ Y2 @ Y0))) & 518.81/75.82 (g_true_only @ Y2 @ Y1))))))))))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])). 518.81/75.82 thf(zip_derived_cl24, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_both @ Y1 @ X2) | (g_false_only @ 518.81/75.82 Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ X2) | 518.81/75.82 (g_true_only @ Y1 @ X2))))) | 518.81/75.82 (((((g_true_only @ Y1 @ X2) | (g_both @ 518.81/75.82 Y1 @ X2))) & 518.81/75.82 (g_true_only @ Y1 @ Y0)))))))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 518.81/75.82 thf(zip_derived_cl27, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_both @ Y0 @ X2) | (g_false_only @ Y0 @ X2))))) | 518.81/75.82 (((g_both @ Y0 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_false_only @ Y0 @ X2) | (g_true_only @ Y0 @ X2))))) | 518.81/75.82 (((((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2))) & 518.81/75.82 (g_true_only @ Y0 @ ('#sk2' @ X2)))))))))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl24])). 518.81/75.82 thf(zip_derived_cl30, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ~ (((((g_false_only @ X4 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_both @ X4 @ X2) | (g_false_only @ X4 @ X2))))) | 518.81/75.82 (((g_both @ X4 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_false_only @ X4 @ X2) | (g_true_only @ X4 @ X2))))) | 518.81/75.82 (((((g_true_only @ X4 @ X2) | (g_both @ X4 @ X2))) & 518.81/75.82 (g_true_only @ X4 @ ('#sk2' @ X2))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl27])). 518.81/75.82 thf(zip_derived_cl35, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ~ (((g_false_only @ X4 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_both @ X4 @ X2) | (g_false_only @ X4 @ X2)))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 518.81/75.82 thf(zip_derived_cl42, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_false_only @ X4 @ ('#sk2' @ X2)) 518.81/75.82 | ~ (((g_both @ X4 @ X2) | (g_false_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl35])). 518.81/75.82 thf(zip_derived_cl54, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_false_only @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.82 thf(zip_derived_cl271, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_true_only @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | (g_both @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl54])). 518.81/75.82 thf(zip_derived_cl36, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ~ (((g_both @ X4 @ ('#sk2' @ X2)) & 518.81/75.82 (((g_false_only @ X4 @ X2) | (g_true_only @ X4 @ X2)))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 518.81/75.82 thf(zip_derived_cl43, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ ('#sk2' @ X2)) 518.81/75.82 | ~ (((g_false_only @ X4 @ X2) | (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl36])). 518.81/75.82 thf(zip_derived_cl55, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_false_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.82 thf(zip_derived_cl764, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl23, plain, 518.81/75.82 (~ (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_both @ Y1 @ Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))) | 518.81/75.82 (((((g_false_only @ Y1 @ Y1) | (g_both @ 518.81/75.82 Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0)))))))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])). 518.81/75.82 thf(zip_derived_cl26, plain, 518.81/75.82 (~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_both @ Y0 @ '#sk1') & 518.81/75.82 (((g_false_only @ Y0 @ Y0) | (g_true_only @ Y0 @ Y0))))) | 518.81/75.82 (((g_false_only @ Y0 @ '#sk1') & 518.81/75.82 (((g_both @ Y0 @ Y0) | (g_true_only @ Y0 @ Y0))))) | 518.81/75.82 (((((g_false_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))) & 518.81/75.82 (g_true_only @ Y0 @ '#sk1'))))))))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl23])). 518.81/75.82 thf(zip_derived_cl29, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((((g_both @ X2 @ '#sk1') & 518.81/75.82 (((g_false_only @ X2 @ X2) | (g_true_only @ X2 @ X2))))) | 518.81/75.82 (((g_false_only @ X2 @ '#sk1') & 518.81/75.82 (((g_both @ X2 @ X2) | (g_true_only @ X2 @ X2))))) | 518.81/75.82 (((((g_false_only @ X2 @ X2) | (g_both @ X2 @ X2))) & 518.81/75.82 (g_true_only @ X2 @ '#sk1')))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 518.81/75.82 thf(zip_derived_cl33, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((g_false_only @ X2 @ '#sk1') & 518.81/75.82 (((g_both @ X2 @ X2) | (g_true_only @ X2 @ X2)))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 518.81/75.82 thf(zip_derived_cl40, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (g_false_only @ X2 @ '#sk1') 518.81/75.82 | ~ (((g_both @ X2 @ X2) | (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl33])). 518.81/75.82 thf(zip_derived_cl50, plain, 518.81/75.82 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.82 thf(zip_derived_cl767, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false_only @ ('#sk2' @ X0) @ X0) 518.81/75.82 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl50])). 518.81/75.82 thf(zip_derived_cl809, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.82 | (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.82 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl767])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl53, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.82 thf(zip_derived_cl270, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_true_only @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | (g_both @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_both @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl53])). 518.81/75.82 thf(zip_derived_cl37, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ~ (((((g_true_only @ X4 @ X2) | (g_both @ X4 @ X2))) & (g_true_only @ 518.81/75.82 X4 @ ('#sk2' @ X2))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl30])). 518.81/75.82 thf(zip_derived_cl44, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (((g_true_only @ X4 @ X2) | (g_both @ X4 @ X2))) 518.81/75.82 | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl37])). 518.81/75.82 thf(zip_derived_cl58, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl497, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_both @ X1 @ X0) | (g_both @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl270, zip_derived_cl58])). 518.81/75.82 thf(zip_derived_cl49, plain, 518.81/75.82 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.82 thf(zip_derived_cl500, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.82 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl49])). 518.81/75.82 thf(zip_derived_cl1472, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk2' @ X0) @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl809, zip_derived_cl500])). 518.81/75.82 thf(zip_derived_cl1474, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.82 | ~ (g_false @ ('#sk2' @ X0) @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk2' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl301, zip_derived_cl1472])). 518.81/75.82 thf(zip_derived_cl2003, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.82 | (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk2' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1891, zip_derived_cl1474])). 518.81/75.82 thf(zip_derived_cl2024, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.82 | (g_true @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl2003])). 518.81/75.82 thf(zip_derived_cl1889, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl34, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((((g_false_only @ X2 @ X2) | (g_both @ X2 @ X2))) & 518.81/75.82 (g_true_only @ X2 @ '#sk1')))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 518.81/75.82 thf(zip_derived_cl41, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (((g_false_only @ X2 @ X2) | (g_both @ X2 @ X2))) 518.81/75.82 | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl34])). 518.81/75.82 thf(zip_derived_cl51, plain, 518.81/75.82 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl268, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ X0 @ X0) 518.81/75.82 | (g_both @ X0 @ X0) 518.81/75.82 | ~ (g_true_only @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl51])). 518.81/75.82 thf(zip_derived_cl52, plain, 518.81/75.82 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl292, plain, 518.81/75.82 (![X0 : $i]: (~ (g_true_only @ X0 @ '#sk1') | (g_true_only @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl268, zip_derived_cl52])). 518.81/75.82 thf(zip_derived_cl1895, plain, 518.81/75.82 (![X0 : $i]: ( (g_false @ X0 @ '#sk1') | (g_true_only @ X0 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl292])). 518.81/75.82 thf(zip_derived_cl10, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.82 thf(zip_derived_cl12, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) | (g_both @ X2 @ X4))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl10])). 518.81/75.82 thf(zip_derived_cl15, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl32, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ~ (((g_both @ X2 @ '#sk1') & 518.81/75.82 (((g_false_only @ X2 @ X2) | (g_true_only @ X2 @ X2)))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl29])). 518.81/75.82 thf(zip_derived_cl39, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (g_both @ X2 @ '#sk1') 518.81/75.82 | ~ (((g_false_only @ X2 @ X2) | (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl32])). 518.81/75.82 thf(zip_derived_cl47, plain, 518.81/75.82 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.82 thf(zip_derived_cl266, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ X0 @ X0) 518.81/75.82 | (g_both @ X0 @ X0) 518.81/75.82 | ~ (g_both @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl47])). 518.81/75.82 thf(zip_derived_cl48, plain, 518.81/75.82 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.82 thf(zip_derived_cl289, plain, 518.81/75.82 (![X0 : $i]: (~ (g_both @ X0 @ '#sk1') | (g_both @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl266, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl290, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false @ X0 @ '#sk1') 518.81/75.82 | ~ (g_true @ X0 @ '#sk1') 518.81/75.82 | (g_both @ X0 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl2157, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ X0 @ X0) 518.81/75.82 | ~ (g_true @ X0 @ '#sk1') 518.81/75.82 | (g_both @ X0 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1895, zip_derived_cl290])). 518.81/75.82 thf(zip_derived_cl2418, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.82 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)) 518.81/75.82 | (g_both @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl2024, zip_derived_cl2157])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl767, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false_only @ ('#sk2' @ X0) @ X0) 518.81/75.82 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl50])). 518.81/75.82 thf(zip_derived_cl814, plain, 518.81/75.82 (~ (g_false_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('eq_fact', [status(thm)], [zip_derived_cl767])). 518.81/75.82 thf(zip_derived_cl815, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl814])). 518.81/75.82 thf(zip_derived_cl18, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_false @ X2 @ X4) | ~ (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl11])). 518.81/75.82 thf(zip_derived_cl818, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_false @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl18])). 518.81/75.82 thf(zip_derived_cl7, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X4) 518.81/75.82 | (g_both @ X2 @ X4) 518.81/75.82 | (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.82 thf(zip_derived_cl815, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl814])). 518.81/75.82 thf(zip_derived_cl289, plain, 518.81/75.82 (![X0 : $i]: (~ (g_both @ X0 @ '#sk1') | (g_both @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl266, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl821, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl497, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_both @ X1 @ X0) | (g_both @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl270, zip_derived_cl58])). 518.81/75.82 thf(zip_derived_cl55, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_false_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.82 thf(zip_derived_cl502, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl873, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | ~ (g_false_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl821, zip_derived_cl502])). 518.81/75.82 thf(zip_derived_cl51, plain, 518.81/75.82 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl898, plain, 518.81/75.82 (~ (g_false_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl873, zip_derived_cl51])). 518.81/75.82 thf(zip_derived_cl899, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl898])). 518.81/75.82 thf(zip_derived_cl821, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl497, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_both @ X1 @ X0) | (g_both @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl270, zip_derived_cl58])). 518.81/75.82 thf(zip_derived_cl56, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.82 thf(zip_derived_cl503, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl56])). 518.81/75.82 thf(zip_derived_cl874, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | ~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl821, zip_derived_cl503])). 518.81/75.82 thf(zip_derived_cl57, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl907, plain, 518.81/75.82 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl934, plain, 518.81/75.82 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl52, plain, 518.81/75.82 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.82 thf(zip_derived_cl950, plain, ( (g_false @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl818, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl15, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.82 thf(zip_derived_cl22, plain, 518.81/75.82 (~ (((((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y1) & 518.81/75.82 (g_false_only @ Y1 @ Y0))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ 518.81/75.82 Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y0) | 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0)))))))))))))))))) & 518.81/75.82 (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) & 518.81/75.82 (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1)))))))))))))))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl0])). 