0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.26 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.M8MX2wEnQt true 0.25/0.47 % Computer : n020.cluster.edu 0.25/0.47 % Model : x86_64 x86_64 0.25/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.25/0.47 % Memory : 8042.1875MB 0.25/0.47 % OS : Linux 3.10.0-693.el7.x86_64 0.25/0.47 % CPULimit : 1440 0.25/0.47 % WCLimit : 180 0.25/0.47 % DateTime : Mon Jul 3 10:21:46 EDT 2023 0.25/0.47 % CPUTime : 0.25/0.47 % Running portfolio for 1440 s 0.25/0.47 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.25/0.48 % Number of cores: 8 0.25/0.48 % Python version: Python 3.6.8 0.25/0.48 % Running in HO mode 0.45/0.78 % Total configuration time : 828 0.45/0.78 % Estimated wc time : 1656 0.45/0.78 % Estimated cpu time (8 cpus) : 207.0 0.45/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.45/0.84 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.45/0.84 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.45/0.85 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.45/0.86 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.45/0.86 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.46/0.87 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.46/0.87 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.46/1.01 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 92.27/12.48 % Solved by lams/40_b.comb.sh. 92.27/12.48 % done 446 iterations in 11.506s 92.27/12.48 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 92.27/12.48 % SZS output start Refutation 92.27/12.48 thf(list_A1402527603le_alt_type, type, list_A1402527603le_alt: $tType). 92.27/12.48 thf(arrow_1389031998le_alt_type, type, arrow_1389031998le_alt: $tType). 92.27/12.48 thf(produc1572197287le_alt_type, type, produc1572197287le_alt: $tType). 92.27/12.48 thf(arrow_1196572341e_indi_type, type, arrow_1196572341e_indi: $tType). 92.27/12.48 thf(member1241905979_alt_o_type, type, member1241905979_alt_o: (produc1572197287le_alt > $o) > 92.27/12.48 ((produc1572197287le_alt > $o) > $o) > $o). 92.27/12.48 thf(produc897867031le_alt_type, type, produc897867031le_alt: arrow_1389031998le_alt > 92.27/12.48 arrow_1389031998le_alt > produc1572197287le_alt). 92.27/12.48 thf(b_type, type, b: arrow_1389031998le_alt). 92.27/12.48 thf(top_to54564308indi_o_type, type, top_to54564308indi_o: arrow_1196572341e_indi > $o). 92.27/12.48 thf(last_A2130988295le_alt_type, type, last_A2130988295le_alt: list_A1402527603le_alt > arrow_1389031998le_alt). 92.27/12.48 thf(hd_Arr731872705le_alt_type, type, hd_Arr731872705le_alt: list_A1402527603le_alt > arrow_1389031998le_alt). 92.27/12.48 thf(c_type, type, c: arrow_1389031998le_alt). 92.27/12.48 thf(cons_A1142416030le_alt_type, type, cons_A1142416030le_alt: arrow_1389031998le_alt > 92.27/12.48 list_A1402527603le_alt > list_A1402527603le_alt). 92.27/12.48 thf('#ty_enc67_type', type, '#ty_enc67': ((produc1572197287le_alt > $o) > $o) > 92.27/12.48 arrow_1196572341e_indi > 92.27/12.48 (produc1572197287le_alt > $o) > $o). 92.27/12.48 thf(member822980838_alt_o_type, type, member822980838_alt_o: (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > 92.27/12.48 ((arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o) > $o). 92.27/12.48 thf(ord_le602483040lt_o_o_type, type, ord_le602483040lt_o_o: ((arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o) > 92.27/12.48 ((arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o) > $o). 92.27/12.48 thf(append1092755459le_alt_type, type, append1092755459le_alt: list_A1402527603le_alt > 92.27/12.48 list_A1402527603le_alt > list_A1402527603le_alt). 92.27/12.48 thf(butlas1188620858le_alt_type, type, butlas1188620858le_alt: list_A1402527603le_alt > list_A1402527603le_alt). 92.27/12.48 thf(arrow_1647925946e_Prof_type, type, arrow_1647925946e_Prof: (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o). 92.27/12.48 thf(member285112084le_alt_type, type, member285112084le_alt: produc1572197287le_alt > 92.27/12.48 (produc1572197287le_alt > $o) > $o). 92.27/12.48 thf(member998036369le_alt_type, type, member998036369le_alt: arrow_1389031998le_alt > 92.27/12.48 (arrow_1389031998le_alt > $o) > $o). 92.27/12.48 thf('#sk11_type', type, '#sk11': arrow_1196572341e_indi). 92.27/12.48 thf(p_type, type, p: arrow_1196572341e_indi > produc1572197287le_alt > $o). 92.27/12.48 thf(nil_Ar52383470le_alt_type, type, nil_Ar52383470le_alt: list_A1402527603le_alt). 92.27/12.48 thf(distin1149997281le_alt_type, type, distin1149997281le_alt: list_A1402527603le_alt > $o). 92.27/12.48 thf(pi_Arr1309696186_alt_o_type, type, pi_Arr1309696186_alt_o: (arrow_1196572341e_indi > $o) > 92.27/12.48 (arrow_1196572341e_indi > 92.27/12.48 (produc1572197287le_alt > $o) > $o) > 92.27/12.48 (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o). 92.27/12.48 thf(arrow_1865170000_below_type, type, arrow_1865170000_below: (produc1572197287le_alt > $o) > 92.27/12.48 arrow_1389031998le_alt > 92.27/12.48 arrow_1389031998le_alt > 92.27/12.48 produc1572197287le_alt > $o). 92.27/12.48 thf(set_Ar1491127311le_alt_type, type, set_Ar1491127311le_alt: list_A1402527603le_alt > 92.27/12.48 arrow_1389031998le_alt > $o). 92.27/12.48 thf(arrow_1982173296le_Lin_type, type, arrow_1982173296le_Lin: (produc1572197287le_alt > $o) > $o). 92.27/12.48 thf(ord_le865407012indi_o_type, type, ord_le865407012indi_o: (arrow_1196572341e_indi > $o) > 92.27/12.48 (arrow_1196572341e_indi > $o) > $o). 92.27/12.48 thf(a_type, type, a: arrow_1389031998le_alt). 92.27/12.48 thf(member1818997282e_indi_type, type, member1818997282e_indi: arrow_1196572341e_indi > 92.27/12.48 (arrow_1196572341e_indi > $o) > $o). 92.27/12.48 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 92.27/12.48 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 92.27/12.48 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 92.27/12.48 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 92.27/12.48 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 92.27/12.48 thf(fact_4_dist, axiom, 92.27/12.48 (distin1149997281le_alt @ 92.27/12.48 ( cons_A1142416030le_alt @ 92.27/12.48 a @ 92.27/12.48 ( cons_A1142416030le_alt @ 92.27/12.48 b @ ( cons_A1142416030le_alt @ c @ nil_Ar52383470le_alt ) ) ))). 92.27/12.48 thf(zip_derived_cl112, plain, 92.27/12.48 ( (distin1149997281le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ a @ 92.27/12.48 (cons_A1142416030le_alt @ b @ 92.27/12.48 (cons_A1142416030le_alt @ c @ nil_Ar52383470le_alt))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_4_dist])). 92.27/12.48 thf(fact_401_append__Nil, axiom, 92.27/12.48 (![Ys_57:list_A1402527603le_alt]: 92.27/12.48 ( ( append1092755459le_alt @ nil_Ar52383470le_alt @ Ys_57 ) = ( Ys_57 ) ))). 92.27/12.48 thf(zip_derived_cl190, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : list_A1402527603le_alt]: 92.27/12.48 (((append1092755459le_alt @ nil_Ar52383470le_alt @ Y0) = 92.27/12.48 (Y0))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_401_append__Nil])). 92.27/12.48 thf(zip_derived_cl191, plain, 92.27/12.48 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 92.27/12.48 (append1092755459le_alt @ nil_Ar52383470le_alt))) @ 92.27/12.48 ('#I')))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl190])). 92.27/12.48 thf(zip_derived_cl443, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((append1092755459le_alt @ nil_Ar52383470le_alt @ X2) = (X2)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl191])). 92.27/12.48 thf(zip_derived_cl444, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 ((append1092755459le_alt @ nil_Ar52383470le_alt @ X2) = (X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl443])). 92.27/12.48 thf(fact_37_list_Osimps_I2_J, axiom, 92.27/12.48 (![A_48:arrow_1389031998le_alt,List_5:list_A1402527603le_alt]: 92.27/12.48 ( ( nil_Ar52383470le_alt ) != ( cons_A1142416030le_alt @ A_48 @ List_5 ) ))). 92.27/12.48 thf(zip_derived_cl78, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : list_A1402527603le_alt]: 92.27/12.48 (((nil_Ar52383470le_alt) != 92.27/12.48 (cons_A1142416030le_alt @ Y0 @ Y1)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_37_list_Osimps_I2_J])). 92.27/12.48 thf(zip_derived_cl79, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (((list_A1402527603le_alt) != 92.27/12.48 (nil_Ar52383470le_alt))))) @ 92.27/12.48 cons_A1142416030le_alt))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl78])). 