0.10/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.13/0.22 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.1QBr4U0hoV true 0.22/0.44 % Computer : n023.cluster.edu 0.22/0.44 % Model : x86_64 x86_64 0.22/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.22/0.44 % Memory : 8042.1875MB 0.22/0.44 % OS : Linux 3.10.0-693.el7.x86_64 0.22/0.44 % CPULimit : 960 0.22/0.44 % WCLimit : 120 0.22/0.44 % DateTime : Tue Aug 9 07:17:28 EDT 2022 0.22/0.44 % CPUTime : 0.22/0.44 % Running portfolio for 960 s 0.22/0.44 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.22/0.44 % Number of cores: 8 0.22/0.44 % Python version: Python 3.6.8 0.22/0.44 % Running in HO mode 0.64/0.76 % Total configuration time : 828 0.64/0.76 % Estimated wc time : 1656 0.64/0.76 % Estimated cpu time (8 cpus) : 207.0 0.66/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.66/0.84 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.66/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.66/0.85 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.66/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.66/0.86 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.66/0.86 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.66/0.86 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.67/0.98 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 90.82/12.41 % Solved by lams/40_b.comb.sh. 90.82/12.41 % done 379 iterations in 11.479s 90.82/12.41 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 90.82/12.41 % SZS output start Refutation 90.82/12.41 thf(list_A2115238852le_alt_type, type, list_A2115238852le_alt: $tType). 90.82/12.41 thf(arrow_475358991le_alt_type, type, arrow_475358991le_alt: $tType). 90.82/12.41 thf(produc1501160679le_alt_type, type, produc1501160679le_alt: $tType). 90.82/12.41 thf(arrow_1429601828e_indi_type, type, arrow_1429601828e_indi: $tType). 90.82/12.41 thf(c_type, type, c: arrow_475358991le_alt). 90.82/12.41 thf(set_Ar577454304le_alt_type, type, set_Ar577454304le_alt: list_A2115238852le_alt > 90.82/12.41 arrow_475358991le_alt > $o). 90.82/12.41 thf(cons_A228743023le_alt_type, type, cons_A228743023le_alt: arrow_475358991le_alt > 90.82/12.41 list_A2115238852le_alt > list_A2115238852le_alt). 90.82/12.41 thf(member84363362le_alt_type, type, member84363362le_alt: arrow_475358991le_alt > 90.82/12.41 (arrow_475358991le_alt > $o) > $o). 90.82/12.41 thf(member2052026769e_indi_type, type, member2052026769e_indi: arrow_1429601828e_indi > 90.82/12.41 (arrow_1429601828e_indi > $o) > $o). 90.82/12.41 thf(arrow_823908191le_Lin_type, type, arrow_823908191le_Lin: (produc1501160679le_alt > $o) > $o). 90.82/12.41 thf(p_type, type, p: arrow_1429601828e_indi > produc1501160679le_alt > $o). 90.82/12.41 thf(distin236324274le_alt_type, type, distin236324274le_alt: list_A2115238852le_alt > $o). 90.82/12.41 thf(a_type, type, a: arrow_475358991le_alt). 90.82/12.41 thf('#ty_enc50_type', type, '#ty_enc50': ((produc1501160679le_alt > $o) > $o) > 90.82/12.41 arrow_1429601828e_indi > 90.82/12.41 (produc1501160679le_alt > $o) > $o). 90.82/12.41 thf('#sk14_type', type, '#sk14': list_A2115238852le_alt > arrow_475358991le_alt). 90.82/12.41 thf('#sk6_type', type, '#sk6': arrow_1429601828e_indi). 90.82/12.41 thf(arrow_734252939e_Prof_type, type, arrow_734252939e_Prof: (arrow_1429601828e_indi > 90.82/12.41 produc1501160679le_alt > $o) > $o). 90.82/12.41 thf('#sk15_type', type, '#sk15': list_A2115238852le_alt > list_A2115238852le_alt). 90.82/12.41 thf(nil_Ar1286194111le_alt_type, type, nil_Ar1286194111le_alt: list_A2115238852le_alt). 90.82/12.41 thf(produc1347929815le_alt_type, type, produc1347929815le_alt: arrow_475358991le_alt > 90.82/12.41 arrow_475358991le_alt > produc1501160679le_alt). 90.82/12.41 thf(top_to988227749indi_o_type, type, top_to988227749indi_o: arrow_1429601828e_indi > $o). 90.82/12.41 thf(member526088951_alt_o_type, type, member526088951_alt_o: (arrow_1429601828e_indi > 90.82/12.41 produc1501160679le_alt > $o) > 90.82/12.41 ((arrow_1429601828e_indi > 90.82/12.41 produc1501160679le_alt > $o) > $o) > $o). 90.82/12.41 thf(last_A1217315288le_alt_type, type, last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 90.82/12.41 thf(append179082452le_alt_type, type, append179082452le_alt: list_A2115238852le_alt > 90.82/12.41 list_A2115238852le_alt > list_A2115238852le_alt). 90.82/12.41 thf(member214075476le_alt_type, type, member214075476le_alt: produc1501160679le_alt > 90.82/12.41 (produc1501160679le_alt > $o) > $o). 90.82/12.41 thf(member377231867_alt_o_type, type, member377231867_alt_o: (produc1501160679le_alt > $o) > 90.82/12.41 ((produc1501160679le_alt > $o) > $o) > $o). 90.82/12.41 thf(pi_Arr1929480907_alt_o_type, type, pi_Arr1929480907_alt_o: (arrow_1429601828e_indi > $o) > 90.82/12.41 (arrow_1429601828e_indi > 90.82/12.41 (produc1501160679le_alt > $o) > $o) > 90.82/12.41 (arrow_1429601828e_indi > 90.82/12.41 produc1501160679le_alt > $o) > $o). 90.82/12.41 thf(butlas274947851le_alt_type, type, butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 90.82/12.41 thf(rev_Ar1106406943le_alt_type, type, rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 90.82/12.41 thf(hd_Arr1965683346le_alt_type, type, hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 90.82/12.41 thf(arrow_2098199487_below_type, type, arrow_2098199487_below: (produc1501160679le_alt > $o) > 90.82/12.41 arrow_475358991le_alt > 90.82/12.41 arrow_475358991le_alt > 90.82/12.41 produc1501160679le_alt > $o). 90.82/12.41 thf(b_type, type, b: arrow_475358991le_alt). 90.82/12.41 thf('#sk32_type', type, '#sk32': (arrow_1429601828e_indi > 90.82/12.41 produc1501160679le_alt > $o) > 90.82/12.41 (arrow_1429601828e_indi > 90.82/12.41 (produc1501160679le_alt > $o) > $o) > 90.82/12.41 (arrow_1429601828e_indi > $o) > arrow_1429601828e_indi). 90.82/12.41 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 90.82/12.41 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 90.82/12.41 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 90.82/12.41 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 90.82/12.41 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 90.82/12.41 thf(fact_4_dist, axiom, 90.82/12.41 (distin236324274le_alt @ 90.82/12.41 ( cons_A228743023le_alt @ 90.82/12.41 a @ 90.82/12.41 ( cons_A228743023le_alt @ 90.82/12.41 b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ))). 90.82/12.41 thf(zip_derived_cl111, plain, 90.82/12.41 ( (distin236324274le_alt @ 90.82/12.41 (cons_A228743023le_alt @ a @ 90.82/12.41 (cons_A228743023le_alt @ b @ 90.82/12.41 (cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_4_dist])). 90.82/12.41 thf(fact_37_list_Osimps_I2_J, axiom, 90.82/12.41 (![A_23:arrow_475358991le_alt,List_4:list_A2115238852le_alt]: 90.82/12.41 ( ( nil_Ar1286194111le_alt ) != ( cons_A228743023le_alt @ A_23 @ List_4 ) ))). 90.82/12.41 thf(zip_derived_cl298, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((nil_Ar1286194111le_alt) != 90.82/12.41 (cons_A228743023le_alt @ Y0 @ Y1)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_37_list_Osimps_I2_J])). 90.82/12.41 thf(zip_derived_cl299, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 90.82/12.41 (nil_Ar1286194111le_alt))))) @ 90.82/12.41 cons_A228743023le_alt))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl298])). 90.82/12.41 thf(zip_derived_cl407, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != 90.82/12.41 (nil_Ar1286194111le_alt))) @ 90.82/12.41 (cons_A228743023le_alt @ X2)))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl299])). 90.82/12.41 thf(zip_derived_cl408, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl407])). 90.82/12.41 thf(zip_derived_cl409, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl408])). 90.82/12.41 thf(fact_467_hd_Osimps, axiom, 90.82/12.41 (![X_26:arrow_475358991le_alt,Xs_44:list_A2115238852le_alt]: 90.82/12.41 ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_26 @ Xs_44 ) ) = 90.82/12.41 ( X_26 ) ))). 90.82/12.41 thf(zip_derived_cl107, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((hd_Arr1965683346le_alt @ 90.82/12.41 (cons_A228743023le_alt @ Y0 @ Y1)) = (Y0)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_467_hd_Osimps])). 90.82/12.41 thf(zip_derived_cl108, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#C') @ 90.82/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.82/12.41 ((('#B') @ ((('#B') @ hd_Arr1965683346le_alt)) @ 90.82/12.41 cons_A228743023le_alt)))))) @ 90.82/12.41 ('#I')))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl107])). 90.82/12.41 thf(zip_derived_cl475, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#C') @ ((('#B') @ (=) @ 90.82/12.41 ((('#B') @ hd_Arr1965683346le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X2))))) @ 90.82/12.41 X2))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])). 90.82/12.41 thf(zip_derived_cl476, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl475])). 90.82/12.41 thf(zip_derived_cl477, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl476])). 90.82/12.41 thf(fact_375_append__Nil, axiom, 90.82/12.41 (![Ys_45:list_A2115238852le_alt]: 90.82/12.41 ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 ) = ( Ys_45 ) ))). 90.82/12.41 thf(zip_derived_cl133, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((append179082452le_alt @ nil_Ar1286194111le_alt @ Y0) = 90.82/12.41 (Y0))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_375_append__Nil])). 90.82/12.41 thf(zip_derived_cl134, plain, 90.82/12.41 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 90.82/12.41 (append179082452le_alt @ nil_Ar1286194111le_alt))) @ 90.82/12.41 ('#I')))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl133])). 90.82/12.41 thf(zip_derived_cl379, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 90.82/12.41 thf(zip_derived_cl380, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 ((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl379])). 90.82/12.41 thf(fact_589_hd__in__set, axiom, 90.82/12.41 (![Xs_9:list_A2115238852le_alt]: 90.82/12.41 ( ( ( Xs_9 ) != ( nil_Ar1286194111le_alt ) ) => 90.82/12.41 ( member84363362le_alt @ 90.82/12.41 ( hd_Arr1965683346le_alt @ Xs_9 ) @ ( set_Ar577454304le_alt @ Xs_9 ) ) ))). 