518.81/75.82 thf(zip_derived_cl25, plain, 518.81/75.82 (( (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y1) & 518.81/75.82 (g_false_only @ Y1 @ Y0))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))) & 518.81/75.82 (g_false_only @ Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0)))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl22])). 518.81/75.82 thf(zip_derived_cl28, plain, 518.81/75.82 (( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ Y0) & (g_false_only @ Y0 @ 518.81/75.82 '#sk3'))) | 518.81/75.82 (((g_true_only @ Y0 @ '#sk3') & (g_true_only @ Y0 @ Y0)))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))) & 518.81/75.82 (g_false_only @ Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0)))))))))))))))))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl25])). 518.81/75.82 thf(zip_derived_cl31, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (((((g_false_only @ X2 @ X2) & (g_false_only @ X2 @ '#sk3'))) | 518.81/75.82 (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ Y2 @ 518.81/75.82 Y0) | (g_true_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))) & 518.81/75.82 (g_false_only @ Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0)))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 518.81/75.82 thf(zip_derived_cl38, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (((g_false_only @ X2 @ X2) & (g_false_only @ X2 @ '#sk3'))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ Y2 @ 518.81/75.82 Y0) | (g_true_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))) & 518.81/75.82 (g_false_only @ Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0)))))))))))))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl31])). 518.81/75.82 thf(zip_derived_cl45, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (g_false_only @ X2 @ X2) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((((g_false_only @ Y2 @ 518.81/75.82 Y0) | (g_true_only @ 518.81/75.82 Y2 @ Y0))) & 518.81/75.82 (g_both @ Y2 @ Y1))) | 518.81/75.82 (((((g_both @ Y2 @ Y0) | 518.81/75.82 (g_false_only @ Y2 @ Y0))) & 518.81/75.82 (g_false_only @ Y2 @ Y1))) | 518.81/75.82 (((g_true_only @ Y2 @ Y1) & 518.81/75.82 (((g_both @ Y2 @ Y0) | 518.81/75.82 (g_true_only @ Y2 @ Y0)))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl38])). 518.81/75.82 thf(zip_derived_cl59, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ '#sk4') | 518.81/75.82 (g_true_only @ Y1 @ '#sk4'))) & 518.81/75.82 (g_both @ Y1 @ Y0))) | 518.81/75.82 (((((g_both @ Y1 @ '#sk4') | 518.81/75.82 (g_false_only @ Y1 @ '#sk4'))) & 518.81/75.82 (g_false_only @ Y1 @ Y0))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_both @ Y1 @ '#sk4') | 518.81/75.82 (g_true_only @ Y1 @ '#sk4'))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl45])). 518.81/75.82 thf(zip_derived_cl61, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((((g_false_only @ Y0 @ '#sk4') | (g_true_only @ 518.81/75.82 Y0 @ '#sk4'))) & 518.81/75.82 (g_both @ Y0 @ X4))) | 518.81/75.82 (((((g_both @ Y0 @ '#sk4') | (g_false_only @ Y0 @ 518.81/75.82 '#sk4'))) & 518.81/75.82 (g_false_only @ Y0 @ X4))) | 518.81/75.82 (((g_true_only @ Y0 @ X4) & 518.81/75.82 (((g_both @ Y0 @ '#sk4') | (g_true_only @ Y0 @ 518.81/75.82 '#sk4')))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl59])). 518.81/75.82 thf(zip_derived_cl63, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((((g_false_only @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_both @ ('#sk5' @ X4) @ X4))) | 518.81/75.82 (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) | 518.81/75.82 (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl61])). 518.81/75.82 thf(zip_derived_cl65, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((g_false_only @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_both @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl63])). 518.81/75.82 thf(zip_derived_cl68, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 518.81/75.82 thf(zip_derived_cl73, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 518.81/75.82 thf(zip_derived_cl73, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 518.81/75.82 thf(zip_derived_cl81, plain, 518.81/75.82 (![X4 : $i]: 518.81/75.82 (~ ('#form6' @ X4) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl84, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( ('#form6' @ X4) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (g_true_only @ X2 @ X2))), 518.81/75.82 inference('renaming', [status(thm)], [zip_derived_cl73, zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl67, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_false_only @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl65])). 518.81/75.82 thf(zip_derived_cl71, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl67])). 518.81/75.82 thf(zip_derived_cl77, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 518.81/75.82 thf(zip_derived_cl88, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl94, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ('#form6' @ X4))), 518.81/75.82 inference('renaming', [status(thm)], [zip_derived_cl84, zip_derived_cl88])). 518.81/75.82 thf(zip_derived_cl104, plain, 518.81/75.82 (( ('#form8') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl105, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (((((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_true_only @ Y1 @ Y0) & 518.81/75.82 (g_false_only @ Y1 @ X2))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (g_true_only @ Y1 @ X2))))))))))))) & 518.81/75.82 (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))))) 518.81/75.82 | ('#form8'))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 518.81/75.82 thf(zip_derived_cl117, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (((??) @ (^[Y0 : $i]: 518.81/75.82 (((!!) @ (^[Y1 : $i]: 518.81/75.82 (((((g_true_only @ Y1 @ Y0) & 518.81/75.82 (g_false_only @ Y1 @ X2))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (g_true_only @ Y1 @ X2))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))) 518.81/75.82 | ('#form8'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl105])). 518.81/75.82 thf(zip_derived_cl131, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 ( (((!!) @ (^[Y0 : $i]: 518.81/75.82 (((((g_true_only @ Y0 @ ('#sk9' @ X2)) & 518.81/75.82 (g_false_only @ Y0 @ X2))) | 518.81/75.82 (((g_false_only @ Y0 @ ('#sk9' @ X2)) & 518.81/75.82 (g_true_only @ Y0 @ X2)))))))) 518.81/75.82 | ('#form8') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl117])). 518.81/75.82 thf(zip_derived_cl141, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((g_true_only @ X4 @ ('#sk9' @ X2)) & (g_false_only @ X4 @ X2))) | 518.81/75.82 (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))) 518.81/75.82 | ('#form8'))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl131])). 518.81/75.82 thf(zip_derived_cl157, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_true_only @ X4 @ ('#sk9' @ X2)) & (g_false_only @ X4 @ X2))) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl141])). 518.81/75.82 thf(zip_derived_cl172, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.82 X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_false_only @ Y1 @ X2))))) | 518.81/75.82 (((g_true_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ X2) | 518.81/75.82 (g_both @ Y1 @ X2))))))))))))))))) 518.81/75.82 | ('#form8') 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 518.81/75.82 thf(zip_derived_cl177, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i]: 518.81/75.82 (~ (((((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ X6) & (g_both @ Y0 @ X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ X6) & 518.81/75.82 (((g_false_only @ Y0 @ X2) | (g_both @ 518.81/75.82 Y0 @ X2))))) | 518.81/75.82 (((g_both @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | 518.81/75.82 (g_false_only @ Y0 @ X2))))) | 518.81/75.82 (((g_true_only @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_both @ 518.81/75.82 Y0 @ X2)))))))))))))) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl172])). 518.81/75.82 thf(zip_derived_cl184, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i]: 518.81/75.82 (~ (((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ X6) & (g_both @ Y0 @ X2)))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ X6) & 518.81/75.82 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.82 (((g_both @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.82 X2))))) | 518.81/75.82 (((g_true_only @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl177])). 518.81/75.82 thf(zip_derived_cl195, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 (~ (((g_both @ X8 @ X6) & (g_both @ X8 @ X2))) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ X6) & 518.81/75.82 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.82 (((g_both @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.82 X2))))) | 518.81/75.82 (((g_true_only @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl184])). 518.81/75.82 thf(zip_derived_cl204, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 (~ (g_both @ X8 @ X6) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((g_false_only @ Y0 @ X6) & 518.81/75.82 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.82 (((g_both @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.82 X2))))) | 518.81/75.82 (((g_true_only @ Y0 @ X6) & 518.81/75.82 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl195])). 518.81/75.82 thf(zip_derived_cl216, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (((((g_false_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) | 518.81/75.82 (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) | 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))))) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl204])). 518.81/75.82 thf(zip_derived_cl218, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (((g_false_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl216])). 518.81/75.82 thf(zip_derived_cl220, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl218])). 518.81/75.82 thf(zip_derived_cl225, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (g_true_only @ X4 @ X2) 518.81/75.82 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl220])). 518.81/75.82 thf(zip_derived_cl233, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.82 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (g_true_only @ X4 @ X2))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl225])). 518.81/75.82 thf(zip_derived_cl221, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl218])). 518.81/75.82 thf(zip_derived_cl226, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.82 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.82 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl221])). 518.81/75.82 thf(zip_derived_cl234, plain, 518.81/75.82 (![X2 : $i, X6 : $i]: 518.81/75.82 (~ ('#form12' @ X2 @ X6) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.82 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl244, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( ('#form12' @ X2 @ X6) 518.81/75.82 | (g_true_only @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.82 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.82 ('#sk11' @ X2 @ X6) @ X2))))), 518.81/75.82 inference('renaming', [status(thm)], 518.81/75.82 [zip_derived_cl233, zip_derived_cl234])). 518.81/75.82 thf(zip_derived_cl255, plain, 518.81/75.82 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.82 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.82 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.82 | ~ (g_both @ X8 @ X2) 518.81/75.82 | ~ (g_both @ X8 @ X6) 518.81/75.82 | (g_true_only @ X4 @ X2) 518.81/75.82 | ('#form12' @ X2 @ X6))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl244])). 518.81/75.82 thf(zip_derived_cl1130, plain, 518.81/75.82 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 518.81/75.82 (~ (g_false @ X1 @ X0) 518.81/75.82 | ~ (g_true @ X1 @ X0) 518.81/75.82 | (g_true_only @ ('#sk11' @ X0 @ X2) @ X0) 518.81/75.82 | (g_false_only @ ('#sk11' @ X0 @ X2) @ X0) 518.81/75.82 | (g_false_only @ ('#sk11' @ X0 @ X2) @ X2) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X3 @ ('#sk9' @ X0)) 518.81/75.82 | ~ (g_both @ X1 @ X2) 518.81/75.82 | (g_true_only @ X3 @ X0) 518.81/75.82 | ('#form12' @ X0 @ X2))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl255])). 518.81/75.82 thf(zip_derived_cl14126, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_true @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X1 @ ('#sk9' @ '#sk1')) 518.81/75.82 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.82 | (g_true_only @ X1 @ '#sk1') 518.81/75.82 | ('#form12' @ '#sk1' @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl950, zip_derived_cl1130])). 518.81/75.82 thf(zip_derived_cl815, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl814])). 518.81/75.82 thf(zip_derived_cl10, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.82 thf(zip_derived_cl13, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | (((($false) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4)))), 518.81/75.82 inference('bool_hoist', [status(thm)], [zip_derived_cl10])). 518.81/75.82 thf(zip_derived_cl14, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_true @ X2 @ X4) | ~ (g_both @ X2 @ X4))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl13])). 518.81/75.82 thf(zip_derived_cl817, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_true @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl815, zip_derived_cl14])). 518.81/75.82 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.82 thf(zip_derived_cl949, plain, ( (g_true @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl817, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl14163, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.82 | ('#form8') 518.81/75.82 | (g_true_only @ X1 @ ('#sk9' @ '#sk1')) 518.81/75.82 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.82 | (g_true_only @ X1 @ '#sk1') 518.81/75.82 | ('#form12' @ '#sk1' @ X0))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl14126, zip_derived_cl949])). 518.81/75.82 thf(zip_derived_cl276, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((g_true_only @ X2 @ X4) 518.81/75.82 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl275])). 518.81/75.82 thf(zip_derived_cl279, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false @ X2 @ X4) 518.81/75.82 | ((g_true_only @ X2 @ X4) 518.81/75.82 = (((((~) @ ($false))) & (g_true @ X2 @ X4)))))), 518.81/75.82 inference('bool_hoist', [status(thm)], [zip_derived_cl276])). 