92.27/12.48 thf(zip_derived_cl482, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#B') @ (((list_A1402527603le_alt) != 92.27/12.48 (nil_Ar52383470le_alt))) @ 92.27/12.48 (cons_A1142416030le_alt @ X2)))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl79])). 92.27/12.48 thf(zip_derived_cl483, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 (((nil_Ar52383470le_alt) != (cons_A1142416030le_alt @ X2 @ X4)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl482])). 92.27/12.48 thf(zip_derived_cl484, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 ((nil_Ar52383470le_alt) != (cons_A1142416030le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl483])). 92.27/12.48 thf(fact_583_hd_Osimps, axiom, 92.27/12.48 (![X_54:arrow_1389031998le_alt,Xs_77:list_A1402527603le_alt]: 92.27/12.48 ( ( hd_Arr731872705le_alt @ ( cons_A1142416030le_alt @ X_54 @ Xs_77 ) ) = 92.27/12.48 ( X_54 ) ))). 92.27/12.48 thf(zip_derived_cl156, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : list_A1402527603le_alt]: 92.27/12.48 (((hd_Arr731872705le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ Y0 @ Y1)) = (Y0)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_583_hd_Osimps])). 92.27/12.48 thf(zip_derived_cl157, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=))) @ 92.27/12.48 ((('#B') @ ((('#B') @ hd_Arr731872705le_alt)) @ 92.27/12.48 cons_A1142416030le_alt)))))) @ 92.27/12.48 ('#I')))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl156])). 92.27/12.48 thf(zip_derived_cl557, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#C') @ ((('#B') @ (=) @ 92.27/12.48 ((('#B') @ hd_Arr731872705le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ X2))))) @ 92.27/12.48 X2))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl157])). 92.27/12.48 thf(zip_derived_cl558, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 (((hd_Arr731872705le_alt @ (cons_A1142416030le_alt @ X2 @ X4)) = (X2)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl557])). 92.27/12.48 thf(zip_derived_cl559, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 ((hd_Arr731872705le_alt @ (cons_A1142416030le_alt @ X2 @ X4)) = (X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl558])). 92.27/12.48 thf(fact_744_hd__in__set, axiom, 92.27/12.48 (![Xs_25:list_A1402527603le_alt]: 92.27/12.48 ( ( ( Xs_25 ) != ( nil_Ar52383470le_alt ) ) => 92.27/12.48 ( member998036369le_alt @ 92.27/12.48 ( hd_Arr731872705le_alt @ Xs_25 ) @ ( set_Ar1491127311le_alt @ Xs_25 ) ) ))). 92.27/12.48 thf(zip_derived_cl228, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : list_A1402527603le_alt]: 92.27/12.48 (((((Y0) != (nil_Ar52383470le_alt))) => 92.27/12.48 (member998036369le_alt @ (hd_Arr731872705le_alt @ Y0) @ 92.27/12.48 (set_Ar1491127311le_alt @ Y0)))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_744_hd__in__set])). 92.27/12.48 thf(zip_derived_cl229, plain, 92.27/12.48 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 92.27/12.48 ((('#C') @ (!=) @ nil_Ar52383470le_alt)))) @ 92.27/12.48 ((('#S') @ ((('#B') @ member998036369le_alt @ 92.27/12.48 hd_Arr731872705le_alt)) @ 92.27/12.48 set_Ar1491127311le_alt))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl228])). 92.27/12.48 thf(zip_derived_cl494, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((((X2) != (nil_Ar52383470le_alt))) => (member998036369le_alt @ 92.27/12.48 (hd_Arr731872705le_alt @ X2) @ (set_Ar1491127311le_alt @ X2))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl229])). 92.27/12.48 thf(zip_derived_cl495, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (~ (((X2) != (nil_Ar52383470le_alt))) 92.27/12.48 | (member998036369le_alt @ (hd_Arr731872705le_alt @ X2) @ 92.27/12.48 (set_Ar1491127311le_alt @ X2)))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl494])). 92.27/12.48 thf(zip_derived_cl496, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((X2) = (nil_Ar52383470le_alt)) 92.27/12.48 | (member998036369le_alt @ (hd_Arr731872705le_alt @ X2) @ 92.27/12.48 (set_Ar1491127311le_alt @ X2)))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl495])). 92.27/12.48 thf(fact_399_append__Cons, axiom, 92.27/12.48 (![X_86:arrow_1389031998le_alt,Xs_140:list_A1402527603le_alt, 92.27/12.48 Ys_59:list_A1402527603le_alt]: 92.27/12.48 ( ( append1092755459le_alt @ 92.27/12.48 ( cons_A1142416030le_alt @ X_86 @ Xs_140 ) @ Ys_59 ) = 92.27/12.48 ( cons_A1142416030le_alt @ 92.27/12.48 X_86 @ ( append1092755459le_alt @ Xs_140 @ Ys_59 ) ) ))). 92.27/12.48 thf(zip_derived_cl180, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ (^[Y2 : list_A1402527603le_alt]: 92.27/12.48 (((append1092755459le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ Y0 @ Y1) @ 92.27/12.48 Y2) = (cons_A1142416030le_alt @ 92.27/12.48 Y0 @ 92.27/12.48 (append1092755459le_alt @ Y1 @ Y2)))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_399_append__Cons])). 92.27/12.48 thf(zip_derived_cl181, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ append1092755459le_alt)) @ 92.27/12.48 cons_A1142416030le_alt)))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#B') @ cons_A1142416030le_alt)))) @ 92.27/12.48 append1092755459le_alt))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl180])). 92.27/12.48 thf(zip_derived_cl814, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=))) @ 92.27/12.48 ((('#B') @ append1092755459le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ X2))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (cons_A1142416030le_alt @ X2))) @ 92.27/12.48 append1092755459le_alt))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl181])). 92.27/12.48 thf(zip_derived_cl815, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 92.27/12.48 (append1092755459le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ X2 @ X4)))) @ 92.27/12.48 ((('#B') @ (cons_A1142416030le_alt @ X2) @ 92.27/12.48 (append1092755459le_alt @ X4)))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl814])). 92.27/12.48 thf(zip_derived_cl816, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt, 92.27/12.48 X6 : list_A1402527603le_alt]: 92.27/12.48 (((append1092755459le_alt @ (cons_A1142416030le_alt @ X2 @ X4) @ 92.27/12.48 X6) = (cons_A1142416030le_alt @ X2 @ 92.27/12.48 (append1092755459le_alt @ X4 @ X6))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl815])). 92.27/12.48 thf(zip_derived_cl817, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt, 92.27/12.48 X6 : list_A1402527603le_alt]: 92.27/12.48 ((append1092755459le_alt @ (cons_A1142416030le_alt @ X2 @ X4) @ X6) 92.27/12.48 = (cons_A1142416030le_alt @ X2 @ (append1092755459le_alt @ X4 @ X6)))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl816])). 92.27/12.48 thf(fact_423_last__snoc, axiom, 92.27/12.48 (![Xs_119:list_A1402527603le_alt,X_77:arrow_1389031998le_alt]: 92.27/12.48 ( ( last_A2130988295le_alt @ 92.27/12.48 ( append1092755459le_alt @ 92.27/12.48 Xs_119 @ ( cons_A1142416030le_alt @ X_77 @ nil_Ar52383470le_alt ) ) ) = 92.27/12.48 ( X_77 ) ))). 92.27/12.48 thf(zip_derived_cl154, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1389031998le_alt]: 92.27/12.48 (((last_A2130988295le_alt @ 92.27/12.48 (append1092755459le_alt @ Y0 @ 92.27/12.48 (cons_A1142416030le_alt @ Y1 @ 92.27/12.48 nil_Ar52383470le_alt))) = 92.27/12.48 (Y1)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_423_last__snoc])). 92.27/12.48 thf(zip_derived_cl155, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=))) @ 92.27/12.48 ((('#B') @ ((('#B') @ last_A2130988295le_alt)) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 append1092755459le_alt)) @ 92.27/12.48 ((('#C') @ cons_A1142416030le_alt @ 92.27/12.48 nil_Ar52383470le_alt)))))))))) @ 92.27/12.48 ('#I')))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl154])). 92.27/12.48 thf(zip_derived_cl626, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 92.27/12.48 ((('#B') @ last_A2130988295le_alt @ 92.27/12.48 ((('#B') @ (append1092755459le_alt @ X2) @ 92.27/12.48 ((('#C') @ cons_A1142416030le_alt @ 92.27/12.48 nil_Ar52383470le_alt)))))))) @ 92.27/12.48 ('#I')))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl155])). 92.27/12.48 thf(zip_derived_cl627, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt, X4 : arrow_1389031998le_alt]: 92.27/12.48 (((last_A2130988295le_alt @ 92.27/12.48 (append1092755459le_alt @ X2 @ 92.27/12.48 (cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt))) = 92.27/12.48 (X4)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl626])). 