0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.20 % Command : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.r6ytOTy177 true 0.19/0.40 % Computer : n015.cluster.edu 0.19/0.40 % Model : x86_64 x86_64 0.19/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.19/0.40 % Memory : 8042.1875MB 0.19/0.40 % OS : Linux 3.10.0-693.el7.x86_64 0.19/0.40 % CPULimit : 1920 0.19/0.40 % WCLimit : 240 0.19/0.40 % DateTime : Wed Jul 30 09:28:19 EDT 2025 0.19/0.40 % CPUTime : 0.19/0.40 % Running portfolio for 1920 s 0.19/0.40 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.19/0.40 % Number of cores: 8 0.19/0.40 % Python version: Python 3.6.8 0.19/0.41 % Running in HO mode 0.39/0.70 % Total configuration time : 828 0.39/0.70 % Estimated wc time : 1656 0.39/0.70 % Estimated cpu time (8 cpus) : 207.0 0.39/0.76 % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s 0.39/0.78 % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s 0.39/0.78 % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s 0.39/0.78 % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s 0.39/0.79 % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s 0.39/0.79 % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s 0.39/0.79 % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.39/0.79 % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s 0.39/0.95 % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s 94.61/12.65 % Solved by lams/40_b.comb.sh. 94.61/12.65 % done 344 iterations in 11.720s 94.61/12.65 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 94.61/12.65 % SZS output start Refutation 94.61/12.65 thf(list_A2115238852le_alt_type, type, list_A2115238852le_alt: $tType). 94.61/12.65 thf(arrow_475358991le_alt_type, type, arrow_475358991le_alt: $tType). 94.61/12.65 thf(produc1501160679le_alt_type, type, produc1501160679le_alt: $tType). 94.61/12.65 thf(arrow_1429601828e_indi_type, type, arrow_1429601828e_indi: $tType). 94.61/12.65 thf(c_type, type, c: arrow_475358991le_alt). 94.61/12.65 thf(set_Ar577454304le_alt_type, type, set_Ar577454304le_alt: list_A2115238852le_alt > 94.61/12.65 arrow_475358991le_alt > $o). 94.61/12.65 thf(cons_A228743023le_alt_type, type, cons_A228743023le_alt: arrow_475358991le_alt > 94.61/12.65 list_A2115238852le_alt > list_A2115238852le_alt). 94.61/12.65 thf(member84363362le_alt_type, type, member84363362le_alt: arrow_475358991le_alt > 94.61/12.65 (arrow_475358991le_alt > $o) > $o). 94.61/12.65 thf(member2052026769e_indi_type, type, member2052026769e_indi: arrow_1429601828e_indi > 94.61/12.65 (arrow_1429601828e_indi > $o) > $o). 94.61/12.65 thf(arrow_823908191le_Lin_type, type, arrow_823908191le_Lin: (produc1501160679le_alt > $o) > $o). 94.61/12.65 thf(p_type, type, p: arrow_1429601828e_indi > produc1501160679le_alt > $o). 94.61/12.65 thf(distin236324274le_alt_type, type, distin236324274le_alt: list_A2115238852le_alt > $o). 94.61/12.65 thf(a_type, type, a: arrow_475358991le_alt). 94.61/12.65 thf('#sk14_type', type, '#sk14': list_A2115238852le_alt > arrow_475358991le_alt). 94.61/12.65 thf('#sk6_type', type, '#sk6': arrow_1429601828e_indi). 94.61/12.65 thf(arrow_734252939e_Prof_type, type, arrow_734252939e_Prof: (arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > $o). 94.61/12.65 thf('#sk15_type', type, '#sk15': list_A2115238852le_alt > list_A2115238852le_alt). 94.61/12.65 thf(nil_Ar1286194111le_alt_type, type, nil_Ar1286194111le_alt: list_A2115238852le_alt). 94.61/12.65 thf(produc1347929815le_alt_type, type, produc1347929815le_alt: arrow_475358991le_alt > 94.61/12.65 arrow_475358991le_alt > produc1501160679le_alt). 94.61/12.65 thf(top_to988227749indi_o_type, type, top_to988227749indi_o: arrow_1429601828e_indi > $o). 94.61/12.65 thf(member526088951_alt_o_type, type, member526088951_alt_o: (arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > 94.61/12.65 ((arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > $o) > $o). 94.61/12.65 thf(last_A1217315288le_alt_type, type, last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 94.61/12.65 thf('#sk33_type', type, '#sk33': (arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > 94.61/12.65 (arrow_1429601828e_indi > 94.61/12.65 (produc1501160679le_alt > $o) > $o) > 94.61/12.65 (arrow_1429601828e_indi > $o) > arrow_1429601828e_indi). 94.61/12.65 thf(append179082452le_alt_type, type, append179082452le_alt: list_A2115238852le_alt > 94.61/12.65 list_A2115238852le_alt > list_A2115238852le_alt). 94.61/12.65 thf(member214075476le_alt_type, type, member214075476le_alt: produc1501160679le_alt > 94.61/12.65 (produc1501160679le_alt > $o) > $o). 94.61/12.65 thf(member377231867_alt_o_type, type, member377231867_alt_o: (produc1501160679le_alt > $o) > 94.61/12.65 ((produc1501160679le_alt > $o) > $o) > $o). 94.61/12.65 thf(pi_Arr1929480907_alt_o_type, type, pi_Arr1929480907_alt_o: (arrow_1429601828e_indi > $o) > 94.61/12.65 (arrow_1429601828e_indi > 94.61/12.65 (produc1501160679le_alt > $o) > $o) > 94.61/12.65 (arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > $o). 94.61/12.65 thf('#ty_enc48_type', type, '#ty_enc48': ((produc1501160679le_alt > $o) > $o) > 94.61/12.65 arrow_1429601828e_indi > 94.61/12.65 (produc1501160679le_alt > $o) > $o). 94.61/12.65 thf(butlas274947851le_alt_type, type, butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 94.61/12.65 thf(rev_Ar1106406943le_alt_type, type, rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 94.61/12.65 thf(hd_Arr1965683346le_alt_type, type, hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 94.61/12.65 thf(arrow_2098199487_below_type, type, arrow_2098199487_below: (produc1501160679le_alt > $o) > 94.61/12.65 arrow_475358991le_alt > 94.61/12.65 arrow_475358991le_alt > 94.61/12.65 produc1501160679le_alt > $o). 94.61/12.65 thf(b_type, type, b: arrow_475358991le_alt). 94.61/12.65 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 94.61/12.65 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 94.61/12.65 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 94.61/12.65 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 94.61/12.65 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 94.61/12.65 thf(fact_4_dist, axiom, 94.61/12.65 (distin236324274le_alt @ 94.61/12.65 ( cons_A228743023le_alt @ 94.61/12.65 a @ 94.61/12.65 ( cons_A228743023le_alt @ 94.61/12.65 b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ))). 94.61/12.65 thf(zip_derived_cl265, plain, 94.61/12.65 ( (distin236324274le_alt @ 94.61/12.65 (cons_A228743023le_alt @ a @ 94.61/12.65 (cons_A228743023le_alt @ b @ 94.61/12.65 (cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_4_dist])). 94.61/12.65 thf(fact_37_list_Osimps_I2_J, axiom, 94.61/12.65 (![A_23:arrow_475358991le_alt,List_4:list_A2115238852le_alt]: 94.61/12.65 ( ( nil_Ar1286194111le_alt ) != ( cons_A228743023le_alt @ A_23 @ List_4 ) ))). 94.61/12.65 thf(zip_derived_cl95, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((nil_Ar1286194111le_alt) != 94.61/12.65 (cons_A228743023le_alt @ Y0 @ Y1)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_37_list_Osimps_I2_J])). 94.61/12.65 thf(zip_derived_cl96, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 94.61/12.65 (nil_Ar1286194111le_alt))))) @ 94.61/12.65 cons_A228743023le_alt))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl95])). 94.61/12.65 thf(zip_derived_cl397, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != 94.61/12.65 (nil_Ar1286194111le_alt))) @ 94.61/12.65 (cons_A228743023le_alt @ X2)))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl96])). 94.61/12.65 thf(zip_derived_cl398, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl397])). 94.61/12.65 thf(zip_derived_cl399, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl398])). 94.61/12.65 thf(fact_467_hd_Osimps, axiom, 94.61/12.65 (![X_26:arrow_475358991le_alt,Xs_44:list_A2115238852le_alt]: 94.61/12.65 ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_26 @ Xs_44 ) ) = 94.61/12.65 ( X_26 ) ))). 94.61/12.65 thf(zip_derived_cl276, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((hd_Arr1965683346le_alt @ 94.61/12.65 (cons_A228743023le_alt @ Y0 @ Y1)) = (Y0)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_467_hd_Osimps])). 94.61/12.65 thf(zip_derived_cl277, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#B') @ ((('#B') @ hd_Arr1965683346le_alt)) @ 94.61/12.65 cons_A228743023le_alt)))))) @ 94.61/12.65 ('#I')))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl276])). 94.61/12.65 thf(zip_derived_cl476, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#C') @ ((('#B') @ (=) @ 94.61/12.65 ((('#B') @ hd_Arr1965683346le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X2))))) @ 94.61/12.65 X2))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl277])). 94.61/12.65 thf(zip_derived_cl477, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl476])). 94.61/12.65 thf(zip_derived_cl478, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl477])). 94.61/12.65 thf(fact_375_append__Nil, axiom, 94.61/12.65 (![Ys_45:list_A2115238852le_alt]: 94.61/12.65 ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 ) = ( Ys_45 ) ))). 94.61/12.65 thf(zip_derived_cl247, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ nil_Ar1286194111le_alt @ Y0) = 94.61/12.65 (Y0))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_375_append__Nil])). 94.61/12.65 thf(zip_derived_cl248, plain, 94.61/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 94.61/12.65 (append179082452le_alt @ nil_Ar1286194111le_alt))) @ 94.61/12.65 ('#I')))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl247])). 