90.82/12.41 thf(zip_derived_cl116, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((((Y0) != (nil_Ar1286194111le_alt))) => 90.82/12.41 (member84363362le_alt @ (hd_Arr1965683346le_alt @ Y0) @ 90.82/12.41 (set_Ar577454304le_alt @ Y0)))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_589_hd__in__set])). 90.82/12.41 thf(zip_derived_cl117, plain, 90.82/12.41 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.82/12.41 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 90.82/12.41 ((('#S') @ ((('#B') @ member84363362le_alt @ 90.82/12.41 hd_Arr1965683346le_alt)) @ 90.82/12.41 set_Ar577454304le_alt))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl116])). 90.82/12.41 thf(zip_derived_cl416, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 90.82/12.41 (hd_Arr1965683346le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl117])). 90.82/12.41 thf(zip_derived_cl417, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (~ (((X2) != (nil_Ar1286194111le_alt))) 90.82/12.41 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 90.82/12.41 (set_Ar577454304le_alt @ X2)))), 90.82/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl416])). 90.82/12.41 thf(zip_derived_cl418, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt)) 90.82/12.41 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 90.82/12.41 (set_Ar577454304le_alt @ X2)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl417])). 90.82/12.41 thf(fact_373_append__Cons, axiom, 90.82/12.41 (![X_50:arrow_475358991le_alt,Xs_99:list_A2115238852le_alt, 90.82/12.41 Ys_47:list_A2115238852le_alt]: 90.82/12.41 ( ( append179082452le_alt @ 90.82/12.41 ( cons_A228743023le_alt @ X_50 @ Xs_99 ) @ Ys_47 ) = 90.82/12.41 ( cons_A228743023le_alt @ 90.82/12.41 X_50 @ ( append179082452le_alt @ Xs_99 @ Ys_47 ) ) ))). 90.82/12.41 thf(zip_derived_cl284, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 90.82/12.41 (((append179082452le_alt @ 90.82/12.41 (cons_A228743023le_alt @ Y0 @ Y1) @ 90.82/12.41 Y2) = (cons_A228743023le_alt @ 90.82/12.41 Y0 @ 90.82/12.41 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_373_append__Cons])). 90.82/12.41 thf(zip_derived_cl285, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 90.82/12.41 cons_A228743023le_alt)))))))) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.82/12.41 ((('#B') @ ('#B') @ cons_A228743023le_alt)))) @ 90.82/12.41 append179082452le_alt))))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl284])). 90.82/12.41 thf(zip_derived_cl681, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.82/12.41 ((('#B') @ append179082452le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X2))))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ (cons_A228743023le_alt @ X2))) @ 90.82/12.41 append179082452le_alt))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl285])). 90.82/12.41 thf(zip_derived_cl682, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 90.82/12.41 (append179082452le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X2 @ X4)))) @ 90.82/12.41 ((('#B') @ (cons_A228743023le_alt @ X2) @ 90.82/12.41 (append179082452le_alt @ X4)))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl681])). 90.82/12.41 thf(zip_derived_cl683, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 90.82/12.41 X6 : list_A2115238852le_alt]: 90.82/12.41 (((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) = 90.82/12.41 (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl682])). 90.82/12.41 thf(zip_derived_cl684, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 90.82/12.41 X6 : list_A2115238852le_alt]: 90.82/12.41 ((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) 90.82/12.41 = (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl683])). 90.82/12.41 thf(fact_394_last__snoc, axiom, 90.82/12.41 (![Xs_80:list_A2115238852le_alt,X_42:arrow_475358991le_alt]: 90.82/12.41 ( ( last_A1217315288le_alt @ 90.82/12.41 ( append179082452le_alt @ 90.82/12.41 Xs_80 @ ( cons_A228743023le_alt @ X_42 @ nil_Ar1286194111le_alt ) ) ) = 90.82/12.41 ( X_42 ) ))). 90.82/12.41 thf(zip_derived_cl231, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.82/12.41 (((last_A1217315288le_alt @ 90.82/12.41 (append179082452le_alt @ Y0 @ 90.82/12.41 (cons_A228743023le_alt @ Y1 @ 90.82/12.41 nil_Ar1286194111le_alt))) = 90.82/12.41 (Y1)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_394_last__snoc])). 90.82/12.41 thf(zip_derived_cl232, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.82/12.41 ((('#B') @ ((('#B') @ last_A1217315288le_alt)) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.82/12.41 append179082452le_alt)) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ 90.82/12.41 nil_Ar1286194111le_alt)))))))))) @ 90.82/12.41 ('#I')))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl231])). 90.82/12.41 thf(zip_derived_cl545, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 90.82/12.41 ((('#B') @ last_A1217315288le_alt @ 90.82/12.41 ((('#B') @ (append179082452le_alt @ X2) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ 90.82/12.41 nil_Ar1286194111le_alt)))))))) @ 90.82/12.41 ('#I')))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl232])). 90.82/12.41 thf(zip_derived_cl546, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.82/12.41 (((last_A1217315288le_alt @ 90.82/12.41 (append179082452le_alt @ X2 @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) = 90.82/12.41 (X4)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl545])). 90.82/12.41 thf(zip_derived_cl547, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.82/12.41 ((last_A1217315288le_alt @ 90.82/12.41 (append179082452le_alt @ X2 @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) 90.82/12.41 = (X4))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl546])). 90.82/12.41 thf(fact_268_mem__def, axiom, 90.82/12.41 (![X_66:produc1501160679le_alt,A_12:( produc1501160679le_alt > $o )]: 90.82/12.41 ( ( member214075476le_alt @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 90.82/12.41 thf(zip_derived_cl30, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : produc1501160679le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : produc1501160679le_alt > $o]: 90.82/12.41 (((member214075476le_alt @ Y0 @ Y1) <=> (Y1 @ 90.82/12.41 Y0)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_268_mem__def])). 90.82/12.41 thf(zip_derived_cl31, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 member214075476le_alt)))) @ 90.82/12.41 ((('#C') @ ('#I')))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl30])). 90.82/12.41 thf(zip_derived_cl468, plain, 90.82/12.41 (![X2 : produc1501160679le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member214075476le_alt @ X2))) @ 90.82/12.41 ((('#C') @ ('#I') @ X2))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl31])). 90.82/12.41 thf(zip_derived_cl469, plain, 90.82/12.41 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 90.82/12.41 (((member214075476le_alt @ X2 @ X4) <=> (X4 @ X2)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl468])). 90.82/12.41 thf(zip_derived_cl470, plain, 90.82/12.41 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 90.82/12.41 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl469])). 90.82/12.41 thf(fact_270_mem__def, axiom, 90.82/12.41 (![X_66:( produc1501160679le_alt > $o ), 90.82/12.41 A_12:( ( produc1501160679le_alt > $o ) > $o )]: 90.82/12.41 ( ( A_12 @ X_66 ) <=> ( member377231867_alt_o @ X_66 @ A_12 ) ))). 90.82/12.41 thf(zip_derived_cl294, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : produc1501160679le_alt > $o]: 90.82/12.41 (((!!) @ (^[Y1 : (produc1501160679le_alt > $o) > $o]: 90.82/12.41 (((Y1 @ Y0) <=> (member377231867_alt_o @ Y0 @ 90.82/12.41 Y1)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_270_mem__def])). 90.82/12.41 thf(zip_derived_cl295, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 ((('#C') @ ('#I'))))))) @ 90.82/12.41 member377231867_alt_o))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl294])). 90.82/12.41 thf(zip_derived_cl497, plain, 90.82/12.41 (![X2 : produc1501160679le_alt > $o]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 90.82/12.41 (member377231867_alt_o @ X2)))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl295])). 90.82/12.41 thf(zip_derived_cl498, plain, 90.82/12.41 (![X2 : produc1501160679le_alt > $o, 90.82/12.41 X4 : (produc1501160679le_alt > $o) > $o]: 90.82/12.41 (((X4 @ X2) <=> (member377231867_alt_o @ X2 @ X4)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl497])). 90.82/12.41 thf(zip_derived_cl499, plain, 90.82/12.41 (![X2 : produc1501160679le_alt > $o, 90.82/12.41 X4 : (produc1501160679le_alt > $o) > $o]: 90.82/12.41 ((X4 @ X2) = (member377231867_alt_o @ X2 @ X4))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl498])). 90.82/12.41 thf(conj_0, conjecture, 90.82/12.41 (![I:arrow_1429601828e_indi]: 90.82/12.41 ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) <=> 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ a @ c ) @ 90.82/12.41 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ))). 90.82/12.41 thf(zf_stmt_0, negated_conjecture, 90.82/12.41 (~( ![I:arrow_1429601828e_indi]: 90.82/12.41 ( ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) <=> 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ a @ c ) @ 90.82/12.41 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ) )), 90.82/12.41 inference('cnf.neg', [status(esa)], [conj_0])). 90.82/12.41 thf(zip_derived_cl343, plain, 90.82/12.41 (~ (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 90.82/12.41 (((member214075476le_alt @ 90.82/12.41 (produc1347929815le_alt @ a @ b) @ (p @ Y0)) <=> 90.82/12.41 (member214075476le_alt @ 90.82/12.41 (produc1347929815le_alt @ a @ c) @ 90.82/12.41 (arrow_2098199487_below @ (p @ Y0) @ c @ b)))))))), 90.82/12.41 inference('cnf', [status(esa)], [zf_stmt_0])). 