92.27/12.48 thf(zip_derived_cl628, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt, X4 : arrow_1389031998le_alt]: 92.27/12.48 ((last_A2130988295le_alt @ 92.27/12.48 (append1092755459le_alt @ X2 @ 92.27/12.48 (cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt))) 92.27/12.48 = (X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl627])). 92.27/12.48 thf(fact_433_snoc__eq__iff__butlast, axiom, 92.27/12.48 (![Xs_118:list_A1402527603le_alt,X_75:arrow_1389031998le_alt, 92.27/12.48 Ys_41:list_A1402527603le_alt]: 92.27/12.48 ( ( ( append1092755459le_alt @ 92.27/12.48 Xs_118 @ ( cons_A1142416030le_alt @ X_75 @ nil_Ar52383470le_alt ) ) = 92.27/12.48 ( Ys_41 ) ) <=> 92.27/12.48 ( ( ( last_A2130988295le_alt @ Ys_41 ) = ( X_75 ) ) & 92.27/12.48 ( ( butlas1188620858le_alt @ Ys_41 ) = ( Xs_118 ) ) & 92.27/12.48 ( ( Ys_41 ) != ( nil_Ar52383470le_alt ) ) ) ))). 92.27/12.48 thf(zip_derived_cl222, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y2 : list_A1402527603le_alt]: 92.27/12.48 (((((append1092755459le_alt @ Y0 @ 92.27/12.48 (cons_A1142416030le_alt @ Y1 @ 92.27/12.48 nil_Ar52383470le_alt)) = 92.27/12.48 (Y2))) <=> 92.27/12.48 (((((last_A2130988295le_alt @ 92.27/12.48 Y2) = (Y1))) & 92.27/12.48 (((butlas1188620858le_alt @ 92.27/12.48 Y2) = (Y0))) & 92.27/12.48 (((Y2) != 92.27/12.48 (nil_Ar52383470le_alt))))))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_433_snoc__eq__iff__butlast])). 92.27/12.48 thf(zip_derived_cl223, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (<=>))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (=))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 append1092755459le_alt)) @ 92.27/12.48 ((('#C') @ cons_A1142416030le_alt @ 92.27/12.48 nil_Ar52383470le_alt)))))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ (&))) @ 92.27/12.48 ((('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 =) @ 92.27/12.48 last_A2130988295le_alt)))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ (=) @ 92.27/12.48 butlas1188620858le_alt)))))))))) @ 92.27/12.48 ((('#C') @ (!=) @ nil_Ar52383470le_alt))))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl222])). 92.27/12.48 thf(zip_derived_cl990, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 ((('#B') @ (=) @ 92.27/12.48 ((('#B') @ (append1092755459le_alt @ X2) @ 92.27/12.48 ((('#C') @ cons_A1142416030le_alt @ 92.27/12.48 nil_Ar52383470le_alt)))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (&))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ( 92.27/12.48 =) @ 92.27/12.48 last_A2130988295le_alt)))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ (=) @ 92.27/12.48 butlas1188620858le_alt)) @ 92.27/12.48 X2)))))) @ 92.27/12.48 ((('#C') @ (!=) @ nil_Ar52383470le_alt))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl223])). 92.27/12.48 thf(zip_derived_cl991, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt, X4 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 92.27/12.48 (((list_A1402527603le_alt) = 92.27/12.48 (append1092755459le_alt @ X2 @ 92.27/12.48 (cons_A1142416030le_alt @ X4 @ 92.27/12.48 nil_Ar52383470le_alt)))))) @ 92.27/12.48 ((('#S') @ ((('#S') @ ((('#B') @ (&) @ 92.27/12.48 ((('#C') @ ((('#B') @ (=) @ 92.27/12.48 last_A2130988295le_alt)) @ 92.27/12.48 X4)))) @ 92.27/12.48 ((('#C') @ ((('#B') @ (=) @ 92.27/12.48 butlas1188620858le_alt)) @ 92.27/12.48 X2)))) @ 92.27/12.48 ((('#C') @ (!=) @ nil_Ar52383470le_alt))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl990])). 92.27/12.48 thf(zip_derived_cl992, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : list_A1402527603le_alt]: 92.27/12.48 (((((append1092755459le_alt @ X2 @ 92.27/12.48 (cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt)) = (X6))) <=> 92.27/12.48 (((((last_A2130988295le_alt @ X6) = (X4))) & 92.27/12.48 (((butlas1188620858le_alt @ X6) = (X2))) & 92.27/12.48 (((X6) != (nil_Ar52383470le_alt)))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl991])). 92.27/12.48 thf(zip_derived_cl993, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : list_A1402527603le_alt]: 92.27/12.48 ((((append1092755459le_alt @ X2 @ 92.27/12.48 (cons_A1142416030le_alt @ X4 @ nil_Ar52383470le_alt)) = (X6))) 92.27/12.48 = (((((last_A2130988295le_alt @ X6) = (X4))) & 92.27/12.48 (((butlas1188620858le_alt @ X6) = (X2))) & 92.27/12.48 (((X6) != (nil_Ar52383470le_alt))))))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl992])). 92.27/12.48 thf(fact_321_mem__def, axiom, 92.27/12.48 (![X_102:( produc1572197287le_alt > $o ), 92.27/12.48 A_36:( ( produc1572197287le_alt > $o ) > $o )]: 92.27/12.48 ( ( member1241905979_alt_o @ X_102 @ A_36 ) <=> ( A_36 @ X_102 ) ))). 92.27/12.48 thf(zip_derived_cl31, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ (^[Y1 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member1241905979_alt_o @ Y0 @ Y1) <=> (Y1 @ 92.27/12.48 Y0)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_321_mem__def])). 92.27/12.48 thf(zip_derived_cl32, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 member1241905979_alt_o)))) @ 92.27/12.48 ((('#C') @ ('#I')))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl31])). 92.27/12.48 thf(zip_derived_cl576, plain, 92.27/12.48 (![X2 : produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member1241905979_alt_o @ X2))) @ 92.27/12.48 ((('#C') @ ('#I') @ X2))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 92.27/12.48 thf(zip_derived_cl577, plain, 92.27/12.48 (![X2 : produc1572197287le_alt > $o, 92.27/12.48 X4 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member1241905979_alt_o @ X2 @ X4) <=> (X4 @ X2)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl576])). 92.27/12.48 thf(zip_derived_cl578, plain, 92.27/12.48 (![X2 : produc1572197287le_alt > $o, 92.27/12.48 X4 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 ((member1241905979_alt_o @ X2 @ X4) = (X4 @ X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl577])). 92.27/12.48 thf(fact_319_mem__def, axiom, 92.27/12.48 (![X_102:produc1572197287le_alt,A_36:( produc1572197287le_alt > $o )]: 92.27/12.48 ( ( A_36 @ X_102 ) <=> ( member285112084le_alt @ X_102 @ A_36 ) ))). 92.27/12.48 thf(zip_derived_cl10, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : produc1572197287le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : produc1572197287le_alt > $o]: 92.27/12.48 (((Y1 @ Y0) <=> (member285112084le_alt @ Y0 @ 92.27/12.48 Y1)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_319_mem__def])). 92.27/12.48 thf(zip_derived_cl11, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 ((('#C') @ ('#I'))))))) @ 92.27/12.48 member285112084le_alt))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl10])). 92.27/12.48 thf(zip_derived_cl474, plain, 92.27/12.48 (![X2 : produc1572197287le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 92.27/12.48 (member285112084le_alt @ X2)))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 92.27/12.48 thf(zip_derived_cl475, plain, 92.27/12.48 (![X2 : produc1572197287le_alt, X4 : produc1572197287le_alt > $o]: 92.27/12.48 (((X4 @ X2) <=> (member285112084le_alt @ X2 @ X4)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl474])). 92.27/12.48 thf(zip_derived_cl476, plain, 92.27/12.48 (![X2 : produc1572197287le_alt, X4 : produc1572197287le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member285112084le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl475])). 92.27/12.48 thf(fact_725_last__in__set, axiom, 92.27/12.48 (![As:list_A1402527603le_alt]: 92.27/12.48 ( ( ( As ) != ( nil_Ar52383470le_alt ) ) => 92.27/12.48 ( member998036369le_alt @ 92.27/12.48 ( last_A2130988295le_alt @ As ) @ ( set_Ar1491127311le_alt @ As ) ) ))). 92.27/12.48 thf(zip_derived_cl260, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : list_A1402527603le_alt]: 92.27/12.48 (((((Y0) != (nil_Ar52383470le_alt))) => 92.27/12.48 (member998036369le_alt @ (last_A2130988295le_alt @ Y0) @ 92.27/12.48 (set_Ar1491127311le_alt @ Y0)))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_725_last__in__set])). 92.27/12.48 thf(zip_derived_cl261, plain, 92.27/12.48 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 92.27/12.48 ((('#C') @ (!