94.61/12.65 thf(zip_derived_cl386, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl248])). 94.61/12.65 thf(zip_derived_cl387, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 ((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl386])). 94.61/12.65 thf(fact_589_hd__in__set, axiom, 94.61/12.65 (![Xs_9:list_A2115238852le_alt]: 94.61/12.65 ( ( ( Xs_9 ) != ( nil_Ar1286194111le_alt ) ) => 94.61/12.65 ( member84363362le_alt @ 94.61/12.65 ( hd_Arr1965683346le_alt @ Xs_9 ) @ ( set_Ar577454304le_alt @ Xs_9 ) ) ))). 94.61/12.65 thf(zip_derived_cl54, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((((Y0) != (nil_Ar1286194111le_alt))) => 94.61/12.65 (member84363362le_alt @ (hd_Arr1965683346le_alt @ Y0) @ 94.61/12.65 (set_Ar577454304le_alt @ Y0)))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_589_hd__in__set])). 94.61/12.65 thf(zip_derived_cl55, plain, 94.61/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member84363362le_alt @ 94.61/12.65 hd_Arr1965683346le_alt)) @ 94.61/12.65 set_Ar577454304le_alt))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl54])). 94.61/12.65 thf(zip_derived_cl412, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 94.61/12.65 (hd_Arr1965683346le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 94.61/12.65 thf(zip_derived_cl413, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (~ (((X2) != (nil_Ar1286194111le_alt))) 94.61/12.65 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 94.61/12.65 (set_Ar577454304le_alt @ X2)))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 94.61/12.65 thf(zip_derived_cl414, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((X2) = (nil_Ar1286194111le_alt)) 94.61/12.65 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 94.61/12.65 (set_Ar577454304le_alt @ X2)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl413])). 94.61/12.65 thf(fact_373_append__Cons, axiom, 94.61/12.65 (![X_50:arrow_475358991le_alt,Xs_99:list_A2115238852le_alt, 94.61/12.65 Ys_47:list_A2115238852le_alt]: 94.61/12.65 ( ( append179082452le_alt @ 94.61/12.65 ( cons_A228743023le_alt @ X_50 @ Xs_99 ) @ Ys_47 ) = 94.61/12.65 ( cons_A228743023le_alt @ 94.61/12.65 X_50 @ ( append179082452le_alt @ Xs_99 @ Ys_47 ) ) ))). 94.61/12.65 thf(zip_derived_cl78, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ 94.61/12.65 (cons_A228743023le_alt @ Y0 @ Y1) @ 94.61/12.65 Y2) = (cons_A228743023le_alt @ 94.61/12.65 Y0 @ 94.61/12.65 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_373_append__Cons])). 94.61/12.65 thf(zip_derived_cl79, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 94.61/12.65 cons_A228743023le_alt)))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ cons_A228743023le_alt)))) @ 94.61/12.65 append179082452le_alt))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl78])). 94.61/12.65 thf(zip_derived_cl672, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#B') @ append179082452le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X2))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (cons_A228743023le_alt @ X2))) @ 94.61/12.65 append179082452le_alt))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 94.61/12.65 thf(zip_derived_cl673, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 94.61/12.65 (append179082452le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X2 @ X4)))) @ 94.61/12.65 ((('#B') @ (cons_A228743023le_alt @ X2) @ 94.61/12.65 (append179082452le_alt @ X4)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl672])). 94.61/12.65 thf(zip_derived_cl674, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) = 94.61/12.65 (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl673])). 94.61/12.65 thf(zip_derived_cl675, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 ((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) 94.61/12.65 = (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl674])). 94.61/12.65 thf(fact_394_last__snoc, axiom, 94.61/12.65 (![Xs_80:list_A2115238852le_alt,X_42:arrow_475358991le_alt]: 94.61/12.65 ( ( last_A1217315288le_alt @ 94.61/12.65 ( append179082452le_alt @ 94.61/12.65 Xs_80 @ ( cons_A228743023le_alt @ X_42 @ nil_Ar1286194111le_alt ) ) ) = 94.61/12.65 ( X_42 ) ))). 94.61/12.65 thf(zip_derived_cl126, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((last_A1217315288le_alt @ 94.61/12.65 (append179082452le_alt @ Y0 @ 94.61/12.65 (cons_A228743023le_alt @ Y1 @ 94.61/12.65 nil_Ar1286194111le_alt))) = 94.61/12.65 (Y1)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_394_last__snoc])). 94.61/12.65 thf(zip_derived_cl127, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#B') @ ((('#B') @ last_A1217315288le_alt)) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 append179082452le_alt)) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt)))))))))) @ 94.61/12.65 ('#I')))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl126])). 94.61/12.65 thf(zip_derived_cl542, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 94.61/12.65 ((('#B') @ last_A1217315288le_alt @ 94.61/12.65 ((('#B') @ (append179082452le_alt @ X2) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt)))))))) @ 94.61/12.65 ('#I')))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl127])). 94.61/12.65 thf(zip_derived_cl543, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 (((last_A1217315288le_alt @ 94.61/12.65 (append179082452le_alt @ X2 @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) = 94.61/12.65 (X4)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl542])). 94.61/12.65 thf(zip_derived_cl544, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 ((last_A1217315288le_alt @ 94.61/12.65 (append179082452le_alt @ X2 @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) 94.61/12.65 = (X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl543])). 94.61/12.65 thf(fact_268_mem__def, axiom, 94.61/12.65 (![X_66:produc1501160679le_alt,A_12:( produc1501160679le_alt > $o )]: 94.61/12.65 ( ( member214075476le_alt @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 94.61/12.65 thf(zip_derived_cl18, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : produc1501160679le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : produc1501160679le_alt > $o]: 94.61/12.65 (((member214075476le_alt @ Y0 @ Y1) <=> (Y1 @ 94.61/12.65 Y0)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_268_mem__def])). 94.61/12.65 thf(zip_derived_cl19, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 member214075476le_alt)))) @ 94.61/12.65 ((('#C') @ ('#I')))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl18])). 94.61/12.65 thf(zip_derived_cl494, plain, 94.61/12.65 (![X2 : produc1501160679le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member214075476le_alt @ X2))) @ 94.61/12.65 ((('#C') @ ('#I') @ X2))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 94.61/12.65 thf(zip_derived_cl495, plain, 94.61/12.65 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 94.61/12.65 (((member214075476le_alt @ X2 @ X4) <=> (X4 @ X2)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl494])). 94.61/12.65 thf(zip_derived_cl496, plain, 94.61/12.65 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 94.61/12.65 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl495])). 94.61/12.65 thf(fact_270_mem__def, axiom, 94.61/12.65 (![X_66:( produc1501160679le_alt > $o ), 94.61/12.65 A_12:( ( produc1501160679le_alt > $o ) > $o )]: 94.61/12.65 ( ( A_12 @ X_66 ) <=> ( member377231867_alt_o @ X_66 @ A_12 ) ))). 94.61/12.65 thf(zip_derived_cl20, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y1 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((Y1 @ Y0) <=> (member377231867_alt_o @ Y0 @ 94.61/12.65 Y1)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_270_mem__def])). 94.61/12.65 thf(zip_derived_cl21, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#C') @ ('#I'))))))) @ 94.61/12.65 member377231867_alt_o))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl20])). 94.61/12.65 thf(zip_derived_cl498, plain, 94.61/12.65 (![X2 : produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 94.61/12.65 (member377231867_alt_o @ X2)))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl21])). 94.61/12.65 thf(zip_derived_cl499, plain, 94.61/12.65 (![X2 : produc1501160679le_alt > $o, 94.61/12.65 X4 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((X4 @ X2) <=> (member377231867_alt_o @ X2 @ X4)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl498])). 94.61/12.65 thf(zip_derived_cl500, plain, 94.61/12.65 (![X2 : produc1501160679le_alt > $o, 94.61/12.65 X4 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 ((X4 @ X2) = (member377231867_alt_o @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl499])). 94.61/12.65 thf(conj_0, conjecture, 94.61/12.65 (![I:arrow_1429601828e_indi]: 94.61/12.65 ( ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ a @ c ) @ 94.61/12.65 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) <=> 94.61/12.65 ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) ))). 94.61/12.65 thf(zf_stmt_0, negated_conjecture, 94.61/12.65 (~( ![I:arrow_1429601828e_indi]: 94.61/12.65 ( ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ a @ c ) @ 94.61/12.65 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) <=> 94.61/12.65 ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) ) )), 94.61/12.65 inference('cnf.neg', [status(esa)], [conj_0])). 