518.81/75.82 thf(zip_derived_cl280, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false @ X2 @ X4) | ((g_true_only @ X2 @ X4) = (g_true @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl279])). 518.81/75.82 thf(zip_derived_cl301, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.82 thf(zip_derived_cl280, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false @ X2 @ X4) | ((g_true_only @ X2 @ X4) = (g_true @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl279])). 518.81/75.82 thf(zip_derived_cl94, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ('#form6' @ X4))), 518.81/75.82 inference('renaming', [status(thm)], [zip_derived_cl84, zip_derived_cl88])). 518.81/75.82 thf(zip_derived_cl104, plain, 518.81/75.82 (( ('#form8') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl106, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ X4) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) & 518.81/75.82 (g_false_only @ ('#sk5' @ X4) @ X4))) 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('renaming', [status(thm)], 518.81/75.82 [zip_derived_cl94, zip_derived_cl104])). 518.81/75.82 thf(zip_derived_cl115, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_false_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ('#form6' @ X4) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 518.81/75.82 thf(zip_derived_cl130, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_both @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ('#form6' @ X4) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl115])). 518.81/75.82 thf(zip_derived_cl898, plain, 518.81/75.82 (~ (g_false_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl873, zip_derived_cl51])). 518.81/75.82 thf(zip_derived_cl906, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ '#sk4'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl130, zip_derived_cl898])). 518.81/75.82 thf(zip_derived_cl907, plain, 518.81/75.82 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl9892, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_both @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl906, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl764, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl57, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl768, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl9895, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ (g_true_only @ ('#sk5' @ X0) @ '#sk4'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl9892, zip_derived_cl768])). 518.81/75.82 thf(zip_derived_cl503, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl56])). 518.81/75.82 thf(zip_derived_cl9930, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_true_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl9895, zip_derived_cl503])). 518.81/75.82 thf(zip_derived_cl9931, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ (g_true @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl280, zip_derived_cl9930])). 518.81/75.82 thf(zip_derived_cl1891, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.82 thf(zip_derived_cl9938, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false @ ('#sk5' @ X0) @ '#sk4'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl9931, zip_derived_cl1891])). 518.81/75.82 thf(zip_derived_cl502, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl9941, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ (g_false_only @ ('#sk5' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl9938, zip_derived_cl502])). 518.81/75.82 thf(zip_derived_cl1541, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: ( (g_true @ X2 @ X4) | ~ (g_true_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 518.81/75.82 thf(zip_derived_cl81, plain, 518.81/75.82 (![X4 : $i]: 518.81/75.82 (~ ('#form6' @ X4) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl82, plain, 518.81/75.82 (![X4 : $i]: ( (g_true_only @ ('#sk5' @ X4) @ X4) | ~ ('#form6' @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl1550, plain, 518.81/75.82 (![X0 : $i]: ( (g_true @ ('#sk5' @ X0) @ X0) | ~ ('#form6' @ X0))), 518.81/75.82 inference('s_sup+', [status(thm)], [zip_derived_cl1541, zip_derived_cl82])). 518.81/75.82 thf(zip_derived_cl297, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 = (g_false_only @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl296])). 518.81/75.82 thf(zip_derived_cl1577, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form6' @ X0) 518.81/75.82 | ((((((~) @ ($true))) & (g_false @ ('#sk5' @ X0) @ X0))) 518.81/75.82 = (g_false_only @ ('#sk5' @ X0) @ X0)))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl1550, zip_derived_cl297])). 518.81/75.82 thf(zip_derived_cl1583, plain, 518.81/75.82 (![X0 : $i]: (~ ('#form6' @ X0) | ~ (g_false_only @ ('#sk5' @ X0) @ X0))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], 518.81/75.82 [zip_derived_cl1577])). 518.81/75.82 thf(zip_derived_cl9970, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false @ ('#sk5' @ X0) @ '#sk4'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl9941, zip_derived_cl1583])). 518.81/75.82 thf(zip_derived_cl9972, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ (g_false @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false @ ('#sk5' @ X0) @ '#sk4'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl301, zip_derived_cl9970])). 518.81/75.82 thf(zip_derived_cl1891, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.82 thf(zip_derived_cl10079, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_true @ ('#sk5' @ X0) @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl9972, zip_derived_cl1891])). 518.81/75.82 thf(zip_derived_cl280, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false @ X2 @ X4) | ((g_true_only @ X2 @ X4) = (g_true @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl279])). 518.81/75.82 thf(zip_derived_cl57, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl340, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_false @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_true_only @ X1 @ X0) 518.81/75.82 | ~ (g_true @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl15, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.82 thf(zip_derived_cl56, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.82 thf(zip_derived_cl273, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_true @ X1 @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl56])). 518.81/75.82 thf(zip_derived_cl422, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_true @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl273])). 518.81/75.82 thf(zip_derived_cl10086, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | ~ (g_true_only @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl10079, zip_derived_cl422])). 518.81/75.82 thf(zip_derived_cl10193, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | ~ (g_true @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl280, zip_derived_cl10086])). 518.81/75.82 thf(zip_derived_cl1891, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.82 thf(zip_derived_cl10416, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | ~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl10193, zip_derived_cl1891])). 518.81/75.82 thf(zip_derived_cl10427, plain, 518.81/75.82 (( (g_false @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('eq_fact', [status(thm)], [zip_derived_cl10416])). 518.81/75.82 thf(zip_derived_cl815, plain, 518.81/75.82 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk2' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl814])). 518.81/75.82 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.82 thf(zip_derived_cl947, plain, ( (g_both @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl116, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_true_only @ X2 @ X2) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (g_both @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ('#form6' @ X4) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl106])). 518.81/75.82 thf(zip_derived_cl47, plain, 518.81/75.82 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.82 thf(zip_derived_cl333, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ X1) 518.81/75.82 | (g_both @ ('#sk5' @ X1) @ X1) 518.81/75.82 | (g_true_only @ X0 @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_false_only @ ('#sk5' @ X1) @ X1) 518.81/75.82 | ~ (g_both @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl116, zip_derived_cl47])). 518.81/75.82 thf(zip_derived_cl48, plain, 518.81/75.82 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.82 thf(zip_derived_cl1978, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_both @ X0 @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk5' @ X1) @ X1) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ X1) @ X1) 518.81/75.82 | ('#form6' @ X1) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl333, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl1980, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl947, zip_derived_cl1978])). 518.81/75.82 thf(zip_derived_cl768, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl5711, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | (g_both @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ (g_true_only @ ('#sk5' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1980, zip_derived_cl768])). 518.81/75.82 thf(zip_derived_cl503, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl56])). 518.81/75.82 thf(zip_derived_cl5722, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_true_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl5711, zip_derived_cl503])). 518.81/75.82 thf(zip_derived_cl764, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl5725, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ (g_false_only @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl5722, zip_derived_cl764])). 518.81/75.82 thf(zip_derived_cl1891, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.82 thf(zip_derived_cl297, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 = (g_false_only @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl296])). 518.81/75.82 thf(zip_derived_cl299, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (((((~) @ (g_true @ X2 @ X4))) & (g_false @ X2 @ X4))) 518.81/75.82 | (g_false_only @ X2 @ X4))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl297])). 518.81/75.82 thf(zip_derived_cl358, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | ~ (g_false @ X2 @ X4) 518.81/75.82 | (g_false_only @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl299])). 518.81/75.82 thf(zip_derived_cl1986, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_true @ X1 @ X0) | (g_true @ X1 @ X0) | (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl1891, zip_derived_cl358])). 518.81/75.82 thf(zip_derived_cl2018, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_false_only @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl1986])). 518.81/75.82 thf(zip_derived_cl5733, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ ('#form8') 518.81/75.82 | (g_true @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl5725, zip_derived_cl2018])). 518.81/75.82 thf(zip_derived_cl10, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.82 thf(zip_derived_cl5779, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (((($true) & (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ X0))) 518.81/75.82 = (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0)))), 518.81/75.82 inference('s_sup+', [status(thm)], [zip_derived_cl5733, zip_derived_cl10])). 518.81/75.82 thf(zip_derived_cl5788, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ((g_false @ ('#sk5' @ ('#sk2' @ X0)) @ X0) 518.81/75.82 = (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], 518.81/75.82 [zip_derived_cl5779])). 518.81/75.82 thf(zip_derived_cl8853, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false @ ('#sk5' @ ('#sk2' @ X0)) @ X0) 518.81/75.82 | (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0) 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('eq_elim', [status(thm)], [zip_derived_cl5788])). 518.81/75.82 thf(zip_derived_cl10437, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ('#form6' @ ('#sk2' @ '#sk4')) 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl10427, zip_derived_cl8853])). 518.81/75.82 thf(zip_derived_cl83, plain, 518.81/75.82 (![X4 : $i]: 518.81/75.82 ( (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))) 518.81/75.82 | ~ ('#form6' @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl95, plain, 518.81/75.82 (![X4 : $i]: 518.81/75.82 ( (g_both @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | ~ ('#form6' @ X4))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl83])). 518.81/75.82 thf(zip_derived_cl82, plain, 518.81/75.82 (![X4 : $i]: ( (g_true_only @ ('#sk5' @ X4) @ X4) | ~ ('#form6' @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl58, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl284, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl58])). 518.81/75.82 thf(zip_derived_cl286, plain, 518.81/75.82 ((~ ('#form6' @ ('#sk2' @ '#sk4')) 518.81/75.82 | (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form6' @ ('#sk2' @ '#sk4')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl95, zip_derived_cl284])). 518.81/75.82 thf(zip_derived_cl287, plain, 518.81/75.82 (( (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form6' @ ('#sk2' @ '#sk4')))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl286])). 518.81/75.82 thf(zip_derived_cl82, plain, 518.81/75.82 (![X4 : $i]: ( (g_true_only @ ('#sk5' @ X4) @ X4) | ~ ('#form6' @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl57, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.82 thf(zip_derived_cl283, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_true_only @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl288, plain, (~ ('#form6' @ ('#sk2' @ '#sk4'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl287, zip_derived_cl283])). 518.81/75.82 thf(zip_derived_cl10439, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_both @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl10437, zip_derived_cl288])). 518.81/75.82 thf(zip_derived_cl10440, plain, 518.81/75.82 (( (g_both @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl10439])). 