=) @ nil_Ar52383470le_alt)))) @ 92.27/12.48 ((('#S') @ ((('#B') @ member998036369le_alt @ 92.27/12.48 last_A2130988295le_alt)) @ 92.27/12.48 set_Ar1491127311le_alt))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl260])). 92.27/12.48 thf(zip_derived_cl497, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((((X2) != (nil_Ar52383470le_alt))) => (member998036369le_alt @ 92.27/12.48 (last_A2130988295le_alt @ X2) @ (set_Ar1491127311le_alt @ X2))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl261])). 92.27/12.48 thf(zip_derived_cl498, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (~ (((X2) != (nil_Ar52383470le_alt))) 92.27/12.48 | (member998036369le_alt @ (last_A2130988295le_alt @ X2) @ 92.27/12.48 (set_Ar1491127311le_alt @ X2)))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl497])). 92.27/12.48 thf(zip_derived_cl499, plain, 92.27/12.48 (![X2 : list_A1402527603le_alt]: 92.27/12.48 (((X2) = (nil_Ar52383470le_alt)) 92.27/12.48 | (member998036369le_alt @ (last_A2130988295le_alt @ X2) @ 92.27/12.48 (set_Ar1491127311le_alt @ X2)))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl498])). 92.27/12.48 thf(fact_316_mem__def, axiom, 92.27/12.48 (![X_102:arrow_1389031998le_alt,A_36:( arrow_1389031998le_alt > $o )]: 92.27/12.48 ( ( A_36 @ X_102 ) <=> ( member998036369le_alt @ X_102 @ A_36 ) ))). 92.27/12.48 thf(zip_derived_cl49, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1389031998le_alt > $o]: 92.27/12.48 (((Y1 @ Y0) <=> (member998036369le_alt @ Y0 @ 92.27/12.48 Y1)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_316_mem__def])). 92.27/12.48 thf(zip_derived_cl50, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 ((('#C') @ ('#I'))))))) @ 92.27/12.48 member998036369le_alt))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl49])). 92.27/12.48 thf(zip_derived_cl579, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ ((('#C') @ ('#I') @ X2)))) @ 92.27/12.48 (member998036369le_alt @ X2)))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 92.27/12.48 thf(zip_derived_cl580, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt > $o]: 92.27/12.48 (((X4 @ X2) <=> (member998036369le_alt @ X2 @ X4)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl579])). 92.27/12.48 thf(zip_derived_cl581, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member998036369le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl580])). 92.27/12.48 thf(fact_708_distinct_Osimps_I2_J, axiom, 92.27/12.48 (![X_31:arrow_1389031998le_alt,Xs_29:list_A1402527603le_alt]: 92.27/12.48 ( ( distin1149997281le_alt @ ( cons_A1142416030le_alt @ X_31 @ Xs_29 ) ) <=> 92.27/12.48 ( ( distin1149997281le_alt @ Xs_29 ) & 92.27/12.48 ( ~( member998036369le_alt @ X_31 @ ( set_Ar1491127311le_alt @ Xs_29 ) ) ) ) ))). 92.27/12.48 thf(zip_derived_cl194, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : list_A1402527603le_alt]: 92.27/12.48 (((distin1149997281le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ Y0 @ Y1)) <=> 92.27/12.48 (((distin1149997281le_alt @ Y1) & 92.27/12.48 (((~) @ (member998036369le_alt @ Y0 @ 92.27/12.48 (set_Ar1491127311le_alt @ Y1))))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_708_distinct_Osimps_I2_J])). 92.27/12.48 thf(zip_derived_cl195, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 ((('#B') @ ((('#B') @ distin1149997281le_alt)) @ 92.27/12.48 cons_A1142416030le_alt)))))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ (&) @ 92.27/12.48 distin1149997281le_alt)))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (~))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ member998036369le_alt)) @ 92.27/12.48 set_Ar1491127311le_alt))))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl194])). 92.27/12.48 thf(zip_derived_cl760, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 92.27/12.48 ((('#B') @ distin1149997281le_alt @ 92.27/12.48 (cons_A1142416030le_alt @ X2))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ (&) @ distin1149997281le_alt)) @ 92.27/12.48 ((('#B') @ (~) @ 92.27/12.48 ((('#B') @ (member998036369le_alt @ X2) @ 92.27/12.48 set_Ar1491127311le_alt))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl195])). 92.27/12.48 thf(zip_derived_cl761, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 (((distin1149997281le_alt @ (cons_A1142416030le_alt @ X2 @ X4)) <=> 92.27/12.48 (((distin1149997281le_alt @ X4) & 92.27/12.48 (((~) @ (member998036369le_alt @ X2 @ 92.27/12.48 (set_Ar1491127311le_alt @ X4))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl760])). 92.27/12.48 thf(zip_derived_cl762, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 ((distin1149997281le_alt @ (cons_A1142416030le_alt @ X2 @ X4)) 92.27/12.48 = (((distin1149997281le_alt @ X4) & 92.27/12.48 (((~) @ (member998036369le_alt @ X2 @ 92.27/12.48 (set_Ar1491127311le_alt @ X4)))))))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl761])). 92.27/12.48 thf(zip_derived_cl581, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member998036369le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl580])). 92.27/12.48 thf(zip_derived_cl763, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : list_A1402527603le_alt]: 92.27/12.48 ((distin1149997281le_alt @ (cons_A1142416030le_alt @ X2 @ X4)) 92.27/12.48 = (((distin1149997281le_alt @ X4) & 92.27/12.48 (((~) @ (set_Ar1491127311le_alt @ X4 @ X2))))))), 92.27/12.48 inference('demod', [status(thm)], [zip_derived_cl762, zip_derived_cl581])). 92.27/12.48 thf(conj_0, conjecture, 92.27/12.48 (![I:arrow_1196572341e_indi]: 92.27/12.48 ( ( member285112084le_alt @ ( produc897867031le_alt @ a @ b ) @ ( p @ I ) ) <=> 92.27/12.48 ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ a @ c ) @ 92.27/12.48 ( arrow_1865170000_below @ ( p @ I ) @ c @ b ) ) ))). 92.27/12.48 thf(zf_stmt_0, negated_conjecture, 92.27/12.48 (~( ![I:arrow_1196572341e_indi]: 92.27/12.48 ( ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ a @ b ) @ ( p @ I ) ) <=> 92.27/12.48 ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ a @ c ) @ 92.27/12.48 ( arrow_1865170000_below @ ( p @ I ) @ c @ b ) ) ) )), 92.27/12.48 inference('cnf.neg', [status(esa)], [conj_0])). 92.27/12.48 thf(zip_derived_cl401, plain, 92.27/12.48 (~ (((!!) @ (^[Y0 : arrow_1196572341e_indi]: 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ a @ b) @ (p @ Y0)) <=> 92.27/12.48 (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ a @ c) @ 92.27/12.48 (arrow_1865170000_below @ (p @ Y0) @ c @ b)))))))), 92.27/12.48 inference('cnf', [status(esa)], [zf_stmt_0])). 92.27/12.48 thf(zip_derived_cl402, plain, 92.27/12.48 (~ (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ 92.27/12.48 ((('#B') @ (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ a @ b)) @ 92.27/12.48 p)))) @ 92.27/12.48 ((('#B') @ (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ a @ c)) @ 92.27/12.48 ((('#C') @ ((('#C') @ ((('#B') @ arrow_1865170000_below @ 92.27/12.48 p)) @ 92.27/12.48 c)) @ 92.27/12.48 b))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl401])). 92.27/12.48 thf(zip_derived_cl462, plain, 92.27/12.48 (~ (((member285112084le_alt @ (produc897867031le_alt @ a @ b) @ 92.27/12.48 (p @ '#sk11')) <=> (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ a @ c) @ 92.27/12.48 (arrow_1865170000_below @ (p @ '#sk11') @ c @ b))))), 92.27/12.48 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl402])). 92.27/12.48 thf(zip_derived_cl463, plain, 92.27/12.48 (((member285112084le_alt @ (produc897867031le_alt @ a @ b) @ 92.27/12.48 (p @ '#sk11')) 92.27/12.48 != (member285112084le_alt @ (produc897867031le_alt @ a @ c) @ 92.27/12.48 (arrow_1865170000_below @ (p @ '#sk11') @ c @ b)))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl462])). 92.27/12.48 thf(zip_derived_cl476, plain, 92.27/12.48 (![X2 : produc1572197287le_alt, X4 : produc1572197287le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member285112084le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl475])). 92.27/12.48 thf(zip_derived_cl476, plain, 92.27/12.48 (![X2 : produc1572197287le_alt, X4 : produc1572197287le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member285112084le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl475])). 92.27/12.48 thf(zip_derived_cl477, plain, 92.27/12.48 (((p @ '#sk11' @ (produc897867031le_alt @ a @ b)) 92.27/12.48 != (arrow_1865170000_below @ (p @ '#sk11') @ c @ b @ 92.27/12.48 (produc897867031le_alt @ a @ c)))), 92.27/12.48 inference('demod', [status(thm)], 92.27/12.48 [zip_derived_cl463, zip_derived_cl476, zip_derived_cl476])). 