94.61/12.65 thf(zip_derived_cl343, plain, 94.61/12.65 (~ (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 94.61/12.65 (((member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ a @ c) @ 94.61/12.65 (arrow_2098199487_below @ (p @ Y0) @ c @ b)) <=> 94.61/12.65 (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ a @ b) @ (p @ Y0)))))))), 94.61/12.65 inference('cnf', [status(esa)], [zf_stmt_0])). 94.61/12.65 thf(zip_derived_cl344, plain, 94.61/12.65 (~ (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 ((('#B') @ (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ a @ c)) @ 94.61/12.65 ((('#C') @ ((('#C') @ ((('#B') @ arrow_2098199487_below @ 94.61/12.65 p)) @ 94.61/12.65 c)) @ 94.61/12.65 b)))))) @ 94.61/12.65 ((('#B') @ (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ a @ b)) @ 94.61/12.65 p))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl343])). 94.61/12.65 thf(zip_derived_cl406, plain, 94.61/12.65 (~ (((member214075476le_alt @ (produc1347929815le_alt @ a @ c) @ 94.61/12.65 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b)) <=> 94.61/12.65 (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 94.61/12.65 (p @ '#sk6'))))), 94.61/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl344])). 94.61/12.65 thf(zip_derived_cl407, plain, 94.61/12.65 (((member214075476le_alt @ (produc1347929815le_alt @ a @ c) @ 94.61/12.65 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b)) 94.61/12.65 != (member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 94.61/12.65 (p @ '#sk6')))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl406])). 94.61/12.65 thf(zip_derived_cl496, plain, 94.61/12.65 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 94.61/12.65 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl495])). 94.61/12.65 thf(zip_derived_cl496, plain, 94.61/12.65 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 94.61/12.65 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl495])). 94.61/12.65 thf(zip_derived_cl497, plain, 94.61/12.65 (((arrow_2098199487_below @ (p @ '#sk6') @ c @ b @ 94.61/12.65 (produc1347929815le_alt @ a @ c)) 94.61/12.65 != (p @ '#sk6' @ (produc1347929815le_alt @ a @ b)))), 94.61/12.65 inference('demod', [status(thm)], 94.61/12.65 [zip_derived_cl407, zip_derived_cl496, zip_derived_cl496])). 94.61/12.65 thf(fact_43_not__Cons__self, axiom, 94.61/12.65 (![Xs_126:list_A2115238852le_alt,X_73:arrow_475358991le_alt]: 94.61/12.65 ( ( Xs_126 ) != ( cons_A228743023le_alt @ X_73 @ Xs_126 ) ))). 94.61/12.65 thf(zip_derived_cl16, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((Y0) != (cons_A228743023le_alt @ Y1 @ Y0)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_43_not__Cons__self])). 94.61/12.65 thf(zip_derived_cl17, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#B') @ (!=))) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl16])). 94.61/12.65 thf(zip_derived_cl428, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ X2))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 94.61/12.65 thf(zip_derived_cl429, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 (((X2) != (cons_A228743023le_alt @ X4 @ X2)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl428])). 94.61/12.65 thf(zip_derived_cl430, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 ((X2) != (cons_A228743023le_alt @ X4 @ X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl429])). 94.61/12.65 thf(fact_376_Nil__is__append__conv, axiom, 94.61/12.65 (![Xs_97:list_A2115238852le_alt,Ys_44:list_A2115238852le_alt]: 94.61/12.65 ( ( ( nil_Ar1286194111le_alt ) = ( append179082452le_alt @ Xs_97 @ Ys_44 ) ) <=> 94.61/12.65 ( ( ( Xs_97 ) = ( nil_Ar1286194111le_alt ) ) & 94.61/12.65 ( ( Ys_44 ) = ( nil_Ar1286194111le_alt ) ) ) ))). 94.61/12.65 thf(zip_derived_cl224, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((((nil_Ar1286194111le_alt) = 94.61/12.65 (append179082452le_alt @ Y0 @ Y1))) <=> 94.61/12.65 (((((Y0) = (nil_Ar1286194111le_alt))) & 94.61/12.65 (((Y1) = (nil_Ar1286194111le_alt)))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_376_Nil__is__append__conv])). 94.61/12.65 thf(zip_derived_cl225, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 94.61/12.65 (nil_Ar1286194111le_alt))))) @ 94.61/12.65 append179082452le_alt)))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (&) @ 94.61/12.65 ((('#C') @ (=) @ nil_Ar1286194111le_alt)))))) @ 94.61/12.65 ((('#C') @ (=) @ nil_Ar1286194111le_alt))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl224])). 94.61/12.65 thf(zip_derived_cl636, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 ((('#B') @ (((list_A2115238852le_alt) = 94.61/12.65 (nil_Ar1286194111le_alt))) @ 94.61/12.65 (append179082452le_alt @ X2))))) @ 94.61/12.65 ((('#B') @ (((&) @ (((X2) = (nil_Ar1286194111le_alt))))) @ 94.61/12.65 ((('#C') @ (=) @ nil_Ar1286194111le_alt))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl225])). 94.61/12.65 thf(zip_derived_cl637, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4))) <=> 94.61/12.65 (((((X2) = (nil_Ar1286194111le_alt))) & 94.61/12.65 (((X4) = (nil_Ar1286194111le_alt)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl636])). 94.61/12.65 thf(zip_derived_cl638, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4))) 94.61/12.65 = (((((X2) = (nil_Ar1286194111le_alt))) & 94.61/12.65 (((X4) = (nil_Ar1286194111le_alt))))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl637])). 94.61/12.65 thf(fact_496_rev__eq__Cons__iff, axiom, 94.61/12.65 (![Xs_25:list_A2115238852le_alt,Y_3:arrow_475358991le_alt, 94.61/12.65 Ys_7:list_A2115238852le_alt]: 94.61/12.65 ( ( ( rev_Ar1106406943le_alt @ Xs_25 ) = 94.61/12.65 ( cons_A228743023le_alt @ Y_3 @ Ys_7 ) ) <=> 94.61/12.65 ( ( Xs_25 ) = 94.61/12.65 ( append179082452le_alt @ 94.61/12.65 ( rev_Ar1106406943le_alt @ Ys_7 ) @ 94.61/12.65 ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) ))). 94.61/12.65 thf(zip_derived_cl87, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 94.61/12.65 (((((rev_Ar1106406943le_alt @ Y0) = 94.61/12.65 (cons_A228743023le_alt @ Y1 @ 94.61/12.65 Y2))) <=> 94.61/12.65 (((Y0) = 94.61/12.65 (append179082452le_alt @ 94.61/12.65 (rev_Ar1106406943le_alt @ Y2) @ 94.61/12.65 (cons_A228743023le_alt @ Y1 @ 94.61/12.65 nil_Ar1286194111le_alt)))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_496_rev__eq__Cons__iff])). 94.61/12.65 thf(zip_derived_cl88, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=) @ 94.61/12.65 rev_Ar1106406943le_alt)))))) @ 94.61/12.65 cons_A228743023le_alt)))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ ((('#B') @ ('#B') @ (=))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 94.61/12.65 rev_Ar1106406943le_alt)))) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt))))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl87])). 94.61/12.65 thf(zip_derived_cl805, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 94.61/12.65 (rev_Ar1106406943le_alt @ 94.61/12.65 X2))))) @ 94.61/12.65 cons_A228743023le_alt)))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = (X2))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 94.61/12.65 rev_Ar1106406943le_alt)))) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 94.61/12.65 thf(zip_derived_cl806, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 ((('#B') @ (((list_A2115238852le_alt) = 94.61/12.65 (rev_Ar1106406943le_alt @ X2))) @ 94.61/12.65 (cons_A228743023le_alt @ X4))))) @ 94.61/12.65 ((('#B') @ (((list_A2115238852le_alt) = (X2))) @ 94.61/12.65 ((('#C') @ ((('#B') @ append179082452le_alt @ 94.61/12.65 rev_Ar1106406943le_alt)) @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl805])). 94.61/12.65 thf(zip_derived_cl807, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 (((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) <=> 94.61/12.65 (((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl806])). 94.61/12.65 thf(zip_derived_cl808, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 ((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) 94.61/12.65 = (((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl807])). 94.61/12.65 thf(fact_495_rev_Osimps_I2_J, axiom, 94.61/12.65 (![X_17:arrow_475358991le_alt,Xs_26:list_A2115238852le_alt]: 94.61/12.65 ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_17 @ Xs_26 ) ) = 94.61/12.65 ( append179082452le_alt @ 94.61/12.65 ( rev_Ar1106406943le_alt @ Xs_26 ) @ 94.61/12.65 ( cons_A228743023le_alt @ X_17 @ nil_Ar1286194111le_alt ) ) ))). 94.61/12.65 thf(zip_derived_cl274, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((rev_Ar1106406943le_alt @ 94.61/12.65 (cons_A228743023le_alt @ Y0 @ Y1)) = 94.61/12.65 (append179082452le_alt @ 94.61/12.65 (rev_Ar1106406943le_alt @ Y1) @ 94.61/12.65 (cons_A228743023le_alt @ Y0 @ 94.61/12.65 nil_Ar1286194111le_alt))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_495_rev_Osimps_I2_J])). 94.61/12.65 thf(zip_derived_cl275, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#B') @ ((('#B') @ rev_Ar1106406943le_alt)) @ 94.61/12.65 cons_A228743023le_alt)))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 94.61/12.65 rev_Ar1106406943le_alt)))) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl274])). 94.61/12.65 thf(zip_derived_cl588, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 94.61/12.65 ((('#B') @ rev_Ar1106406943le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X2))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ append179082452le_alt @ 94.61/12.65 rev_Ar1106406943le_alt)) @ 94.61/12.65 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl275])). 