518.81/75.82 thf(zip_derived_cl947, plain, ( (g_both @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl934, plain, 518.81/75.82 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl88, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl89, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (((((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ Y0) & (g_both @ Y0 @ X2)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((((g_false_only @ Y0 @ Y0) | (g_both @ 518.81/75.82 Y0 @ Y0))) & 518.81/75.82 (g_true_only @ Y0 @ X2))) | 518.81/75.82 (((g_false_only @ Y0 @ X2) & 518.81/75.82 (((g_true_only @ Y0 @ Y0) | (g_both @ 518.81/75.82 Y0 @ Y0))))) | 518.81/75.82 (((g_both @ Y0 @ X2) & 518.81/75.82 (((g_false_only @ Y0 @ Y0) | 518.81/75.82 (g_true_only @ Y0 @ Y0)))))))))))))) 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 518.81/75.82 thf(zip_derived_cl100, plain, 518.81/75.82 (![X2 : $i]: 518.81/75.82 (~ (((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ Y0) & (g_both @ Y0 @ X2)))))) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((((g_false_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))) & 518.81/75.82 (g_true_only @ Y0 @ X2))) | 518.81/75.82 (((g_false_only @ Y0 @ X2) & 518.81/75.82 (((g_true_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))))) | 518.81/75.82 (((g_both @ Y0 @ X2) & 518.81/75.82 (((g_false_only @ Y0 @ Y0) | (g_true_only @ Y0 @ 518.81/75.82 Y0)))))))))) 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl89])). 518.81/75.82 thf(zip_derived_cl111, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (((g_both @ X4 @ X4) & (g_both @ X4 @ X2))) 518.81/75.82 | ('#form7') 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((((g_false_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))) & 518.81/75.82 (g_true_only @ Y0 @ X2))) | 518.81/75.82 (((g_false_only @ Y0 @ X2) & 518.81/75.82 (((g_true_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))))) | 518.81/75.82 (((g_both @ Y0 @ X2) & 518.81/75.82 (((g_false_only @ Y0 @ Y0) | (g_true_only @ Y0 @ 518.81/75.82 Y0)))))))))))), 518.81/75.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 518.81/75.82 thf(zip_derived_cl126, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((((g_false_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))) & 518.81/75.82 (g_true_only @ Y0 @ X2))) | 518.81/75.82 (((g_false_only @ Y0 @ X2) & 518.81/75.82 (((g_true_only @ Y0 @ Y0) | (g_both @ Y0 @ Y0))))) | 518.81/75.82 (((g_both @ Y0 @ X2) & 518.81/75.82 (((g_false_only @ Y0 @ Y0) | (g_true_only @ Y0 @ 518.81/75.82 Y0)))))))))) 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl111])). 518.81/75.82 thf(zip_derived_cl140, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))) & 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ X2))) | 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))) | 518.81/75.82 (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))))) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4))), 518.81/75.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl126])). 518.81/75.82 thf(zip_derived_cl156, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))) & 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ X2))) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl140])). 518.81/75.82 thf(zip_derived_cl171, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl156])). 518.81/75.82 thf(zip_derived_cl176, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_true_only @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl171])). 518.81/75.82 thf(zip_derived_cl183, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl176])). 518.81/75.82 thf(zip_derived_cl193, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl183])). 518.81/75.82 thf(zip_derived_cl943, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk10' @ X0) @ X0) 518.81/75.82 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X0) @ X0) 518.81/75.82 | (g_true_only @ ('#sk10' @ X0) @ ('#sk10' @ X0)) 518.81/75.82 | (g_false_only @ ('#sk10' @ X0) @ ('#sk10' @ X0)))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl193])). 518.81/75.82 thf(zip_derived_cl10770, plain, 518.81/75.82 (( (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl947, zip_derived_cl943])). 518.81/75.82 thf(zip_derived_cl947, plain, ( (g_both @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl934, plain, 518.81/75.82 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl175, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_both @ ('#sk10' @ X2) @ X2) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl171])). 518.81/75.82 thf(zip_derived_cl182, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))) 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ X2))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl175])). 518.81/75.82 thf(zip_derived_cl192, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X2) @ X2))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl182])). 518.81/75.82 thf(zip_derived_cl942, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk10' @ X0) @ ('#sk10' @ X0)) 518.81/75.82 | (g_both @ ('#sk10' @ X0) @ ('#sk10' @ X0)) 518.81/75.82 | (g_both @ ('#sk10' @ X0) @ X0) 518.81/75.82 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl192])). 518.81/75.82 thf(zip_derived_cl10711, plain, 518.81/75.82 (( (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl947, zip_derived_cl942])). 518.81/75.82 thf(zip_derived_cl947, plain, ( (g_both @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl940])). 518.81/75.82 thf(zip_derived_cl934, plain, 518.81/75.82 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl170, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl156])). 518.81/75.82 thf(zip_derived_cl174, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (((g_false_only @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | (g_both @ 518.81/75.82 ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl170])). 518.81/75.82 thf(zip_derived_cl179, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk10' @ X2) @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | (((g_both @ ('#sk10' @ X2) @ X2) & 518.81/75.82 (((g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) | 518.81/75.82 (g_true_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))))) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl174])). 518.81/75.82 thf(zip_derived_cl186, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_both @ ('#sk10' @ X2) @ X2) 518.81/75.82 | (g_false_only @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | (g_both @ ('#sk10' @ X2) @ ('#sk10' @ X2)) 518.81/75.82 | ~ (g_both @ X4 @ X4) 518.81/75.82 | ~ (g_both @ X4 @ X2) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_false_only @ ('#sk10' @ X2) @ X2))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl179])). 518.81/75.82 thf(zip_derived_cl941, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_both @ ('#sk10' @ X0) @ X0) 518.81/75.82 | (g_false_only @ ('#sk10' @ X0) @ ('#sk10' @ X0)) 518.81/75.82 | (g_both @ ('#sk10' @ X0) @ ('#sk10' @ X0)) 518.81/75.82 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_false_only @ ('#sk10' @ X0) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl186])). 518.81/75.82 thf(zip_derived_cl10654, plain, 518.81/75.82 (( (g_both @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl947, zip_derived_cl941])). 518.81/75.82 thf(zip_derived_cl289, plain, 518.81/75.82 (![X0 : $i]: (~ (g_both @ X0 @ '#sk1') | (g_both @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl266, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl11246, plain, 518.81/75.82 (( (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7') 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl10654, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl51, plain, 518.81/75.82 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl11250, plain, 518.81/75.82 (( (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | ('#form7') 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ~ (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl11246, zip_derived_cl51])). 518.81/75.82 thf(zip_derived_cl52, plain, 518.81/75.82 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.82 thf(zip_derived_cl11292, plain, 518.81/75.82 ((~ (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11250, zip_derived_cl52])). 518.81/75.82 thf(zip_derived_cl768, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 (~ (g_false_only @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl11293, plain, 518.81/75.82 (( ('#form7') | ~ (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11292, zip_derived_cl768])). 518.81/75.82 thf(zip_derived_cl1889, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.82 thf(zip_derived_cl11295, plain, 518.81/75.82 (( ('#form7') | (g_false @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl11293, zip_derived_cl1889])). 518.81/75.82 thf(zip_derived_cl301, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true @ X2 @ X4) 518.81/75.82 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.82 thf(zip_derived_cl1889, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.82 thf(zip_derived_cl50, plain, 518.81/75.82 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.82 thf(zip_derived_cl1893, plain, 518.81/75.82 (![X0 : $i]: ( (g_false @ X0 @ X0) | ~ (g_false_only @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl50])). 518.81/75.82 thf(zip_derived_cl1916, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( (g_true @ X0 @ '#sk1') 518.81/75.82 | (g_false @ X0 @ X0) 518.81/75.82 | ~ (g_false @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl301, zip_derived_cl1893])). 518.81/75.82 thf(zip_derived_cl15, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.82 thf(zip_derived_cl1889, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.82 thf(zip_derived_cl48, plain, 518.81/75.82 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.82 thf(zip_derived_cl1892, plain, 518.81/75.82 (![X0 : $i]: ( (g_false @ X0 @ X0) | ~ (g_both @ X0 @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl1909, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_false @ X0 @ '#sk1') 518.81/75.82 | ~ (g_true @ X0 @ '#sk1') 518.81/75.82 | (g_false @ X0 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl1892])). 518.81/75.82 thf(zip_derived_cl2135, plain, 518.81/75.82 (![X0 : $i]: (~ (g_false @ X0 @ '#sk1') | (g_false @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl1916, zip_derived_cl1909])). 518.81/75.82 thf(zip_derived_cl11302, plain, 518.81/75.82 (( ('#form7') | (g_false @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl11295, zip_derived_cl2135])). 518.81/75.82 thf(zip_derived_cl276, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((g_true_only @ X2 @ X4) 518.81/75.82 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl275])). 518.81/75.82 thf(zip_derived_cl11304, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | ((g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 = (((((~) @ ($true))) & (g_true @ ('#sk10' @ '#sk1') @ 518.81/75.82 ('#sk10' @ '#sk1'))))))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl11302, zip_derived_cl276])). 518.81/75.82 thf(zip_derived_cl11311, plain, 518.81/75.82 (( ('#form7') | ~ (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], 518.81/75.82 [zip_derived_cl11304])). 518.81/75.82 thf(zip_derived_cl11558, plain, 518.81/75.82 (( (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7') 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl10711, zip_derived_cl11311])). 518.81/75.82 thf(zip_derived_cl11293, plain, 518.81/75.82 (( ('#form7') | ~ (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11292, zip_derived_cl768])). 518.81/75.82 thf(zip_derived_cl11559, plain, 518.81/75.82 (( (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_both @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl11558, zip_derived_cl11293])). 518.81/75.82 thf(zip_derived_cl289, plain, 518.81/75.82 (![X0 : $i]: (~ (g_both @ X0 @ '#sk1') | (g_both @ X0 @ X0))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl266, zip_derived_cl48])). 518.81/75.82 thf(zip_derived_cl11560, plain, 518.81/75.82 (( ('#form7') | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11559, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl49, plain, 518.81/75.82 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.82 thf(zip_derived_cl11569, plain, 518.81/75.82 (( ('#form7') | ~ (g_false_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl11560, zip_derived_cl49])). 518.81/75.82 thf(zip_derived_cl12030, plain, 518.81/75.82 (( (g_false_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl10770, zip_derived_cl11569])). 518.81/75.82 thf(zip_derived_cl11560, plain, 518.81/75.82 (( ('#form7') | (g_both @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11559, zip_derived_cl289])). 518.81/75.82 thf(zip_derived_cl502, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl11563, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | ~ (g_false_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl11560, zip_derived_cl502])). 518.81/75.82 thf(zip_derived_cl12031, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1') 518.81/75.82 | (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12030, zip_derived_cl11563])). 518.81/75.82 thf(zip_derived_cl11293, plain, 518.81/75.82 (( ('#form7') | ~ (g_true_only @ ('#sk10' @ '#sk1') @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl11292, zip_derived_cl768])). 518.81/75.82 thf(zip_derived_cl12032, plain, 518.81/75.82 (( (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')) | ('#form7'))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12031, zip_derived_cl11293])). 518.81/75.82 thf(zip_derived_cl11311, plain, 518.81/75.82 (( ('#form7') | ~ (g_true_only @ ('#sk10' @ '#sk1') @ ('#sk10' @ '#sk1')))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], 518.81/75.82 [zip_derived_cl11304])). 518.81/75.82 thf(zip_derived_cl12033, plain, ( ('#form7')), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12032, zip_derived_cl11311])). 518.81/75.82 thf(zip_derived_cl12095, plain, 518.81/75.82 (( (g_both @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') | ~ ('#form8'))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl10440, zip_derived_cl12033])). 518.81/75.82 thf(zip_derived_cl78, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_false_only @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ 518.81/75.82 Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ 518.81/75.82 Y1) | (g_true_only @ 518.81/75.82 Y1 @ Y1))))))))))))))))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl71])). 518.81/75.82 thf(zip_derived_cl88, plain, 518.81/75.82 (( ('#form7') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((??) @ (^[Y1 : $i]: 518.81/75.82 (((g_both @ Y1 @ Y1) & (g_both @ Y1 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))) & 518.81/75.82 (g_true_only @ Y1 @ Y0))) | 518.81/75.82 (((g_false_only @ Y1 @ Y0) & 518.81/75.82 (((g_true_only @ Y1 @ Y1) | 518.81/75.82 (g_both @ Y1 @ Y1))))) | 518.81/75.82 (((g_both @ Y1 @ Y0) & 518.81/75.82 (((g_false_only @ Y1 @ Y1) | 518.81/75.82 (g_true_only @ Y1 @ Y1))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl91, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ ('#form7') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ X4))), 518.81/75.82 inference('renaming', [status(thm)], [zip_derived_cl78, zip_derived_cl88])). 