90.82/12.41 thf(zip_derived_cl344, plain, 90.82/12.41 (~ (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 90.82/12.41 ((('#B') @ (member214075476le_alt @ 90.82/12.41 (produc1347929815le_alt @ a @ b)) @ 90.82/12.41 p)))) @ 90.82/12.41 ((('#B') @ (member214075476le_alt @ 90.82/12.41 (produc1347929815le_alt @ a @ c)) @ 90.82/12.41 ((('#C') @ ((('#C') @ ((('#B') @ arrow_2098199487_below @ 90.82/12.41 p)) @ 90.82/12.41 c)) @ 90.82/12.41 b))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl343])). 90.82/12.41 thf(zip_derived_cl405, plain, 90.82/12.41 (~ (((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 90.82/12.41 (p @ '#sk6')) <=> (member214075476le_alt @ 90.82/12.41 (produc1347929815le_alt @ a @ c) @ 90.82/12.41 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b))))), 90.82/12.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl344])). 90.82/12.41 thf(zip_derived_cl406, plain, 90.82/12.41 (((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 90.82/12.41 (p @ '#sk6')) 90.82/12.41 != (member214075476le_alt @ (produc1347929815le_alt @ a @ c) @ 90.82/12.41 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl405])). 90.82/12.41 thf(zip_derived_cl470, plain, 90.82/12.41 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 90.82/12.41 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl469])). 90.82/12.41 thf(zip_derived_cl470, plain, 90.82/12.41 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 90.82/12.41 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl469])). 90.82/12.41 thf(zip_derived_cl471, plain, 90.82/12.41 (((p @ '#sk6' @ (produc1347929815le_alt @ a @ b)) 90.82/12.41 != (arrow_2098199487_below @ (p @ '#sk6') @ c @ b @ 90.82/12.41 (produc1347929815le_alt @ a @ c)))), 90.82/12.41 inference('demod', [status(thm)], 90.82/12.41 [zip_derived_cl406, zip_derived_cl470, zip_derived_cl470])). 90.82/12.41 thf(fact_43_not__Cons__self, axiom, 90.82/12.41 (![Xs_126:list_A2115238852le_alt,X_73:arrow_475358991le_alt]: 90.82/12.41 ( ( Xs_126 ) != ( cons_A228743023le_alt @ X_73 @ Xs_126 ) ))). 90.82/12.41 thf(zip_derived_cl149, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.82/12.41 (((Y0) != (cons_A228743023le_alt @ Y1 @ Y0)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_43_not__Cons__self])). 90.82/12.41 thf(zip_derived_cl150, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#B') @ (!=))) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl149])). 90.82/12.41 thf(zip_derived_cl427, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ X2))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl150])). 90.82/12.41 thf(zip_derived_cl428, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.82/12.41 (((X2) != (cons_A228743023le_alt @ X4 @ X2)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl427])). 90.82/12.41 thf(zip_derived_cl429, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.82/12.41 ((X2) != (cons_A228743023le_alt @ X4 @ X2))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl428])). 90.82/12.41 thf(fact_376_Nil__is__append__conv, axiom, 90.82/12.41 (![Xs_97:list_A2115238852le_alt,Ys_44:list_A2115238852le_alt]: 90.82/12.41 ( ( ( ( Ys_44 ) = ( nil_Ar1286194111le_alt ) ) & 90.82/12.41 ( ( Xs_97 ) = ( nil_Ar1286194111le_alt ) ) ) <=> 90.82/12.41 ( ( nil_Ar1286194111le_alt ) = ( append179082452le_alt @ Xs_97 @ Ys_44 ) ) ))). 90.82/12.41 thf(zip_derived_cl313, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((((((Y1) = (nil_Ar1286194111le_alt))) & 90.82/12.41 (((Y0) = (nil_Ar1286194111le_alt))))) <=> 90.82/12.41 (((nil_Ar1286194111le_alt) = 90.82/12.41 (append179082452le_alt @ Y0 @ Y1)))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_376_Nil__is__append__conv])). 90.82/12.41 thf(zip_derived_cl314, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 ((('#B') @ ((('#C') @ ((('#B') @ (&) @ 90.82/12.41 ((('#C') @ (=) @ 90.82/12.41 nil_Ar1286194111le_alt)))))) @ 90.82/12.41 ((('#C') @ (=) @ nil_Ar1286194111le_alt)))))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 90.82/12.41 (nil_Ar1286194111le_alt))))) @ 90.82/12.41 append179082452le_alt))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl313])). 90.82/12.41 thf(zip_derived_cl601, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 90.82/12.41 ((('#C') @ ((('#B') @ (&) @ 90.82/12.41 ((('#C') @ (=) @ 90.82/12.41 nil_Ar1286194111le_alt)))) @ 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt))))))) @ 90.82/12.41 ((('#B') @ (((list_A2115238852le_alt) = 90.82/12.41 (nil_Ar1286194111le_alt))) @ 90.82/12.41 (append179082452le_alt @ X2)))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl314])). 90.82/12.41 thf(zip_derived_cl602, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((((((X4) = (nil_Ar1286194111le_alt))) & 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt))))) <=> 90.82/12.41 (((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4)))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl601])). 90.82/12.41 thf(zip_derived_cl603, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((((((X4) = (nil_Ar1286194111le_alt))) & 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt))))) 90.82/12.41 = (((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4))))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl602])). 90.82/12.41 thf(fact_496_rev__eq__Cons__iff, axiom, 90.82/12.41 (![Xs_25:list_A2115238852le_alt,Y_3:arrow_475358991le_alt, 90.82/12.41 Ys_7:list_A2115238852le_alt]: 90.82/12.41 ( ( ( rev_Ar1106406943le_alt @ Xs_25 ) = 90.82/12.41 ( cons_A228743023le_alt @ Y_3 @ Ys_7 ) ) <=> 90.82/12.41 ( ( Xs_25 ) = 90.82/12.41 ( append179082452le_alt @ 90.82/12.41 ( rev_Ar1106406943le_alt @ Ys_7 ) @ 90.82/12.41 ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) ))). 90.82/12.41 thf(zip_derived_cl80, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 90.82/12.41 (((((rev_Ar1106406943le_alt @ Y0) = 90.82/12.41 (cons_A228743023le_alt @ Y1 @ 90.82/12.41 Y2))) <=> 90.82/12.41 (((Y0) = 90.82/12.41 (append179082452le_alt @ 90.82/12.41 (rev_Ar1106406943le_alt @ Y2) @ 90.82/12.41 (cons_A228743023le_alt @ Y1 @ 90.82/12.41 nil_Ar1286194111le_alt)))))))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_496_rev__eq__Cons__iff])). 90.82/12.41 thf(zip_derived_cl81, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.82/12.41 ((('#B') @ ('#B') @ 90.82/12.41 ((('#B') @ (=) @ 90.82/12.41 rev_Ar1106406943le_alt)))))) @ 90.82/12.41 cons_A228743023le_alt)))))))) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ ((('#B') @ ('#B') @ (=))))) @ 90.82/12.41 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 90.82/12.41 rev_Ar1106406943le_alt)))) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ 90.82/12.41 nil_Ar1286194111le_alt))))))))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl80])). 90.82/12.41 thf(zip_derived_cl817, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 90.82/12.41 (rev_Ar1106406943le_alt @ 90.82/12.41 X2))))) @ 90.82/12.41 cons_A228743023le_alt)))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = (X2))))) @ 90.82/12.41 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 90.82/12.41 rev_Ar1106406943le_alt)))) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ 90.82/12.41 nil_Ar1286194111le_alt))))))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl81])). 90.82/12.41 thf(zip_derived_cl818, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 90.82/12.41 ((('#B') @ (((list_A2115238852le_alt) = 90.82/12.41 (rev_Ar1106406943le_alt @ X2))) @ 90.82/12.41 (cons_A228743023le_alt @ X4))))) @ 90.82/12.41 ((('#B') @ (((list_A2115238852le_alt) = (X2))) @ 90.82/12.41 ((('#C') @ ((('#B') @ append179082452le_alt @ 90.82/12.41 rev_Ar1106406943le_alt)) @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl817])). 90.82/12.41 thf(zip_derived_cl819, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 90.82/12.41 X6 : list_A2115238852le_alt]: 90.82/12.41 (((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) <=> 90.82/12.41 (((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl818])). 90.82/12.41 thf(zip_derived_cl820, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 90.82/12.41 X6 : list_A2115238852le_alt]: 90.82/12.41 ((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) 90.82/12.41 = (((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl819])). 90.82/12.41 thf(fact_495_rev_Osimps_I2_J, axiom, 90.82/12.41 (![X_17:arrow_475358991le_alt,Xs_26:list_A2115238852le_alt]: 90.82/12.41 ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_17 @ Xs_26 ) ) = 90.82/12.41 ( append179082452le_alt @ 90.82/12.41 ( rev_Ar1106406943le_alt @ Xs_26 ) @ 90.82/12.41 ( cons_A228743023le_alt @ X_17 @ nil_Ar1286194111le_alt ) ) ))). 90.82/12.41 thf(zip_derived_cl84, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((rev_Ar1106406943le_alt @ 90.82/12.41 (cons_A228743023le_alt @ Y0 @ Y1)) = 90.82/12.41 (append179082452le_alt @ 90.82/12.41 (rev_Ar1106406943le_alt @ Y1) @ 90.82/12.41 (cons_A228743023le_alt @ Y0 @ 90.82/12.41 nil_Ar1286194111le_alt))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_495_rev_Osimps_I2_J])). 90.82/12.41 thf(zip_derived_cl85, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.82/12.41 ((('#B') @ ((('#B') @ rev_Ar1106406943le_alt)) @ 90.82/12.41 cons_A228743023le_alt)))))) @ 90.82/12.41 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 90.82/12.41 rev_Ar1106406943le_alt)))) @ 90.82/12.41 ((('#C') @ cons_A228743023le_alt @ 90.82/12.41 nil_Ar1286194111le_alt))))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl84])). 90.82/12.41 thf(zip_derived_cl584, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 90.82/12.41 ((('#B') @ rev_Ar1106406943le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X2))))) @ 90.82/12.41 ((('#C') @ ((('#B') @ append179082452le_alt @ 90.82/12.41 rev_Ar1106406943le_alt)) @ 90.82/12.41 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 90.82/12.41 thf(zip_derived_cl585, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = 90.82/12.41 (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 90.82/12.41 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl584])). 90.82/12.41 thf(zip_derived_cl586, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 90.82/12.41 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 90.82/12.41 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl585])). 