94.61/12.65 thf(zip_derived_cl589, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = 94.61/12.65 (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 94.61/12.65 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl588])). 94.61/12.65 thf(zip_derived_cl590, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 94.61/12.65 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 94.61/12.65 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl589])). 94.61/12.65 thf(zip_derived_cl809, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 ((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) 94.61/12.65 = (((X2) = (rev_Ar1106406943le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ X6)))))), 94.61/12.65 inference('demod', [status(thm)], [zip_derived_cl808, zip_derived_cl590])). 94.61/12.65 thf(fact_79_list_Oexhaust, axiom, 94.61/12.65 (![Y_26:list_A2115238852le_alt]: 94.61/12.65 ( ( ( Y_26 ) != ( nil_Ar1286194111le_alt ) ) => 94.61/12.65 ( ~( ![A:arrow_475358991le_alt,List:list_A2115238852le_alt]: 94.61/12.65 ( ( Y_26 ) != ( cons_A228743023le_alt @ A @ List ) ) ) ) ))). 94.61/12.65 thf(zip_derived_cl290, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((((Y0) != (nil_Ar1286194111le_alt))) => 94.61/12.65 (((~) @ (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 94.61/12.65 (((Y0) != 94.61/12.65 (cons_A228743023le_alt @ 94.61/12.65 Y1 @ Y2))))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_79_list_Oexhaust])). 94.61/12.65 thf(zip_derived_cl291, plain, 94.61/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 94.61/12.65 ((('#B') @ (~) @ 94.61/12.65 ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ (!=))))) @ 94.61/12.65 cons_A228743023le_alt))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl290])). 94.61/12.65 thf(zip_derived_cl620, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((((X2) != (nil_Ar1286194111le_alt))) => 94.61/12.65 (((~) @ (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 94.61/12.65 (X2))))) @ 94.61/12.65 cons_A228743023le_alt))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl291])). 94.61/12.65 thf(zip_derived_cl621, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (~ (((X2) != (nil_Ar1286194111le_alt))) 94.61/12.65 | ~ (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 94.61/12.65 (X2))))) @ 94.61/12.65 cons_A228743023le_alt)))))))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl620])). 94.61/12.65 thf(zip_derived_cl622, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((X2) = (nil_Ar1286194111le_alt)) 94.61/12.65 | ~ (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 94.61/12.65 (X2))))) @ 94.61/12.65 cons_A228743023le_alt)))))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl621])). 94.61/12.65 thf(zip_derived_cl623, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (~ (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 94.61/12.65 (cons_A228743023le_alt @ ('#sk14' @ X2)))))) 94.61/12.65 | ((X2) = (nil_Ar1286194111le_alt)))), 94.61/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl622])). 94.61/12.65 thf(zip_derived_cl624, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (~ (((X2) != (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2)))) 94.61/12.65 | ((X2) = (nil_Ar1286194111le_alt)))), 94.61/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl623])). 94.61/12.65 thf(zip_derived_cl625, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((X2) = (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2))) 94.61/12.65 | ((X2) = (nil_Ar1286194111le_alt)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl624])). 94.61/12.65 thf(fact_572_last__in__set, axiom, 94.61/12.65 (![As:list_A2115238852le_alt]: 94.61/12.65 ( ( ( As ) != ( nil_Ar1286194111le_alt ) ) => 94.61/12.65 ( member84363362le_alt @ 94.61/12.65 ( last_A1217315288le_alt @ As ) @ ( set_Ar577454304le_alt @ As ) ) ))). 94.61/12.65 thf(zip_derived_cl282, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((((Y0) != (nil_Ar1286194111le_alt))) => 94.61/12.65 (member84363362le_alt @ (last_A1217315288le_alt @ Y0) @ 94.61/12.65 (set_Ar577454304le_alt @ Y0)))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_572_last__in__set])). 94.61/12.65 thf(zip_derived_cl283, plain, 94.61/12.65 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member84363362le_alt @ 94.61/12.65 last_A1217315288le_alt)) @ 94.61/12.65 set_Ar577454304le_alt))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl282])). 94.61/12.65 thf(zip_derived_cl415, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 94.61/12.65 (last_A1217315288le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl283])). 94.61/12.65 thf(zip_derived_cl416, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (~ (((X2) != (nil_Ar1286194111le_alt))) 94.61/12.65 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 94.61/12.65 (set_Ar577454304le_alt @ X2)))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl415])). 94.61/12.65 thf(zip_derived_cl417, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((X2) = (nil_Ar1286194111le_alt)) 94.61/12.65 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 94.61/12.65 (set_Ar577454304le_alt @ X2)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl416])). 94.61/12.65 thf(fact_264_mem__def, axiom, 94.61/12.65 (![X_66:arrow_475358991le_alt,A_12:( arrow_475358991le_alt > $o )]: 94.61/12.65 ( ( A_12 @ X_66 ) <=> ( member84363362le_alt @ X_66 @ A_12 ) ))). 94.61/12.65 thf(zip_derived_cl122, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt > $o]: 94.61/12.65 (((Y1 @ Y0) <=> (member84363362le_alt @ Y0 @ 94.61/12.65 Y1)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_264_mem__def])). 94.61/12.65 thf(zip_derived_cl123, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#C') @ ('#I'))))))) @ 94.61/12.65 member84363362le_alt))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl122])). 94.61/12.65 thf(zip_derived_cl525, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 94.61/12.65 (member84363362le_alt @ X2)))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl123])). 94.61/12.65 thf(zip_derived_cl526, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 94.61/12.65 (((X4 @ X2) <=> (member84363362le_alt @ X2 @ X4)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl525])). 94.61/12.65 thf(zip_derived_cl527, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 94.61/12.65 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl526])). 94.61/12.65 thf(fact_556_distinct_Osimps_I2_J, axiom, 94.61/12.65 (![X_8:arrow_475358991le_alt,Xs_13:list_A2115238852le_alt]: 94.61/12.65 ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_13 ) ) <=> 94.61/12.65 ( ( distin236324274le_alt @ Xs_13 ) & 94.61/12.65 ( ~( member84363362le_alt @ X_8 @ ( set_Ar577454304le_alt @ Xs_13 ) ) ) ) ))). 94.61/12.65 thf(zip_derived_cl120, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((distin236324274le_alt @ 94.61/12.65 (cons_A228743023le_alt @ Y0 @ Y1)) <=> 94.61/12.65 (((distin236324274le_alt @ Y1) & 94.61/12.65 (((~) @ (member84363362le_alt @ Y0 @ 94.61/12.65 (set_Ar577454304le_alt @ Y1))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_556_distinct_Osimps_I2_J])). 94.61/12.65 thf(zip_derived_cl121, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ distin236324274le_alt)) @ 94.61/12.65 cons_A228743023le_alt)))))) @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 94.61/12.65 distin236324274le_alt)))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (~))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ member84363362le_alt)) @ 94.61/12.65 set_Ar577454304le_alt))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl120])). 94.61/12.65 thf(zip_derived_cl645, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 ((('#B') @ distin236324274le_alt @ 94.61/12.65 (cons_A228743023le_alt @ X2))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ (&) @ distin236324274le_alt)) @ 94.61/12.65 ((('#B') @ (~) @ 94.61/12.65 ((('#B') @ (member84363362le_alt @ X2) @ 94.61/12.65 set_Ar577454304le_alt))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl121])). 94.61/12.65 thf(zip_derived_cl646, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) <=> 94.61/12.65 (((distin236324274le_alt @ X4) & 94.61/12.65 (((~) @ (member84363362le_alt @ X2 @ (set_Ar577454304le_alt @ X4))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl645])). 94.61/12.65 thf(zip_derived_cl647, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 94.61/12.65 = (((distin236324274le_alt @ X4) & 94.61/12.65 (((~) @ (member84363362le_alt @ X2 @ 94.61/12.65 (set_Ar577454304le_alt @ X4)))))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl646])). 94.61/12.65 thf(zip_derived_cl527, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 94.61/12.65 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl526])). 94.61/12.65 thf(zip_derived_cl648, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 94.61/12.65 = (((distin236324274le_alt @ X4) & 94.61/12.65 (((~) @ (set_Ar577454304le_alt @ X4 @ X2))))))), 94.61/12.65 inference('demod', [status(thm)], [zip_derived_cl647, zip_derived_cl527])). 94.61/12.65 thf(fact_12_in__below, axiom, 94.61/12.65 (![X:arrow_475358991le_alt,Y:arrow_475358991le_alt, 94.61/12.65 L_1:( produc1501160679le_alt > $o ),A_24:arrow_475358991le_alt, 94.61/12.65 B_17:arrow_475358991le_alt]: 94.61/12.65 ( ( ( A_24 ) != ( B_17 ) ) => 94.61/12.65 ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin ) => 94.61/12.65 ( ( ( ( X ) != ( Y ) ) & 94.61/12.65 ( ( ( Y ) != ( A_24 ) ) => 94.61/12.65 ( ( ( ( X ) != ( A_24 ) ) => 94.61/12.65 ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) & 94.61/12.65 ( ( ( X ) = ( A_24 ) ) => 94.61/12.65 ( ( ( Y ) = ( B_17 ) ) | 94.61/12.65 ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ B_17 @ Y ) @ L_1 ) ) ) ) ) & 94.61/12.65 ( ( ( Y ) = ( A_24 ) ) => 94.61/12.65 ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ X @ B_17 ) @ L_1 ) ) ) <=> 94.61/12.65 ( member214075476le_alt @ 94.61/12.65 ( produc1347929815le_alt @ X @ Y ) @ 94.61/12.65 ( arrow_2098199487_below @ L_1 @ A_24 @ B_17 ) ) ) ) ))). 