518.81/75.82 thf(zip_derived_cl81, plain, 518.81/75.82 (![X4 : $i]: 518.81/75.82 (~ ('#form6' @ X4) 518.81/75.82 | (((g_true_only @ ('#sk5' @ X4) @ X4) & 518.81/75.82 (((g_both @ ('#sk5' @ X4) @ '#sk4') | (g_true_only @ 518.81/75.82 ('#sk5' @ X4) @ '#sk4'))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl101, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( ('#form6' @ X4) 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | ~ ('#form7'))), 518.81/75.82 inference('renaming', [status(thm)], [zip_derived_cl91, zip_derived_cl81])). 518.81/75.82 thf(zip_derived_cl104, plain, 518.81/75.82 (( ('#form8') 518.81/75.82 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.82 (((((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.82 (((!!) @ (^[Y2 : $i]: 518.81/75.82 (((((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))) | 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (g_true_only @ 518.81/75.82 Y2 @ Y0))))))))))))) & 518.81/75.82 (((??) @ (^[Y1 : $i]: 518.81/75.82 (((((??) @ (^[Y2 : $i]: 518.81/75.82 (((g_both @ Y2 @ Y1) & 518.81/75.82 (g_both @ Y2 @ Y0)))))) & 518.81/75.82 (((~) @ (((??) @ (^[Y2 : $i]: 518.81/75.82 (((((g_false_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_false_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_both @ Y2 @ 518.81/75.82 Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_false_only @ 518.81/75.82 Y2 @ Y0))))) | 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y1) & 518.81/75.82 (((g_true_only @ 518.81/75.82 Y2 @ Y0) | 518.81/75.82 (g_both @ 518.81/75.82 Y2 @ Y0)))))))))))))))))))))))), 518.81/75.82 define([status(thm)])). 518.81/75.82 thf(zip_derived_cl112, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (((g_true_only @ X2 @ '#sk3') & (g_true_only @ X2 @ X2))) 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ X4) 518.81/75.82 | ('#form6' @ X4))), 518.81/75.82 inference('renaming', [status(thm)], 518.81/75.82 [zip_derived_cl101, zip_derived_cl104])). 518.81/75.82 thf(zip_derived_cl128, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ( (g_true_only @ X2 @ X2) 518.81/75.82 | ('#form6' @ X4) 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ X4) 518.81/75.82 | (g_false_only @ X2 @ X2) 518.81/75.82 | (g_true_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X4) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl112])). 518.81/75.82 thf(zip_derived_cl898, plain, 518.81/75.82 (~ (g_false_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl873, zip_derived_cl51])). 518.81/75.82 thf(zip_derived_cl904, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | ('#form6' @ X0) 518.81/75.82 | (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl128, zip_derived_cl898])). 518.81/75.82 thf(zip_derived_cl907, plain, 518.81/75.82 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.82 thf(zip_derived_cl9790, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( ('#form6' @ X0) 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | (g_true_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl904, zip_derived_cl907])). 518.81/75.82 thf(zip_derived_cl12033, plain, ( ('#form7')), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12032, zip_derived_cl11311])). 518.81/75.82 thf(zip_derived_cl12071, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 ( ('#form6' @ X0) 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ X0) 518.81/75.82 | (g_true_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ X0) @ '#sk4') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl9790, zip_derived_cl12033])). 518.81/75.82 thf(zip_derived_cl53, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 (~ (g_both @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.82 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.82 thf(zip_derived_cl23533, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form8') 518.81/75.82 | (g_false_only @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl12071, zip_derived_cl53])). 518.81/75.82 thf(zip_derived_cl284, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ ('#form6' @ ('#sk2' @ X0)) 518.81/75.82 | ~ (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl82, zip_derived_cl58])). 518.81/75.82 thf(zip_derived_cl23614, plain, 518.81/75.82 (![X0 : $i]: 518.81/75.82 (~ (g_both @ ('#sk5' @ ('#sk2' @ X0)) @ X0) 518.81/75.82 | (g_true_only @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ ('#sk2' @ X0)) @ '#sk4') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('clc', [status(thm)], [zip_derived_cl23533, zip_derived_cl284])). 518.81/75.82 thf(zip_derived_cl23625, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | (g_false_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl12095, zip_derived_cl23614])). 518.81/75.82 thf(zip_derived_cl23633, plain, 518.81/75.82 (( (g_false_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl23625])). 518.81/75.82 thf(zip_derived_cl10440, plain, 518.81/75.82 (( (g_both @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('simplify', [status(thm)], [zip_derived_cl10439])). 518.81/75.82 thf(zip_derived_cl502, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.82 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.82 thf(zip_derived_cl10445, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ (g_false_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4'))), 518.81/75.82 inference('s_sup-', [status(thm)], 518.81/75.82 [zip_derived_cl10440, zip_derived_cl502])). 518.81/75.82 thf(zip_derived_cl12033, plain, ( ('#form7')), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12032, zip_derived_cl11311])). 518.81/75.82 thf(zip_derived_cl12097, plain, 518.81/75.82 ((~ ('#form8') | ~ (g_false_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4'))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl10445, zip_derived_cl12033])). 518.81/75.82 thf(zip_derived_cl23635, plain, 518.81/75.82 ((~ ('#form8') | (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4'))), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl23633, zip_derived_cl12097])). 518.81/75.82 thf(zip_derived_cl10427, plain, 518.81/75.82 (( (g_false @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ ('#form8'))), 518.81/75.82 inference('eq_fact', [status(thm)], [zip_derived_cl10416])). 518.81/75.82 thf(zip_derived_cl276, plain, 518.81/75.82 (![X2 : $i, X4 : $i]: 518.81/75.82 ((g_true_only @ X2 @ X4) 518.81/75.82 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.82 inference('simplify nested equalities', [status(thm)], 518.81/75.82 [zip_derived_cl275])). 518.81/75.82 thf(zip_derived_cl10435, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ((g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4') 518.81/75.82 = (((((~) @ ($true))) & (g_true @ ('#sk5' @ ('#sk2' @ '#sk4')) @ 518.81/75.82 '#sk4')))))), 518.81/75.82 inference('s_sup+', [status(thm)], 518.81/75.82 [zip_derived_cl10427, zip_derived_cl276])). 518.81/75.82 thf(zip_derived_cl10438, plain, 518.81/75.82 ((~ ('#form8') 518.81/75.82 | ~ ('#form7') 518.81/75.82 | ~ (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4'))), 518.81/75.82 inference('simplify boolean subterms', [status(thm)], 518.81/75.82 [zip_derived_cl10435])). 518.81/75.82 thf(zip_derived_cl12033, plain, ( ('#form7')), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl12032, zip_derived_cl11311])). 518.81/75.82 thf(zip_derived_cl12094, plain, 518.81/75.82 ((~ ('#form8') | ~ (g_true_only @ ('#sk5' @ ('#sk2' @ '#sk4')) @ '#sk4'))), 518.81/75.82 inference('demod', [status(thm)], 518.81/75.82 [zip_derived_cl10438, zip_derived_cl12033])). 518.81/75.82 thf(zip_derived_cl23636, plain, (~ ('#form8')), 518.81/75.82 inference('clc', [status(thm)], 518.81/75.82 [zip_derived_cl23635, zip_derived_cl12094])). 518.81/75.82 thf(zip_derived_cl63676, plain, 518.81/75.82 (![X0 : $i, X1 : $i]: 518.81/75.82 ( (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.82 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.83 | (g_true_only @ X1 @ ('#sk9' @ '#sk1')) 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_true_only @ X1 @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ X0))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl14163, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl63699, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ ('#sk9' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ ('#sk2' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2418, zip_derived_cl63676])). 518.81/75.83 thf(zip_derived_cl907, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl1889, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.83 thf(zip_derived_cl2418, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)) 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2024, zip_derived_cl2157])). 518.81/75.83 thf(zip_derived_cl947, plain, ( (g_both @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('demod', [status(thm)], [zip_derived_cl815, zip_derived_cl940])). 518.81/75.83 thf(zip_derived_cl173, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (((??) @ (^[Y0 : $i]: 518.81/75.83 (((((??) @ (^[Y1 : $i]: 518.81/75.83 (((g_both @ Y1 @ Y0) & (g_both @ Y1 @ 518.81/75.83 X2)))))) & 518.81/75.83 (((~) @ (((??) @ (^[Y1 : $i]: 518.81/75.83 (((((g_false_only @ Y1 @ Y0) & 518.81/75.83 (((g_false_only @ Y1 @ 518.81/75.83 X2) | (g_both @ Y1 @ X2))))) | 518.81/75.83 (((g_both @ Y1 @ Y0) & 518.81/75.83 (((g_true_only @ Y1 @ X2) | 518.81/75.83 (g_false_only @ Y1 @ X2))))) | 518.81/75.83 (((g_true_only @ Y1 @ Y0) & 518.81/75.83 (((g_true_only @ Y1 @ X2) | 518.81/75.83 (g_both @ Y1 @ X2))))))))))))))))) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 518.81/75.83 thf(zip_derived_cl178, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i]: 518.81/75.83 (~ (((((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ X6) & (g_both @ Y0 @ X2)))))) & 518.81/75.83 (((~) @ (((??) @ (^[Y0 : $i]: 518.81/75.83 (((((g_false_only @ Y0 @ X6) & 518.81/75.83 (((g_false_only @ Y0 @ X2) | (g_both @ 518.81/75.83 Y0 @ X2))))) | 518.81/75.83 (((g_both @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | 518.81/75.83 (g_false_only @ Y0 @ X2))))) | 518.81/75.83 (((g_true_only @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_both @ 518.81/75.83 Y0 @ X2)))))))))))))) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2))), 518.81/75.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl173])). 518.81/75.83 thf(zip_derived_cl185, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i]: 518.81/75.83 (~ (((??) @ (^[Y0 : $i]: (((g_both @ Y0 @ X6) & (g_both @ Y0 @ X2)))))) 518.81/75.83 | (((??) @ (^[Y0 : $i]: 518.81/75.83 (((((g_false_only @ Y0 @ X6) & 518.81/75.83 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.83 (((g_both @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.83 X2))))) | 518.81/75.83 (((g_true_only @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl178])). 518.81/75.83 thf(zip_derived_cl196, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 (~ (((g_both @ X8 @ X6) & (g_both @ X8 @ X2))) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | (((??) @ (^[Y0 : $i]: 518.81/75.83 (((((g_false_only @ Y0 @ X6) & 518.81/75.83 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.83 (((g_both @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.83 X2))))) | 518.81/75.83 (((g_true_only @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))))), 518.81/75.83 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])). 518.81/75.83 thf(zip_derived_cl205, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 (~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (((??) @ (^[Y0 : $i]: 518.81/75.83 (((((g_false_only @ Y0 @ X6) & 518.81/75.83 (((g_false_only @ Y0 @ X2) | (g_both @ Y0 @ X2))))) | 518.81/75.83 (((g_both @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_false_only @ Y0 @ 518.81/75.83 X2))))) | 518.81/75.83 (((g_true_only @ Y0 @ X6) & 518.81/75.83 (((g_true_only @ Y0 @ X2) | (g_both @ Y0 @ X2)))))))))) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl196])). 518.81/75.83 thf(zip_derived_cl217, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (((((g_false_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) | 518.81/75.83 (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) | 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6))), 518.81/75.83 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl205])). 518.81/75.83 thf(zip_derived_cl219, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (((g_false_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl217])). 518.81/75.83 thf(zip_derived_cl223, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (((g_false_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 518.81/75.83 thf(zip_derived_cl229, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl223])). 518.81/75.83 thf(zip_derived_cl234, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl240, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2))), 518.81/75.83 inference('renaming', [status(thm)], 518.81/75.83 [zip_derived_cl229, zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl253, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_true_only @ X4 @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl240])). 518.81/75.83 thf(zip_derived_cl226, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | ('#form8') 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl221])). 518.81/75.83 thf(zip_derived_cl234, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl237, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2))), 518.81/75.83 inference('renaming', [status(thm)], 518.81/75.83 [zip_derived_cl226, zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl245, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_false_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_true_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | ('#form8') 518.81/75.83 | ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl237])). 518.81/75.83 thf(zip_derived_cl256, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form13' @ X2 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl264, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( ('#form13' @ X2 @ X6) 518.81/75.83 | ('#form12' @ X2 @ X6) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_true_only @ X4 @ X2))), 518.81/75.83 inference('renaming', [status(thm)], 518.81/75.83 [zip_derived_cl253, zip_derived_cl256])). 