0.12/0.12 % 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.iyYlzO8Va1 true 0.22/0.44 % Computer : n004.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 : 1440 0.22/0.44 % WCLimit : 180 0.22/0.44 % DateTime : Mon Jul 3 10:13:15 EDT 2023 0.22/0.44 % CPUTime : 0.22/0.44 % Running portfolio for 1440 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 0.29/0.71 % Total configuration time : 828 0.29/0.71 % Estimated wc time : 1656 0.29/0.71 % Estimated cpu time (8 cpus) : 207.0 1.23/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.23/0.81 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.35/0.83 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.35/0.83 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.43/0.83 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.43/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.43/0.84 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 1.43/0.84 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.46/0.93 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 98.62/13.31 % Solved by lams/40_b.comb.sh. 98.62/13.31 % done 448 iterations in 12.384s 98.62/13.31 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 98.62/13.31 % SZS output start Refutation 98.62/13.31 thf(list_A2115238852le_alt_type, type, list_A2115238852le_alt: $tType). 98.62/13.31 thf(arrow_475358991le_alt_type, type, arrow_475358991le_alt: $tType). 98.62/13.31 thf(produc1501160679le_alt_type, type, produc1501160679le_alt: $tType). 98.62/13.31 thf(arrow_1429601828e_indi_type, type, arrow_1429601828e_indi: $tType). 98.62/13.31 thf(c_type, type, c: arrow_475358991le_alt). 98.62/13.31 thf(set_Ar577454304le_alt_type, type, set_Ar577454304le_alt: list_A2115238852le_alt > 98.62/13.31 arrow_475358991le_alt > $o). 98.62/13.31 thf(cons_A228743023le_alt_type, type, cons_A228743023le_alt: arrow_475358991le_alt > 98.62/13.31 list_A2115238852le_alt > list_A2115238852le_alt). 98.62/13.31 thf(member84363362le_alt_type, type, member84363362le_alt: arrow_475358991le_alt > 98.62/13.31 (arrow_475358991le_alt > $o) > $o). 98.62/13.31 thf(member2052026769e_indi_type, type, member2052026769e_indi: arrow_1429601828e_indi > 98.62/13.31 (arrow_1429601828e_indi > $o) > $o). 98.62/13.31 thf(arrow_823908191le_Lin_type, type, arrow_823908191le_Lin: (produc1501160679le_alt > $o) > $o). 98.62/13.31 thf(p_type, type, p: arrow_1429601828e_indi > produc1501160679le_alt > $o). 98.62/13.31 thf(distin236324274le_alt_type, type, distin236324274le_alt: list_A2115238852le_alt > $o). 98.62/13.31 thf(a_type, type, a: arrow_475358991le_alt). 98.62/13.31 thf('#sk14_type', type, '#sk14': list_A2115238852le_alt > arrow_475358991le_alt). 98.62/13.31 thf('#sk6_type', type, '#sk6': arrow_1429601828e_indi). 98.62/13.31 thf(arrow_734252939e_Prof_type, type, arrow_734252939e_Prof: (arrow_1429601828e_indi > 98.62/13.31 produc1501160679le_alt > $o) > $o). 98.62/13.31 thf('#sk15_type', type, '#sk15': list_A2115238852le_alt > list_A2115238852le_alt). 98.62/13.31 thf(nil_Ar1286194111le_alt_type, type, nil_Ar1286194111le_alt: list_A2115238852le_alt). 98.62/13.31 thf(produc1347929815le_alt_type, type, produc1347929815le_alt: arrow_475358991le_alt > 98.62/13.31 arrow_475358991le_alt > produc1501160679le_alt). 98.62/13.31 thf(top_to988227749indi_o_type, type, top_to988227749indi_o: arrow_1429601828e_indi > $o). 98.62/13.31 thf(member526088951_alt_o_type, type, member526088951_alt_o: (arrow_1429601828e_indi > 98.62/13.31 produc1501160679le_alt > $o) > 98.62/13.31 ((arrow_1429601828e_indi > 98.62/13.31 produc1501160679le_alt > $o) > $o) > $o). 98.62/13.31 thf(last_A1217315288le_alt_type, type, last_A1217315288le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 98.62/13.31 thf(append179082452le_alt_type, type, append179082452le_alt: list_A2115238852le_alt > 98.62/13.31 list_A2115238852le_alt > list_A2115238852le_alt). 98.62/13.31 thf(member214075476le_alt_type, type, member214075476le_alt: produc1501160679le_alt > 98.62/13.31 (produc1501160679le_alt > $o) > $o). 98.62/13.31 thf(member377231867_alt_o_type, type, member377231867_alt_o: (produc1501160679le_alt > $o) > 98.62/13.31 ((produc1501160679le_alt > $o) > $o) > $o). 98.62/13.31 thf(pi_Arr1929480907_alt_o_type, type, pi_Arr1929480907_alt_o: (arrow_1429601828e_indi > $o) > 98.62/13.31 (arrow_1429601828e_indi > 98.62/13.31 (produc1501160679le_alt > $o) > $o) > 98.62/13.31 (arrow_1429601828e_indi > 98.62/13.31 produc1501160679le_alt > $o) > $o). 98.62/13.31 thf('#ty_enc48_type', type, '#ty_enc48': ((produc1501160679le_alt > $o) > $o) > 98.62/13.31 arrow_1429601828e_indi > 98.62/13.31 (produc1501160679le_alt > $o) > $o). 98.62/13.31 thf(butlas274947851le_alt_type, type, butlas274947851le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 98.62/13.31 thf(rev_Ar1106406943le_alt_type, type, rev_Ar1106406943le_alt: list_A2115238852le_alt > list_A2115238852le_alt). 98.62/13.31 thf(hd_Arr1965683346le_alt_type, type, hd_Arr1965683346le_alt: list_A2115238852le_alt > arrow_475358991le_alt). 98.62/13.31 thf(arrow_2098199487_below_type, type, arrow_2098199487_below: (produc1501160679le_alt > $o) > 98.62/13.31 arrow_475358991le_alt > 98.62/13.31 arrow_475358991le_alt > 98.62/13.31 produc1501160679le_alt > $o). 98.62/13.31 thf(b_type, type, b: arrow_475358991le_alt). 98.62/13.31 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 98.62/13.31 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 98.62/13.31 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 98.62/13.31 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 98.62/13.31 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 98.62/13.31 thf(fact_4_dist, axiom, 98.62/13.31 (distin236324274le_alt @ 98.62/13.31 ( cons_A228743023le_alt @ 98.62/13.31 a @ 98.62/13.31 ( cons_A228743023le_alt @ 98.62/13.31 b @ ( cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt ) ) ))). 98.62/13.31 thf(zip_derived_cl284, plain, 98.62/13.31 ( (distin236324274le_alt @ 98.62/13.31 (cons_A228743023le_alt @ a @ 98.62/13.31 (cons_A228743023le_alt @ b @ 98.62/13.31 (cons_A228743023le_alt @ c @ nil_Ar1286194111le_alt))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_4_dist])). 98.62/13.31 thf(fact_37_list_Osimps_I2_J, axiom, 98.62/13.31 (![A_23:arrow_475358991le_alt,List_4:list_A2115238852le_alt]: 98.62/13.31 ( ( nil_Ar1286194111le_alt ) != ( cons_A228743023le_alt @ A_23 @ List_4 ) ))). 98.62/13.31 thf(zip_derived_cl290, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((nil_Ar1286194111le_alt) != 98.62/13.31 (cons_A228743023le_alt @ Y0 @ Y1)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_37_list_Osimps_I2_J])). 98.62/13.31 thf(zip_derived_cl291, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 98.62/13.31 (nil_Ar1286194111le_alt))))) @ 98.62/13.31 cons_A228743023le_alt))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl290])). 98.62/13.31 thf(zip_derived_cl400, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != 98.62/13.31 (nil_Ar1286194111le_alt))) @ 98.62/13.31 (cons_A228743023le_alt @ X2)))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl291])). 98.62/13.31 thf(zip_derived_cl401, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl400])). 98.62/13.31 thf(zip_derived_cl402, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((nil_Ar1286194111le_alt) != (cons_A228743023le_alt @ X2 @ X4))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl401])). 98.62/13.31 thf(fact_467_hd_Osimps, axiom, 98.62/13.31 (![X_26:arrow_475358991le_alt,Xs_44:list_A2115238852le_alt]: 98.62/13.31 ( ( hd_Arr1965683346le_alt @ ( cons_A228743023le_alt @ X_26 @ Xs_44 ) ) = 98.62/13.31 ( X_26 ) ))). 98.62/13.31 thf(zip_derived_cl27, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((hd_Arr1965683346le_alt @ 98.62/13.31 (cons_A228743023le_alt @ Y0 @ Y1)) = (Y0)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_467_hd_Osimps])). 98.62/13.31 thf(zip_derived_cl28, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#C') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.31 ((('#B') @ ((('#B') @ hd_Arr1965683346le_alt)) @ 98.62/13.31 cons_A228743023le_alt)))))) @ 98.62/13.31 ('#I')))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl27])). 98.62/13.31 thf(zip_derived_cl475, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#C') @ ((('#B') @ (=) @ 98.62/13.31 ((('#B') @ hd_Arr1965683346le_alt @ 98.62/13.31 (cons_A228743023le_alt @ X2))))) @ 98.62/13.31 X2))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 98.62/13.31 thf(zip_derived_cl476, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl475])). 98.62/13.31 thf(zip_derived_cl477, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((hd_Arr1965683346le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = (X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl476])). 98.62/13.31 thf(fact_375_append__Nil, axiom, 98.62/13.31 (![Ys_45:list_A2115238852le_alt]: 98.62/13.31 ( ( append179082452le_alt @ nil_Ar1286194111le_alt @ Ys_45 ) = ( Ys_45 ) ))). 98.62/13.31 thf(zip_derived_cl214, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((append179082452le_alt @ nil_Ar1286194111le_alt @ Y0) = 98.62/13.31 (Y0))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_375_append__Nil])). 98.62/13.31 thf(zip_derived_cl215, plain, 98.62/13.31 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 98.62/13.31 (append179082452le_alt @ nil_Ar1286194111le_alt))) @ 98.62/13.31 ('#I')))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl214])). 