90.82/12.41 thf(zip_derived_cl821, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 90.82/12.41 X6 : list_A2115238852le_alt]: 90.82/12.41 ((((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6))) 90.82/12.41 = (((X2) = (rev_Ar1106406943le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X4 @ X6)))))), 90.82/12.41 inference('demod', [status(thm)], [zip_derived_cl820, zip_derived_cl586])). 90.82/12.41 thf(fact_79_list_Oexhaust, axiom, 90.82/12.41 (![Y_26:list_A2115238852le_alt]: 90.82/12.41 ( ( ( Y_26 ) != ( nil_Ar1286194111le_alt ) ) => 90.82/12.41 ( ~( ![A:arrow_475358991le_alt,List:list_A2115238852le_alt]: 90.82/12.41 ( ( Y_26 ) != ( cons_A228743023le_alt @ A @ List ) ) ) ) ))). 90.82/12.41 thf(zip_derived_cl215, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((((Y0) != (nil_Ar1286194111le_alt))) => 90.82/12.41 (((~) @ (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 90.82/12.41 (((Y0) != 90.82/12.41 (cons_A228743023le_alt @ 90.82/12.41 Y1 @ Y2))))))))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_79_list_Oexhaust])). 90.82/12.41 thf(zip_derived_cl216, plain, 90.82/12.41 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.82/12.41 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 90.82/12.41 ((('#B') @ (~) @ 90.82/12.41 ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.82/12.41 ((('#B') @ ('#B') @ (!=))))) @ 90.82/12.41 cons_A228743023le_alt))))))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl215])). 90.82/12.41 thf(zip_derived_cl595, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((((X2) != (nil_Ar1286194111le_alt))) => 90.82/12.41 (((~) @ (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 90.82/12.41 (X2))))) @ 90.82/12.41 cons_A228743023le_alt))))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl216])). 90.82/12.41 thf(zip_derived_cl596, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (~ (((X2) != (nil_Ar1286194111le_alt))) 90.82/12.41 | ~ (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 90.82/12.41 (X2))))) @ 90.82/12.41 cons_A228743023le_alt)))))))), 90.82/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl595])). 90.82/12.41 thf(zip_derived_cl597, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt)) 90.82/12.41 | ~ (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 90.82/12.41 (X2))))) @ 90.82/12.41 cons_A228743023le_alt)))))))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl596])). 90.82/12.41 thf(zip_derived_cl598, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (~ (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 90.82/12.41 (cons_A228743023le_alt @ ('#sk14' @ X2)))))) 90.82/12.41 | ((X2) = (nil_Ar1286194111le_alt)))), 90.82/12.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl597])). 90.82/12.41 thf(zip_derived_cl599, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (~ (((X2) != (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2)))) 90.82/12.41 | ((X2) = (nil_Ar1286194111le_alt)))), 90.82/12.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl598])). 90.82/12.41 thf(zip_derived_cl600, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((X2) = (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2))) 90.82/12.41 | ((X2) = (nil_Ar1286194111le_alt)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl599])). 90.82/12.41 thf(fact_572_last__in__set, axiom, 90.82/12.41 (![As:list_A2115238852le_alt]: 90.82/12.41 ( ( ( As ) != ( nil_Ar1286194111le_alt ) ) => 90.82/12.41 ( member84363362le_alt @ 90.82/12.41 ( last_A1217315288le_alt @ As ) @ ( set_Ar577454304le_alt @ As ) ) ))). 90.82/12.41 thf(zip_derived_cl183, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.82/12.41 (((((Y0) != (nil_Ar1286194111le_alt))) => 90.82/12.41 (member84363362le_alt @ (last_A1217315288le_alt @ Y0) @ 90.82/12.41 (set_Ar577454304le_alt @ Y0)))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_572_last__in__set])). 90.82/12.41 thf(zip_derived_cl184, plain, 90.82/12.41 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.82/12.41 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 90.82/12.41 ((('#S') @ ((('#B') @ member84363362le_alt @ 90.82/12.41 last_A1217315288le_alt)) @ 90.82/12.41 set_Ar577454304le_alt))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl183])). 90.82/12.41 thf(zip_derived_cl419, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 90.82/12.41 (last_A1217315288le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl184])). 90.82/12.41 thf(zip_derived_cl420, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (~ (((X2) != (nil_Ar1286194111le_alt))) 90.82/12.41 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 90.82/12.41 (set_Ar577454304le_alt @ X2)))), 90.82/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl419])). 90.82/12.41 thf(zip_derived_cl421, plain, 90.82/12.41 (![X2 : list_A2115238852le_alt]: 90.82/12.41 (((X2) = (nil_Ar1286194111le_alt)) 90.82/12.41 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 90.82/12.41 (set_Ar577454304le_alt @ X2)))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl420])). 90.82/12.41 thf(fact_264_mem__def, axiom, 90.82/12.41 (![X_66:arrow_475358991le_alt,A_12:( arrow_475358991le_alt > $o )]: 90.82/12.41 ( ( A_12 @ X_66 ) <=> ( member84363362le_alt @ X_66 @ A_12 ) ))). 90.82/12.41 thf(zip_derived_cl315, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt > $o]: 90.82/12.41 (((Y1 @ Y0) <=> (member84363362le_alt @ Y0 @ 90.82/12.41 Y1)))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_264_mem__def])). 90.82/12.41 thf(zip_derived_cl316, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 ((('#C') @ ('#I'))))))) @ 90.82/12.41 member84363362le_alt))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl315])). 90.82/12.41 thf(zip_derived_cl500, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 90.82/12.41 (member84363362le_alt @ X2)))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl316])). 90.82/12.41 thf(zip_derived_cl501, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 90.82/12.41 (((X4 @ X2) <=> (member84363362le_alt @ X2 @ X4)))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl500])). 90.82/12.41 thf(zip_derived_cl502, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 90.82/12.41 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl501])). 90.82/12.41 thf(fact_556_distinct_Osimps_I2_J, axiom, 90.82/12.41 (![X_8:arrow_475358991le_alt,Xs_13:list_A2115238852le_alt]: 90.82/12.41 ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_13 ) ) <=> 90.82/12.41 ( ( distin236324274le_alt @ Xs_13 ) & 90.82/12.41 ( ~( member84363362le_alt @ X_8 @ ( set_Ar577454304le_alt @ Xs_13 ) ) ) ) ))). 90.82/12.41 thf(zip_derived_cl223, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.82/12.41 (((distin236324274le_alt @ 90.82/12.41 (cons_A228743023le_alt @ Y0 @ Y1)) <=> 90.82/12.41 (((distin236324274le_alt @ Y1) & 90.82/12.41 (((~) @ (member84363362le_alt @ Y0 @ 90.82/12.41 (set_Ar577454304le_alt @ Y1))))))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_556_distinct_Osimps_I2_J])). 90.82/12.41 thf(zip_derived_cl224, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.82/12.41 ((('#B') @ ((('#B') @ distin236324274le_alt)) @ 90.82/12.41 cons_A228743023le_alt)))))) @ 90.82/12.41 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 90.82/12.41 distin236324274le_alt)))) @ 90.82/12.41 ((('#B') @ ((('#B') @ (~))) @ 90.82/12.41 ((('#C') @ ((('#B') @ ('#B') @ member84363362le_alt)) @ 90.82/12.41 set_Ar577454304le_alt))))))))))))), 90.82/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl223])). 90.82/12.41 thf(zip_derived_cl638, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 90.82/12.41 ((('#B') @ distin236324274le_alt @ 90.82/12.41 (cons_A228743023le_alt @ X2))))) @ 90.82/12.41 ((('#S') @ ((('#B') @ (&) @ distin236324274le_alt)) @ 90.82/12.41 ((('#B') @ (~) @ 90.82/12.41 ((('#B') @ (member84363362le_alt @ X2) @ 90.82/12.41 set_Ar577454304le_alt))))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl224])). 90.82/12.41 thf(zip_derived_cl639, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 (((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) <=> 90.82/12.41 (((distin236324274le_alt @ X4) & 90.82/12.41 (((~) @ (member84363362le_alt @ X2 @ (set_Ar577454304le_alt @ X4))))))))), 90.82/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl638])). 90.82/12.41 thf(zip_derived_cl640, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 90.82/12.41 = (((distin236324274le_alt @ X4) & 90.82/12.41 (((~) @ (member84363362le_alt @ X2 @ 90.82/12.41 (set_Ar577454304le_alt @ X4)))))))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl639])). 90.82/12.41 thf(zip_derived_cl502, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 90.82/12.41 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 90.82/12.41 inference('simplify nested equalities', [status(thm)], 90.82/12.41 [zip_derived_cl501])). 90.82/12.41 thf(zip_derived_cl641, plain, 90.82/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.82/12.41 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 90.82/12.41 = (((distin236324274le_alt @ X4) & 90.82/12.41 (((~) @ (set_Ar577454304le_alt @ X4 @ X2))))))), 90.82/12.41 inference('demod', [status(thm)], [zip_derived_cl640, zip_derived_cl502])). 90.82/12.41 thf(fact_12_in__below, axiom, 90.82/12.41 (![X:arrow_475358991le_alt,Y:arrow_475358991le_alt, 90.82/12.41 L_1:( produc1501160679le_alt > $o ),A_24:arrow_475358991le_alt, 90.82/12.41 B_17:arrow_475358991le_alt]: 90.82/12.41 ( ( ( A_24 ) != ( B_17 ) ) => 90.82/12.41 ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin ) => 90.82/12.41 ( ( ( ( ( Y ) != ( A_24 ) ) => 90.82/12.41 ( ( ( ( X ) != ( A_24 ) ) => 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) & 90.82/12.41 ( ( ( X ) = ( A_24 ) ) => 90.82/12.41 ( ( ( Y ) = ( B_17 ) ) | 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ B_17 @ Y ) @ L_1 ) ) ) ) ) & 90.82/12.41 ( ( ( Y ) = ( A_24 ) ) => 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ X @ B_17 ) @ L_1 ) ) & 90.82/12.41 ( ( X ) != ( Y ) ) ) <=> 90.82/12.41 ( member214075476le_alt @ 90.82/12.41 ( produc1347929815le_alt @ X @ Y ) @ 90.82/12.41 ( arrow_2098199487_below @ L_1 @ A_24 @ B_17 ) ) ) ) ))). 