92.27/12.48 thf(fact_376_UNIV__I, axiom, 92.27/12.48 (![X_90:arrow_1196572341e_indi]: 92.27/12.48 ( member1818997282e_indi @ X_90 @ top_to54564308indi_o ))). 92.27/12.48 thf(zip_derived_cl230, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi]: 92.27/12.48 (member1818997282e_indi @ Y0 @ top_to54564308indi_o))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_376_UNIV__I])). 92.27/12.48 thf(zip_derived_cl231, plain, 92.27/12.48 ( (((!!) @ ((('#C') @ member1818997282e_indi @ top_to54564308indi_o))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl230])). 92.27/12.48 thf(zip_derived_cl416, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi]: 92.27/12.48 (member1818997282e_indi @ X2 @ top_to54564308indi_o)), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl231])). 92.27/12.48 thf(fact_12_in__below, axiom, 92.27/12.48 (![X:arrow_1389031998le_alt,Y:arrow_1389031998le_alt, 92.27/12.48 L_4:( produc1572197287le_alt > $o ),A:arrow_1389031998le_alt, 92.27/12.48 B:arrow_1389031998le_alt]: 92.27/12.48 ( ( ( A ) != ( B ) ) => 92.27/12.48 ( ( member1241905979_alt_o @ L_4 @ arrow_1982173296le_Lin ) => 92.27/12.48 ( ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ X @ Y ) @ 92.27/12.48 ( arrow_1865170000_below @ L_4 @ A @ B ) ) <=> 92.27/12.48 ( ( ( X ) != ( Y ) ) & 92.27/12.48 ( ( ( Y ) != ( A ) ) => 92.27/12.48 ( ( ( ( X ) = ( A ) ) => 92.27/12.48 ( ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ B @ Y ) @ L_4 ) | 92.27/12.48 ( ( Y ) = ( B ) ) ) ) & 92.27/12.48 ( ( ( X ) != ( A ) ) => 92.27/12.48 ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ X @ Y ) @ L_4 ) ) ) ) & 92.27/12.48 ( ( ( Y ) = ( A ) ) => 92.27/12.48 ( member285112084le_alt @ 92.27/12.48 ( produc897867031le_alt @ X @ B ) @ L_4 ) ) ) ) ) ))). 92.27/12.48 thf(zip_derived_cl310, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y2 : produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ (^[Y3 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ (^[Y4 : arrow_1389031998le_alt]: 92.27/12.48 (((( 92.27/12.48 (Y3) != 92.27/12.48 (Y4))) => 92.27/12.48 (( 92.27/12.48 (member1241905979_alt_o @ 92.27/12.48 Y2 @ 92.27/12.48 arrow_1982173296le_Lin) => 92.27/12.48 (( 92.27/12.48 (member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 produc897867031le_alt @ 92.27/12.48 Y0 @ Y1) @ 92.27/12.48 ( 92.27/12.48 arrow_1865170000_below @ 92.27/12.48 Y2 @ 92.27/12.48 Y3 @ Y4)) <=> 92.27/12.48 (( 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (Y0) != 92.27/12.48 (Y1))) & 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (( 92.27/12.48 (Y1) != 92.27/12.48 (Y3))) => 92.27/12.48 (( 92.27/12.48 (( 92.27/12.48 (( 92.27/12.48 (Y0) = 92.27/12.48 (Y3))) => 92.27/12.48 (( 92.27/12.48 (member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 produc897867031le_alt @ 92.27/12.48 Y4 @ Y1) @ 92.27/12.48 Y2) | 92.27/12.48 (( 92.27/12.48 (Y1) = 92.27/12.48 (Y4))))))) & 92.27/12.48 (( 92.27/12.48 (( 92.27/12.48 (Y0) != 92.27/12.48 (Y3))) => 92.27/12.48 (member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 produc897867031le_alt @ 92.27/12.48 Y0 @ Y1) @ 92.27/12.48 Y2))))))) & 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (( 92.27/12.48 (Y1) = 92.27/12.48 (Y3))) => 92.27/12.48 (member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 produc897867031le_alt @ 92.27/12.48 Y0 @ Y4) @ 92.27/12.48 Y2))))))))))))))))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_12_in__below])). 92.27/12.48 thf(zip_derived_cl311, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ (( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>))) @ 92.27/12.48 ( 92.27/12.48 !=))))))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 ((('#C') @ member1241905979_alt_o @ 92.27/12.48 arrow_1982173296le_Lin)))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 '#S'))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#S'))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 (('#B') @ (<=>))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ member285112084le_alt)) @ 92.27/12.48 produc897867031le_alt)))))))))) @ 92.27/12.48 arrow_1865170000_below)))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 '#S'))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 (('#B') @ ('#S'))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 &))) @ 92.27/12.48 ( 92.27/12.48 !=))))))))))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>))) @ 92.27/12.48 ( 92.27/12.48 !=))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#S'))) @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#S'))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C'))))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 &))))))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>))) @ 92.27/12.48 ( 92.27/12.48 =))))))))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#S') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#S'))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 |))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ member285112084le_alt)) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ produc897867031le_alt)))))))))))) @ 92.27/12.48 ( 92.27/12.48 =))))))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>))) @ 92.27/12.48 ( 92.27/12.48 !=))))))))) @ 92.27/12.48 ((('#B') @ (( 92.27/12.48 ('#B') @ member285112084le_alt)) @ 92.27/12.48 produc897867031le_alt)))))))))))))))))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ('#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ (=>))) @ 92.27/12.48 (=))))))))))) @ 92.27/12.48 ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ member285112084le_alt)) @ 92.27/12.48 produc897867031le_alt))))))))))))))))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl310])). 92.27/12.48 thf(zip_derived_cl1284, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ (=>))) @ 92.27/12.48 (!=))))))))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 ((('#C') @ member1241905979_alt_o @ 92.27/12.48 arrow_1982173296le_Lin)))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 '#S'))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 <=>))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ 92.27/12.48 X2))))))))) @ 92.27/12.48 arrow_1865170000_below)))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 '#S'))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 &) @ 92.27/12.48 (((arrow_1389031998le_alt) != 92.27/12.48 (X2))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 =>))) @ 92.27/12.48 (!=))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#S'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C'))))) @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 &))))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#C') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (arrow_1389031998le_alt) = 92.27/12.48 (X2))))))))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#S') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#S'))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 |))))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 '#C') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ member285112084le_alt)) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ produc897867031le_alt)))))))))))) @ 92.27/12.48 ( 92.27/12.48 =))))))))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ( 92.27/12.48 (('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 (( 92.27/12.48 (arrow_1389031998le_alt) != 92.27/12.48 (X2))))))))) @ 92.27/12.48 ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ 92.27/12.48 X2))))))))))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#B'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 (=))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2)))))))))))))))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl311])). 92.27/12.48 thf(zip_derived_cl1285, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 (!