98.62/13.31 thf(zip_derived_cl377, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 98.62/13.31 thf(zip_derived_cl378, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 ((append179082452le_alt @ nil_Ar1286194111le_alt @ X2) = (X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl377])). 98.62/13.31 thf(fact_589_hd__in__set, axiom, 98.62/13.31 (![Xs_9:list_A2115238852le_alt]: 98.62/13.31 ( ( ( Xs_9 ) != ( nil_Ar1286194111le_alt ) ) => 98.62/13.31 ( member84363362le_alt @ 98.62/13.31 ( hd_Arr1965683346le_alt @ Xs_9 ) @ ( set_Ar577454304le_alt @ Xs_9 ) ) ))). 98.62/13.31 thf(zip_derived_cl273, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((((Y0) != (nil_Ar1286194111le_alt))) => 98.62/13.31 (member84363362le_alt @ (hd_Arr1965683346le_alt @ Y0) @ 98.62/13.31 (set_Ar577454304le_alt @ Y0)))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_589_hd__in__set])). 98.62/13.31 thf(zip_derived_cl274, plain, 98.62/13.31 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 98.62/13.31 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 98.62/13.31 ((('#S') @ ((('#B') @ member84363362le_alt @ 98.62/13.31 hd_Arr1965683346le_alt)) @ 98.62/13.31 set_Ar577454304le_alt))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl273])). 98.62/13.31 thf(zip_derived_cl415, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 98.62/13.31 (hd_Arr1965683346le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl274])). 98.62/13.31 thf(zip_derived_cl416, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (~ (((X2) != (nil_Ar1286194111le_alt))) 98.62/13.31 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 98.62/13.31 (set_Ar577454304le_alt @ X2)))), 98.62/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl415])). 98.62/13.31 thf(zip_derived_cl417, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((X2) = (nil_Ar1286194111le_alt)) 98.62/13.31 | (member84363362le_alt @ (hd_Arr1965683346le_alt @ X2) @ 98.62/13.31 (set_Ar577454304le_alt @ X2)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl416])). 98.62/13.31 thf(fact_373_append__Cons, axiom, 98.62/13.31 (![X_50:arrow_475358991le_alt,Xs_99:list_A2115238852le_alt, 98.62/13.31 Ys_47:list_A2115238852le_alt]: 98.62/13.31 ( ( append179082452le_alt @ 98.62/13.31 ( cons_A228743023le_alt @ X_50 @ Xs_99 ) @ Ys_47 ) = 98.62/13.31 ( cons_A228743023le_alt @ 98.62/13.31 X_50 @ ( append179082452le_alt @ Xs_99 @ Ys_47 ) ) ))). 98.62/13.31 thf(zip_derived_cl17, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 98.62/13.31 (((append179082452le_alt @ 98.62/13.31 (cons_A228743023le_alt @ Y0 @ Y1) @ 98.62/13.31 Y2) = (cons_A228743023le_alt @ 98.62/13.31 Y0 @ 98.62/13.31 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_373_append__Cons])). 98.62/13.31 thf(zip_derived_cl18, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 98.62/13.31 cons_A228743023le_alt)))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ cons_A228743023le_alt)))) @ 98.62/13.31 append179082452le_alt))))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl17])). 98.62/13.31 thf(zip_derived_cl537, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.31 ((('#B') @ append179082452le_alt @ 98.62/13.31 (cons_A228743023le_alt @ X2))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (cons_A228743023le_alt @ X2))) @ 98.62/13.31 append179082452le_alt))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 98.62/13.31 thf(zip_derived_cl538, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 98.62/13.31 (append179082452le_alt @ 98.62/13.31 (cons_A228743023le_alt @ X2 @ X4)))) @ 98.62/13.31 ((('#B') @ (cons_A228743023le_alt @ X2) @ 98.62/13.31 (append179082452le_alt @ X4)))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl537])). 98.62/13.31 thf(zip_derived_cl539, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 98.62/13.31 X6 : list_A2115238852le_alt]: 98.62/13.31 (((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) = 98.62/13.31 (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl538])). 98.62/13.31 thf(zip_derived_cl540, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt, 98.62/13.31 X6 : list_A2115238852le_alt]: 98.62/13.31 ((append179082452le_alt @ (cons_A228743023le_alt @ X2 @ X4) @ X6) 98.62/13.31 = (cons_A228743023le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl539])). 98.62/13.31 thf(fact_394_last__snoc, axiom, 98.62/13.31 (![Xs_80:list_A2115238852le_alt,X_42:arrow_475358991le_alt]: 98.62/13.31 ( ( last_A1217315288le_alt @ 98.62/13.31 ( append179082452le_alt @ 98.62/13.31 Xs_80 @ ( cons_A228743023le_alt @ X_42 @ nil_Ar1286194111le_alt ) ) ) = 98.62/13.31 ( X_42 ) ))). 98.62/13.31 thf(zip_derived_cl200, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.31 (((last_A1217315288le_alt @ 98.62/13.31 (append179082452le_alt @ Y0 @ 98.62/13.31 (cons_A228743023le_alt @ Y1 @ 98.62/13.31 nil_Ar1286194111le_alt))) = 98.62/13.31 (Y1)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_394_last__snoc])). 98.62/13.31 thf(zip_derived_cl201, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.31 ((('#B') @ ((('#B') @ last_A1217315288le_alt)) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 append179082452le_alt)) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ 98.62/13.31 nil_Ar1286194111le_alt)))))))))) @ 98.62/13.31 ('#I')))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl200])). 98.62/13.31 thf(zip_derived_cl553, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 98.62/13.31 ((('#B') @ last_A1217315288le_alt @ 98.62/13.31 ((('#B') @ (append179082452le_alt @ X2) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ 98.62/13.31 nil_Ar1286194111le_alt)))))))) @ 98.62/13.31 ('#I')))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl201])). 98.62/13.31 thf(zip_derived_cl554, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 (((last_A1217315288le_alt @ 98.62/13.31 (append179082452le_alt @ X2 @ 98.62/13.31 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) = 98.62/13.31 (X4)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl553])). 98.62/13.31 thf(zip_derived_cl555, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 ((last_A1217315288le_alt @ 98.62/13.31 (append179082452le_alt @ X2 @ 98.62/13.31 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt))) 98.62/13.31 = (X4))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl554])). 98.62/13.31 thf(fact_268_mem__def, axiom, 98.62/13.31 (![X_66:produc1501160679le_alt,A_12:( produc1501160679le_alt > $o )]: 98.62/13.31 ( ( member214075476le_alt @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 98.62/13.31 thf(zip_derived_cl143, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : produc1501160679le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : produc1501160679le_alt > $o]: 98.62/13.31 (((member214075476le_alt @ Y0 @ Y1) <=> (Y1 @ 98.62/13.31 Y0)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_268_mem__def])). 98.62/13.31 thf(zip_derived_cl144, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 member214075476le_alt)))) @ 98.62/13.31 ((('#C') @ ('#I')))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl143])). 98.62/13.31 thf(zip_derived_cl501, plain, 98.62/13.31 (![X2 : produc1501160679le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member214075476le_alt @ X2))) @ 98.62/13.31 ((('#C') @ ('#I') @ X2))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl144])). 98.62/13.31 thf(zip_derived_cl502, plain, 98.62/13.31 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 98.62/13.31 (((member214075476le_alt @ X2 @ X4) <=> (X4 @ X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl501])). 98.62/13.31 thf(zip_derived_cl503, plain, 98.62/13.31 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 98.62/13.31 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl502])). 98.62/13.31 thf(fact_0__096P_A_058_AProf_096, axiom, 98.62/13.31 (member526088951_alt_o @ p @ arrow_734252939e_Prof)). 98.62/13.31 thf(zip_derived_cl332, plain, 98.62/13.31 ( (member526088951_alt_o @ p @ arrow_734252939e_Prof)), 98.62/13.31 inference('cnf', [status(esa)], [fact_0__096P_A_058_AProf_096])). 98.62/13.31 thf(conj_0, conjecture, 98.62/13.31 (![I:arrow_1429601828e_indi]: 98.62/13.31 ( ( member214075476le_alt @ ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) <=> 98.62/13.31 ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ a @ c ) @ 98.62/13.31 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ))). 98.62/13.31 thf(zf_stmt_0, negated_conjecture, 98.62/13.31 (~( ![I:arrow_1429601828e_indi]: 98.62/13.31 ( ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ a @ b ) @ ( p @ I ) ) <=> 98.62/13.31 ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ a @ c ) @ 98.62/13.31 ( arrow_2098199487_below @ ( p @ I ) @ c @ b ) ) ) )), 98.62/13.31 inference('cnf.neg', [status(esa)], [conj_0])). 98.62/13.31 thf(zip_derived_cl343, plain, 98.62/13.31 (~ (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 98.62/13.31 (((member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ a @ b) @ (p @ Y0)) <=> 98.62/13.31 (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ a @ c) @ 98.62/13.31 (arrow_2098199487_below @ (p @ Y0) @ c @ b)))))))), 98.62/13.31 inference('cnf', [status(esa)], [zf_stmt_0])). 98.62/13.31 thf(zip_derived_cl344, plain, 98.62/13.31 (~ (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.31 ((('#B') @ (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ a @ b)) @ 98.62/13.31 p)))) @ 98.62/13.31 ((('#B') @ (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ a @ c)) @ 98.62/13.31 ((('#C') @ ((('#C') @ ((('#B') @ arrow_2098199487_below @ 98.62/13.31 p)) @ 98.62/13.31 c)) @ 98.62/13.31 b))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl343])). 