90.82/12.41 thf(zip_derived_cl46, plain, 90.82/12.41 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y2 : produc1501160679le_alt > $o]: 90.82/12.41 (((!!) @ (^[Y3 : arrow_475358991le_alt]: 90.82/12.41 (((!!) @ (^[Y4 : arrow_475358991le_alt]: 90.82/12.41 (((( 90.82/12.41 (Y3) != 90.82/12.41 (Y4))) => 90.82/12.41 (( 90.82/12.41 (member377231867_alt_o @ 90.82/12.41 Y2 @ 90.82/12.41 arrow_823908191le_Lin) => 90.82/12.41 (( 90.82/12.41 (( 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 (( 90.82/12.41 (Y1) != 90.82/12.41 (Y3))) => 90.82/12.41 (( 90.82/12.41 (( 90.82/12.41 (( 90.82/12.41 (Y0) != 90.82/12.41 (Y3))) => 90.82/12.41 (member214075476le_alt @ 90.82/12.41 ( 90.82/12.41 produc1347929815le_alt @ 90.82/12.41 Y0 @ Y1) @ 90.82/12.41 Y2))) & 90.82/12.41 (( 90.82/12.41 (( 90.82/12.41 (Y0) = 90.82/12.41 (Y3))) => 90.82/12.41 (( 90.82/12.41 (( 90.82/12.41 (Y1) = 90.82/12.41 (Y4))) | 90.82/12.41 (member214075476le_alt @ 90.82/12.41 ( 90.82/12.41 produc1347929815le_alt @ 90.82/12.41 Y4 @ Y1) @ 90.82/12.41 Y2))))))))) & 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 (( 90.82/12.41 (Y1) = 90.82/12.41 (Y3))) => 90.82/12.41 (member214075476le_alt @ 90.82/12.41 ( 90.82/12.41 produc1347929815le_alt @ 90.82/12.41 Y0 @ Y4) @ 90.82/12.41 Y2))) & 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 (Y0) != 90.82/12.41 (Y1))))) <=> 90.82/12.41 (member214075476le_alt @ 90.82/12.41 ( 90.82/12.41 produc1347929815le_alt @ 90.82/12.41 Y0 @ Y1) @ 90.82/12.41 ( 90.82/12.41 arrow_2098199487_below @ 90.82/12.41 Y2 @ 90.82/12.41 Y3 @ Y4)))))))))))))))))))))))), 90.82/12.41 inference('cnf', [status(esa)], [fact_12_in__below])). 90.82/12.41 thf(zip_derived_cl47, plain, 90.82/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.82/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ (( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 =>))) @ 90.82/12.41 ( 90.82/12.41 !=))))))))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ((('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ((('#B') @ ( 90.82/12.41 =>) @ 90.82/12.41 ((('#C') @ member377231867_alt_o @ 90.82/12.41 arrow_823908191le_Lin)))))))))))) @ 90.82/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.82/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.82/12.41 '#S'))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))))))) @ 90.82/12.41 ((('#B') @ ((('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 (('#B') @ (<=>))))))))) @ 90.82/12.41 ((('#S') @ ((('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ((('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 '#C'))) @ 90.82/12.41 ((('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 '#C'))))) @ 90.82/12.41 ((('#B') @ ( 90.82/12.41 (('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#C'))))))) @ 90.82/12.41 (( 90.82/12.41 ('#S') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 &))))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#S') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B'))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 =>))) @ 90.82/12.41 ( 90.82/12.41 !=))))))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#S') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S'))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B'))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 &))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#S') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#C') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 =>))) @ 90.82/12.41 ( 90.82/12.41 !=))))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ member214075476le_alt)) @ 90.82/12.41 produc1347929815le_alt)))))))))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#C') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#C') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B'))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 =>))) @ 90.82/12.41 ( 90.82/12.41 =))))))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#S') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#B') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 '#S') @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.82/12.41 |))) @ 90.82/12.41 ( 90.82/12.41 =))))))) @ 90.82/12.41 ( 90.82/12.41 ( 90.82/12.41 ('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt)) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ produc1347929815le_alt)))))))))))))))))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>))) @ 90.86/12.41 ( 90.86/12.41 =))))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt)) @ 90.86/12.41 produc1347929815le_alt)))))))))))))))) @ 90.86/12.41 (!=))))))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ member214075476le_alt)) @ 90.86/12.41 produc1347929815le_alt)))))))))) @ 90.86/12.41 arrow_2098199487_below))))))))))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl46])). 90.86/12.41 thf(zip_derived_cl723, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ (=>))) @ 90.86/12.41 (!=))))))))) @ 90.86/12.41 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ (=>) @ 90.86/12.41 ((('#C') @ member377231867_alt_o @ 90.86/12.41 arrow_823908191le_Lin)))))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.86/12.41 '#S'))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 <=>))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ('#C'))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#C'))))) @ 90.86/12.41 ((('#S') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S'))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 &))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>))) @ 90.86/12.41 ( 90.86/12.41 !=))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B'))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 &))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) != 90.86/12.41 (X2))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 produc1347929815le_alt @ 90.86/12.41 X2))))))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X2))))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 |))) @ 90.86/12.41 ( 90.86/12.41 =))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt)) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ produc1347929815le_alt)))))))))))))))))))))) @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#C') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>))) @ 90.86/12.41 ( 90.86/12.41 =))))))))) @ 90.86/12.41 (( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 produc1347929815le_alt @ 90.86/12.41 X2))))))))))))))) @ 90.86/12.41 (((arrow_475358991le_alt) != 90.86/12.41 (X2))))))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2))))))))) @ 90.86/12.41 arrow_2098199487_below))))))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl47])). 90.86/12.41 thf(zip_derived_cl724, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 (!=))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ (=>) @ 90.86/12.41 ((('#C') @ member377231867_alt_o @ 90.86/12.41 arrow_823908191le_Lin)))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.86/12.41 <=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ ( 90.86/12.41 '#C'))) @ 90.86/12.41 ((('#S') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#S'))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 &))))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#S') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) != 90.86/12.41 (X4))))))))) @ 90.86/12.41 ((('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B'))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 &))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) != 90.86/12.41 (X2))))))) @ 90.86/12.41 ( 90.86/12.41 member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 produc1347929815le_alt @ 90.86/12.41 X2 @ X4)))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X2))))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 |) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X4))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ produc1347929815le_alt @ 90.86/12.41 X4)))))))))))))))))))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#C') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 (((arrow_475358991le_alt) = 90.86/12.41 (X4))))))))) @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 (('#B') @ member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ 90.86/12.41 X2))))))))))))) @ 90.86/12.41 (((X2) != (X4))))))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ 90.86/12.41 X2 @ X4)))))) @ 90.86/12.41 arrow_2098199487_below))))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl723])). 90.86/12.41 thf(zip_derived_cl725, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ (!=))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (((=>) @ (member377231867_alt_o @ 90.86/12.41 X6 @ 90.86/12.41 arrow_823908191le_Lin))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#S') @ ((('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 &))) @ 90.86/12.41 ((('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) != 90.86/12.41 (X4))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 &) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) != 90.86/12.41 (X2))))) @ 90.86/12.41 ( 90.86/12.41 member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 produc1347929815le_alt @ 90.86/12.41 X2 @ X4) @ 90.86/12.41 X6))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X2))))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#S') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 |) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X4))))) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ produc1347929815le_alt @ 90.86/12.41 X4)))) @ 90.86/12.41 X6)))))))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 =>) @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X4))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 produc1347929815le_alt @ 90.86/12.41 X2))) @ 90.86/12.41 X6)))))))) @ 90.86/12.41 (((X2) != (X4))))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ 90.86/12.41 X2 @ X4)))) @ 90.86/12.41 (arrow_2098199487_below @ X6)))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl724])). 