=))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 ((('#C') @ member1241905979_alt_o @ 92.27/12.48 arrow_1982173296le_Lin)))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 <=>))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ 92.27/12.48 X2 @ X4)))))) @ 92.27/12.48 arrow_1865170000_below)))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ ( 92.27/12.48 ((&) @ ( 92.27/12.48 ((X2) != 92.27/12.48 (X4))))))))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (arrow_1389031998le_alt) != 92.27/12.48 (X4))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ('#C'))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 (('#B') @ (&))))) @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 (('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 (( 92.27/12.48 ('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 (arrow_1389031998le_alt) = 92.27/12.48 (X2))))))))) @ 92.27/12.48 ((('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#S') @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ ( 92.27/12.48 |))) @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ produc897867031le_alt @ 92.27/12.48 X4)))))))))) @ 92.27/12.48 (( 92.27/12.48 (arrow_1389031998le_alt) = 92.27/12.48 (X4))))))))))))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 (((arrow_1389031998le_alt) != 92.27/12.48 (X2))))))) @ 92.27/12.48 (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ 92.27/12.48 X2 @ X4)))))))))))))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (((arrow_1389031998le_alt) = 92.27/12.48 (X4))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2)))))))))))))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1284])). 92.27/12.48 thf(zip_derived_cl1286, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ (!=))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (((=>) @ (member1241905979_alt_o @ 92.27/12.48 X6 @ 92.27/12.48 arrow_1982173296le_Lin))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ 92.27/12.48 X2 @ X4)))) @ 92.27/12.48 (arrow_1865170000_below @ X6))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (((&) @ ( 92.27/12.48 ((X2) != (X4))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (((arrow_1389031998le_alt) != 92.27/12.48 (X4))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ( 92.27/12.48 &))) @ 92.27/12.48 ((('#C') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 =>) @ 92.27/12.48 (((arrow_1389031998le_alt) = 92.27/12.48 (X2))))))) @ 92.27/12.48 ((('#S') @ ( 92.27/12.48 (('#B') @ ( 92.27/12.48 |) @ 92.27/12.48 ((('#C') @ ( 92.27/12.48 (('#B') @ member285112084le_alt @ 92.27/12.48 ((('#C') @ produc897867031le_alt @ 92.27/12.48 X4)))) @ 92.27/12.48 X6)))) @ 92.27/12.48 (((arrow_1389031998le_alt) = 92.27/12.48 (X4))))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ (=>) @ 92.27/12.48 (((arrow_1389031998le_alt) != 92.27/12.48 (X2))))) @ 92.27/12.48 (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ 92.27/12.48 X4) @ 92.27/12.48 X6))))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (((arrow_1389031998le_alt) = (X4))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2))) @ 92.27/12.48 X6))))))))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1285])). 92.27/12.48 thf(zip_derived_cl1287, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 92.27/12.48 (((arrow_1389031998le_alt) != (X8))))) @ 92.27/12.48 ((('#B') @ (((=>) @ (member1241905979_alt_o @ X6 @ 92.27/12.48 arrow_1982173296le_Lin))) @ 92.27/12.48 ((('#S') @ ((('#B') @ (<=>) @ 92.27/12.48 ((('#B') @ (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ 92.27/12.48 X4)) @ 92.27/12.48 (arrow_1865170000_below @ X6 @ X8))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ (((&) @ (((X2) != (X4))))) @ 92.27/12.48 ((('#B') @ (((=>) @ (((X4) != (X8))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ (&) @ 92.27/12.48 ((('#B') @ (((=>) @ ( 92.27/12.48 ((X2) = (X8))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ( 92.27/12.48 |) @ 92.27/12.48 ((('#C') @ ( 92.27/12.48 ( 92.27/12.48 ('#B') @ member285112084le_alt @ 92.27/12.48 ( 92.27/12.48 ( 92.27/12.48 ('#C') @ produc897867031le_alt @ 92.27/12.48 X4)))) @ 92.27/12.48 X6)))) @ 92.27/12.48 (((arrow_1389031998le_alt) = 92.27/12.48 (X4))))))))) @ 92.27/12.48 (((((X2) != (X8))) => 92.27/12.48 (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ 92.27/12.48 X6))))))))) @ 92.27/12.48 ((('#B') @ (((=>) @ (((X4) = (X8))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2))) @ 92.27/12.48 X6))))))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1286])). 92.27/12.48 thf(zip_derived_cl1288, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (((((X8) != (X10))) => 92.27/12.48 (((member1241905979_alt_o @ X6 @ arrow_1982173296le_Lin) => 92.27/12.48 (((member285112084le_alt @ (produc897867031le_alt @ X2 @ X4) @ 92.27/12.48 (arrow_1865170000_below @ X6 @ X8 @ X10)) <=> 92.27/12.48 (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6)))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1287])). 92.27/12.48 thf(zip_derived_cl578, plain, 92.27/12.48 (![X2 : produc1572197287le_alt > $o, 92.27/12.48 X4 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 ((member1241905979_alt_o @ X2 @ X4) = (X4 @ X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl577])). 92.27/12.48 thf(zip_derived_cl476, plain, 92.27/12.48 (![X2 : produc1572197287le_alt, X4 : produc1572197287le_alt > $o]: 92.27/12.48 ((X4 @ X2) = (member285112084le_alt @ X2 @ X4))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl475])). 92.27/12.48 thf(zip_derived_cl1289, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (((((X8) != (X10))) => 92.27/12.48 (((arrow_1982173296le_Lin @ X6) => 92.27/12.48 (((arrow_1865170000_below @ X6 @ X8 @ X10 @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4)) <=> 92.27/12.48 (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6)))))))))))), 92.27/12.48 inference('demod', [status(thm)], 92.27/12.48 [zip_derived_cl1288, zip_derived_cl578, zip_derived_cl476])). 92.27/12.48 thf(zip_derived_cl1290, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (~ (((X8) != (X10))) 92.27/12.48 | (((arrow_1982173296le_Lin @ X6) => 92.27/12.48 (((arrow_1865170000_below @ X6 @ X8 @ X10 @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4)) <=> 92.27/12.48 (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6))))))))))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1289])). 92.27/12.48 thf(zip_derived_cl1291, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (((X8) = (X10)) 92.27/12.48 | (((arrow_1982173296le_Lin @ X6) => 92.27/12.48 (((arrow_1865170000_below @ X6 @ X8 @ X10 @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4)) <=> 92.27/12.48 (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6))))))))))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl1290])). 92.27/12.48 thf(zip_derived_cl1292, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (~ (arrow_1982173296le_Lin @ X6) 92.27/12.48 | (((arrow_1865170000_below @ X6 @ X8 @ X10 @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4)) <=> 92.27/12.48 (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6))))))) 92.27/12.48 | ((X8) = (X10)))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1291])). 92.27/12.48 thf(zip_derived_cl1293, plain, 92.27/12.48 (![X2 : arrow_1389031998le_alt, X4 : arrow_1389031998le_alt, 92.27/12.48 X6 : produc1572197287le_alt > $o, X8 : arrow_1389031998le_alt, 92.27/12.48 X10 : arrow_1389031998le_alt]: 92.27/12.48 (~ (arrow_1982173296le_Lin @ X6) 92.27/12.48 | ((arrow_1865170000_below @ X6 @ X8 @ X10 @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4)) 92.27/12.48 = (((((X2) != (X4))) & 92.27/12.48 (((((X4) != (X8))) => 92.27/12.48 (((((((X2) = (X8))) => 92.27/12.48 (((member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X10 @ X4) @ X6) | 92.27/12.48 (((X4) = (X10))))))) & 92.27/12.48 (((((X2) != (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X4) @ X6))))))) & 92.27/12.48 (((((X4) = (X8))) => (member285112084le_alt @ 92.27/12.48 (produc897867031le_alt @ X2 @ X10) @ X6)))))) 92.27/12.48 | ((X8) = (X10)))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl1292])). 92.27/12.48 thf(fact_320_mem__def, axiom, 92.27/12.48 (![X_102:( arrow_1196572341e_indi > produc1572197287le_alt > $o ), 92.27/12.48 A_36:( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o )]: 92.27/12.48 ( ( member822980838_alt_o @ X_102 @ A_36 ) <=> ( A_36 @ X_102 ) ))). 92.27/12.48 thf(zip_derived_cl214, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi > produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ (^[Y1 : (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member822980838_alt_o @ Y0 @ Y1) <=> (Y1 @ 92.27/12.48 Y0)))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_320_mem__def])). 