98.62/13.31 thf(zip_derived_cl379, plain, 98.62/13.31 (~ (((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 98.62/13.31 (p @ '#sk6')) <=> (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ a @ c) @ 98.62/13.31 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b))))), 98.62/13.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl344])). 98.62/13.31 thf(zip_derived_cl380, plain, 98.62/13.31 (((member214075476le_alt @ (produc1347929815le_alt @ a @ b) @ 98.62/13.31 (p @ '#sk6')) 98.62/13.31 != (member214075476le_alt @ (produc1347929815le_alt @ a @ c) @ 98.62/13.31 (arrow_2098199487_below @ (p @ '#sk6') @ c @ b)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl379])). 98.62/13.31 thf(zip_derived_cl503, plain, 98.62/13.31 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 98.62/13.31 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl502])). 98.62/13.31 thf(zip_derived_cl503, plain, 98.62/13.31 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 98.62/13.31 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl502])). 98.62/13.31 thf(zip_derived_cl504, plain, 98.62/13.31 (((p @ '#sk6' @ (produc1347929815le_alt @ a @ b)) 98.62/13.31 != (arrow_2098199487_below @ (p @ '#sk6') @ c @ b @ 98.62/13.31 (produc1347929815le_alt @ a @ c)))), 98.62/13.31 inference('demod', [status(thm)], 98.62/13.31 [zip_derived_cl380, zip_derived_cl503, zip_derived_cl503])). 98.62/13.31 thf(fact_43_not__Cons__self, axiom, 98.62/13.31 (![Xs_126:list_A2115238852le_alt,X_73:arrow_475358991le_alt]: 98.62/13.31 ( ( Xs_126 ) != ( cons_A228743023le_alt @ X_73 @ Xs_126 ) ))). 98.62/13.31 thf(zip_derived_cl113, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.31 (((Y0) != (cons_A228743023le_alt @ Y1 @ Y0)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_43_not__Cons__self])). 98.62/13.31 thf(zip_derived_cl114, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#B') @ (!=))) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl113])). 98.62/13.31 thf(zip_derived_cl409, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ X2))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 98.62/13.31 thf(zip_derived_cl410, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 (((X2) != (cons_A228743023le_alt @ X4 @ X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl409])). 98.62/13.31 thf(zip_derived_cl411, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 ((X2) != (cons_A228743023le_alt @ X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl410])). 98.62/13.31 thf(fact_376_Nil__is__append__conv, axiom, 98.62/13.31 (![Xs_97:list_A2115238852le_alt,Ys_44:list_A2115238852le_alt]: 98.62/13.31 ( ( ( ( Xs_97 ) = ( nil_Ar1286194111le_alt ) ) & 98.62/13.31 ( ( Ys_44 ) = ( nil_Ar1286194111le_alt ) ) ) <=> 98.62/13.31 ( ( nil_Ar1286194111le_alt ) = ( append179082452le_alt @ Xs_97 @ Ys_44 ) ) ))). 98.62/13.31 thf(zip_derived_cl19, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((((((Y0) = (nil_Ar1286194111le_alt))) & 98.62/13.31 (((Y1) = (nil_Ar1286194111le_alt))))) <=> 98.62/13.31 (((nil_Ar1286194111le_alt) = 98.62/13.31 (append179082452le_alt @ Y0 @ Y1)))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_376_Nil__is__append__conv])). 98.62/13.31 thf(zip_derived_cl20, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ (&) @ 98.62/13.31 ((('#C') @ (=) @ 98.62/13.31 nil_Ar1286194111le_alt)))))) @ 98.62/13.31 ((('#C') @ (=) @ nil_Ar1286194111le_alt)))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 98.62/13.31 (nil_Ar1286194111le_alt))))) @ 98.62/13.31 append179082452le_alt))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl19])). 98.62/13.31 thf(zip_derived_cl577, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.31 ((('#B') @ (((&) @ (((X2) = 98.62/13.31 (nil_Ar1286194111le_alt))))) @ 98.62/13.31 ((('#C') @ (=) @ nil_Ar1286194111le_alt)))))) @ 98.62/13.31 ((('#B') @ (((list_A2115238852le_alt) = 98.62/13.31 (nil_Ar1286194111le_alt))) @ 98.62/13.31 (append179082452le_alt @ X2)))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl20])). 98.62/13.31 thf(zip_derived_cl578, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((((((X2) = (nil_Ar1286194111le_alt))) & 98.62/13.31 (((X4) = (nil_Ar1286194111le_alt))))) <=> 98.62/13.31 (((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4)))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl577])). 98.62/13.31 thf(zip_derived_cl579, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((((((X2) = (nil_Ar1286194111le_alt))) & 98.62/13.31 (((X4) = (nil_Ar1286194111le_alt))))) 98.62/13.31 = (((nil_Ar1286194111le_alt) = (append179082452le_alt @ X2 @ X4))))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl578])). 98.62/13.31 thf(fact_496_rev__eq__Cons__iff, axiom, 98.62/13.31 (![Xs_25:list_A2115238852le_alt,Y_3:arrow_475358991le_alt, 98.62/13.31 Ys_7:list_A2115238852le_alt]: 98.62/13.31 ( ( ( Xs_25 ) = 98.62/13.31 ( append179082452le_alt @ 98.62/13.31 ( rev_Ar1106406943le_alt @ Ys_7 ) @ 98.62/13.31 ( cons_A228743023le_alt @ Y_3 @ nil_Ar1286194111le_alt ) ) ) <=> 98.62/13.31 ( ( rev_Ar1106406943le_alt @ Xs_25 ) = 98.62/13.31 ( cons_A228743023le_alt @ Y_3 @ Ys_7 ) ) ))). 98.62/13.31 thf(zip_derived_cl91, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 98.62/13.31 (((((Y0) = 98.62/13.31 (append179082452le_alt @ 98.62/13.31 (rev_Ar1106406943le_alt @ Y2) @ 98.62/13.31 (cons_A228743023le_alt @ Y1 @ 98.62/13.31 nil_Ar1286194111le_alt)))) <=> 98.62/13.31 (((rev_Ar1106406943le_alt @ Y0) = 98.62/13.31 (cons_A228743023le_alt @ Y1 @ 98.62/13.31 Y2))))))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_496_rev__eq__Cons__iff])). 98.62/13.31 thf(zip_derived_cl92, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ (=))))) @ 98.62/13.31 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 98.62/13.31 rev_Ar1106406943le_alt)))) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ 98.62/13.31 nil_Ar1286194111le_alt)))))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ (=) @ rev_Ar1106406943le_alt)))))) @ 98.62/13.31 cons_A228743023le_alt))))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl91])). 98.62/13.31 thf(zip_derived_cl765, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 98.62/13.31 (X2))))) @ 98.62/13.31 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 98.62/13.31 rev_Ar1106406943le_alt)))) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ 98.62/13.31 nil_Ar1286194111le_alt)))))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) = 98.62/13.31 (rev_Ar1106406943le_alt @ X2))))) @ 98.62/13.31 cons_A228743023le_alt))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])). 98.62/13.31 thf(zip_derived_cl766, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.31 ((('#B') @ (((list_A2115238852le_alt) = (X2))) @ 98.62/13.31 ((('#C') @ ((('#B') @ append179082452le_alt @ 98.62/13.31 rev_Ar1106406943le_alt)) @ 98.62/13.31 (cons_A228743023le_alt @ X4 @ 98.62/13.31 nil_Ar1286194111le_alt))))))) @ 98.62/13.31 ((('#B') @ (((list_A2115238852le_alt) = 98.62/13.31 (rev_Ar1106406943le_alt @ X2))) @ 98.62/13.31 (cons_A228743023le_alt @ X4)))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl765])). 98.62/13.31 thf(zip_derived_cl767, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : list_A2115238852le_alt]: 98.62/13.31 (((((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 98.62/13.31 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))) <=> 98.62/13.31 (((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ X6)))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl766])). 98.62/13.31 thf(zip_derived_cl768, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : list_A2115238852le_alt]: 98.62/13.31 ((((X2) = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X6) @ 98.62/13.31 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)))) 98.62/13.31 = (((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ 98.62/13.31 X6))))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl767])). 98.62/13.31 thf(fact_495_rev_Osimps_I2_J, axiom, 98.62/13.31 (![X_17:arrow_475358991le_alt,Xs_26:list_A2115238852le_alt]: 98.62/13.31 ( ( rev_Ar1106406943le_alt @ ( cons_A228743023le_alt @ X_17 @ Xs_26 ) ) = 98.62/13.31 ( append179082452le_alt @ 98.62/13.31 ( rev_Ar1106406943le_alt @ Xs_26 ) @ 98.62/13.31 ( cons_A228743023le_alt @ X_17 @ nil_Ar1286194111le_alt ) ) ))). 98.62/13.31 thf(zip_derived_cl111, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((rev_Ar1106406943le_alt @ 98.62/13.31 (cons_A228743023le_alt @ Y0 @ Y1)) = 98.62/13.31 (append179082452le_alt @ 98.62/13.31 (rev_Ar1106406943le_alt @ Y1) @ 98.62/13.31 (cons_A228743023le_alt @ Y0 @ 98.62/13.31 nil_Ar1286194111le_alt))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_495_rev_Osimps_I2_J])). 98.62/13.31 thf(zip_derived_cl112, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.31 ((('#B') @ ((('#B') @ rev_Ar1106406943le_alt)) @ 98.62/13.31 cons_A228743023le_alt)))))) @ 98.62/13.31 ((('#B') @ ((('#C') @ ((('#B') @ append179082452le_alt @ 98.62/13.31 rev_Ar1106406943le_alt)))) @ 98.62/13.31 ((('#C') @ cons_A228743023le_alt @ 98.62/13.31 nil_Ar1286194111le_alt))))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl111])). 