518.81/75.83 thf(zip_derived_cl1479, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( ('#form13' @ '#sk1' @ X0) 518.81/75.83 | ('#form12' @ '#sk1' @ X0) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X1 @ '#sk1') 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_true_only @ X1 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl947, zip_derived_cl264])). 518.81/75.83 thf(zip_derived_cl21872, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | ('#form13' @ '#sk1' @ ('#sk2' @ '#sk1')) 518.81/75.83 | ('#form12' @ '#sk1' @ ('#sk2' @ '#sk1')) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2418, zip_derived_cl1479])). 518.81/75.83 thf(zip_derived_cl907, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl256, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form13' @ X2 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl258, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.83 | ~ ('#form13' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl256])). 518.81/75.83 thf(zip_derived_cl265, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | ~ ('#form13' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl258])). 518.81/75.83 thf(zip_derived_cl257, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ X2 @ X6) @ X6) | ~ ('#form13' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl256])). 518.81/75.83 thf(zip_derived_cl55, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_false_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl320, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ ('#form13' @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_false_only @ ('#sk11' @ X1 @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl1524, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ ('#form13' @ X0 @ ('#sk2' @ X0)) 518.81/75.83 | (g_true_only @ ('#sk11' @ X0 @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ ('#form13' @ X0 @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl265, zip_derived_cl320])). 518.81/75.83 thf(zip_derived_cl1530, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X0 @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ ('#form13' @ X0 @ ('#sk2' @ X0)))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1524])). 518.81/75.83 thf(zip_derived_cl257, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ X2 @ X6) @ X6) | ~ ('#form13' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl256])). 518.81/75.83 thf(zip_derived_cl56, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl321, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ ('#form13' @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_true_only @ ('#sk11' @ X1 @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl257, zip_derived_cl56])). 518.81/75.83 thf(zip_derived_cl1537, plain, 518.81/75.83 (![X0 : $i]: ~ ('#form13' @ X0 @ ('#sk2' @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1530, zip_derived_cl321])). 518.81/75.83 thf(zip_derived_cl234, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl236, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.83 | ~ ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl247, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_both @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | ~ ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl236])). 518.81/75.83 thf(zip_derived_cl235, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X6) | ~ ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl58, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_both @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.83 thf(zip_derived_cl309, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ ('#form12' @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_both @ ('#sk11' @ X1 @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl58])). 518.81/75.83 thf(zip_derived_cl991, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ ('#form12' @ X0 @ ('#sk2' @ X0)) 518.81/75.83 | (g_true_only @ ('#sk11' @ X0 @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ ('#form12' @ X0 @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl247, zip_derived_cl309])). 518.81/75.83 thf(zip_derived_cl995, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X0 @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ ('#form12' @ X0 @ ('#sk2' @ X0)))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl991])). 518.81/75.83 thf(zip_derived_cl235, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X6) | ~ ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl57, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.83 thf(zip_derived_cl308, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ ('#form12' @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_true_only @ ('#sk11' @ X1 @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl235, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl1460, plain, 518.81/75.83 (![X0 : $i]: ~ ('#form12' @ X0 @ ('#sk2' @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl995, zip_derived_cl308])). 518.81/75.83 thf(zip_derived_cl21897, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( ('#form8') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl21872, zip_derived_cl907, zip_derived_cl940, 518.81/75.83 zip_derived_cl1537, zip_derived_cl1460])). 518.81/75.83 thf(zip_derived_cl23636, plain, (~ ('#form8')), 518.81/75.83 inference('clc', [status(thm)], 518.81/75.83 [zip_derived_cl23635, zip_derived_cl12094])). 518.81/75.83 thf(zip_derived_cl26089, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl21897, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl768, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl26131, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl26089, zip_derived_cl768])). 518.81/75.83 thf(zip_derived_cl503, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl56])). 518.81/75.83 thf(zip_derived_cl26142, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl26131, zip_derived_cl503])). 518.81/75.83 thf(zip_derived_cl26144, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1889, zip_derived_cl26142])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl1889, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.83 thf(zip_derived_cl57, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true_only @ X4 @ X2) | ~ (g_true_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl44])). 518.81/75.83 thf(zip_derived_cl1898, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_false @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl1891, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.83 thf(zip_derived_cl301, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_true @ X2 @ X4) 518.81/75.83 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl280, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false @ X2 @ X4) | ((g_true_only @ X2 @ X4) = (g_true @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl279])). 518.81/75.83 thf(zip_derived_cl765, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) 518.81/75.83 | (g_false @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | (g_true @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup+', [status(thm)], [zip_derived_cl764, zip_derived_cl280])). 518.81/75.83 thf(zip_derived_cl301, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_true @ X2 @ X4) 518.81/75.83 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.83 thf(zip_derived_cl54, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_false_only @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.83 thf(zip_derived_cl382, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_true @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_false_only @ X1 @ X0) 518.81/75.83 | ~ (g_false @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl54])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl55, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_false_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl272, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_true @ X1 @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_false_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl421, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false @ X1 @ ('#sk2' @ X0)) | ~ (g_false_only @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl382, zip_derived_cl272])). 518.81/75.83 thf(zip_derived_cl1108, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_true @ X1 @ ('#sk2' @ X0)) | ~ (g_false_only @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl765, zip_derived_cl421])). 518.81/75.83 thf(zip_derived_cl7, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false_only @ X2 @ X4) 518.81/75.83 | (g_both @ X2 @ X4) 518.81/75.83 | (g_true_only @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.83 thf(zip_derived_cl280, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false @ X2 @ X4) | ((g_true_only @ X2 @ X4) = (g_true @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl279])). 518.81/75.83 thf(zip_derived_cl50, plain, 518.81/75.83 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.83 thf(zip_derived_cl338, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false @ X0 @ X0) 518.81/75.83 | ~ (g_true @ X0 @ X0) 518.81/75.83 | ~ (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl280, zip_derived_cl50])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl49, plain, 518.81/75.83 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.83 thf(zip_derived_cl267, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ X0 @ X0) 518.81/75.83 | ~ (g_true @ X0 @ X0) 518.81/75.83 | ~ (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl49])). 518.81/75.83 thf(zip_derived_cl352, plain, 518.81/75.83 (![X0 : $i]: (~ (g_false_only @ X0 @ '#sk1') | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl338, zip_derived_cl267])). 518.81/75.83 thf(zip_derived_cl353, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ X0 @ '#sk1') 518.81/75.83 | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl352])). 518.81/75.83 thf(zip_derived_cl1113, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1108, zip_derived_cl353])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl48, plain, 518.81/75.83 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.83 thf(zip_derived_cl766, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_both @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl48])). 518.81/75.83 thf(zip_derived_cl1120, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1113, zip_derived_cl766])). 518.81/75.83 thf(zip_derived_cl1122, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl301, zip_derived_cl1120])). 518.81/75.83 thf(zip_derived_cl1997, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1891, zip_derived_cl1122])). 518.81/75.83 thf(zip_derived_cl2022, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | (g_true @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1997])). 518.81/75.83 thf(zip_derived_cl10, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.83 thf(zip_derived_cl2329, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | (((($true) & (g_false @ ('#sk2' @ X0) @ X0))) 518.81/75.83 = (g_both @ ('#sk2' @ X0) @ X0)))), 518.81/75.83 inference('s_sup+', [status(thm)], [zip_derived_cl2022, zip_derived_cl10])). 518.81/75.83 thf(zip_derived_cl2334, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ((g_false @ ('#sk2' @ X0) @ X0) = (g_both @ ('#sk2' @ X0) @ X0)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], 518.81/75.83 [zip_derived_cl2329])). 518.81/75.83 thf(zip_derived_cl292, plain, 518.81/75.83 (![X0 : $i]: (~ (g_true_only @ X0 @ '#sk1') | (g_true_only @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl268, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl4032, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (((g_false @ ('#sk2' @ X0) @ X0) = (g_both @ ('#sk2' @ X0) @ X0)) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2334, zip_derived_cl292])). 518.81/75.83 thf(zip_derived_cl4122, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.83 inference('eq_elim', [status(thm)], [zip_derived_cl4032])). 518.81/75.83 thf(zip_derived_cl4719, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | (g_both @ ('#sk2' @ ('#sk2' @ X0)) @ ('#sk2' @ X0)) 518.81/75.83 | (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ ('#sk2' @ ('#sk2' @ X0))))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1898, zip_derived_cl4122])). 518.81/75.83 thf(zip_derived_cl56, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl8554, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ ('#sk2' @ ('#sk2' @ X0))) 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl4719, zip_derived_cl56])). 518.81/75.83 thf(zip_derived_cl50, plain, 518.81/75.83 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.83 thf(zip_derived_cl8558, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl8554, zip_derived_cl50])). 518.81/75.83 thf(zip_derived_cl8574, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl764, zip_derived_cl8558])). 518.81/75.83 thf(zip_derived_cl26195, plain, 518.81/75.83 (( (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1') 518.81/75.83 | (g_false @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl26144, zip_derived_cl8574])). 518.81/75.83 thf(zip_derived_cl2018, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false_only @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1986])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl2022, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | (g_true @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1997])). 518.81/75.83 thf(zip_derived_cl422, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_true @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl273])). 518.81/75.83 thf(zip_derived_cl2332, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2022, zip_derived_cl422])). 518.81/75.83 thf(zip_derived_cl2338, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl764, zip_derived_cl2332])). 518.81/75.83 thf(zip_derived_cl2356, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2018, zip_derived_cl2338])). 518.81/75.83 thf(zip_derived_cl2018, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false_only @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1986])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl1898, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_false @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl1889, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_true_only @ X1 @ X0) | (g_false @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1620, zip_derived_cl18])). 