94.61/12.65 thf(zip_derived_cl116, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y3 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y4 : arrow_475358991le_alt]: 94.61/12.65 (((( 94.61/12.65 (Y3) != 94.61/12.65 (Y4))) => 94.61/12.65 (( 94.61/12.65 (member377231867_alt_o @ 94.61/12.65 Y2 @ 94.61/12.65 arrow_823908191le_Lin) => 94.61/12.65 (( 94.61/12.65 (( 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (Y0) != 94.61/12.65 (Y1))) & 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (( 94.61/12.65 (Y1) != 94.61/12.65 (Y3))) => 94.61/12.65 (( 94.61/12.65 (( 94.61/12.65 (( 94.61/12.65 (Y0) != 94.61/12.65 (Y3))) => 94.61/12.65 (member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 Y0 @ Y1) @ 94.61/12.65 Y2))) & 94.61/12.65 (( 94.61/12.65 (( 94.61/12.65 (Y0) = 94.61/12.65 (Y3))) => 94.61/12.65 (( 94.61/12.65 (( 94.61/12.65 (Y1) = 94.61/12.65 (Y4))) | 94.61/12.65 (member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 Y4 @ Y1) @ 94.61/12.65 Y2))))))))) & 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (( 94.61/12.65 (Y1) = 94.61/12.65 (Y3))) => 94.61/12.65 (member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 Y0 @ Y4) @ 94.61/12.65 Y2))))) <=> 94.61/12.65 (member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 Y0 @ Y1) @ 94.61/12.65 ( 94.61/12.65 arrow_2098199487_below @ 94.61/12.65 Y2 @ 94.61/12.65 Y3 @ Y4)))))))))))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_12_in__below])). 94.61/12.65 thf(zip_derived_cl117, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ (( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 !=))))))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ((('#C') @ member377231867_alt_o @ 94.61/12.65 arrow_823908191le_Lin)))))))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 '#S'))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S'))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 (('#B') @ (<=>))))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#S'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#S'))))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S'))))))) @ 94.61/12.65 (( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &))) @ 94.61/12.65 ( 94.61/12.65 !=))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 !=))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S'))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 !=))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ member214075476le_alt)) @ 94.61/12.65 produc1347929815le_alt)))))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 =))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 |))) @ 94.61/12.65 ( 94.61/12.65 =))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ member214075476le_alt)) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ produc1347929815le_alt)))))))))))))))))))))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 =))))))))))) @ 94.61/12.65 ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ member214075476le_alt)) @ 94.61/12.65 produc1347929815le_alt)))))))))))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ member214075476le_alt)) @ 94.61/12.65 produc1347929815le_alt)))))))))) @ 94.61/12.65 arrow_2098199487_below))))))))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl116])). 94.61/12.65 thf(zip_derived_cl1103, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ (=>))) @ 94.61/12.65 (!=))))))))) @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ member377231867_alt_o @ 94.61/12.65 arrow_823908191le_Lin)))))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 '#S'))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 <=>))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#S'))))) @ 94.61/12.65 ((('#S') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) != 94.61/12.65 (X2))))))))))) @ 94.61/12.65 ((('#S') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ( 94.61/12.65 !=))))))))) @ 94.61/12.65 (( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S'))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B'))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) != 94.61/12.65 (X2))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 X2))))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) = 94.61/12.65 (X2))))))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 |))) @ 94.61/12.65 ( 94.61/12.65 =))))))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ member214075476le_alt)) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ produc1347929815le_alt)))))))))))))))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#C') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 (=))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2))))))))))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2))))))))) @ 94.61/12.65 arrow_2098199487_below))))))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 94.61/12.65 thf(zip_derived_cl1104, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 (!=))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ member377231867_alt_o @ 94.61/12.65 arrow_823908191le_Lin)))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 <=>))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ( 94.61/12.65 '#S'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 ((&) @ ( 94.61/12.65 ((X2) != (X4))))))))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#S') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 (((arrow_475358991le_alt) != 94.61/12.65 (X4))))))))) @ 94.61/12.65 ((('#S') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &))) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) != 94.61/12.65 (X2))))))) @ 94.61/12.65 ( 94.61/12.65 member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 X2 @ X4)))))))))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#C') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 (( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) = 94.61/12.65 (X2))))))))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#S') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 |) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) = 94.61/12.65 (X4))))))) @ 94.61/12.65 (( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ produc1347929815le_alt @ 94.61/12.65 X4)))))))))))))))))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) = 94.61/12.65 (X4))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2))))))))))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2 @ X4)))))) @ 94.61/12.65 arrow_2098199487_below))))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1103])). 94.61/12.65 thf(zip_derived_cl1105, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ (!=))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (((=>) @ (member377231867_alt_o @ 94.61/12.65 X6 @ 94.61/12.65 arrow_823908191le_Lin))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ( 94.61/12.65 ((&) @ ( 94.61/12.65 ((X2) != 94.61/12.65 (X4))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) != 94.61/12.65 (X4))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 &) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 ( 94.61/12.65 ('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 (arrow_475358991le_alt) != 94.61/12.65 (X2))))) @ 94.61/12.65 ( 94.61/12.65 member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 produc1347929815le_alt @ 94.61/12.65 X2 @ X4) @ 94.61/12.65 X6))))))) @ 94.61/12.65 ((('#C') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 =>) @ 94.61/12.65 (((arrow_475358991le_alt) = 94.61/12.65 (X2))))))) @ 94.61/12.65 ((('#S') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 |) @ 94.61/12.65 (((arrow_475358991le_alt) = 94.61/12.65 (X4))))) @ 94.61/12.65 ((('#C') @ ( 94.61/12.65 (('#B') @ member214075476le_alt @ 94.61/12.65 ((('#C') @ produc1347929815le_alt @ 94.61/12.65 X4)))) @ 94.61/12.65 X6)))))))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=>) @ 94.61/12.65 (((arrow_475358991le_alt) = 94.61/12.65 (X4))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2))) @ 94.61/12.65 X6)))))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2 @ X4)))) @ 94.61/12.65 (arrow_2098199487_below @ X6)))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1104])). 94.61/12.65 thf(zip_derived_cl1106, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 (((arrow_475358991le_alt) != (X8))))) @ 94.61/12.65 ((('#B') @ (((=>) @ (member377231867_alt_o @ X6 @ 94.61/12.65 arrow_823908191le_Lin))) @ 94.61/12.65 ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 ((('#S') @ ((('#B') @ (((&) @ (((X2) != 94.61/12.65 (X4))))) @ 94.61/12.65 ((('#B') @ (((=>) @ (( 94.61/12.65 (X4) != 94.61/12.65 (X8))))) @ 94.61/12.65 ((('#B') @ (((&) @ ( 94.61/12.65 ((((X2) != (X8))) => 94.61/12.65 (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2 @ X4) @ 94.61/12.65 X6))))) @ 94.61/12.65 ((('#B') @ (((=>) @ ( 94.61/12.65 ((X2) = (X8))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ( 94.61/12.65 |) @ 94.61/12.65 (((arrow_475358991le_alt) = 94.61/12.65 (X4))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ member214075476le_alt @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ produc1347929815le_alt @ 94.61/12.65 X4)))) @ 94.61/12.65 X6)))))))))))) @ 94.61/12.65 ((('#B') @ (((=>) @ (((X4) = (X8))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ 94.61/12.65 X2))) @ 94.61/12.65 X6)))))))) @ 94.61/12.65 ((('#B') @ (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4)) @ 94.61/12.65 (arrow_2098199487_below @ X6 @ X8)))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1105])). 