98.62/13.31 thf(zip_derived_cl574, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 98.62/13.31 ((('#B') @ rev_Ar1106406943le_alt @ 98.62/13.31 (cons_A228743023le_alt @ X2))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ append179082452le_alt @ 98.62/13.31 rev_Ar1106406943le_alt)) @ 98.62/13.31 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl112])). 98.62/13.31 thf(zip_derived_cl575, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) = 98.62/13.31 (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 98.62/13.31 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl574])). 98.62/13.31 thf(zip_derived_cl576, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 98.62/13.31 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 98.62/13.31 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl575])). 98.62/13.31 thf(zip_derived_cl769, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : list_A2115238852le_alt]: 98.62/13.31 ((((X2) = (rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X4 @ X6)))) 98.62/13.31 = (((rev_Ar1106406943le_alt @ X2) = (cons_A228743023le_alt @ X4 @ 98.62/13.31 X6))))), 98.62/13.31 inference('demod', [status(thm)], [zip_derived_cl768, zip_derived_cl576])). 98.62/13.31 thf(fact_79_list_Oexhaust, axiom, 98.62/13.31 (![Y_26:list_A2115238852le_alt]: 98.62/13.31 ( ( ( Y_26 ) != ( nil_Ar1286194111le_alt ) ) => 98.62/13.31 ( ~( ![A:arrow_475358991le_alt,List:list_A2115238852le_alt]: 98.62/13.31 ( ( Y_26 ) != ( cons_A228743023le_alt @ A @ List ) ) ) ) ))). 98.62/13.31 thf(zip_derived_cl186, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((((Y0) != (nil_Ar1286194111le_alt))) => 98.62/13.31 (((~) @ (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 98.62/13.31 (((Y0) != 98.62/13.31 (cons_A228743023le_alt @ 98.62/13.31 Y1 @ Y2))))))))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_79_list_Oexhaust])). 98.62/13.31 thf(zip_derived_cl187, plain, 98.62/13.31 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 98.62/13.31 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 98.62/13.31 ((('#B') @ (~) @ 98.62/13.31 ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ (!=))))) @ 98.62/13.31 cons_A228743023le_alt))))))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl186])). 98.62/13.31 thf(zip_derived_cl599, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((((X2) != (nil_Ar1286194111le_alt))) => 98.62/13.31 (((~) @ (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 98.62/13.31 (X2))))) @ 98.62/13.31 cons_A228743023le_alt))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl187])). 98.62/13.31 thf(zip_derived_cl600, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (~ (((X2) != (nil_Ar1286194111le_alt))) 98.62/13.31 | ~ (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 98.62/13.31 (X2))))) @ 98.62/13.31 cons_A228743023le_alt)))))))), 98.62/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl599])). 98.62/13.31 thf(zip_derived_cl601, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((X2) = (nil_Ar1286194111le_alt)) 98.62/13.31 | ~ (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((list_A2115238852le_alt) != 98.62/13.31 (X2))))) @ 98.62/13.31 cons_A228743023le_alt)))))))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl600])). 98.62/13.31 thf(zip_derived_cl602, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (~ (((!!) @ ((('#B') @ (((list_A2115238852le_alt) != (X2))) @ 98.62/13.31 (cons_A228743023le_alt @ ('#sk14' @ X2)))))) 98.62/13.31 | ((X2) = (nil_Ar1286194111le_alt)))), 98.62/13.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl601])). 98.62/13.31 thf(zip_derived_cl603, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (~ (((X2) != (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2)))) 98.62/13.31 | ((X2) = (nil_Ar1286194111le_alt)))), 98.62/13.31 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl602])). 98.62/13.31 thf(zip_derived_cl604, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((X2) = (cons_A228743023le_alt @ ('#sk14' @ X2) @ ('#sk15' @ X2))) 98.62/13.31 | ((X2) = (nil_Ar1286194111le_alt)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl603])). 98.62/13.31 thf(fact_572_last__in__set, axiom, 98.62/13.31 (![As:list_A2115238852le_alt]: 98.62/13.31 ( ( ( As ) != ( nil_Ar1286194111le_alt ) ) => 98.62/13.31 ( member84363362le_alt @ 98.62/13.31 ( last_A1217315288le_alt @ As ) @ ( set_Ar577454304le_alt @ As ) ) ))). 98.62/13.31 thf(zip_derived_cl239, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.31 (((((Y0) != (nil_Ar1286194111le_alt))) => 98.62/13.31 (member84363362le_alt @ (last_A1217315288le_alt @ Y0) @ 98.62/13.31 (set_Ar577454304le_alt @ Y0)))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_572_last__in__set])). 98.62/13.31 thf(zip_derived_cl240, plain, 98.62/13.31 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 98.62/13.31 ((('#C') @ (!=) @ nil_Ar1286194111le_alt)))) @ 98.62/13.31 ((('#S') @ ((('#B') @ member84363362le_alt @ 98.62/13.31 last_A1217315288le_alt)) @ 98.62/13.31 set_Ar577454304le_alt))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl239])). 98.62/13.31 thf(zip_derived_cl412, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((((X2) != (nil_Ar1286194111le_alt))) => (member84363362le_alt @ 98.62/13.31 (last_A1217315288le_alt @ X2) @ (set_Ar577454304le_alt @ X2))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl240])). 98.62/13.31 thf(zip_derived_cl413, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (~ (((X2) != (nil_Ar1286194111le_alt))) 98.62/13.31 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 98.62/13.31 (set_Ar577454304le_alt @ X2)))), 98.62/13.31 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl412])). 98.62/13.31 thf(zip_derived_cl414, plain, 98.62/13.31 (![X2 : list_A2115238852le_alt]: 98.62/13.31 (((X2) = (nil_Ar1286194111le_alt)) 98.62/13.31 | (member84363362le_alt @ (last_A1217315288le_alt @ X2) @ 98.62/13.31 (set_Ar577454304le_alt @ X2)))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl413])). 98.62/13.31 thf(fact_264_mem__def, axiom, 98.62/13.31 (![X_66:arrow_475358991le_alt,A_12:( arrow_475358991le_alt > $o )]: 98.62/13.31 ( ( A_12 @ X_66 ) <=> ( member84363362le_alt @ X_66 @ A_12 ) ))). 98.62/13.31 thf(zip_derived_cl192, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : arrow_475358991le_alt > $o]: 98.62/13.31 (((Y1 @ Y0) <=> (member84363362le_alt @ Y0 @ 98.62/13.31 Y1)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_264_mem__def])). 98.62/13.31 thf(zip_derived_cl193, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 ((('#C') @ ('#I'))))))) @ 98.62/13.31 member84363362le_alt))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl192])). 98.62/13.31 thf(zip_derived_cl508, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 98.62/13.31 (member84363362le_alt @ X2)))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl193])). 98.62/13.31 thf(zip_derived_cl509, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 98.62/13.31 (((X4 @ X2) <=> (member84363362le_alt @ X2 @ X4)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl508])). 98.62/13.31 thf(zip_derived_cl510, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 98.62/13.31 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl509])). 98.62/13.31 thf(fact_556_distinct_Osimps_I2_J, axiom, 98.62/13.31 (![X_8:arrow_475358991le_alt,Xs_13:list_A2115238852le_alt]: 98.62/13.31 ( ( distin236324274le_alt @ ( cons_A228743023le_alt @ X_8 @ Xs_13 ) ) <=> 98.62/13.31 ( ( ~( member84363362le_alt @ X_8 @ ( set_Ar577454304le_alt @ Xs_13 ) ) ) & 98.62/13.31 ( distin236324274le_alt @ Xs_13 ) ) ))). 98.62/13.31 thf(zip_derived_cl330, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.31 (((distin236324274le_alt @ 98.62/13.31 (cons_A228743023le_alt @ Y0 @ Y1)) <=> 98.62/13.31 (((((~) @ (member84363362le_alt @ Y0 @ 98.62/13.31 (set_Ar577454304le_alt @ Y1)))) & 98.62/13.31 (distin236324274le_alt @ Y1)))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_556_distinct_Osimps_I2_J])). 98.62/13.31 thf(zip_derived_cl331, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 ((('#B') @ ((('#B') @ distin236324274le_alt)) @ 98.62/13.31 cons_A228743023le_alt)))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (&))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (~))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 member84363362le_alt)) @ 98.62/13.31 set_Ar577454304le_alt)))))))) @ 98.62/13.31 distin236324274le_alt))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl330])). 98.62/13.31 thf(zip_derived_cl651, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.31 ((('#B') @ distin236324274le_alt @ 98.62/13.31 (cons_A228743023le_alt @ X2))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ (&) @ 98.62/13.31 ((('#B') @ (~) @ 98.62/13.31 ((('#B') @ (member84363362le_alt @ X2) @ 98.62/13.31 set_Ar577454304le_alt)))))) @ 98.62/13.31 distin236324274le_alt))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl331])). 98.62/13.31 thf(zip_derived_cl652, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 (((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) <=> 98.62/13.31 (((((~) @ (member84363362le_alt @ X2 @ (set_Ar577454304le_alt @ X4)))) & 98.62/13.31 (distin236324274le_alt @ X4)))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl651])). 98.62/13.31 thf(zip_derived_cl653, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 98.62/13.31 = (((((~) @ (member84363362le_alt @ X2 @ 98.62/13.31 (set_Ar577454304le_alt @ X4)))) & 98.62/13.31 (distin236324274le_alt @ X4))))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl652])). 