90.86/12.41 thf(zip_derived_cl726, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 (((arrow_475358991le_alt) != (X8))))) @ 90.86/12.41 ((('#B') @ (((=>) @ (member377231867_alt_o @ X6 @ 90.86/12.41 arrow_823908191le_Lin))) @ 90.86/12.41 ((('#S') @ ((('#B') @ (<=>) @ 90.86/12.41 ((('#C') @ ((('#S') @ ((('#B') @ (&) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 ((=>) @ ( 90.86/12.41 ((X4) != (X8))))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 ((&) @ ( 90.86/12.41 ((((X2) != 90.86/12.41 (X8))) => 90.86/12.41 (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ 90.86/12.41 X2 @ X4) @ 90.86/12.41 X6))))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 ((=>) @ ( 90.86/12.41 ((X2) = (X8))))) @ 90.86/12.41 ((('#S') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 |) @ 90.86/12.41 (( 90.86/12.41 (arrow_475358991le_alt) = 90.86/12.41 (X4))))) @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ member214075476le_alt @ 90.86/12.41 ( 90.86/12.41 ( 90.86/12.41 ('#C') @ produc1347929815le_alt @ 90.86/12.41 X4)))) @ 90.86/12.41 X6)))))))))))) @ 90.86/12.41 ((('#B') @ (((=>) @ (( 90.86/12.41 (X4) = 90.86/12.41 (X8))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ 90.86/12.41 X2))) @ 90.86/12.41 X6)))))) @ 90.86/12.41 (((X2) != (X4))))))) @ 90.86/12.41 ((('#B') @ (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4)) @ 90.86/12.41 (arrow_2098199487_below @ X6 @ X8)))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl725])). 90.86/12.41 thf(zip_derived_cl727, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (((((X8) != (X10))) => 90.86/12.41 (((member377231867_alt_o @ X6 @ arrow_823908191le_Lin) => 90.86/12.41 (((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) <=> 90.86/12.41 (member214075476le_alt @ (produc1347929815le_alt @ X2 @ X4) @ 90.86/12.41 (arrow_2098199487_below @ X6 @ X8 @ X10))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl726])). 90.86/12.41 thf(zip_derived_cl499, plain, 90.86/12.41 (![X2 : produc1501160679le_alt > $o, 90.86/12.41 X4 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 ((X4 @ X2) = (member377231867_alt_o @ X2 @ X4))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl498])). 90.86/12.41 thf(zip_derived_cl470, plain, 90.86/12.41 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 90.86/12.41 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl469])). 90.86/12.41 thf(zip_derived_cl728, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (((((X8) != (X10))) => 90.86/12.41 (((arrow_823908191le_Lin @ X6) => 90.86/12.41 (((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) <=> 90.86/12.41 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4))))))))), 90.86/12.41 inference('demod', [status(thm)], 90.86/12.41 [zip_derived_cl727, zip_derived_cl499, zip_derived_cl470])). 90.86/12.41 thf(zip_derived_cl729, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (~ (((X8) != (X10))) 90.86/12.41 | (((arrow_823908191le_Lin @ X6) => 90.86/12.41 (((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) <=> 90.86/12.41 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4)))))))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl728])). 90.86/12.41 thf(zip_derived_cl730, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (((X8) = (X10)) 90.86/12.41 | (((arrow_823908191le_Lin @ X6) => 90.86/12.41 (((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) <=> 90.86/12.41 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4)))))))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl729])). 90.86/12.41 thf(zip_derived_cl731, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (~ (arrow_823908191le_Lin @ X6) 90.86/12.41 | (((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) <=> 90.86/12.41 (arrow_2098199487_below @ X6 @ X8 @ X10 @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4)))) 90.86/12.41 | ((X8) = (X10)))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl730])). 90.86/12.41 thf(zip_derived_cl732, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 90.86/12.41 X10 : arrow_475358991le_alt]: 90.86/12.41 (~ (arrow_823908191le_Lin @ X6) 90.86/12.41 | ((((((((X4) != (X8))) => 90.86/12.41 (((((((X2) != (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4) @ X6))) & 90.86/12.41 (((((X2) = (X8))) => 90.86/12.41 (((((X4) = (X10))) | (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X10 @ X4) @ X6))))))))) & 90.86/12.41 (((((X4) = (X8))) => (member214075476le_alt @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 90.86/12.41 (((X2) != (X4))))) 90.86/12.41 = (arrow_2098199487_below @ X6 @ X8 @ X10 @ 90.86/12.41 (produc1347929815le_alt @ X2 @ X4))) 90.86/12.41 | ((X8) = (X10)))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl731])). 90.86/12.41 thf(zip_derived_cl586, plain, 90.86/12.41 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 90.86/12.41 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 90.86/12.41 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 90.86/12.41 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl585])). 90.86/12.41 thf(fact_372_append__assoc, axiom, 90.86/12.41 (![Xs_100:list_A2115238852le_alt,Ys_48:list_A2115238852le_alt, 90.86/12.41 Zs_5:list_A2115238852le_alt]: 90.86/12.41 ( ( append179082452le_alt @ 90.86/12.41 ( append179082452le_alt @ Xs_100 @ Ys_48 ) @ Zs_5 ) = 90.86/12.41 ( append179082452le_alt @ 90.86/12.41 Xs_100 @ ( append179082452le_alt @ Ys_48 @ Zs_5 ) ) ))). 90.86/12.41 thf(zip_derived_cl65, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 90.86/12.41 (((append179082452le_alt @ 90.86/12.41 (append179082452le_alt @ Y0 @ Y1) @ 90.86/12.41 Y2) = (append179082452le_alt @ 90.86/12.41 Y0 @ 90.86/12.41 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_372_append__assoc])). 90.86/12.41 thf(zip_derived_cl66, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 90.86/12.41 append179082452le_alt)))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ append179082452le_alt)))) @ 90.86/12.41 append179082452le_alt))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl65])). 90.86/12.41 thf(zip_derived_cl677, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.86/12.41 ((('#B') @ append179082452le_alt @ 90.86/12.41 (append179082452le_alt @ X2))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (append179082452le_alt @ X2))) @ 90.86/12.41 append179082452le_alt))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 90.86/12.41 thf(zip_derived_cl678, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 90.86/12.41 (append179082452le_alt @ 90.86/12.41 (append179082452le_alt @ X2 @ X4)))) @ 90.86/12.41 ((('#B') @ (append179082452le_alt @ X2) @ 90.86/12.41 (append179082452le_alt @ X4)))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl677])). 90.86/12.41 thf(zip_derived_cl679, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 90.86/12.41 X6 : list_A2115238852le_alt]: 90.86/12.41 (((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) = 90.86/12.41 (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl678])). 90.86/12.41 thf(zip_derived_cl680, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 90.86/12.41 X6 : list_A2115238852le_alt]: 90.86/12.41 ((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) 90.86/12.41 = (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl679])). 90.86/12.41 thf(fact_289_Prof__def, axiom, 90.86/12.41 (( arrow_734252939e_Prof ) = 90.86/12.41 ( pi_Arr1929480907_alt_o @ 90.86/12.41 top_to988227749indi_o @ 90.86/12.41 ( ^[Uu:arrow_1429601828e_indi]: ( arrow_823908191le_Lin ) ) ))). 90.86/12.41 thf(zip_derived_cl32, plain, 90.86/12.41 (((arrow_734252939e_Prof) 90.86/12.41 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 90.86/12.41 (^[Y0 : arrow_1429601828e_indi]: (arrow_823908191le_Lin))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_289_Prof__def])). 90.86/12.41 thf(zip_derived_cl33, plain, 90.86/12.41 (((arrow_734252939e_Prof) 90.86/12.41 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 90.86/12.41 ((('#K') @ arrow_823908191le_Lin))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl32])). 90.86/12.41 thf(zip_derived_cl9370, plain, 90.86/12.41 (((arrow_734252939e_Prof) 90.86/12.41 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 90.86/12.41 ('#ty_enc50' @ arrow_823908191le_Lin)))), 90.86/12.41 inference('remove_ty_args', [status(thm)], [zip_derived_cl33])). 90.86/12.41 thf(fact_114_funcset__mem, axiom, 90.86/12.41 (![X_71:arrow_1429601828e_indi, 90.86/12.41 F_13:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 90.86/12.41 A_18:( arrow_1429601828e_indi > $o ), 90.86/12.41 B_15:( ( produc1501160679le_alt > $o ) > $o )]: 90.86/12.41 ( ( member526088951_alt_o @ 90.86/12.41 F_13 @ 90.86/12.41 ( pi_Arr1929480907_alt_o @ 90.86/12.41 A_18 @ ( ^[Uu:arrow_1429601828e_indi]: ( B_15 ) ) ) ) => 90.86/12.41 ( ( member2052026769e_indi @ X_71 @ A_18 ) => 90.86/12.41 ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ))). 90.86/12.41 thf(zip_derived_cl155, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 90.86/12.41 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 90.86/12.41 produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((!!) @ (^[Y3 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ 90.86/12.41 Y1 @ 90.86/12.41 (pi_Arr1929480907_alt_o @ 90.86/12.41 Y2 @ 90.86/12.41 (^[Y4 : arrow_1429601828e_indi]: 90.86/12.41 (Y3)))) => 90.86/12.41 (((member2052026769e_indi @ 90.86/12.41 Y0 @ Y2) => 90.86/12.41 (member377231867_alt_o @ 90.86/12.41 (Y1 @ Y0) @ Y3)))))))))))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_114_funcset__mem])). 90.86/12.41 thf(zip_derived_cl156, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 90.86/12.41 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ( 90.86/12.41 (('#B') @ (=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 member526088951_alt_o)))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 pi_Arr1929480907_alt_o)) @ 90.86/12.41 ('#K'))))))))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 member2052026769e_indi)))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ member377231867_alt_o)) @ 90.86/12.41 ((('#C') @ ('#I')))))))))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl155])). 