518.81/75.83 thf(zip_derived_cl301, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_true @ X2 @ X4) 518.81/75.83 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.83 thf(zip_derived_cl51, plain, 518.81/75.83 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.83 thf(zip_derived_cl377, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ X0 @ X0) 518.81/75.83 | ~ (g_false @ X0 @ X0) 518.81/75.83 | ~ (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl51])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl52, plain, 518.81/75.83 (![X2 : $i]: (~ (g_both @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.83 thf(zip_derived_cl269, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ X0 @ X0) 518.81/75.83 | ~ (g_true @ X0 @ X0) 518.81/75.83 | ~ (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl393, plain, 518.81/75.83 (![X0 : $i]: (~ (g_true_only @ X0 @ '#sk1') | ~ (g_false @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl377, zip_derived_cl269])). 518.81/75.83 thf(zip_derived_cl1897, plain, 518.81/75.83 (![X0 : $i]: ( (g_false @ X0 @ '#sk1') | ~ (g_false @ X0 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1889, zip_derived_cl393])). 518.81/75.83 thf(zip_derived_cl1953, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_false @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1898, zip_derived_cl1897])). 518.81/75.83 thf(zip_derived_cl1973, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | (g_false @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl764, zip_derived_cl1953])). 518.81/75.83 thf(zip_derived_cl2118, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | (g_false @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2018, zip_derived_cl1973])). 518.81/75.83 thf(zip_derived_cl422, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_true @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl340, zip_derived_cl273])). 518.81/75.83 thf(zip_derived_cl6181, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2118, zip_derived_cl422])). 518.81/75.83 thf(zip_derived_cl7766, plain, 518.81/75.83 (( (g_true @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1') 518.81/75.83 | (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2356, zip_derived_cl6181])). 518.81/75.83 thf(zip_derived_cl2018, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false_only @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1986])). 518.81/75.83 thf(zip_derived_cl764, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_false_only @ X1 @ X0) | (g_true_only @ X1 @ ('#sk2' @ X0)))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl271, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl1898, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_false @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl4032, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (((g_false @ ('#sk2' @ X0) @ X0) = (g_both @ ('#sk2' @ X0) @ X0)) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2334, zip_derived_cl292])). 518.81/75.83 thf(zip_derived_cl48, plain, 518.81/75.83 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_both @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 518.81/75.83 thf(zip_derived_cl4109, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (((g_false @ ('#sk2' @ X0) @ X0) = (g_both @ ('#sk2' @ X0) @ X0)) 518.81/75.83 | ~ (g_both @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl4032, zip_derived_cl48])). 518.81/75.83 thf(zip_derived_cl4140, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_both @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('eq_elim', [status(thm)], [zip_derived_cl4109])). 518.81/75.83 thf(zip_derived_cl4150, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | (g_both @ ('#sk2' @ ('#sk2' @ X0)) @ ('#sk2' @ X0)) 518.81/75.83 | ~ (g_both @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1898, zip_derived_cl4140])). 518.81/75.83 thf(zip_derived_cl56, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl4729, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_both @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl4150, zip_derived_cl56])). 518.81/75.83 thf(zip_derived_cl4730, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1') 518.81/75.83 | ~ (g_true @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl4729])). 518.81/75.83 thf(zip_derived_cl1898, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_false @ X1 @ ('#sk2' @ X0)) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl1891, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1889, zip_derived_cl1541])). 518.81/75.83 thf(zip_derived_cl301, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_true @ X2 @ X4) 518.81/75.83 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.83 thf(zip_derived_cl301, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_true @ X2 @ X4) 518.81/75.83 | ((g_false @ X2 @ X4) = (g_false_only @ X2 @ X4)))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl300])). 518.81/75.83 thf(zip_derived_cl767, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl764, zip_derived_cl50])). 518.81/75.83 thf(zip_derived_cl810, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl767])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl500, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl49])). 518.81/75.83 thf(zip_derived_cl518, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_true @ ('#sk2' @ X0) @ X0) 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl500])). 518.81/75.83 thf(zip_derived_cl929, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl810, zip_derived_cl518])). 518.81/75.83 thf(zip_derived_cl931, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl301, zip_derived_cl929])). 518.81/75.83 thf(zip_derived_cl2002, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | (g_true @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1891, zip_derived_cl931])). 518.81/75.83 thf(zip_derived_cl2023, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false @ ('#sk2' @ X0) @ X0) | (g_true @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl2002])). 518.81/75.83 thf(zip_derived_cl2052, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | (g_true @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1898, zip_derived_cl2023])). 518.81/75.83 thf(zip_derived_cl4732, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ X0)) @ X0) 518.81/75.83 | ~ (g_false @ ('#sk2' @ ('#sk2' @ X0)) @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl4730, zip_derived_cl2052])). 518.81/75.83 thf(zip_derived_cl4735, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | ~ (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl764, zip_derived_cl4732])). 518.81/75.83 thf(zip_derived_cl4739, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | ~ (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2018, zip_derived_cl4735])). 518.81/75.83 thf(zip_derived_cl7775, plain, 518.81/75.83 ( (g_true @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1')), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl7766, zip_derived_cl4739])). 518.81/75.83 thf(zip_derived_cl10, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ((((g_true @ X2 @ X4) & (g_false @ X2 @ X4))) = (g_both @ X2 @ X4))), 518.81/75.83 inference('simplify nested equalities', [status(thm)], [zip_derived_cl9])). 518.81/75.83 thf(zip_derived_cl7776, plain, 518.81/75.83 ((((($true) & (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ 518.81/75.83 '#sk1'))) 518.81/75.83 = (g_both @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1'))), 518.81/75.83 inference('s_sup+', [status(thm)], [zip_derived_cl7775, zip_derived_cl10])). 518.81/75.83 thf(zip_derived_cl7784, plain, 518.81/75.83 (((g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1') 518.81/75.83 = (g_both @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1'))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], 518.81/75.83 [zip_derived_cl7776])). 518.81/75.83 thf(zip_derived_cl503, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_true_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl56])). 518.81/75.83 thf(zip_derived_cl7794, plain, 518.81/75.83 ((~ (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl7784, zip_derived_cl503])). 518.81/75.83 thf(zip_derived_cl6181, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1') 518.81/75.83 | ~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2118, zip_derived_cl422])). 518.81/75.83 thf(zip_derived_cl7860, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1')), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl7794, zip_derived_cl6181])). 518.81/75.83 thf(zip_derived_cl26239, plain, 518.81/75.83 ( (g_false @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl26195, zip_derived_cl7860])). 518.81/75.83 thf(zip_derived_cl276, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ((g_true_only @ X2 @ X4) 518.81/75.83 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.83 inference('simplify nested equalities', [status(thm)], 518.81/75.83 [zip_derived_cl275])). 518.81/75.83 thf(zip_derived_cl26240, plain, 518.81/75.83 (((g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 = (((((~) @ ($true))) & (g_true @ 518.81/75.83 ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))))), 518.81/75.83 inference('s_sup+', [status(thm)], 518.81/75.83 [zip_derived_cl26239, zip_derived_cl276])). 518.81/75.83 thf(zip_derived_cl26246, plain, 518.81/75.83 (~ (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], 518.81/75.83 [zip_derived_cl26240])). 518.81/75.83 thf(zip_derived_cl934, plain, 518.81/75.83 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.83 thf(zip_derived_cl14, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: ( (g_true @ X2 @ X4) | ~ (g_both @ X2 @ X4))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl13])). 518.81/75.83 thf(zip_derived_cl935, plain, 518.81/75.83 ( (g_true @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl14])). 518.81/75.83 thf(zip_derived_cl26089, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl21897, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl352, plain, 518.81/75.83 (![X0 : $i]: (~ (g_false_only @ X0 @ '#sk1') | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl338, zip_derived_cl267])). 518.81/75.83 thf(zip_derived_cl26093, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl26089, zip_derived_cl352])). 518.81/75.83 thf(zip_derived_cl26446, plain, 518.81/75.83 (( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl935, zip_derived_cl26093])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl26463, plain, 518.81/75.83 (( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl26446, zip_derived_cl940])). 518.81/75.83 thf(zip_derived_cl7, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false_only @ X2 @ X4) 518.81/75.83 | (g_both @ X2 @ X4) 518.81/75.83 | (g_true_only @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.83 thf(zip_derived_cl1120, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ '#sk1') 518.81/75.83 | ~ (g_false_only @ ('#sk2' @ X0) @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1113, zip_derived_cl766])). 518.81/75.83 thf(zip_derived_cl1121, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1120])). 518.81/75.83 thf(zip_derived_cl934, plain, 518.81/75.83 ( (g_both @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], [zip_derived_cl899, zip_derived_cl907])). 518.81/75.83 thf(zip_derived_cl222, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | (((g_false_only @ X4 @ ('#sk9' @ X2)) & (g_true_only @ X4 @ X2))) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl219])). 518.81/75.83 thf(zip_derived_cl228, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_true_only @ X4 @ X2) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl222])). 518.81/75.83 thf(zip_derived_cl234, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl239, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( ('#form12' @ X2 @ X6) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (g_true_only @ X4 @ X2))), 518.81/75.83 inference('renaming', [status(thm)], 518.81/75.83 [zip_derived_cl228, zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl250, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | (g_true_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl239])). 518.81/75.83 thf(zip_derived_cl1058, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ X0 @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X1 @ X0) 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_false_only @ X1 @ X0) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ X0 @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | ('#form12' @ X0 @ ('#sk2' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl250])). 518.81/75.83 thf(zip_derived_cl12811, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | ('#form12' @ '#sk1' @ ('#sk2' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl1121, zip_derived_cl1058])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl1460, plain, 518.81/75.83 (![X0 : $i]: ~ ('#form12' @ X0 @ ('#sk2' @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl995, zip_derived_cl308])). 518.81/75.83 thf(zip_derived_cl12832, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl12811, zip_derived_cl940, zip_derived_cl940, 518.81/75.83 zip_derived_cl1460])). 518.81/75.83 thf(zip_derived_cl23636, plain, (~ ('#form8')), 518.81/75.83 inference('clc', [status(thm)], 518.81/75.83 [zip_derived_cl23635, zip_derived_cl12094])). 518.81/75.83 thf(zip_derived_cl33332, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl12832, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl54, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_false_only @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.83 thf(zip_derived_cl33390, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | ~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33332, zip_derived_cl54])). 518.81/75.83 thf(zip_derived_cl55, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_false_only @ X4 @ X2) | ~ (g_both @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl43])). 518.81/75.83 thf(zip_derived_cl33402, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl33390, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl33407, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl26463, zip_derived_cl33402])). 518.81/75.83 thf(zip_derived_cl2338, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 (~ (g_false_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ X0))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl764, zip_derived_cl2332])). 518.81/75.83 thf(zip_derived_cl33438, plain, 518.81/75.83 (( (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33407, zip_derived_cl2338])). 518.81/75.83 thf(zip_derived_cl7860, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1')), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl7794, zip_derived_cl6181])). 