98.62/13.31 thf(zip_derived_cl510, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt > $o]: 98.62/13.31 ((X4 @ X2) = (member84363362le_alt @ X2 @ X4))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl509])). 98.62/13.31 thf(zip_derived_cl654, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.31 ((distin236324274le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 98.62/13.31 = (((((~) @ (set_Ar577454304le_alt @ X4 @ X2))) & 98.62/13.31 (distin236324274le_alt @ X4))))), 98.62/13.31 inference('demod', [status(thm)], [zip_derived_cl653, zip_derived_cl510])). 98.62/13.31 thf(fact_269_mem__def, axiom, 98.62/13.31 (![X_66:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 98.62/13.31 A_12:( ( arrow_1429601828e_indi > produc1501160679le_alt > $o ) > $o )]: 98.62/13.31 ( ( member526088951_alt_o @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 98.62/13.31 thf(zip_derived_cl125, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ (^[Y1 : (arrow_1429601828e_indi > 98.62/13.31 produc1501160679le_alt > $o) > $o]: 98.62/13.31 (((member526088951_alt_o @ Y0 @ Y1) <=> (Y1 @ 98.62/13.31 Y0)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_269_mem__def])). 98.62/13.31 thf(zip_derived_cl126, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 member526088951_alt_o)))) @ 98.62/13.31 ((('#C') @ ('#I')))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl125])). 98.62/13.31 thf(zip_derived_cl472, plain, 98.62/13.31 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member526088951_alt_o @ X2))) @ 98.62/13.31 ((('#C') @ ('#I') @ X2))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl126])). 98.62/13.31 thf(zip_derived_cl473, plain, 98.62/13.31 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.31 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 98.62/13.31 (((member526088951_alt_o @ X2 @ X4) <=> (X4 @ X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl472])). 98.62/13.31 thf(zip_derived_cl474, plain, 98.62/13.31 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.31 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 98.62/13.31 ((member526088951_alt_o @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl473])). 98.62/13.31 thf(fact_270_mem__def, axiom, 98.62/13.31 (![X_66:( produc1501160679le_alt > $o ), 98.62/13.31 A_12:( ( produc1501160679le_alt > $o ) > $o )]: 98.62/13.31 ( ( member377231867_alt_o @ X_66 @ A_12 ) <=> ( A_12 @ X_66 ) ))). 98.62/13.31 thf(zip_derived_cl149, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ (^[Y1 : (produc1501160679le_alt > $o) > $o]: 98.62/13.31 (((member377231867_alt_o @ Y0 @ Y1) <=> (Y1 @ 98.62/13.31 Y0)))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_270_mem__def])). 98.62/13.31 thf(zip_derived_cl150, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 member377231867_alt_o)))) @ 98.62/13.31 ((('#C') @ ('#I')))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl149])). 98.62/13.31 thf(zip_derived_cl505, plain, 98.62/13.31 (![X2 : produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member377231867_alt_o @ X2))) @ 98.62/13.31 ((('#C') @ ('#I') @ X2))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl150])). 98.62/13.31 thf(zip_derived_cl506, plain, 98.62/13.31 (![X2 : produc1501160679le_alt > $o, 98.62/13.31 X4 : (produc1501160679le_alt > $o) > $o]: 98.62/13.31 (((member377231867_alt_o @ X2 @ X4) <=> (X4 @ X2)))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl505])). 98.62/13.31 thf(zip_derived_cl507, plain, 98.62/13.31 (![X2 : produc1501160679le_alt > $o, 98.62/13.31 X4 : (produc1501160679le_alt > $o) > $o]: 98.62/13.31 ((member377231867_alt_o @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl506])). 98.62/13.31 thf(fact_12_in__below, axiom, 98.62/13.31 (![X:arrow_475358991le_alt,Y:arrow_475358991le_alt, 98.62/13.31 L_1:( produc1501160679le_alt > $o ),A_24:arrow_475358991le_alt, 98.62/13.31 B_17:arrow_475358991le_alt]: 98.62/13.31 ( ( ( A_24 ) != ( B_17 ) ) => 98.62/13.31 ( ( member377231867_alt_o @ L_1 @ arrow_823908191le_Lin ) => 98.62/13.31 ( ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ X @ Y ) @ 98.62/13.31 ( arrow_2098199487_below @ L_1 @ A_24 @ B_17 ) ) <=> 98.62/13.31 ( ( ( ( Y ) != ( A_24 ) ) => 98.62/13.31 ( ( ( ( X ) = ( A_24 ) ) => 98.62/13.31 ( ( ( Y ) = ( B_17 ) ) | 98.62/13.31 ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ B_17 @ Y ) @ L_1 ) ) ) & 98.62/13.31 ( ( ( X ) != ( A_24 ) ) => 98.62/13.31 ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ X @ Y ) @ L_1 ) ) ) ) & 98.62/13.31 ( ( ( Y ) = ( A_24 ) ) => 98.62/13.31 ( member214075476le_alt @ 98.62/13.31 ( produc1347929815le_alt @ X @ B_17 ) @ L_1 ) ) & 98.62/13.31 ( ( X ) != ( Y ) ) ) ) ) ))). 98.62/13.31 thf(zip_derived_cl184, plain, 98.62/13.31 ( (((!!) @ (^[Y0 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y2 : produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ (^[Y3 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ (^[Y4 : arrow_475358991le_alt]: 98.62/13.31 (((( 98.62/13.31 (Y3) != 98.62/13.31 (Y4))) => 98.62/13.31 (( 98.62/13.31 (member377231867_alt_o @ 98.62/13.31 Y2 @ 98.62/13.31 arrow_823908191le_Lin) => 98.62/13.31 (( 98.62/13.31 (member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 produc1347929815le_alt @ 98.62/13.31 Y0 @ Y1) @ 98.62/13.31 ( 98.62/13.31 arrow_2098199487_below @ 98.62/13.31 Y2 @ 98.62/13.31 Y3 @ Y4)) <=> 98.62/13.31 (( 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (( 98.62/13.31 (Y1) != 98.62/13.31 (Y3))) => 98.62/13.31 (( 98.62/13.31 (( 98.62/13.31 (( 98.62/13.31 (Y0) = 98.62/13.31 (Y3))) => 98.62/13.31 (( 98.62/13.31 (( 98.62/13.31 (Y1) = 98.62/13.31 (Y4))) | 98.62/13.31 (member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 produc1347929815le_alt @ 98.62/13.31 Y4 @ Y1) @ 98.62/13.31 Y2))))) & 98.62/13.31 (( 98.62/13.31 (( 98.62/13.31 (Y0) != 98.62/13.31 (Y3))) => 98.62/13.31 (member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 produc1347929815le_alt @ 98.62/13.31 Y0 @ Y1) @ 98.62/13.31 Y2))))))) & 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (( 98.62/13.31 (Y1) = 98.62/13.31 (Y3))) => 98.62/13.31 (member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 produc1347929815le_alt @ 98.62/13.31 Y0 @ Y4) @ 98.62/13.31 Y2))) & 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (Y0) != 98.62/13.31 (Y1))))))))))))))))))))))))))), 98.62/13.31 inference('cnf', [status(esa)], [fact_12_in__below])). 98.62/13.31 thf(zip_derived_cl185, plain, 98.62/13.31 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ (( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 !=))))))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ((('#C') @ member377231867_alt_o @ 98.62/13.31 arrow_823908191le_Lin)))))))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 '#S'))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S'))))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ (<=>))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 (( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt)) @ 98.62/13.31 produc1347929815le_alt)))))))))) @ 98.62/13.31 arrow_2098199487_below)))))))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#C'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 '#C'))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ('#C'))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#S'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#S'))))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S'))))))) @ 98.62/13.31 (( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 &))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 !=))))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S'))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C'))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 &))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 =))))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 |))) @ 98.62/13.31 ( 98.62/13.31 =))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt)) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ produc1347929815le_alt)))))))))))))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 !=))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt)) @ 98.62/13.31 produc1347929815le_alt)))))))))))))))))) @ 98.62/13.31 ((('#B') @ ((('#C') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 =))))))))))) @ 98.62/13.31 ((('#B') @ ('#C') @ 98.62/13.31 ((('#B') @ ((('#B') @ member214075476le_alt)) @ 98.62/13.31 produc1347929815le_alt)))))))))))))))) @ 98.62/13.31 (!=)))))))))))))))))))), 98.62/13.31 inference('lams2combs', [status(thm)], [zip_derived_cl184])). 98.62/13.31 thf(zip_derived_cl1106, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ (=>))) @ 98.62/13.31 (!=))))))))) @ 98.62/13.31 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ (=>) @ 98.62/13.31 ((('#C') @ member377231867_alt_o @ 98.62/13.31 arrow_823908191le_Lin)))))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 '#S'))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 <=>))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2))))))))) @ 98.62/13.31 arrow_2098199487_below)))))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#C') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#C'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 '#C'))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#S'))))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 &))))))) @ 98.62/13.31 ((('#S') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 ( 98.62/13.31 !