90.86/12.41 thf(zip_derived_cl925, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 member526088951_alt_o)))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 pi_Arr1929480907_alt_o)) @ 90.86/12.41 ('#K'))))))))))) @ 90.86/12.41 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ (=>) @ 90.86/12.41 (member2052026769e_indi @ X2))))))) @ 90.86/12.41 ((('#B') @ member377231867_alt_o @ 90.86/12.41 ((('#C') @ ('#I') @ X2))))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl156])). 90.86/12.41 thf(zip_derived_cl926, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (member526088951_alt_o @ 90.86/12.41 X4))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 pi_Arr1929480907_alt_o)) @ 90.86/12.41 ('#K'))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ (=>) @ 90.86/12.41 (member2052026769e_indi @ X2))))) @ 90.86/12.41 (member377231867_alt_o @ (X4 @ X2))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl925])). 90.86/12.41 thf(zip_derived_cl927, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#B') @ (member526088951_alt_o @ X4) @ 90.86/12.41 ((('#B') @ (pi_Arr1929480907_alt_o @ X6) @ 90.86/12.41 ('#K'))))))) @ 90.86/12.41 ((('#B') @ (((=>) @ (member2052026769e_indi @ X2 @ X6))) @ 90.86/12.41 (member377231867_alt_o @ (X4 @ X2))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl926])). 90.86/12.41 thf(zip_derived_cl928, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ X4 @ 90.86/12.41 (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)))) => 90.86/12.41 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 90.86/12.41 (X4 @ X2) @ X8)))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl927])). 90.86/12.41 thf(fact_269_mem__def, axiom, 90.86/12.41 (![X_66:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 90.86/12.41 A_12:( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )]: 90.86/12.41 ( ( member526088951_alt_o @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 90.86/12.41 thf(zip_derived_cl331, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ (^[Y1 : (arrow_1429601828e_indi > 90.86/12.41 produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ Y0 @ Y1) <=> (Y1 @ 90.86/12.41 Y0)))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_269_mem__def])). 90.86/12.41 thf(zip_derived_cl332, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.86/12.41 member526088951_alt_o)))) @ 90.86/12.41 ((('#C') @ ('#I')))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl331])). 90.86/12.41 thf(zip_derived_cl532, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member526088951_alt_o @ X2))) @ 90.86/12.41 ((('#C') @ ('#I') @ X2))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl332])). 90.86/12.41 thf(zip_derived_cl533, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ X2 @ X4) <=> (X4 @ X2)))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl532])). 90.86/12.41 thf(zip_derived_cl534, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 90.86/12.41 ((member526088951_alt_o @ X2 @ X4) = (X4 @ X2))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl533])). 90.86/12.41 thf(zip_derived_cl929, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) => 90.86/12.41 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 90.86/12.41 (X4 @ X2) @ X8)))))), 90.86/12.41 inference('demod', [status(thm)], [zip_derived_cl928, zip_derived_cl534])). 90.86/12.41 thf(zip_derived_cl930, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) 90.86/12.41 | (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 90.86/12.41 (X4 @ X2) @ X8))))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl929])). 90.86/12.41 thf(zip_derived_cl931, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (~ (member2052026769e_indi @ X2 @ X6) 90.86/12.41 | (member377231867_alt_o @ (X4 @ X2) @ X8) 90.86/12.41 | ~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl930])). 90.86/12.41 thf(zip_derived_cl9386, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (~ (member2052026769e_indi @ X2 @ X6) 90.86/12.41 | (member377231867_alt_o @ (X4 @ X2) @ X8) 90.86/12.41 | ~ (pi_Arr1929480907_alt_o @ X6 @ ('#ty_enc50' @ X8) @ X4))), 90.86/12.41 inference('remove_ty_args', [status(thm)], [zip_derived_cl931])). 90.86/12.41 thf(fact_365_snoc__eq__iff__butlast, axiom, 90.86/12.41 (![Xs_106:list_A2115238852le_alt,X_51:arrow_475358991le_alt, 90.86/12.41 Ys_54:list_A2115238852le_alt]: 90.86/12.41 ( ( ( ( last_A1217315288le_alt @ Ys_54 ) = ( X_51 ) ) & 90.86/12.41 ( ( butlas274947851le_alt @ Ys_54 ) = ( Xs_106 ) ) & 90.86/12.41 ( ( Ys_54 ) != ( nil_Ar1286194111le_alt ) ) ) <=> 90.86/12.41 ( ( append179082452le_alt @ 90.86/12.41 Xs_106 @ ( cons_A228743023le_alt @ X_51 @ nil_Ar1286194111le_alt ) ) = 90.86/12.41 ( Ys_54 ) ) ))). 90.86/12.41 thf(zip_derived_cl337, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 90.86/12.41 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 90.86/12.41 (((((((last_A1217315288le_alt @ 90.86/12.41 Y2) = (Y1))) & 90.86/12.41 (((butlas274947851le_alt @ 90.86/12.41 Y2) = (Y0))) & 90.86/12.41 (((Y2) != 90.86/12.41 (nil_Ar1286194111le_alt))))) <=> 90.86/12.41 (((append179082452le_alt @ Y0 @ 90.86/12.41 (cons_A228743023le_alt @ Y1 @ 90.86/12.41 nil_Ar1286194111le_alt)) = 90.86/12.41 (Y2))))))))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_365_snoc__eq__iff__butlast])). 90.86/12.41 thf(zip_derived_cl338, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#C') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 &))) @ 90.86/12.41 (( 90.86/12.41 ('#C') @ ( 90.86/12.41 ( 90.86/12.41 ('#B') @ ( 90.86/12.41 =) @ 90.86/12.41 last_A1217315288le_alt)))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 =) @ 90.86/12.41 butlas274947851le_alt)))))))))) @ 90.86/12.41 ((('#C') @ (!=) @ 90.86/12.41 nil_Ar1286194111le_alt)))))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (=))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ append179082452le_alt)) @ 90.86/12.41 ((('#C') @ cons_A228743023le_alt @ 90.86/12.41 nil_Ar1286194111le_alt))))))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl337])). 90.86/12.41 thf(zip_derived_cl844, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (<=>))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ (&))) @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 =) @ 90.86/12.41 last_A1217315288le_alt)))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 =) @ 90.86/12.41 butlas274947851le_alt)) @ 90.86/12.41 X2)))))) @ 90.86/12.41 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))))))) @ 90.86/12.41 ((('#B') @ (=) @ 90.86/12.41 ((('#B') @ (append179082452le_alt @ X2) @ 90.86/12.41 ((('#C') @ cons_A228743023le_alt @ 90.86/12.41 nil_Ar1286194111le_alt))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl338])). 90.86/12.41 thf(zip_derived_cl845, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 90.86/12.41 ((('#S') @ ((('#S') @ ((('#B') @ (&) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 =) @ 90.86/12.41 last_A1217315288le_alt)) @ 90.86/12.41 X4)))) @ 90.86/12.41 ((('#C') @ ((('#B') @ (=) @ 90.86/12.41 butlas274947851le_alt)) @ 90.86/12.41 X2)))) @ 90.86/12.41 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))))) @ 90.86/12.41 (((list_A2115238852le_alt) = (append179082452le_alt @ 90.86/12.41 X2 @ 90.86/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl844])). 90.86/12.41 thf(zip_derived_cl846, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : list_A2115238852le_alt]: 90.86/12.41 (((((((last_A1217315288le_alt @ X6) = (X4))) & 90.86/12.41 (((butlas274947851le_alt @ X6) = (X2))) & 90.86/12.41 (((X6) != (nil_Ar1286194111le_alt))))) <=> 90.86/12.41 (((append179082452le_alt @ X2 @ 90.86/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6)))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl845])). 90.86/12.41 thf(zip_derived_cl847, plain, 90.86/12.41 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 90.86/12.41 X6 : list_A2115238852le_alt]: 90.86/12.41 ((((((last_A1217315288le_alt @ X6) = (X4))) & 90.86/12.41 (((butlas274947851le_alt @ X6) = (X2))) & 90.86/12.41 (((X6) != (nil_Ar1286194111le_alt))))) 90.86/12.41 = (((append179082452le_alt @ X2 @ 90.86/12.41 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6))))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl846])). 90.86/12.41 thf(fact_324_iso__tuple__UNIV__I, axiom, 90.86/12.41 (![X_54:arrow_1429601828e_indi]: 90.86/12.41 ( member2052026769e_indi @ X_54 @ top_to988227749indi_o ))). 90.86/12.41 thf(zip_derived_cl181, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 90.86/12.41 (member2052026769e_indi @ Y0 @ top_to988227749indi_o))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_324_iso__tuple__UNIV__I])). 90.86/12.41 thf(zip_derived_cl182, plain, 90.86/12.41 ( (((!!) @ ((('#C') @ member2052026769e_indi @ top_to988227749indi_o))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl181])). 90.86/12.41 thf(zip_derived_cl366, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi]: 90.86/12.41 (member2052026769e_indi @ X2 @ top_to988227749indi_o)), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl182])). 90.86/12.41 thf(fact_0__096P_A_058_AProf_096, axiom, 90.86/12.41 (member526088951_alt_o @ p @ arrow_734252939e_Prof)). 90.86/12.41 thf(zip_derived_cl52, plain, 90.86/12.41 ( (member526088951_alt_o @ p @ arrow_734252939e_Prof)), 90.86/12.41 inference('cnf', [status(esa)], [fact_0__096P_A_058_AProf_096])). 90.86/12.41 thf(fact_184_Pi__I, axiom, 90.86/12.41 (![F_11:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 90.86/12.41 B_13:( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o ), 90.86/12.41 A_16:( arrow_1429601828e_indi > $o )]: 90.86/12.41 ( ( ![X_2:arrow_1429601828e_indi]: 90.86/12.41 ( ( member2052026769e_indi @ X_2 @ A_16 ) => 90.86/12.41 ( member377231867_alt_o @ ( F_11 @ X_2 ) @ ( B_13 @ X_2 ) ) ) ) => 90.86/12.41 ( member526088951_alt_o @ 90.86/12.41 F_11 @ ( pi_Arr1929480907_alt_o @ A_16 @ B_13 ) ) ))). 