92.27/12.48 thf(zip_derived_cl215, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (<=>))) @ 92.27/12.48 member822980838_alt_o)))) @ 92.27/12.48 ((('#C') @ ('#I')))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl214])). 92.27/12.48 thf(zip_derived_cl613, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (<=>) @ (member822980838_alt_o @ X2))) @ 92.27/12.48 ((('#C') @ ('#I') @ X2))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl215])). 92.27/12.48 thf(zip_derived_cl614, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member822980838_alt_o @ X2 @ X4) <=> (X4 @ X2)))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl613])). 92.27/12.48 thf(zip_derived_cl615, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 ((member822980838_alt_o @ X2 @ X4) = (X4 @ X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl614])). 92.27/12.48 thf(fact_130_funcset__mem, axiom, 92.27/12.48 (![X_106:arrow_1196572341e_indi, 92.27/12.48 F_20:( arrow_1196572341e_indi > produc1572197287le_alt > $o ), 92.27/12.48 A_43:( arrow_1196572341e_indi > $o ), 92.27/12.48 B_34:( ( produc1572197287le_alt > $o ) > $o )]: 92.27/12.48 ( ( member822980838_alt_o @ 92.27/12.48 F_20 @ 92.27/12.48 ( pi_Arr1309696186_alt_o @ 92.27/12.48 A_43 @ ( ^[Uu:arrow_1196572341e_indi]: ( B_34 ) ) ) ) => 92.27/12.48 ( ( member1818997282e_indi @ X_106 @ A_43 ) => 92.27/12.48 ( member1241905979_alt_o @ ( F_20 @ X_106 ) @ B_34 ) ) ))). 92.27/12.48 thf(zip_derived_cl182, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ (^[Y2 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((!!) @ (^[Y3 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member822980838_alt_o @ 92.27/12.48 Y1 @ 92.27/12.48 (pi_Arr1309696186_alt_o @ 92.27/12.48 Y2 @ 92.27/12.48 (^[Y4 : arrow_1196572341e_indi]: 92.27/12.48 (Y3)))) => 92.27/12.48 (((member1818997282e_indi @ 92.27/12.48 Y0 @ Y2) => 92.27/12.48 (member1241905979_alt_o @ 92.27/12.48 (Y1 @ Y0) @ Y3)))))))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_130_funcset__mem])). 92.27/12.48 thf(zip_derived_cl183, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ( 92.27/12.48 (('#B') @ (=>))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 member822980838_alt_o)))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ( 92.27/12.48 '#B') @ 92.27/12.48 pi_Arr1309696186_alt_o)) @ 92.27/12.48 ('#K'))))))))))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#B'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 member1818997282e_indi)))))))) @ 92.27/12.48 ((('#B') @ ((('#B') @ member1241905979_alt_o)) @ 92.27/12.48 ((('#C') @ ('#I')))))))))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl182])). 92.27/12.48 thf(zip_derived_cl1087, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#S'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#B') @ 92.27/12.48 member822980838_alt_o)))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 pi_Arr1309696186_alt_o)) @ 92.27/12.48 ('#K'))))))))))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (member1818997282e_indi @ X2))))))) @ 92.27/12.48 ((('#B') @ member1241905979_alt_o @ 92.27/12.48 ((('#C') @ ('#I') @ X2))))))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl183])). 92.27/12.48 thf(zip_derived_cl1088, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (member822980838_alt_o @ 92.27/12.48 X4))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 pi_Arr1309696186_alt_o)) @ 92.27/12.48 ('#K'))))))))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (member1818997282e_indi @ X2))))) @ 92.27/12.48 (member1241905979_alt_o @ (X4 @ X2))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1087])). 92.27/12.48 thf(zip_derived_cl1089, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 92.27/12.48 ((('#B') @ (member822980838_alt_o @ X4) @ 92.27/12.48 ((('#B') @ (pi_Arr1309696186_alt_o @ X6) @ 92.27/12.48 ('#K'))))))) @ 92.27/12.48 ((('#B') @ (((=>) @ (member1818997282e_indi @ X2 @ X6))) @ 92.27/12.48 (member1241905979_alt_o @ (X4 @ X2))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1088])). 92.27/12.48 thf(zip_derived_cl1090, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o, 92.27/12.48 X8 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((member822980838_alt_o @ X4 @ 92.27/12.48 (pi_Arr1309696186_alt_o @ X6 @ ((('#K') @ X8)))) => 92.27/12.48 (((member1818997282e_indi @ X2 @ X6) => (member1241905979_alt_o @ 92.27/12.48 (X4 @ X2) @ X8)))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1089])). 92.27/12.48 thf(zip_derived_cl615, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 ((member822980838_alt_o @ X2 @ X4) = (X4 @ X2))), 92.27/12.48 inference('simplify nested equalities', [status(thm)], 92.27/12.48 [zip_derived_cl614])). 92.27/12.48 thf(zip_derived_cl1091, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o, 92.27/12.48 X8 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((pi_Arr1309696186_alt_o @ X6 @ ((('#K') @ X8)) @ X4) => 92.27/12.48 (((member1818997282e_indi @ X2 @ X6) => (member1241905979_alt_o @ 92.27/12.48 (X4 @ X2) @ X8)))))), 92.27/12.48 inference('demod', [status(thm)], [zip_derived_cl1090, zip_derived_cl615])). 92.27/12.48 thf(zip_derived_cl1092, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o, 92.27/12.48 X8 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (~ (pi_Arr1309696186_alt_o @ X6 @ ((('#K') @ X8)) @ X4) 92.27/12.48 | (((member1818997282e_indi @ X2 @ X6) => (member1241905979_alt_o @ 92.27/12.48 (X4 @ X2) @ X8))))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1091])). 92.27/12.48 thf(zip_derived_cl1093, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o, 92.27/12.48 X8 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (~ (member1818997282e_indi @ X2 @ X6) 92.27/12.48 | (member1241905979_alt_o @ (X4 @ X2) @ X8) 92.27/12.48 | ~ (pi_Arr1309696186_alt_o @ X6 @ ((('#K') @ X8)) @ X4))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1092])). 92.27/12.48 thf(zip_derived_cl10079, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi, 92.27/12.48 X4 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X6 : arrow_1196572341e_indi > $o, 92.27/12.48 X8 : (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (~ (member1818997282e_indi @ X2 @ X6) 92.27/12.48 | (member1241905979_alt_o @ (X4 @ X2) @ X8) 92.27/12.48 | ~ (pi_Arr1309696186_alt_o @ X6 @ ('#ty_enc67' @ X8) @ X4))), 92.27/12.48 inference('remove_ty_args', [status(thm)], [zip_derived_cl1093])). 92.27/12.48 thf(fact_0__096P_A_058_AProf_096, axiom, 92.27/12.48 (member822980838_alt_o @ p @ arrow_1647925946e_Prof)). 92.27/12.48 thf(zip_derived_cl73, plain, 92.27/12.48 ( (member822980838_alt_o @ p @ arrow_1647925946e_Prof)), 92.27/12.48 inference('cnf', [status(esa)], [fact_0__096P_A_058_AProf_096])). 92.27/12.48 thf(fact_340_Prof__def, axiom, 92.27/12.48 (( arrow_1647925946e_Prof ) = 92.27/12.48 ( pi_Arr1309696186_alt_o @ 92.27/12.48 top_to54564308indi_o @ 92.27/12.48 ( ^[Uu:arrow_1196572341e_indi]: ( arrow_1982173296le_Lin ) ) ))). 92.27/12.48 thf(zip_derived_cl296, plain, 92.27/12.48 (((arrow_1647925946e_Prof) 92.27/12.48 = (pi_Arr1309696186_alt_o @ top_to54564308indi_o @ 92.27/12.48 (^[Y0 : arrow_1196572341e_indi]: (arrow_1982173296le_Lin))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_340_Prof__def])). 92.27/12.48 thf(zip_derived_cl297, plain, 92.27/12.48 (((arrow_1647925946e_Prof) 92.27/12.48 = (pi_Arr1309696186_alt_o @ top_to54564308indi_o @ 92.27/12.48 ((('#K') @ arrow_1982173296le_Lin))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl296])). 92.27/12.48 thf(zip_derived_cl10063, plain, 92.27/12.48 (((arrow_1647925946e_Prof) 92.27/12.48 = (pi_Arr1309696186_alt_o @ top_to54564308indi_o @ 92.27/12.48 ('#ty_enc67' @ arrow_1982173296le_Lin)))), 92.27/12.48 inference('remove_ty_args', [status(thm)], [zip_derived_cl297])). 92.27/12.48 thf(fact_967_in__mono, axiom, 92.27/12.48 (![X_6:( arrow_1196572341e_indi > produc1572197287le_alt > $o ), 92.27/12.48 A_4:( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o ), 92.27/12.48 B_1:( ( arrow_1196572341e_indi > produc1572197287le_alt > $o ) > $o )]: 92.27/12.48 ( ( ord_le602483040lt_o_o @ A_4 @ B_1 ) => 92.27/12.48 ( ( member822980838_alt_o @ X_6 @ A_4 ) => 92.27/12.48 ( member822980838_alt_o @ X_6 @ B_1 ) ) ))). 