=))))))))) @ 98.62/13.31 (( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S'))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C'))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 &))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X2))))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 |))) @ 98.62/13.31 ( 98.62/13.31 =))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt)) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ produc1347929815le_alt)))))))))))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) != 98.62/13.31 (X2))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 produc1347929815le_alt @ 98.62/13.31 X2))))))))))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 =>))) @ 98.62/13.31 (=))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2))))))))))))))) @ 98.62/13.31 (((arrow_475358991le_alt) != (X2)))))))))))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl185])). 98.62/13.31 thf(zip_derived_cl1107, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.31 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=>))) @ 98.62/13.31 (!=))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ (=>) @ 98.62/13.31 ((('#C') @ member377231867_alt_o @ 98.62/13.31 arrow_823908191le_Lin)))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 <=>))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ ((('#B') @ ( 98.62/13.31 member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2 @ X4)))))) @ 98.62/13.31 arrow_2098199487_below)))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#C') @ 98.62/13.31 ((('#B') @ ((('#B') @ ('#C'))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ ( 98.62/13.31 '#S'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 (('#B') @ (&))))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#S') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 (((arrow_475358991le_alt) != 98.62/13.31 (X4))))))))) @ 98.62/13.31 ((('#S') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#S') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 '#C'))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 &))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X2))))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 |) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X4))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ produc1347929815le_alt @ 98.62/13.31 X4)))))))))))))))) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 (('#C') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 (( 98.62/13.31 (arrow_475358991le_alt) != 98.62/13.31 (X2))))))) @ 98.62/13.31 (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2 @ X4)))))))))))))) @ 98.62/13.31 ((('#B') @ ((('#C') @ ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X4))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2))))))))))))) @ 98.62/13.31 (((X2) != (X4)))))))))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1106])). 98.62/13.31 thf(zip_derived_cl1108, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : produc1501160679le_alt > $o]: 98.62/13.31 (((!!) @ ((('#B') @ (!!) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (=>))) @ (!=))))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (((=>) @ (member377231867_alt_o @ 98.62/13.31 X6 @ 98.62/13.31 arrow_823908191le_Lin))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.31 ((('#B') @ ((('#B') @ (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2 @ X4)))) @ 98.62/13.31 (arrow_2098199487_below @ X6))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#C') @ 98.62/13.31 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.31 ((('#B') @ ((('#B') @ (&))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) != 98.62/13.31 (X4))))))) @ 98.62/13.31 ((('#S') @ ((('#B') @ ( 98.62/13.31 '#C') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 &))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 '#B') @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X2))))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#S') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ ( 98.62/13.31 |) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X4))))) @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ produc1347929815le_alt @ 98.62/13.31 X4)))) @ 98.62/13.31 X6)))))))))) @ 98.62/13.31 ((('#C') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 =>) @ 98.62/13.31 (((arrow_475358991le_alt) != 98.62/13.31 (X2))))) @ 98.62/13.31 (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2 @ X4) @ 98.62/13.31 X6))))))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.31 ((('#B') @ (=>) @ 98.62/13.31 (((arrow_475358991le_alt) = 98.62/13.31 (X4))))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2))) @ 98.62/13.31 X6)))))))) @ 98.62/13.31 (((X2) != (X4)))))))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1107])). 98.62/13.31 thf(zip_derived_cl1109, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt]: 98.62/13.31 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 98.62/13.31 (((arrow_475358991le_alt) != (X8))))) @ 98.62/13.31 ((('#B') @ (((=>) @ (member377231867_alt_o @ X6 @ 98.62/13.31 arrow_823908191le_Lin))) @ 98.62/13.31 ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.31 ((('#B') @ (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ X2 @ 98.62/13.31 X4)) @ 98.62/13.31 (arrow_2098199487_below @ X6 @ X8))))) @ 98.62/13.31 ((('#C') @ ((('#S') @ ((('#B') @ (&) @ 98.62/13.31 ((('#B') @ (((=>) @ (( 98.62/13.31 (X4) != 98.62/13.31 (X8))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ ( 98.62/13.31 &) @ 98.62/13.31 ((('#B') @ ( 98.62/13.31 ((=>) @ ( 98.62/13.31 ((X2) = (X8))))) @ 98.62/13.31 ((('#S') @ ( 98.62/13.31 (('#B') @ ( 98.62/13.31 |) @ 98.62/13.31 (( 98.62/13.31 (arrow_475358991le_alt) = 98.62/13.31 (X4))))) @ 98.62/13.31 ((('#C') @ ( 98.62/13.31 ( 98.62/13.31 ('#B') @ member214075476le_alt @ 98.62/13.31 ( 98.62/13.31 ( 98.62/13.31 ('#C') @ produc1347929815le_alt @ 98.62/13.31 X4)))) @ 98.62/13.31 X6)))))))) @ 98.62/13.31 (((((X2) != (X8))) => 98.62/13.31 (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2 @ X4) @ 98.62/13.31 X6))))))))) @ 98.62/13.31 ((('#B') @ (((=>) @ (((X4) = (X8))))) @ 98.62/13.31 ((('#C') @ ((('#B') @ member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ 98.62/13.31 X2))) @ 98.62/13.31 X6)))))) @ 98.62/13.31 (((X2) != (X4)))))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1108])). 98.62/13.31 thf(zip_derived_cl1110, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.31 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.31 X10 : arrow_475358991le_alt]: 98.62/13.31 (((((X8) != (X10))) => 98.62/13.31 (((member377231867_alt_o @ X6 @ arrow_823908191le_Lin) => 98.62/13.31 (((member214075476le_alt @ (produc1347929815le_alt @ X2 @ X4) @ 98.62/13.31 (arrow_2098199487_below @ X6 @ X8 @ X10)) <=> 98.62/13.31 (((((((X4) != (X8))) => 98.62/13.31 (((((((X2) = (X8))) => 98.62/13.31 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.31 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.31 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.31 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.31 (((X2) != (X4)))))))))))), 98.62/13.31 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1109])). 98.62/13.31 thf(zip_derived_cl507, plain, 98.62/13.31 (![X2 : produc1501160679le_alt > $o, 98.62/13.31 X4 : (produc1501160679le_alt > $o) > $o]: 98.62/13.31 ((member377231867_alt_o @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl506])). 98.62/13.31 thf(zip_derived_cl503, plain, 98.62/13.31 (![X2 : produc1501160679le_alt, X4 : produc1501160679le_alt > $o]: 98.62/13.31 ((member214075476le_alt @ X2 @ X4) = (X4 @ X2))), 98.62/13.31 inference('simplify nested equalities', [status(thm)], 98.62/13.31 [zip_derived_cl502])). 98.62/13.31 thf(zip_derived_cl1111, plain, 98.62/13.31 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.32 X10 : arrow_475358991le_alt]: 98.62/13.32 (((((X8) != (X10))) => 98.62/13.32 (((arrow_823908191le_Lin @ X6) => 98.62/13.32 (((arrow_2098199487_below @ X6 @ X8 @ X10 @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4)) <=> 98.62/13.32 (((((((X4) != (X8))) => 98.62/13.32 (((((((X2) = (X8))) => 98.62/13.32 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.32 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.32 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.32 (((X2) != (X4)))))))))))), 98.62/13.32 inference('demod', [status(thm)], 98.62/13.32 [zip_derived_cl1110, zip_derived_cl507, zip_derived_cl503])). 98.62/13.32 thf(zip_derived_cl1112, plain, 98.62/13.32 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.32 X10 : arrow_475358991le_alt]: 98.62/13.32 (~ (((X8) != (X10))) 98.62/13.32 | (((arrow_823908191le_Lin @ X6) => 98.62/13.32 (((arrow_2098199487_below @ X6 @ X8 @ X10 @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4)) <=> 98.62/13.32 (((((((X4) != (X8))) => 98.62/13.32 (((((((X2) = (X8))) => 98.62/13.32 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.32 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.32 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.32 (((X2) != (X4))))))))))), 98.62/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1111])). 