94.61/12.65 thf(zip_derived_cl1107, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (((((X8) != (X10))) => 94.61/12.65 (((member377231867_alt_o @ X6 @ arrow_823908191le_Lin) => 94.61/12.65 (((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) <=> 94.61/12.65 (member214075476le_alt @ (produc1347929815le_alt @ X2 @ X4) @ 94.61/12.65 (arrow_2098199487_below @ X6 @ X8 @ X10))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1106])). 94.61/12.65 thf(zip_derived_cl500, plain, 94.61/12.65 (![X2 : produc1501160679le_alt > $o, 94.61/12.65 X4 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 ((X4 @ X2) = (member377231867_alt_o @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl499])). 94.61/12.65 thf(zip_derived_cl496, plain, 94.61/12.65 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 94.61/12.65 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl495])). 94.61/12.65 thf(zip_derived_cl1108, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (((((X8) != (X10))) => 94.61/12.65 (((arrow_823908191le_Lin @ X6) => 94.61/12.65 (((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) <=> 94.61/12.65 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4))))))))), 94.61/12.65 inference('demod', [status(thm)], 94.61/12.65 [zip_derived_cl1107, zip_derived_cl500, zip_derived_cl496])). 94.61/12.65 thf(zip_derived_cl1109, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (~ (((X8) != (X10))) 94.61/12.65 | (((arrow_823908191le_Lin @ X6) => 94.61/12.65 (((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) <=> 94.61/12.65 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4)))))))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1108])). 94.61/12.65 thf(zip_derived_cl1110, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (((X8) = (X10)) 94.61/12.65 | (((arrow_823908191le_Lin @ X6) => 94.61/12.65 (((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) <=> 94.61/12.65 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4)))))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl1109])). 94.61/12.65 thf(zip_derived_cl1111, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (~ (arrow_823908191le_Lin @ X6) 94.61/12.65 | (((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) <=> 94.61/12.65 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4)))) 94.61/12.65 | ((X8) = (X10)))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1110])). 94.61/12.65 thf(zip_derived_cl1112, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 94.61/12.65 X10 : arrow_475358991le_alt]: 94.61/12.65 (~ (arrow_823908191le_Lin @ X6) 94.61/12.65 | ((((((X2) != (X4))) & 94.61/12.65 (((((X4) != (X8))) => 94.61/12.65 (((((((X2) != (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 94.61/12.65 (((((X2) = (X8))) => 94.61/12.65 (((((X4) = (X10))) | (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 94.61/12.65 (((((X4) = (X8))) => (member214075476le_alt @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X10) @ X6))))) 94.61/12.65 = (arrow_2098199487_below @ X6 @ X8 @ X10 @ 94.61/12.65 (produc1347929815le_alt @ X2 @ X4))) 94.61/12.65 | ((X8) = (X10)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl1111])). 94.61/12.65 thf(zip_derived_cl590, plain, 94.61/12.65 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 94.61/12.65 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 94.61/12.65 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl589])). 94.61/12.65 thf(fact_372_append__assoc, axiom, 94.61/12.65 (![Xs_100:list_A2115238852le_alt,Ys_48:list_A2115238852le_alt, 94.61/12.65 Zs_5:list_A2115238852le_alt]: 94.61/12.65 ( ( append179082452le_alt @ 94.61/12.65 ( append179082452le_alt @ Xs_100 @ Ys_48 ) @ Zs_5 ) = 94.61/12.65 ( append179082452le_alt @ 94.61/12.65 Xs_100 @ ( append179082452le_alt @ Ys_48 @ Zs_5 ) ) ))). 94.61/12.65 thf(zip_derived_cl118, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ 94.61/12.65 (append179082452le_alt @ Y0 @ Y1) @ 94.61/12.65 Y2) = (append179082452le_alt @ 94.61/12.65 Y0 @ 94.61/12.65 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_372_append__assoc])). 94.61/12.65 thf(zip_derived_cl119, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 94.61/12.65 append179082452le_alt)))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ append179082452le_alt)))) @ 94.61/12.65 append179082452le_alt))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl118])). 94.61/12.65 thf(zip_derived_cl695, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#B') @ append179082452le_alt @ 94.61/12.65 (append179082452le_alt @ X2))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (append179082452le_alt @ X2))) @ 94.61/12.65 append179082452le_alt))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl119])). 94.61/12.65 thf(zip_derived_cl696, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 94.61/12.65 (append179082452le_alt @ 94.61/12.65 (append179082452le_alt @ X2 @ X4)))) @ 94.61/12.65 ((('#B') @ (append179082452le_alt @ X2) @ 94.61/12.65 (append179082452le_alt @ X4)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl695])). 94.61/12.65 thf(zip_derived_cl697, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 (((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) = 94.61/12.65 (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl696])). 94.61/12.65 thf(zip_derived_cl698, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 ((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) 94.61/12.65 = (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl697])). 94.61/12.65 thf(fact_289_Prof__def, axiom, 94.61/12.65 (( arrow_734252939e_Prof ) = 94.61/12.65 ( pi_Arr1929480907_alt_o @ 94.61/12.65 top_to988227749indi_o @ 94.61/12.65 ( ^[Uu:arrow_1429601828e_indi]: ( arrow_823908191le_Lin ) ) ))). 94.61/12.65 thf(zip_derived_cl72, plain, 94.61/12.65 (((arrow_734252939e_Prof) 94.61/12.65 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 94.61/12.65 (^[Y0 : arrow_1429601828e_indi]: (arrow_823908191le_Lin))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_289_Prof__def])). 94.61/12.65 thf(zip_derived_cl73, plain, 94.61/12.65 (((arrow_734252939e_Prof) 94.61/12.65 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 94.61/12.65 ((('#K') @ arrow_823908191le_Lin))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl72])). 94.61/12.65 thf(zip_derived_cl7427, plain, 94.61/12.65 (((arrow_734252939e_Prof) 94.61/12.65 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 94.61/12.65 ('#ty_enc48' @ arrow_823908191le_Lin)))), 94.61/12.65 inference('remove_ty_args', [status(thm)], [zip_derived_cl73])). 94.61/12.65 thf(fact_114_funcset__mem, axiom, 94.61/12.65 (![X_71:arrow_1429601828e_indi, 94.61/12.65 F_13:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 94.61/12.65 A_18:( arrow_1429601828e_indi > $o ), 94.61/12.65 B_15:( ( produc1501160679le_alt > $o ) > $o )]: 94.61/12.65 ( ( member526088951_alt_o @ 94.61/12.65 F_13 @ 94.61/12.65 ( pi_Arr1929480907_alt_o @ 94.61/12.65 A_18 @ ( ^[Uu:arrow_1429601828e_indi]: ( B_15 ) ) ) ) => 94.61/12.65 ( ( member2052026769e_indi @ X_71 @ A_18 ) => 94.61/12.65 ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ))). 94.61/12.65 thf(zip_derived_cl255, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((!!) @ (^[Y3 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((member526088951_alt_o @ 94.61/12.65 Y1 @ 94.61/12.65 (pi_Arr1929480907_alt_o @ 94.61/12.65 Y2 @ 94.61/12.65 (^[Y4 : arrow_1429601828e_indi]: 94.61/12.65 (Y3)))) => 94.61/12.65 (((member2052026769e_indi @ 94.61/12.65 Y0 @ Y2) => 94.61/12.65 (member377231867_alt_o @ 94.61/12.65 (Y1 @ Y0) @ Y3)))))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_114_funcset__mem])). 94.61/12.65 thf(zip_derived_cl256, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ( 94.61/12.65 (('#B') @ (=>))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 member526088951_alt_o)))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 pi_Arr1929480907_alt_o)) @ 94.61/12.65 ('#K'))))))))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 member2052026769e_indi)))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ member377231867_alt_o)) @ 94.61/12.65 ((('#C') @ ('#I')))))))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl255])). 94.61/12.65 thf(zip_derived_cl906, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 member526088951_alt_o)))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 pi_Arr1929480907_alt_o)) @ 94.61/12.65 ('#K'))))))))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=>) @ 94.61/12.65 (member2052026769e_indi @ X2))))))) @ 94.61/12.65 ((('#B') @ member377231867_alt_o @ 94.61/12.65 ((('#C') @ ('#I') @ X2))))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl256])). 94.61/12.65 thf(zip_derived_cl907, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (member526088951_alt_o @ 94.61/12.65 X4))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 pi_Arr1929480907_alt_o)) @ 94.61/12.65 ('#K'))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ (=>) @ 94.61/12.65 (member2052026769e_indi @ X2))))) @ 94.61/12.65 (member377231867_alt_o @ (X4 @ X2))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl906])). 