518.81/75.83 thf(zip_derived_cl7860, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ ('#sk2' @ ('#sk2' @ '#sk1'))) @ '#sk1')), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl7794, zip_derived_cl6181])). 518.81/75.83 thf(zip_derived_cl33498, plain, 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl33438, zip_derived_cl7860, zip_derived_cl7860])). 518.81/75.83 thf(zip_derived_cl502, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl33512, plain, 518.81/75.83 (~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33498, zip_derived_cl502])). 518.81/75.83 thf(zip_derived_cl1460, plain, 518.81/75.83 (![X0 : $i]: ~ ('#form12' @ X0 @ ('#sk2' @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl995, zip_derived_cl308])). 518.81/75.83 thf(zip_derived_cl63738, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ ('#sk9' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl63699, zip_derived_cl907, zip_derived_cl940, 518.81/75.83 zip_derived_cl26246, zip_derived_cl33512, zip_derived_cl1460])). 518.81/75.83 thf(zip_derived_cl935, plain, 518.81/75.83 ( (g_true @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl14])). 518.81/75.83 thf(zip_derived_cl33332, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl12832, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl352, plain, 518.81/75.83 (![X0 : $i]: (~ (g_false_only @ X0 @ '#sk1') | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl338, zip_derived_cl267])). 518.81/75.83 thf(zip_derived_cl33336, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | ~ (g_true @ X0 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33332, zip_derived_cl352])). 518.81/75.83 thf(zip_derived_cl33823, plain, 518.81/75.83 (( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl935, zip_derived_cl33336])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl33844, plain, 518.81/75.83 (( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl33823, zip_derived_cl940])). 518.81/75.83 thf(zip_derived_cl53, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_both @ X4 @ X2) | ~ (g_false_only @ X4 @ ('#sk2' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl42])). 518.81/75.83 thf(zip_derived_cl33851, plain, 518.81/75.83 (( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1')) 518.81/75.83 | ~ (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33844, zip_derived_cl53])). 518.81/75.83 thf(zip_derived_cl33498, plain, 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl33438, zip_derived_cl7860, zip_derived_cl7860])). 518.81/75.83 thf(zip_derived_cl33858, plain, 518.81/75.83 ( (g_both @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl33851, zip_derived_cl33498])). 518.81/75.83 thf(zip_derived_cl502, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: (~ (g_both @ X1 @ X0) | ~ (g_false_only @ X1 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl497, zip_derived_cl55])). 518.81/75.83 thf(zip_derived_cl33864, plain, 518.81/75.83 (~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33858, zip_derived_cl502])). 518.81/75.83 thf(zip_derived_cl63746, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_true_only @ X0 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('clc', [status(thm)], 518.81/75.83 [zip_derived_cl63738, zip_derived_cl33864])). 518.81/75.83 thf(zip_derived_cl7, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ( (g_false_only @ X2 @ X4) 518.81/75.83 | (g_both @ X2 @ X4) 518.81/75.83 | (g_true_only @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl6])). 518.81/75.83 thf(zip_derived_cl1893, plain, 518.81/75.83 (![X0 : $i]: ( (g_false @ X0 @ X0) | ~ (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl50])). 518.81/75.83 thf(zip_derived_cl1915, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | (g_both @ X0 @ '#sk1') 518.81/75.83 | (g_false @ X0 @ X0))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl7, zip_derived_cl1893])). 518.81/75.83 thf(zip_derived_cl1892, plain, 518.81/75.83 (![X0 : $i]: ( (g_false @ X0 @ X0) | ~ (g_both @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl1889, zip_derived_cl48])). 518.81/75.83 thf(zip_derived_cl3195, plain, 518.81/75.83 (![X0 : $i]: ( (g_false @ X0 @ X0) | (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl1915, zip_derived_cl1892])). 518.81/75.83 thf(zip_derived_cl276, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 ((g_true_only @ X2 @ X4) 518.81/75.83 = (((((~) @ (g_false @ X2 @ X4))) & (g_true @ X2 @ X4))))), 518.81/75.83 inference('simplify nested equalities', [status(thm)], 518.81/75.83 [zip_derived_cl275])). 518.81/75.83 thf(zip_derived_cl3196, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ X0 @ '#sk1') 518.81/75.83 | ((g_true_only @ X0 @ X0) 518.81/75.83 = (((((~) @ ($true))) & (g_true @ X0 @ X0)))))), 518.81/75.83 inference('s_sup+', [status(thm)], 518.81/75.83 [zip_derived_cl3195, zip_derived_cl276])). 518.81/75.83 thf(zip_derived_cl3216, plain, 518.81/75.83 (![X0 : $i]: ( (g_true_only @ X0 @ '#sk1') | ~ (g_true_only @ X0 @ X0))), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], 518.81/75.83 [zip_derived_cl3196])). 518.81/75.83 thf(zip_derived_cl63755, plain, 518.81/75.83 (( (g_true_only @ ('#sk9' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk9' @ '#sk1') @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl63746, zip_derived_cl3216])). 518.81/75.83 thf(zip_derived_cl63811, plain, 518.81/75.83 ( (g_true_only @ ('#sk9' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl63755])). 518.81/75.83 thf(zip_derived_cl292, plain, 518.81/75.83 (![X0 : $i]: (~ (g_true_only @ X0 @ '#sk1') | (g_true_only @ X0 @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl268, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl63938, plain, 518.81/75.83 ( (g_true_only @ ('#sk9' @ '#sk1') @ ('#sk9' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl63811, zip_derived_cl292])). 518.81/75.83 thf(zip_derived_cl50, plain, 518.81/75.83 (![X2 : $i]: (~ (g_true_only @ X2 @ X2) | ~ (g_false_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl40])). 518.81/75.83 thf(zip_derived_cl63954, plain, 518.81/75.83 (~ (g_false_only @ ('#sk9' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl63938, zip_derived_cl50])). 518.81/75.83 thf(zip_derived_cl2418, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ X0) @ X0) 518.81/75.83 | (g_true_only @ ('#sk2' @ X0) @ ('#sk2' @ X0)) 518.81/75.83 | (g_both @ ('#sk2' @ X0) @ ('#sk2' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2024, zip_derived_cl2157])). 518.81/75.83 thf(zip_derived_cl950, plain, ( (g_false @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl818, zip_derived_cl940])). 518.81/75.83 thf(zip_derived_cl15, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: 518.81/75.83 (~ (g_true @ X2 @ X4) | ~ (g_false @ X2 @ X4) | (g_both @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl12])). 518.81/75.83 thf(zip_derived_cl227, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_false_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl222])). 518.81/75.83 thf(zip_derived_cl234, plain, 518.81/75.83 (![X2 : $i, X6 : $i]: 518.81/75.83 (~ ('#form12' @ X2 @ X6) 518.81/75.83 | (((g_true_only @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_both @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))))), 518.81/75.83 define([status(thm)])). 518.81/75.83 thf(zip_derived_cl238, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( ('#form12' @ X2 @ X6) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (((g_both @ ('#sk11' @ X2 @ X6) @ X6) & 518.81/75.83 (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))))) 518.81/75.83 | (g_false_only @ X4 @ ('#sk9' @ X2)))), 518.81/75.83 inference('renaming', [status(thm)], 518.81/75.83 [zip_derived_cl227, zip_derived_cl234])). 518.81/75.83 thf(zip_derived_cl249, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (((g_true_only @ ('#sk11' @ X2 @ X6) @ X2) | (g_false_only @ 518.81/75.83 ('#sk11' @ X2 @ X6) @ X2))) 518.81/75.83 | (g_false_only @ X4 @ ('#sk9' @ X2)) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | ('#form12' @ X2 @ X6))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl238])). 518.81/75.83 thf(zip_derived_cl261, plain, 518.81/75.83 (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X2) 518.81/75.83 | ('#form12' @ X2 @ X6) 518.81/75.83 | (g_false_only @ ('#sk11' @ X2 @ X6) @ X6) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X4 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X2) 518.81/75.83 | ~ (g_both @ X8 @ X6) 518.81/75.83 | (g_false_only @ X4 @ ('#sk9' @ X2)))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl249])). 518.81/75.83 thf(zip_derived_cl1364, plain, 518.81/75.83 (![X0 : $i, X1 : $i, X2 : $i, X3 : $i]: 518.81/75.83 (~ (g_false @ X1 @ X0) 518.81/75.83 | ~ (g_true @ X1 @ X0) 518.81/75.83 | (g_true_only @ ('#sk11' @ X0 @ X2) @ X0) 518.81/75.83 | (g_false_only @ ('#sk11' @ X0 @ X2) @ X0) 518.81/75.83 | ('#form12' @ X0 @ X2) 518.81/75.83 | (g_false_only @ ('#sk11' @ X0 @ X2) @ X2) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X3 @ X0) 518.81/75.83 | ~ (g_both @ X1 @ X2) 518.81/75.83 | (g_false_only @ X3 @ ('#sk9' @ X0)))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl15, zip_derived_cl261])). 518.81/75.83 thf(zip_derived_cl17910, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 (~ (g_true @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ X0) 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X1 @ '#sk1') 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_false_only @ X1 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl950, zip_derived_cl1364])). 518.81/75.83 thf(zip_derived_cl949, plain, ( (g_true @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl817, zip_derived_cl940])). 518.81/75.83 thf(zip_derived_cl17959, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ X0) 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.83 | ('#form8') 518.81/75.83 | (g_false_only @ X1 @ '#sk1') 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_false_only @ X1 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl17910, zip_derived_cl949])). 518.81/75.83 thf(zip_derived_cl23636, plain, (~ ('#form8')), 518.81/75.83 inference('clc', [status(thm)], 518.81/75.83 [zip_derived_cl23635, zip_derived_cl12094])). 518.81/75.83 thf(zip_derived_cl80541, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ X0) 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ X0) @ X0) 518.81/75.83 | (g_false_only @ X1 @ '#sk1') 518.81/75.83 | ~ (g_both @ ('#sk2' @ '#sk1') @ X0) 518.81/75.83 | (g_false_only @ X1 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl17959, zip_derived_cl23636])). 518.81/75.83 thf(zip_derived_cl80566, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1') 518.81/75.83 | (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1') 518.81/75.83 | ('#form12' @ '#sk1' @ ('#sk2' @ '#sk1')) 518.81/75.83 | (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl2418, zip_derived_cl80541])). 518.81/75.83 thf(zip_derived_cl907, plain, 518.81/75.83 (~ (g_true_only @ ('#sk2' @ '#sk1') @ ('#sk2' @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl874, zip_derived_cl57])). 518.81/75.83 thf(zip_derived_cl940, plain, (~ (g_true_only @ ('#sk2' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl934, zip_derived_cl52])). 518.81/75.83 thf(zip_derived_cl26246, plain, 518.81/75.83 (~ (g_true_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('simplify boolean subterms', [status(thm)], 518.81/75.83 [zip_derived_cl26240])). 518.81/75.83 thf(zip_derived_cl33512, plain, 518.81/75.83 (~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33498, zip_derived_cl502])). 518.81/75.83 thf(zip_derived_cl1460, plain, 518.81/75.83 (![X0 : $i]: ~ ('#form12' @ X0 @ ('#sk2' @ X0))), 518.81/75.83 inference('clc', [status(thm)], [zip_derived_cl995, zip_derived_cl308])). 518.81/75.83 thf(zip_derived_cl80607, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1')) 518.81/75.83 | (g_false_only @ X0 @ '#sk1') 518.81/75.83 | (g_false_only @ X0 @ ('#sk9' @ '#sk1')))), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl80566, zip_derived_cl907, zip_derived_cl940, 518.81/75.83 zip_derived_cl26246, zip_derived_cl33512, zip_derived_cl1460])). 518.81/75.83 thf(zip_derived_cl33864, plain, 518.81/75.83 (~ (g_false_only @ ('#sk11' @ '#sk1' @ ('#sk2' @ '#sk1')) @ 518.81/75.83 ('#sk2' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl33858, zip_derived_cl502])). 518.81/75.83 thf(zip_derived_cl80615, plain, 518.81/75.83 (![X0 : $i]: 518.81/75.83 ( (g_false_only @ X0 @ ('#sk9' @ '#sk1')) 518.81/75.83 | (g_false_only @ X0 @ '#sk1'))), 518.81/75.83 inference('clc', [status(thm)], 518.81/75.83 [zip_derived_cl80607, zip_derived_cl33864])). 518.81/75.83 thf(zip_derived_cl63811, plain, 518.81/75.83 ( (g_true_only @ ('#sk9' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl63755])). 518.81/75.83 thf(zip_derived_cl2018, plain, 518.81/75.83 (![X0 : $i, X1 : $i]: ( (g_false_only @ X1 @ X0) | (g_true @ X1 @ X0))), 518.81/75.83 inference('simplify', [status(thm)], [zip_derived_cl1986])). 518.81/75.83 thf(zip_derived_cl51, plain, 518.81/75.83 (![X2 : $i]: (~ (g_false_only @ X2 @ X2) | ~ (g_true_only @ X2 @ '#sk1'))), 518.81/75.83 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl41])). 518.81/75.83 thf(zip_derived_cl2067, plain, 518.81/75.83 (![X0 : $i]: ( (g_true @ X0 @ X0) | ~ (g_true_only @ X0 @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], [zip_derived_cl2018, zip_derived_cl51])). 518.81/75.83 thf(zip_derived_cl63940, plain, 518.81/75.83 ( (g_true @ ('#sk9' @ '#sk1') @ ('#sk9' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl63811, zip_derived_cl2067])). 518.81/75.83 thf(zip_derived_cl1609, plain, 518.81/75.83 (![X2 : $i, X4 : $i]: (~ (g_true @ X2 @ X4) | ~ (g_false_only @ X2 @ X4))), 518.81/75.83 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl298])). 518.81/75.83 thf(zip_derived_cl64066, plain, 518.81/75.83 (~ (g_false_only @ ('#sk9' @ '#sk1') @ ('#sk9' @ '#sk1'))), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl63940, zip_derived_cl1609])). 518.81/75.83 thf(zip_derived_cl80660, plain, 518.81/75.83 ( (g_false_only @ ('#sk9' @ '#sk1') @ '#sk1')), 518.81/75.83 inference('s_sup-', [status(thm)], 518.81/75.83 [zip_derived_cl80615, zip_derived_cl64066])). 518.81/75.83 thf(zip_derived_cl80854, plain, ($false), 518.81/75.83 inference('demod', [status(thm)], 518.81/75.83 [zip_derived_cl63954, zip_derived_cl80660])). 518.81/75.83 518.81/75.83 % SZS output end Refutation 518.81/75.83 518.81/75.83 518.81/75.83 % Terminating... 518.81/75.86 % Runner terminated. 518.81/75.87 % Zipperpin 1.5 exiting 518.81/75.88 EOF