98.62/13.32 thf(zip_derived_cl1113, plain, 98.62/13.32 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.32 X10 : arrow_475358991le_alt]: 98.62/13.32 (((X8) = (X10)) 98.62/13.32 | (((arrow_823908191le_Lin @ X6) => 98.62/13.32 (((arrow_2098199487_below @ X6 @ X8 @ X10 @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4)) <=> 98.62/13.32 (((((((X4) != (X8))) => 98.62/13.32 (((((((X2) = (X8))) => 98.62/13.32 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.32 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.32 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.32 (((X2) != (X4))))))))))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl1112])). 98.62/13.32 thf(zip_derived_cl1114, plain, 98.62/13.32 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.32 X10 : arrow_475358991le_alt]: 98.62/13.32 (~ (arrow_823908191le_Lin @ X6) 98.62/13.32 | (((arrow_2098199487_below @ X6 @ X8 @ X10 @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4)) <=> 98.62/13.32 (((((((X4) != (X8))) => 98.62/13.32 (((((((X2) = (X8))) => 98.62/13.32 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.32 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.32 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.32 (((X2) != (X4))))))) 98.62/13.32 | ((X8) = (X10)))), 98.62/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1113])). 98.62/13.32 thf(zip_derived_cl1115, plain, 98.62/13.32 (![X2 : arrow_475358991le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : produc1501160679le_alt > $o, X8 : arrow_475358991le_alt, 98.62/13.32 X10 : arrow_475358991le_alt]: 98.62/13.32 (~ (arrow_823908191le_Lin @ X6) 98.62/13.32 | ((arrow_2098199487_below @ X6 @ X8 @ X10 @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4)) 98.62/13.32 = (((((((X4) != (X8))) => 98.62/13.32 (((((((X2) = (X8))) => 98.62/13.32 (((((X4) = (X10))) | (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X10 @ X4) @ X6))))) & 98.62/13.32 (((((X2) != (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X4) @ X6))))))) & 98.62/13.32 (((((X4) = (X8))) => (member214075476le_alt @ 98.62/13.32 (produc1347929815le_alt @ X2 @ X10) @ X6))) & 98.62/13.32 (((X2) != (X4)))))) 98.62/13.32 | ((X8) = (X10)))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl1114])). 98.62/13.32 thf(zip_derived_cl576, plain, 98.62/13.32 (![X2 : arrow_475358991le_alt, X4 : list_A2115238852le_alt]: 98.62/13.32 ((rev_Ar1106406943le_alt @ (cons_A228743023le_alt @ X2 @ X4)) 98.62/13.32 = (append179082452le_alt @ (rev_Ar1106406943le_alt @ X4) @ 98.62/13.32 (cons_A228743023le_alt @ X2 @ nil_Ar1286194111le_alt)))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl575])). 98.62/13.32 thf(fact_324_iso__tuple__UNIV__I, axiom, 98.62/13.32 (![X_54:arrow_1429601828e_indi]: 98.62/13.32 ( member2052026769e_indi @ X_54 @ top_to988227749indi_o ))). 98.62/13.32 thf(zip_derived_cl0, plain, 98.62/13.32 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 98.62/13.32 (member2052026769e_indi @ Y0 @ top_to988227749indi_o))))), 98.62/13.32 inference('cnf', [status(esa)], [fact_324_iso__tuple__UNIV__I])). 98.62/13.32 thf(zip_derived_cl1, plain, 98.62/13.32 ( (((!!) @ ((('#C') @ member2052026769e_indi @ top_to988227749indi_o))))), 98.62/13.32 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 98.62/13.32 thf(zip_derived_cl351, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi]: 98.62/13.32 (member2052026769e_indi @ X2 @ top_to988227749indi_o)), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 98.62/13.32 thf(fact_372_append__assoc, axiom, 98.62/13.32 (![Xs_100:list_A2115238852le_alt,Ys_48:list_A2115238852le_alt, 98.62/13.32 Zs_5:list_A2115238852le_alt]: 98.62/13.32 ( ( append179082452le_alt @ 98.62/13.32 ( append179082452le_alt @ Xs_100 @ Ys_48 ) @ Zs_5 ) = 98.62/13.32 ( append179082452le_alt @ 98.62/13.32 Xs_100 @ ( append179082452le_alt @ Ys_48 @ Zs_5 ) ) ))). 98.62/13.32 thf(zip_derived_cl243, plain, 98.62/13.32 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ (^[Y1 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 98.62/13.32 (((append179082452le_alt @ 98.62/13.32 (append179082452le_alt @ Y0 @ Y1) @ 98.62/13.32 Y2) = (append179082452le_alt @ 98.62/13.32 Y0 @ 98.62/13.32 (append179082452le_alt @ Y1 @ Y2)))))))))))))), 98.62/13.32 inference('cnf', [status(esa)], [fact_372_append__assoc])). 98.62/13.32 thf(zip_derived_cl244, plain, 98.62/13.32 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.32 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 98.62/13.32 ((('#B') @ ((('#B') @ append179082452le_alt)) @ 98.62/13.32 append179082452le_alt)))))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ ('#B') @ append179082452le_alt)))) @ 98.62/13.32 append179082452le_alt))))))))))), 98.62/13.32 inference('lams2combs', [status(thm)], [zip_derived_cl243])). 98.62/13.32 thf(zip_derived_cl676, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.32 ((('#B') @ append179082452le_alt @ 98.62/13.32 (append179082452le_alt @ X2))))))) @ 98.62/13.32 ((('#B') @ ((('#B') @ (append179082452le_alt @ X2))) @ 98.62/13.32 append179082452le_alt))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl244])). 98.62/13.32 thf(zip_derived_cl677, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 98.62/13.32 (append179082452le_alt @ 98.62/13.32 (append179082452le_alt @ X2 @ X4)))) @ 98.62/13.32 ((('#B') @ (append179082452le_alt @ X2) @ 98.62/13.32 (append179082452le_alt @ X4)))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl676])). 98.62/13.32 thf(zip_derived_cl678, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 98.62/13.32 X6 : list_A2115238852le_alt]: 98.62/13.32 (((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) = 98.62/13.32 (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl677])). 98.62/13.32 thf(zip_derived_cl679, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : list_A2115238852le_alt, 98.62/13.32 X6 : list_A2115238852le_alt]: 98.62/13.32 ((append179082452le_alt @ (append179082452le_alt @ X2 @ X4) @ X6) 98.62/13.32 = (append179082452le_alt @ X2 @ (append179082452le_alt @ X4 @ X6)))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl678])). 98.62/13.32 thf(fact_289_Prof__def, axiom, 98.62/13.32 (( arrow_734252939e_Prof ) = 98.62/13.32 ( pi_Arr1929480907_alt_o @ 98.62/13.32 top_to988227749indi_o @ 98.62/13.32 ( ^[Uu:arrow_1429601828e_indi]: ( arrow_823908191le_Lin ) ) ))). 98.62/13.32 thf(zip_derived_cl11, plain, 98.62/13.32 (((arrow_734252939e_Prof) 98.62/13.32 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 98.62/13.32 (^[Y0 : arrow_1429601828e_indi]: (arrow_823908191le_Lin))))), 98.62/13.32 inference('cnf', [status(esa)], [fact_289_Prof__def])). 98.62/13.32 thf(zip_derived_cl12, plain, 98.62/13.32 (((arrow_734252939e_Prof) 98.62/13.32 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 98.62/13.32 ((('#K') @ arrow_823908191le_Lin))))), 98.62/13.32 inference('lams2combs', [status(thm)], [zip_derived_cl11])). 98.62/13.32 thf(zip_derived_cl11020, plain, 98.62/13.32 (((arrow_734252939e_Prof) 98.62/13.32 = (pi_Arr1929480907_alt_o @ top_to988227749indi_o @ 98.62/13.32 ('#ty_enc48' @ arrow_823908191le_Lin)))), 98.62/13.32 inference('remove_ty_args', [status(thm)], [zip_derived_cl12])). 98.62/13.32 thf(fact_114_funcset__mem, axiom, 98.62/13.32 (![X_71:arrow_1429601828e_indi, 98.62/13.32 F_13:( arrow_1429601828e_indi > produc1501160679le_alt > $o ), 98.62/13.32 A_18:( arrow_1429601828e_indi > $o ), 98.62/13.32 B_15:( ( produc1501160679le_alt > $o ) > $o )]: 98.62/13.32 ( ( member526088951_alt_o @ 98.62/13.32 F_13 @ 98.62/13.32 ( pi_Arr1929480907_alt_o @ 98.62/13.32 A_18 @ ( ^[Uu:arrow_1429601828e_indi]: ( B_15 ) ) ) ) => 98.62/13.32 ( ( member2052026769e_indi @ X_71 @ A_18 ) => 98.62/13.32 ( member377231867_alt_o @ ( F_13 @ X_71 ) @ B_15 ) ) ))). 98.62/13.32 thf(zip_derived_cl15, plain, 98.62/13.32 ( (((!!) @ (^[Y0 : arrow_1429601828e_indi]: 98.62/13.32 (((!!) @ (^[Y1 : arrow_1429601828e_indi > 98.62/13.32 produc1501160679le_alt > $o]: 98.62/13.32 (((!!) @ (^[Y2 : arrow_1429601828e_indi > $o]: 98.62/13.32 (((!!) @ (^[Y3 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (((member526088951_alt_o @ 98.62/13.32 Y1 @ 98.62/13.32 (pi_Arr1929480907_alt_o @ 98.62/13.32 Y2 @ 98.62/13.32 (^[Y4 : arrow_1429601828e_indi]: 98.62/13.32 (Y3)))) => 98.62/13.32 (((member2052026769e_indi @ 98.62/13.32 Y0 @ Y2) => 98.62/13.32 (member377231867_alt_o @ 98.62/13.32 (Y1 @ Y0) @ Y3)))))))))))))))))), 98.62/13.32 inference('cnf', [status(esa)], [fact_114_funcset__mem])). 98.62/13.32 thf(zip_derived_cl16, plain, 98.62/13.32 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.32 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 98.62/13.32 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.32 ((('#B') @ ((('#B') @ ( 98.62/13.32 (('#B') @ (=>))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ( 98.62/13.32 '#B') @ 98.62/13.32 ((('#B') @ ( 98.62/13.32 '#B') @ 98.62/13.32 member526088951_alt_o)))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ( 98.62/13.32 '#B') @ 98.62/13.32 pi_Arr1929480907_alt_o)) @ 98.62/13.32 ('#K'))))))))))))) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ ('#C') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#B'))) @ 98.62/13.32 ((('#B') @ ((('#B') @ (=>))) @ 98.62/13.32 member2052026769e_indi)))))))) @ 98.62/13.32 ((('#B') @ ((('#B') @ member377231867_alt_o)) @ 98.62/13.32 ((('#C') @ ('#I')))))))))))))))))), 98.62/13.32 inference('lams2combs', [status(thm)], [zip_derived_cl15])). 