92.27/12.48 thf(zip_derived_cl63, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi > produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ (^[Y1 : (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((!!) @ (^[Y2 : (arrow_1196572341e_indi > 92.27/12.48 produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((ord_le602483040lt_o_o @ Y1 @ 92.27/12.48 Y2) => 92.27/12.48 (((member822980838_alt_o @ Y0 @ 92.27/12.48 Y1) => 92.27/12.48 (member822980838_alt_o @ Y0 @ 92.27/12.48 Y2))))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_967_in__mono])). 92.27/12.48 thf(zip_derived_cl64, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 ord_le602483040lt_o_o)))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ('#B'))) @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 member822980838_alt_o)))))) @ 92.27/12.48 member822980838_alt_o))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl63])). 92.27/12.48 thf(zip_derived_cl742, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 ord_le602483040lt_o_o)))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ (=>) @ 92.27/12.48 (member822980838_alt_o @ X2))))) @ 92.27/12.48 (member822980838_alt_o @ X2)))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 92.27/12.48 thf(zip_derived_cl743, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (ord_le602483040lt_o_o @ X4))) @ 92.27/12.48 ((('#B') @ (((=>) @ (member822980838_alt_o @ X2 @ X4))) @ 92.27/12.48 (member822980838_alt_o @ X2)))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl742])). 92.27/12.48 thf(zip_derived_cl744, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o, 92.27/12.48 X6 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((ord_le602483040lt_o_o @ X4 @ X6) => 92.27/12.48 (((member822980838_alt_o @ X2 @ X4) => (member822980838_alt_o @ 92.27/12.48 X2 @ X6)))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl743])). 92.27/12.48 thf(zip_derived_cl745, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o, 92.27/12.48 X6 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 (~ (ord_le602483040lt_o_o @ X4 @ X6) 92.27/12.48 | (((member822980838_alt_o @ X2 @ X4) => (member822980838_alt_o @ 92.27/12.48 X2 @ X6))))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl744])). 92.27/12.48 thf(zip_derived_cl746, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > produc1572197287le_alt > $o, 92.27/12.48 X4 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o, 92.27/12.48 X6 : (arrow_1196572341e_indi > produc1572197287le_alt > $o) > $o]: 92.27/12.48 (~ (member822980838_alt_o @ X2 @ X4) 92.27/12.48 | (member822980838_alt_o @ X2 @ X6) 92.27/12.48 | ~ (ord_le602483040lt_o_o @ X4 @ X6))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl745])). 92.27/12.48 thf(fact_349_top1I, axiom, 92.27/12.48 (![X_97:arrow_1196572341e_indi]: ( top_to54564308indi_o @ X_97 ))). 92.27/12.48 thf(zip_derived_cl374, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi]: (top_to54564308indi_o @ Y0))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_349_top1I])). 92.27/12.48 thf(zip_derived_cl375, plain, ( (((!!) @ top_to54564308indi_o))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl374])). 92.27/12.48 thf(zip_derived_cl405, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi]: (top_to54564308indi_o @ X2)), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl375])). 92.27/12.48 thf(fact_989_top__greatest, axiom, 92.27/12.48 (![A_3:( arrow_1196572341e_indi > $o )]: 92.27/12.48 ( ord_le865407012indi_o @ A_3 @ top_to54564308indi_o ))). 92.27/12.48 thf(zip_derived_cl238, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi > $o]: 92.27/12.48 (ord_le865407012indi_o @ Y0 @ top_to54564308indi_o))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_989_top__greatest])). 92.27/12.48 thf(zip_derived_cl239, plain, 92.27/12.48 ( (((!!) @ ((('#C') @ ord_le865407012indi_o @ top_to54564308indi_o))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl238])). 92.27/12.48 thf(zip_derived_cl419, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > $o]: 92.27/12.48 (ord_le865407012indi_o @ X2 @ top_to54564308indi_o)), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl239])). 92.27/12.48 thf(fact_921_Pi__anti__mono, axiom, 92.27/12.48 (![B_8:( arrow_1196572341e_indi > ( produc1572197287le_alt > $o ) > $o ), 92.27/12.48 A_12:( arrow_1196572341e_indi > $o ), 92.27/12.48 A_11:( arrow_1196572341e_indi > $o )]: 92.27/12.48 ( ( ord_le865407012indi_o @ A_12 @ A_11 ) => 92.27/12.48 ( ord_le602483040lt_o_o @ 92.27/12.48 ( pi_Arr1309696186_alt_o @ A_11 @ B_8 ) @ 92.27/12.48 ( pi_Arr1309696186_alt_o @ A_12 @ B_8 ) ) ))). 92.27/12.48 thf(zip_derived_cl92, plain, 92.27/12.48 ( (((!!) @ (^[Y0 : arrow_1196572341e_indi > (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((!!) @ (^[Y1 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((!!) @ (^[Y2 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((ord_le865407012indi_o @ Y1 @ 92.27/12.48 Y2) => (ord_le602483040lt_o_o @ 92.27/12.48 (pi_Arr1309696186_alt_o @ Y2 @ Y0) @ 92.27/12.48 (pi_Arr1309696186_alt_o @ Y1 @ Y0)))))))))))))), 92.27/12.48 inference('cnf', [status(esa)], [fact_921_Pi__anti__mono])). 92.27/12.48 thf(zip_derived_cl93, plain, 92.27/12.48 ( (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#B') @ ((('#B') @ (!!))) @ 92.27/12.48 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 ord_le865407012indi_o)))))) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#B') @ 92.27/12.48 ((('#B') @ ('#C') @ 92.27/12.48 ((('#B') @ ((('#B') @ ord_le602483040lt_o_o)) @ 92.27/12.48 ((('#C') @ pi_Arr1309696186_alt_o)))))))) @ 92.27/12.48 ((('#C') @ pi_Arr1309696186_alt_o))))))))))))), 92.27/12.48 inference('lams2combs', [status(thm)], [zip_derived_cl92])). 92.27/12.48 thf(zip_derived_cl860, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > (produc1572197287le_alt > $o) > $o]: 92.27/12.48 (((!!) @ ((('#B') @ (!!) @ 92.27/12.48 ((('#S') @ ((('#B') @ ('#S') @ 92.27/12.48 ((('#B') @ ((('#B') @ (=>))) @ 92.27/12.48 ord_le865407012indi_o)))) @ 92.27/12.48 ((('#B') @ ((('#C') @ ((('#B') @ ord_le602483040lt_o_o @ 92.27/12.48 ((('#C') @ pi_Arr1309696186_alt_o @ 92.27/12.48 X2)))))) @ 92.27/12.48 ((('#C') @ pi_Arr1309696186_alt_o @ X2))))))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 92.27/12.48 thf(zip_derived_cl861, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > (produc1572197287le_alt > $o) > $o, 92.27/12.48 X4 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ (ord_le865407012indi_o @ X4))) @ 92.27/12.48 ((('#C') @ ((('#B') @ ord_le602483040lt_o_o @ 92.27/12.48 ((('#C') @ pi_Arr1309696186_alt_o @ X2)))) @ 92.27/12.48 (pi_Arr1309696186_alt_o @ X4 @ X2)))))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl860])). 92.27/12.48 thf(zip_derived_cl862, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > (produc1572197287le_alt > $o) > $o, 92.27/12.48 X4 : arrow_1196572341e_indi > $o, X6 : arrow_1196572341e_indi > $o]: 92.27/12.48 (((ord_le865407012indi_o @ X4 @ X6) => (ord_le602483040lt_o_o @ 92.27/12.48 (pi_Arr1309696186_alt_o @ X6 @ X2) @ 92.27/12.48 (pi_Arr1309696186_alt_o @ X4 @ X2))))), 92.27/12.48 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl861])). 92.27/12.48 thf(zip_derived_cl863, plain, 92.27/12.48 (![X2 : arrow_1196572341e_indi > (produc1572197287le_alt > $o) > $o, 92.27/12.48 X4 : arrow_1196572341e_indi > $o, X6 : arrow_1196572341e_indi > $o]: 92.27/12.48 (~ (ord_le865407012indi_o @ X4 @ X6) 92.27/12.48 | (ord_le602483040lt_o_o @ (pi_Arr1309696186_alt_o @ X6 @ X2) @ 92.27/12.48 (pi_Arr1309696186_alt_o @ X4 @ X2)))), 92.27/12.48 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl862])). 92.27/12.48 thf(zip_derived_cl10084, plain, ($false), 92.27/12.48 inference('eprover', [status(thm)], 92.27/12.48 [zip_derived_cl112, zip_derived_cl444, zip_derived_cl484, 92.27/12.48 zip_derived_cl559, zip_derived_cl496, zip_derived_cl817, 92.27/12.48 zip_derived_cl628, zip_derived_cl993, zip_derived_cl578, 92.27/12.48 zip_derived_cl476, zip_derived_cl499, zip_derived_cl581, 92.27/12.48 zip_derived_cl763, zip_derived_cl477, zip_derived_cl416, 92.27/12.48 zip_derived_cl1293, zip_derived_cl615, zip_derived_cl10079, 92.27/12.48 zip_derived_cl73, zip_derived_cl10063, zip_derived_cl746, 92.27/12.48 zip_derived_cl405, zip_derived_cl419, zip_derived_cl863])). 92.27/12.48 92.27/12.48 % SZS output end Refutation 92.27/12.48 92.27/12.48 92.27/12.48 % Terminating... 92.98/12.67 % Runner terminated. 92.98/12.67 % Zipperpin 1.5 exiting 92.98/12.67 EOF