94.61/12.65 thf(zip_derived_cl908, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#B') @ (member526088951_alt_o @ X4) @ 94.61/12.65 ((('#B') @ (pi_Arr1929480907_alt_o @ X6) @ 94.61/12.65 ('#K'))))))) @ 94.61/12.65 ((('#B') @ (((=>) @ (member2052026769e_indi @ X2 @ X6))) @ 94.61/12.65 (member377231867_alt_o @ (X4 @ X2))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl907])). 94.61/12.65 thf(zip_derived_cl909, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((member526088951_alt_o @ X4 @ 94.61/12.65 (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)))) => 94.61/12.65 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 94.61/12.65 (X4 @ X2) @ X8)))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl908])). 94.61/12.65 thf(fact_269_mem__def, axiom, 94.61/12.65 (![X_66:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 94.61/12.65 A_12:( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )]: 94.61/12.65 ( ( A_12 @ X_66 ) <=> ( member526088951_alt_o @ X_66 @ A_12 ) ))). 94.61/12.65 thf(zip_derived_cl243, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y1 : (arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((Y1 @ Y0) <=> (member526088951_alt_o @ Y0 @ 94.61/12.65 Y1)))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_269_mem__def])). 94.61/12.65 thf(zip_derived_cl244, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#C') @ ('#I'))))))) @ 94.61/12.65 member526088951_alt_o))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl243])). 94.61/12.65 thf(zip_derived_cl536, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 94.61/12.65 (member526088951_alt_o @ X2)))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl244])). 94.61/12.65 thf(zip_derived_cl537, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((X4 @ X2) <=> (member526088951_alt_o @ X2 @ X4)))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl536])). 94.61/12.65 thf(zip_derived_cl538, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 94.61/12.65 ((X4 @ X2) = (member526088951_alt_o @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl537])). 94.61/12.65 thf(zip_derived_cl910, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) => 94.61/12.65 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 94.61/12.65 (X4 @ X2) @ X8)))))), 94.61/12.65 inference('demod', [status(thm)], [zip_derived_cl909, zip_derived_cl538])). 94.61/12.65 thf(zip_derived_cl911, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) 94.61/12.65 | (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 94.61/12.65 (X4 @ X2) @ X8))))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl910])). 94.61/12.65 thf(zip_derived_cl912, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (~ (member2052026769e_indi @ X2 @ X6) 94.61/12.65 | (member377231867_alt_o @ (X4 @ X2) @ X8) 94.61/12.65 | ~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])). 94.61/12.65 thf(zip_derived_cl7441, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (~ (member2052026769e_indi @ X2 @ X6) 94.61/12.65 | (member377231867_alt_o @ (X4 @ X2) @ X8) 94.61/12.65 | ~ (pi_Arr1929480907_alt_o @ X6 @ ('#ty_enc48' @ X8) @ X4))), 94.61/12.65 inference('remove_ty_args', [status(thm)], [zip_derived_cl912])). 94.61/12.65 thf(fact_365_snoc__eq__iff__butlast, axiom, 94.61/12.65 (![Xs_106:list_A2115238852le_alt,X_51:arrow_475358991le_alt, 94.61/12.65 Ys_54:list_A2115238852le_alt]: 94.61/12.65 ( ( ( append179082452le_alt @ 94.61/12.65 Xs_106 @ ( cons_A228743023le_alt @ X_51 @ nil_Ar1286194111le_alt ) ) = 94.61/12.65 ( Ys_54 ) ) <=> 94.61/12.65 ( ( ( Ys_54 ) != ( nil_Ar1286194111le_alt ) ) & 94.61/12.65 ( ( last_A1217315288le_alt @ Ys_54 ) = ( X_51 ) ) & 94.61/12.65 ( ( butlas274947851le_alt @ Ys_54 ) = ( Xs_106 ) ) ) ))). 94.61/12.65 thf(zip_derived_cl76, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 94.61/12.65 (((((append179082452le_alt @ Y0 @ 94.61/12.65 (cons_A228743023le_alt @ Y1 @ 94.61/12.65 nil_Ar1286194111le_alt)) = 94.61/12.65 (Y2))) <=> 94.61/12.65 (((((Y2) != 94.61/12.65 (nil_Ar1286194111le_alt))) & 94.61/12.65 (((last_A1217315288le_alt @ 94.61/12.65 Y2) = (Y1))) & 94.61/12.65 (((butlas274947851le_alt @ 94.61/12.65 Y2) = (Y0))))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_365_snoc__eq__iff__butlast])). 94.61/12.65 thf(zip_derived_cl77, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (=))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 append179082452le_alt)) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt)))))))))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#S') @ (( 94.61/12.65 ('#B') @ ( 94.61/12.65 &) @ 94.61/12.65 ( 94.61/12.65 ( 94.61/12.65 ('#C') @ ( 94.61/12.65 !=) @ 94.61/12.65 nil_Ar1286194111le_alt)))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ( 94.61/12.65 =) @ 94.61/12.65 last_A1217315288le_alt)))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=) @ butlas274947851le_alt))))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl76])). 94.61/12.65 thf(zip_derived_cl801, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (<=>))) @ 94.61/12.65 ((('#B') @ (=) @ 94.61/12.65 ((('#B') @ (append179082452le_alt @ X2) @ 94.61/12.65 ((('#C') @ cons_A228743023le_alt @ 94.61/12.65 nil_Ar1286194111le_alt)))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 94.61/12.65 ((('#C') @ ( 94.61/12.65 !=) @ 94.61/12.65 nil_Ar1286194111le_alt)))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=) @ 94.61/12.65 last_A1217315288le_alt)))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=) @ butlas274947851le_alt)) @ 94.61/12.65 X2))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl77])). 94.61/12.65 thf(zip_derived_cl802, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 94.61/12.65 (((list_A2115238852le_alt) = 94.61/12.65 (append179082452le_alt @ X2 @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ 94.61/12.65 nil_Ar1286194111le_alt)))))) @ 94.61/12.65 ((('#S') @ ((('#S') @ ((('#B') @ (&) @ 94.61/12.65 ((('#C') @ (!=) @ 94.61/12.65 nil_Ar1286194111le_alt)))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=) @ 94.61/12.65 last_A1217315288le_alt)) @ 94.61/12.65 X4)))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=) @ butlas274947851le_alt)) @ X2))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl801])). 94.61/12.65 thf(zip_derived_cl803, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 (((((append179082452le_alt @ X2 @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6))) <=> 94.61/12.65 (((((X6) != (nil_Ar1286194111le_alt))) & 94.61/12.65 (((last_A1217315288le_alt @ X6) = (X4))) & 94.61/12.65 (((butlas274947851le_alt @ X6) = (X2)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl802])). 94.61/12.65 thf(zip_derived_cl804, plain, 94.61/12.65 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 94.61/12.65 X6 : list_A2115238852le_alt]: 94.61/12.65 ((((append179082452le_alt @ X2 @ 94.61/12.65 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6))) 94.61/12.65 = (((((X6) != (nil_Ar1286194111le_alt))) & 94.61/12.65 (((last_A1217315288le_alt @ X6) = (X4))) & 94.61/12.65 (((butlas274947851le_alt @ X6) = (X2))))))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl803])). 94.61/12.65 thf(fact_316_UNIV__I, axiom, 94.61/12.65 (![X_55:arrow_1429601828e_indi]: 94.61/12.65 ( member2052026769e_indi @ X_55 @ top_to988227749indi_o ))). 94.61/12.65 thf(zip_derived_cl68, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 94.61/12.65 (member2052026769e_indi @ Y0 @ top_to988227749indi_o))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_316_UNIV__I])). 94.61/12.65 thf(zip_derived_cl69, plain, 94.61/12.65 ( (((!!) @ ((('#C') @ member2052026769e_indi @ top_to988227749indi_o))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl68])). 94.61/12.65 thf(zip_derived_cl354, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi]: 94.61/12.65 (member2052026769e_indi @ X2 @ top_to988227749indi_o)), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl69])). 94.61/12.65 thf(fact_0__096P_A_058_AProf_096, axiom, 94.61/12.65 (member526088951_alt_o @ p @ arrow_734252939e_Prof)). 94.61/12.65 thf(zip_derived_cl86, plain, 94.61/12.65 ( (member526088951_alt_o @ p @ arrow_734252939e_Prof)), 94.61/12.65 inference('cnf', [status(esa)], [fact_0__096P_A_058_AProf_096])). 94.61/12.65 thf(fact_250_Pi__I_H, axiom, 94.61/12.65 (![F_9:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 94.61/12.65 B_11:( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ), 94.61/12.65 A_14:( arrow_1429601828e_indi > $o )]: 94.61/12.65 ( ( ![X_2:arrow_1429601828e_indi]: 94.61/12.65 ( ( member2052026769e_indi @ X_2 @ A_14 ) => 94.61/12.65 ( member377231867_alt_o @ ( F_9 @ X_2 ) @ ( B_11 @ X_2 ) ) ) ) => 94.61/12.65 ( member526088951_alt_o @ F_9 @ ( pi_Arr1929480907_alt_o @ A_14 @ B_11 ) ) ))). 94.61/12.65 thf(zip_derived_cl150, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 94.61/12.65 (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((((!!) @ (^[Y3 : arrow_1429601828e_indi]: 94.61/12.65 (((member2052026769e_indi @ 94.61/12.65 Y3 @ Y2) => 94.61/12.65 (member377231867_alt_o @ 94.61/12.65 (Y0 @ Y3) @ 94.61/12.65 (Y1 @ Y3))))))) => 94.61/12.65 (member526088951_alt_o @ Y0 @ 94.61/12.65 (pi_Arr1929480907_alt_o @ Y2 @ Y1)))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_250_Pi__I_H])). 