98.62/13.32 thf(zip_derived_cl494, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi]: 98.62/13.32 (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.32 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ ('#B') @ 98.62/13.32 member526088951_alt_o)))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 pi_Arr1929480907_alt_o)) @ 98.62/13.32 ('#K'))))))))))) @ 98.62/13.32 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ (=>) @ 98.62/13.32 (member2052026769e_indi @ X2))))))) @ 98.62/13.32 ((('#B') @ member377231867_alt_o @ 98.62/13.32 ((('#C') @ ('#I') @ X2))))))))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 98.62/13.32 thf(zip_derived_cl495, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o]: 98.62/13.32 (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ (=>))) @ 98.62/13.32 ((('#B') @ ((('#B') @ (member526088951_alt_o @ 98.62/13.32 X4))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 pi_Arr1929480907_alt_o)) @ 98.62/13.32 ('#K'))))))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ (=>) @ 98.62/13.32 (member2052026769e_indi @ X2))))) @ 98.62/13.32 (member377231867_alt_o @ (X4 @ X2))))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl494])). 98.62/13.32 thf(zip_derived_cl496, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o]: 98.62/13.32 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 98.62/13.32 ((('#B') @ (member526088951_alt_o @ X4) @ 98.62/13.32 ((('#B') @ (pi_Arr1929480907_alt_o @ X6) @ 98.62/13.32 ('#K'))))))) @ 98.62/13.32 ((('#B') @ (((=>) @ (member2052026769e_indi @ X2 @ X6))) @ 98.62/13.32 (member377231867_alt_o @ (X4 @ X2))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl495])). 98.62/13.32 thf(zip_derived_cl497, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o, 98.62/13.32 X8 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (((member526088951_alt_o @ X4 @ 98.62/13.32 (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)))) => 98.62/13.32 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 98.62/13.32 (X4 @ X2) @ X8)))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl496])). 98.62/13.32 thf(zip_derived_cl474, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X4 : (arrow_1429601828e_indi > produc1501160679le_alt > $o) > $o]: 98.62/13.32 ((member526088951_alt_o @ X2 @ X4) = (X4 @ X2))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl473])). 98.62/13.32 thf(zip_derived_cl498, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o, 98.62/13.32 X8 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (((pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) => 98.62/13.32 (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 98.62/13.32 (X4 @ X2) @ X8)))))), 98.62/13.32 inference('demod', [status(thm)], [zip_derived_cl497, zip_derived_cl474])). 98.62/13.32 thf(zip_derived_cl499, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o, 98.62/13.32 X8 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4) 98.62/13.32 | (((member2052026769e_indi @ X2 @ X6) => (member377231867_alt_o @ 98.62/13.32 (X4 @ X2) @ X8))))), 98.62/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl498])). 98.62/13.32 thf(zip_derived_cl500, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o, 98.62/13.32 X8 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (~ (member2052026769e_indi @ X2 @ X6) 98.62/13.32 | (member377231867_alt_o @ (X4 @ X2) @ X8) 98.62/13.32 | ~ (pi_Arr1929480907_alt_o @ X6 @ ((('#K') @ X8)) @ X4))), 98.62/13.32 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl499])). 98.62/13.32 thf(zip_derived_cl11028, plain, 98.62/13.32 (![X2 : arrow_1429601828e_indi, 98.62/13.32 X4 : arrow_1429601828e_indi > produc1501160679le_alt > $o, 98.62/13.32 X6 : arrow_1429601828e_indi > $o, 98.62/13.32 X8 : (produc1501160679le_alt > $o) > $o]: 98.62/13.32 (~ (member2052026769e_indi @ X2 @ X6) 98.62/13.32 | (member377231867_alt_o @ (X4 @ X2) @ X8) 98.62/13.32 | ~ (pi_Arr1929480907_alt_o @ X6 @ ('#ty_enc48' @ X8) @ X4))), 98.62/13.32 inference('remove_ty_args', [status(thm)], [zip_derived_cl500])). 98.62/13.32 thf(fact_365_snoc__eq__iff__butlast, axiom, 98.62/13.32 (![Xs_106:list_A2115238852le_alt,X_51:arrow_475358991le_alt, 98.62/13.32 Ys_54:list_A2115238852le_alt]: 98.62/13.32 ( ( ( append179082452le_alt @ 98.62/13.32 Xs_106 @ ( cons_A228743023le_alt @ X_51 @ nil_Ar1286194111le_alt ) ) = 98.62/13.32 ( Ys_54 ) ) <=> 98.62/13.32 ( ( ( butlas274947851le_alt @ Ys_54 ) = ( Xs_106 ) ) & 98.62/13.32 ( ( last_A1217315288le_alt @ Ys_54 ) = ( X_51 ) ) & 98.62/13.32 ( ( Ys_54 ) != ( nil_Ar1286194111le_alt ) ) ) ))). 98.62/13.32 thf(zip_derived_cl188, plain, 98.62/13.32 ( (((!!) @ (^[Y0 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ (^[Y1 : arrow_475358991le_alt]: 98.62/13.32 (((!!) @ (^[Y2 : list_A2115238852le_alt]: 98.62/13.32 (((((append179082452le_alt @ Y0 @ 98.62/13.32 (cons_A228743023le_alt @ Y1 @ 98.62/13.32 nil_Ar1286194111le_alt)) = 98.62/13.32 (Y2))) <=> 98.62/13.32 (((((butlas274947851le_alt @ 98.62/13.32 Y2) = (Y0))) & 98.62/13.32 (((last_A1217315288le_alt @ 98.62/13.32 Y2) = (Y1))) & 98.62/13.32 (((Y2) != 98.62/13.32 (nil_Ar1286194111le_alt))))))))))))))))), 98.62/13.32 inference('cnf', [status(esa)], [fact_365_snoc__eq__iff__butlast])). 98.62/13.32 thf(zip_derived_cl189, plain, 98.62/13.32 ( (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#B') @ ((('#B') @ (!!))) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.32 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 98.62/13.32 ((('#B') @ ((('#B') @ (=))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 append179082452le_alt)) @ 98.62/13.32 ((('#C') @ cons_A228743023le_alt @ 98.62/13.32 nil_Ar1286194111le_alt)))))))))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#C') @ 98.62/13.32 ((('#B') @ ((('#B') @ ('#S'))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#B') @ 98.62/13.32 ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ (&))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ( 98.62/13.32 =) @ 98.62/13.32 butlas274947851le_alt)))))))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ (=) @ 98.62/13.32 last_A1217315288le_alt)))))))))) @ 98.62/13.32 ((('#C') @ (!=) @ nil_Ar1286194111le_alt))))))))))))), 98.62/13.32 inference('lams2combs', [status(thm)], [zip_derived_cl188])). 98.62/13.32 thf(zip_derived_cl839, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt]: 98.62/13.32 (((!!) @ ((('#B') @ (!!) @ 98.62/13.32 ((('#S') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#B') @ (<=>))) @ 98.62/13.32 ((('#B') @ (=) @ 98.62/13.32 ((('#B') @ (append179082452le_alt @ X2) @ 98.62/13.32 ((('#C') @ cons_A228743023le_alt @ 98.62/13.32 nil_Ar1286194111le_alt)))))))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ ('#S') @ 98.62/13.32 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 98.62/13.32 ((('#C') @ ( 98.62/13.32 (('#B') @ ( 98.62/13.32 =) @ 98.62/13.32 butlas274947851le_alt)) @ 98.62/13.32 X2)))))) @ 98.62/13.32 ((('#C') @ ((('#B') @ (=) @ 98.62/13.32 last_A1217315288le_alt)))))))) @ 98.62/13.32 ((('#C') @ (!=) @ nil_Ar1286194111le_alt))))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl189])). 98.62/13.32 thf(zip_derived_cl840, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt]: 98.62/13.32 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 98.62/13.32 (((list_A2115238852le_alt) = 98.62/13.32 (append179082452le_alt @ X2 @ 98.62/13.32 (cons_A228743023le_alt @ X4 @ 98.62/13.32 nil_Ar1286194111le_alt)))))) @ 98.62/13.32 ((('#S') @ ((('#S') @ ((('#B') @ (&) @ 98.62/13.32 ((('#C') @ ((('#B') @ (=) @ 98.62/13.32 butlas274947851le_alt)) @ 98.62/13.32 X2)))) @ 98.62/13.32 ((('#C') @ ((('#B') @ (=) @ 98.62/13.32 last_A1217315288le_alt)) @ 98.62/13.32 X4)))) @ 98.62/13.32 ((('#C') @ (!=) @ nil_Ar1286194111le_alt))))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl839])). 98.62/13.32 thf(zip_derived_cl841, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : list_A2115238852le_alt]: 98.62/13.32 (((((append179082452le_alt @ X2 @ 98.62/13.32 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6))) <=> 98.62/13.32 (((((butlas274947851le_alt @ X6) = (X2))) & 98.62/13.32 (((last_A1217315288le_alt @ X6) = (X4))) & 98.62/13.32 (((X6) != (nil_Ar1286194111le_alt)))))))), 98.62/13.32 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl840])). 98.62/13.32 thf(zip_derived_cl842, plain, 98.62/13.32 (![X2 : list_A2115238852le_alt, X4 : arrow_475358991le_alt, 98.62/13.32 X6 : list_A2115238852le_alt]: 98.62/13.32 ((((append179082452le_alt @ X2 @ 98.62/13.32 (cons_A228743023le_alt @ X4 @ nil_Ar1286194111le_alt)) = (X6))) 98.62/13.32 = (((((butlas274947851le_alt @ X6) = (X2))) & 98.62/13.32 (((last_A1217315288le_alt @ X6) = (X4))) & 98.62/13.32 (((X6) != (nil_Ar1286194111le_alt))))))), 98.62/13.32 inference('simplify nested equalities', [status(thm)], 98.62/13.32 [zip_derived_cl841])). 98.62/13.32 thf(zip_derived_cl11040, plain, ($false), 98.62/13.32 inference('eprover', [status(thm)], 98.62/13.32 [zip_derived_cl284, zip_derived_cl402, zip_derived_cl477, 98.62/13.32 zip_derived_cl378, zip_derived_cl417, zip_derived_cl540, 98.62/13.32 zip_derived_cl555, zip_derived_cl503, zip_derived_cl332, 98.62/13.32 zip_derived_cl504, zip_derived_cl411, zip_derived_cl579, 98.62/13.32 zip_derived_cl769, zip_derived_cl604, zip_derived_cl414, 98.62/13.32 zip_derived_cl510, zip_derived_cl654, zip_derived_cl474, 98.62/13.32 zip_derived_cl507, zip_derived_cl1115, zip_derived_cl576, 98.62/13.32 zip_derived_cl351, zip_derived_cl679, zip_derived_cl11020, 98.62/13.32 zip_derived_cl11028, zip_derived_cl842])). 98.62/13.32 98.62/13.32 % SZS output end Refutation 98.62/13.32 98.62/13.32 98.62/13.32 % Terminating... 98.62/13.40 % Runner terminated. 98.62/13.42 % Zipperpin 1.5 exiting 98.62/13.43 EOF