90.86/12.41 thf(zip_derived_cl61, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 90.86/12.41 (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((((!!) @ (^[Y3 : arrow_1429601828e_indi]: 90.86/12.41 (((member2052026769e_indi @ 90.86/12.41 Y3 @ Y2) => 90.86/12.41 (member377231867_alt_o @ 90.86/12.41 (Y0 @ Y3) @ 90.86/12.41 (Y1 @ Y3))))))) => 90.86/12.41 (member526088951_alt_o @ Y0 @ 90.86/12.41 (pi_Arr1929480907_alt_o @ Y2 @ Y1)))))))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_184_Pi__I])). 90.86/12.41 thf(zip_derived_cl62, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#C') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ( 90.86/12.41 =>))) @ 90.86/12.41 ((('#C') @ member2052026769e_indi)))))))))) @ 90.86/12.41 ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ member377231867_alt_o)))))))))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ member526088951_alt_o)))) @ 90.86/12.41 ((('#C') @ pi_Arr1929480907_alt_o))))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl61])). 90.86/12.41 thf(zip_derived_cl867, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#B') @ ((('#C') @ ((('#B') @ ( 90.86/12.41 '#S') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ (=>))) @ 90.86/12.41 ((('#C') @ member2052026769e_indi)))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ member377231867_alt_o @ 90.86/12.41 X2)))))))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (member526088951_alt_o @ X2))) @ 90.86/12.41 ((('#C') @ pi_Arr1929480907_alt_o))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 90.86/12.41 thf(zip_derived_cl868, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#B') @ (!!) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 ((('#C') @ member2052026769e_indi)))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ member377231867_alt_o @ 90.86/12.41 X2)) @ 90.86/12.41 X4)))))))) @ 90.86/12.41 ((('#B') @ (member526088951_alt_o @ X2) @ 90.86/12.41 ((('#C') @ pi_Arr1929480907_alt_o @ X4))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl867])). 90.86/12.41 thf(zip_derived_cl869, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#C') @ member2052026769e_indi @ X6)))) @ 90.86/12.41 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) => 90.86/12.41 (member526088951_alt_o @ X2 @ (pi_Arr1929480907_alt_o @ X6 @ X4))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl868])). 90.86/12.41 thf(zip_derived_cl534, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 90.86/12.41 ((member526088951_alt_o @ X2 @ X4) = (X4 @ X2))), 90.86/12.41 inference('simplify nested equalities', [status(thm)], 90.86/12.41 [zip_derived_cl533])). 90.86/12.41 thf(zip_derived_cl870, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#C') @ member2052026769e_indi @ X6)))) @ 90.86/12.41 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) => 90.86/12.41 (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2)))), 90.86/12.41 inference('demod', [status(thm)], [zip_derived_cl869, zip_derived_cl534])). 90.86/12.41 thf(zip_derived_cl871, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#C') @ member2052026769e_indi @ X6)))) @ 90.86/12.41 ((('#S') @ ((('#B') @ member377231867_alt_o @ X2)) @ X4)))))) 90.86/12.41 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl870])). 90.86/12.41 thf(zip_derived_cl872, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (~ (((member2052026769e_indi @ ('#sk32' @ X2 @ X4 @ X6) @ X6) => 90.86/12.41 (member377231867_alt_o @ (X2 @ ('#sk32' @ X2 @ X4 @ X6)) @ 90.86/12.41 (X4 @ ('#sk32' @ X2 @ X4 @ X6))))) 90.86/12.41 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 90.86/12.41 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl871])). 90.86/12.41 thf(zip_derived_cl874, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X4 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (~ (member377231867_alt_o @ (X2 @ ('#sk32' @ X2 @ X4 @ X6)) @ 90.86/12.41 (X4 @ ('#sk32' @ X2 @ X4 @ X6))) 90.86/12.41 | (pi_Arr1929480907_alt_o @ X6 @ X4 @ X2))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl872])). 90.86/12.41 thf(fact_78_PiE, axiom, 90.86/12.41 (![X_72:arrow_1429601828e_indi, 90.86/12.41 F_15:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 90.86/12.41 A_19:( arrow_1429601828e_indi > $o ), 90.86/12.41 B_16:( arrow_1429601828e_indi > ( produc1501160679le_alt > $o ) > $o )]: 90.86/12.41 ( ( member526088951_alt_o @ 90.86/12.41 F_15 @ ( pi_Arr1929480907_alt_o @ A_19 @ B_16 ) ) => 90.86/12.41 ( ( ~( member377231867_alt_o @ ( F_15 @ X_72 ) @ ( B_16 @ X_72 ) ) ) => 90.86/12.41 ( ~( member2052026769e_indi @ X_72 @ A_19 ) ) ) ))). 90.86/12.41 thf(zip_derived_cl0, plain, 90.86/12.41 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 90.86/12.41 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 90.86/12.41 produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((!!) @ (^[Y3 : arrow_1429601828e_indi > 90.86/12.41 (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ 90.86/12.41 Y1 @ 90.86/12.41 (pi_Arr1929480907_alt_o @ 90.86/12.41 Y2 @ Y3)) => 90.86/12.41 (((((~) @ (member377231867_alt_o @ 90.86/12.41 (Y1 @ Y0) @ 90.86/12.41 (Y3 @ Y0)))) => 90.86/12.41 (((~) @ (member2052026769e_indi @ 90.86/12.41 Y0 @ Y2)))))))))))))))))))), 90.86/12.41 inference('cnf', [status(esa)], [fact_78_PiE])). 90.86/12.41 thf(zip_derived_cl1, plain, 90.86/12.41 ( (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 90.86/12.41 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ( 90.86/12.41 (('#B') @ (=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 '#B') @ 90.86/12.41 member526088951_alt_o)))) @ 90.86/12.41 pi_Arr1929480907_alt_o)))))))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#C'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ ( 90.86/12.41 ~))))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ ('#B'))) @ 90.86/12.41 ((('#B') @ ( 90.86/12.41 (('#B') @ member377231867_alt_o)) @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 '#I'))))))))) @ 90.86/12.41 ((('#C') @ ('#I'))))))))))))))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (~))) @ member2052026769e_indi))))))))))))))), 90.86/12.41 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 90.86/12.41 thf(zip_derived_cl350, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#B') @ ((('#B') @ (!!))) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ ('#S'))) @ 90.86/12.41 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#B') @ 90.86/12.41 member526088951_alt_o)))) @ 90.86/12.41 pi_Arr1929480907_alt_o)))))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ ('#C') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (~))) @ 90.86/12.41 ((('#C') @ ((('#B') @ ('#B') @ 90.86/12.41 ((('#B') @ member377231867_alt_o @ 90.86/12.41 ((('#C') @ ( 90.86/12.41 '#I') @ X2)))))) @ 90.86/12.41 ((('#C') @ ('#I') @ X2)))))))))))) @ 90.86/12.41 ((('#B') @ (~) @ (member2052026769e_indi @ X2)))))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 90.86/12.41 thf(zip_derived_cl351, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 90.86/12.41 (((!!) @ ((('#B') @ (!!) @ 90.86/12.41 ((('#S') @ ((('#B') @ ('#S') @ 90.86/12.41 ((('#B') @ ((('#B') @ (=>))) @ 90.86/12.41 ((('#B') @ ((('#B') @ (member526088951_alt_o @ 90.86/12.41 X4))) @ 90.86/12.41 pi_Arr1929480907_alt_o)))))) @ 90.86/12.41 ((('#B') @ ((('#C') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#B') @ (~) @ 90.86/12.41 ((('#B') @ (member377231867_alt_o @ 90.86/12.41 (X4 @ X2)) @ 90.86/12.41 ((('#C') @ ('#I') @ X2)))))))))) @ 90.86/12.41 ((('#B') @ (~) @ (member2052026769e_indi @ X2)))))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl350])). 90.86/12.41 thf(zip_derived_cl352, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o]: 90.86/12.41 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#B') @ (member526088951_alt_o @ X4) @ 90.86/12.41 (pi_Arr1929480907_alt_o @ X6))))) @ 90.86/12.41 ((('#C') @ ((('#B') @ (=>) @ 90.86/12.41 ((('#B') @ (~) @ 90.86/12.41 ((('#B') @ (member377231867_alt_o @ 90.86/12.41 (X4 @ X2)) @ 90.86/12.41 ((('#C') @ ('#I') @ X2)))))))) @ 90.86/12.41 (((~) @ (member2052026769e_indi @ X2 @ X6)))))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl351])). 90.86/12.41 thf(zip_derived_cl353, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (((member526088951_alt_o @ X4 @ 90.86/12.41 (pi_Arr1929480907_alt_o @ X6 @ X8)) => 90.86/12.41 (((((~) @ (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)))) => 90.86/12.41 (((~) @ (member2052026769e_indi @ X2 @ X6)))))))), 90.86/12.41 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl352])). 90.86/12.41 thf(zip_derived_cl354, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 90.86/12.41 (~ (member526088951_alt_o @ X4 @ (pi_Arr1929480907_alt_o @ X6 @ X8)) 90.86/12.41 | (((((~) @ (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)))) => 90.86/12.41 (((~) @ (member2052026769e_indi @ X2 @ X6))))))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl353])). 90.86/12.41 thf(zip_derived_cl355, plain, 90.86/12.41 (![X2 : arrow_1429601828e_indi, 90.86/12.41 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 90.86/12.41 X6 : arrow_1429601828e_indi > $o, 90.86/12.41 X8 : arrow_1429601828e_indi > (produc1501160679le_alt > $o) > $o]: 90.86/12.41 ( (member377231867_alt_o @ (X4 @ X2) @ (X8 @ X2)) 90.86/12.41 | ~ (member2052026769e_indi @ X2 @ X6) 90.86/12.41 | ~ (member526088951_alt_o @ X4 @ (pi_Arr1929480907_alt_o @ X6 @ X8)))), 90.86/12.41 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl354])). 90.86/12.41 thf(zip_derived_cl9389, plain, ($false), 90.86/12.41 inference('eprover', [status(thm)], 90.86/12.41 [zip_derived_cl111, zip_derived_cl409, zip_derived_cl477, 90.86/12.41 zip_derived_cl380, zip_derived_cl418, zip_derived_cl684, 90.86/12.41 zip_derived_cl547, zip_derived_cl470, zip_derived_cl499, 90.86/12.41 zip_derived_cl471, zip_derived_cl429, zip_derived_cl603, 90.86/12.41 zip_derived_cl821, zip_derived_cl600, zip_derived_cl421, 90.86/12.41 zip_derived_cl502, zip_derived_cl641, zip_derived_cl732, 90.86/12.41 zip_derived_cl586, zip_derived_cl680, zip_derived_cl9370, 90.86/12.41 zip_derived_cl9386, zip_derived_cl847, zip_derived_cl366, 90.86/12.41 zip_derived_cl52, zip_derived_cl874, zip_derived_cl355])). 90.86/12.41 90.86/12.41 % SZS output end Refutation 90.86/12.41 90.86/12.41 90.86/12.41 % Terminating... 91.70/12.52 % Runner terminated. 91.70/12.53 % Zipperpin 1.5 exiting 91.70/12.53 EOF