94.61/12.65 thf(zip_derived_cl151, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#C') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ( 94.61/12.65 =>))) @ 94.61/12.65 ((('#C') @ member2052026769e_indi)))))))))) @ 94.61/12.65 ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ member377231867_alt_o)))))))))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ member526088951_alt_o)))) @ 94.61/12.65 ((('#C') @ pi_Arr1929480907_alt_o))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl150])). 94.61/12.65 thf(zip_derived_cl846, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ ( 94.61/12.65 '#S') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ (=>))) @ 94.61/12.65 ((('#C') @ member2052026769e_indi)))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member377231867_alt_o @ 94.61/12.65 X2)))))))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (member526088951_alt_o @ X2))) @ 94.61/12.65 ((('#C') @ pi_Arr1929480907_alt_o))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl151])). 94.61/12.65 thf(zip_derived_cl847, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#B') @ (!!) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 ((('#C') @ member2052026769e_indi)))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member377231867_alt_o @ 94.61/12.65 X2)) @ 94.61/12.65 X4)))))))) @ 94.61/12.65 ((('#B') @ (member526088951_alt_o @ X2) @ 94.61/12.65 ((('#C') @ pi_Arr1929480907_alt_o @ X4))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl846])). 94.61/12.65 thf(zip_derived_cl848, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ member2052026769e_indi @ X6)))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) => 94.61/12.65 (member526088951_alt_o @ X2 @ (pi_Arr1929480907_alt_o @ X6 @ X4))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl847])). 94.61/12.65 thf(zip_derived_cl538, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 94.61/12.65 ((X4 @ X2) = (member526088951_alt_o @ X2 @ X4))), 94.61/12.65 inference('simplify nested equalities', [status(thm)], 94.61/12.65 [zip_derived_cl537])). 94.61/12.65 thf(zip_derived_cl849, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ member2052026769e_indi @ X6)))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) => 94.61/12.65 (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2)))), 94.61/12.65 inference('demod', [status(thm)], [zip_derived_cl848, zip_derived_cl538])). 94.61/12.65 thf(zip_derived_cl850, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#C') @ member2052026769e_indi @ X6)))) @ 94.61/12.65 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) 94.61/12.65 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl849])). 94.61/12.65 thf(zip_derived_cl851, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (~ (((member2052026769e_indi @ ('#sk33' @ X2 @ X4 @ X6) @ X6) => 94.61/12.65 (member377231867_alt_o @ (X2 @ ('#sk33' @ X2 @ X4 @ X6)) @ 94.61/12.65 (X4 @ ('#sk33' @ X2 @ X4 @ X6))))) 94.61/12.65 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 94.61/12.65 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl850])). 94.61/12.65 thf(zip_derived_cl853, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (~ (member377231867_alt_o @ (X2 @ ('#sk33' @ X2 @ X4 @ X6)) @ 94.61/12.65 (X4 @ ('#sk33' @ X2 @ X4 @ X6))) 94.61/12.65 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl851])). 94.61/12.65 thf(fact_78_PiE, axiom, 94.61/12.65 (![X_72:arrow_1429601828e_indi, 94.61/12.65 F_15:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 94.61/12.65 A_19:( arrow_1429601828e_indi > $o ), 94.61/12.65 B_16:( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o )]: 94.61/12.65 ( ( member526088951_alt_o @ 94.61/12.65 F_15 @ ( pi_Arr1929480907_alt_o @ A_19 @ B_16 ) ) => 94.61/12.65 ( ( ~( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) ) ) => 94.61/12.65 ( ~( member2052026769e_indi @ X_72 @ A_19 ) ) ) ))). 94.61/12.65 thf(zip_derived_cl2, plain, 94.61/12.65 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 94.61/12.65 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 94.61/12.65 produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((!!) @ (^[Y3 : arrow_1429601828e_indi > 94.61/12.65 (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((member526088951_alt_o @ 94.61/12.65 Y1 @ 94.61/12.65 (pi_Arr1929480907_alt_o @ 94.61/12.65 Y2 @ Y3)) => 94.61/12.65 (((((~) @ (member377231867_alt_o @ 94.61/12.65 (Y1 @ Y0) @ 94.61/12.65 (Y3 @ Y0)))) => 94.61/12.65 (((~) @ (member2052026769e_indi @ 94.61/12.65 Y0 @ Y2)))))))))))))))))))), 94.61/12.65 inference('cnf', [status(esa)], [fact_78_PiE])). 94.61/12.65 thf(zip_derived_cl3, plain, 94.61/12.65 ( (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 94.61/12.65 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ( 94.61/12.65 (('#B') @ (=>))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 '#B') @ 94.61/12.65 member526088951_alt_o)))) @ 94.61/12.65 pi_Arr1929480907_alt_o)))))))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#C'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ ( 94.61/12.65 ~))))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ ('#B'))) @ 94.61/12.65 ((('#B') @ ( 94.61/12.65 (('#B') @ member377231867_alt_o)) @ 94.61/12.65 ((('#C') @ ( 94.61/12.65 '#I'))))))))) @ 94.61/12.65 ((('#C') @ ('#I'))))))))))))))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (~))) @ member2052026769e_indi))))))))))))))), 94.61/12.65 inference('lams2combs', [status(thm)], [zip_derived_cl2])). 94.61/12.65 thf(zip_derived_cl371, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#B') @ ((('#B') @ (!!))) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ ('#S'))) @ 94.61/12.65 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#B') @ 94.61/12.65 member526088951_alt_o)))) @ 94.61/12.65 pi_Arr1929480907_alt_o)))))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ ('#C') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (~))) @ 94.61/12.65 ((('#C') @ ((('#B') @ ('#B') @ 94.61/12.65 ((('#B') @ member377231867_alt_o @ 94.61/12.65 ((('#C') @ ( 94.61/12.65 '#I') @ X2)))))) @ 94.61/12.65 ((('#C') @ ('#I') @ X2)))))))))))) @ 94.61/12.65 ((('#B') @ (~) @ (member2052026769e_indi @ X2)))))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 94.61/12.65 thf(zip_derived_cl372, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 94.61/12.65 (((!!) @ ((('#B') @ (!!) @ 94.61/12.65 ((('#S') @ ((('#B') @ ('#S') @ 94.61/12.65 ((('#B') @ ((('#B') @ (=>))) @ 94.61/12.65 ((('#B') @ ((('#B') @ (member526088951_alt_o @ 94.61/12.65 X4))) @ 94.61/12.65 pi_Arr1929480907_alt_o)))))) @ 94.61/12.65 ((('#B') @ ((('#C') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#B') @ (~) @ 94.61/12.65 ((('#B') @ (member377231867_alt_o @ 94.61/12.65 (X4 @ X2)) @ 94.61/12.65 ((('#C') @ ('#I') @ X2)))))))))) @ 94.61/12.65 ((('#B') @ (~) @ (member2052026769e_indi @ X2)))))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl371])). 94.61/12.65 thf(zip_derived_cl373, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o]: 94.61/12.65 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#B') @ (member526088951_alt_o @ X4) @ 94.61/12.65 (pi_Arr1929480907_alt_o @ X6))))) @ 94.61/12.65 ((('#C') @ ((('#B') @ (=>) @ 94.61/12.65 ((('#B') @ (~) @ 94.61/12.65 ((('#B') @ (member377231867_alt_o @ 94.61/12.65 (X4 @ X2)) @ 94.61/12.65 ((('#C') @ ('#I') @ X2)))))))) @ 94.61/12.65 (((~) @ (member2052026769e_indi @ X2 @ X6)))))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl372])). 94.61/12.65 thf(zip_derived_cl374, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (((member526088951_alt_o @ X4 @ 94.61/12.65 (pi_Arr1929480907_alt_o @ X6 @ X8)) => 94.61/12.65 (((((~) @ (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)))) => 94.61/12.65 (((~) @ (member2052026769e_indi @ X2 @ X6)))))))), 94.61/12.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl373])). 94.61/12.65 thf(zip_derived_cl375, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 94.61/12.65 (~ (member526088951_alt_o @ X4 @ (pi_Arr1929480907_alt_o @ X6 @ X8)) 94.61/12.65 | (((((~) @ (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)))) => 94.61/12.65 (((~) @ (member2052026769e_indi @ X2 @ X6))))))), 94.61/12.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl374])). 94.61/12.65 thf(zip_derived_cl376, plain, 94.61/12.65 (![X2 : arrow_1429601828e_indi, 94.61/12.65 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 94.61/12.65 X6 : arrow_1429601828e_indi > $o, 94.61/12.65 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 94.61/12.66 ( (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)) 94.61/12.66 | ~ (member2052026769e_indi @ X2 @ X6) 94.61/12.66 | ~ (member526088951_alt_o @ X4 @ (pi_Arr1929480907_alt_o @ X6 @ X8)))), 94.61/12.66 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl375])). 94.61/12.66 thf(zip_derived_cl7445, plain, ($false), 94.61/12.66 inference('eprover', [status(thm)], 94.61/12.66 [zip_derived_cl265, zip_derived_cl399, zip_derived_cl478, 94.61/12.66 zip_derived_cl387, zip_derived_cl414, zip_derived_cl675, 94.61/12.66 zip_derived_cl544, zip_derived_cl496, zip_derived_cl500, 94.61/12.66 zip_derived_cl497, zip_derived_cl430, zip_derived_cl638, 94.61/12.66 zip_derived_cl809, zip_derived_cl625, zip_derived_cl417, 94.61/12.66 zip_derived_cl527, zip_derived_cl648, zip_derived_cl1112, 94.61/12.66 zip_derived_cl590, zip_derived_cl698, zip_derived_cl7427, 94.61/12.66 zip_derived_cl7441, zip_derived_cl804, zip_derived_cl354, 94.61/12.66 zip_derived_cl86, zip_derived_cl853, zip_derived_cl376])). 94.61/12.66 94.61/12.66 % SZS output end Refutation 94.61/12.66 94.61/12.66 94.61/12.66 % Terminating... 94.90/12.73 % Runner terminated. 94.90/12.75 % Zipperpin 1.5 exiting 94.90/12.75 EOF