0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.08 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.JxmEwGH6Xn true 0.21/0.46 % Computer : n003.cluster.edu 0.21/0.46 % Model : x86_64 x86_64 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.21/0.46 % Memory : 8046.5625MB 0.21/0.46 % OS : Linux 6.8.0-71-generic 0.21/0.46 % CPULimit : 1440 0.21/0.46 % WCLimit : 180 0.21/0.46 % DateTime : Mon Jul 27 13:02:54 UTC 2026 0.21/0.47 % CPUTime : 0.21/0.47 % Running portfolio for 1440 s 0.21/0.47 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.21/0.47 % Number of cores: 8 0.21/0.48 % Python version: Python 3.12.3 0.21/0.48 % Running in HO mode 0.45/0.83 % Total configuration time : 828 0.45/0.83 % Estimated wc time : 1656 0.45/0.83 % Estimated cpu time (8 cpus) : 207.0 0.48/0.93 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.48/1.03 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.48/1.03 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.48/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.48/1.04 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.48/1.05 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.48/1.05 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.48/1.05 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.37/1.11 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 2.59/1.18 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 135.73/20.25 % Solved by lams/40_b.comb.sh. 135.73/20.25 % done 542 iterations in 19.041s 135.73/20.25 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 135.73/20.25 % SZS output start Refutation 135.73/20.25 thf(del_type, type, del: $tType). 135.73/20.25 thf(tp__ty_2Enum_2Enum_type, type, tp__ty_2Enum_2Enum: $tType). 135.73/20.25 thf(tp__ty_2Einteger_2Eint_type, type, tp__ty_2Einteger_2Eint: $tType). 135.73/20.25 thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $i). 135.73/20.25 thf(c_2Ewords_2Eword__2comp_type, type, c_2Ewords_2Eword__2comp: del > $i). 135.73/20.25 thf(mem_type, type, mem: $i > del > $o). 135.73/20.25 thf(c_2Ebool_2ECOND_type, type, c_2Ebool_2ECOND: del > $i). 135.73/20.25 thf(c_2Ewords_2En2w_type, type, c_2Ewords_2En2w: del > $i). 135.73/20.25 thf(inj__ty_2Enum_2Enum_type, type, inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i). 135.73/20.25 thf(c_2Einteger_2Eint__lt_type, type, c_2Einteger_2Eint__lt: $i). 135.73/20.25 thf(ty_2Einteger_2Eint_type, type, ty_2Einteger_2Eint: del). 135.73/20.25 thf(p_type, type, p: $i > $o). 135.73/20.25 thf(surj__ty_2Einteger_2Eint_type, type, surj__ty_2Einteger_2Eint: $i > tp__ty_2Einteger_2Eint). 135.73/20.25 thf(c_2Eprim__rec_2E_3C_type, type, c_2Eprim__rec_2E_3C: $i). 135.73/20.25 thf(fo__c_2Enum_2E0_type, type, fo__c_2Enum_2E0: tp__ty_2Enum_2Enum). 135.73/20.25 thf(c_2Ebool_2EF_type, type, c_2Ebool_2EF: $i). 135.73/20.25 thf(c_2Einteger__word_2Ei2w_type, type, c_2Einteger__word_2Ei2w: del > $i). 135.73/20.25 thf('#sk2_type', type, '#sk2': del). 135.73/20.25 thf(ap_type, type, ap: $i > $i > $i). 135.73/20.25 thf(c_2Einteger_2Eint__of__num_type, type, c_2Einteger_2Eint__of__num: $i). 135.73/20.25 thf(arr_type, type, arr: del > del > del). 135.73/20.25 thf(ty_2Efcp_2Ecart_type, type, ty_2Efcp_2Ecart: del > del > del). 135.73/20.25 thf(c_2Einteger_2ENum_type, type, c_2Einteger_2ENum: $i). 135.73/20.25 thf(bool_type, type, bool: del). 135.73/20.25 thf(c_2Einteger_2Eint__neg_type, type, c_2Einteger_2Eint__neg: $i). 135.73/20.25 thf(surj__ty_2Enum_2Enum_type, type, surj__ty_2Enum_2Enum: $i > tp__ty_2Enum_2Enum). 135.73/20.25 thf(inj__ty_2Einteger_2Eint_type, type, inj__ty_2Einteger_2Eint: tp__ty_2Einteger_2Eint > $i). 135.73/20.25 thf(ty_2Enum_2Enum_type, type, ty_2Enum_2Enum: del). 135.73/20.25 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 135.73/20.25 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 135.73/20.25 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 135.73/20.25 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 135.73/20.25 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 135.73/20.25 thf(conj_thm_2Einteger__word_2Ei2w__0, conjecture, 135.73/20.25 (![A_27a:del]: 135.73/20.25 ( ( ap @ 135.73/20.25 ( c_2Einteger__word_2Ei2w @ A_27a ) @ 135.73/20.25 ( ap @ 135.73/20.25 c_2Einteger_2Eint__of__num @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) = 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ))). 135.73/20.25 thf(zf_stmt_0, negated_conjecture, 135.73/20.25 (~( ![A_27a:del]: 135.73/20.25 ( ( ap @ 135.73/20.25 ( c_2Einteger__word_2Ei2w @ A_27a ) @ 135.73/20.25 ( ap @ 135.73/20.25 c_2Einteger_2Eint__of__num @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) = 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) )), 135.73/20.25 inference('cnf.neg', [status(esa)], [conj_thm_2Einteger__word_2Ei2w__0])). 135.73/20.25 thf(zip_derived_cl65, plain, 135.73/20.25 (~ (((!!) @ (^[Y0 : del]: 135.73/20.25 (((ap @ (c_2Einteger__word_2Ei2w @ Y0) @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = 135.73/20.25 (ap @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))), 135.73/20.25 inference('cnf', [status(esa)], [zf_stmt_0])). 135.73/20.25 thf(zip_derived_cl66, plain, 135.73/20.25 (~ (((!!) @ ((('#S') @ ((('#B') @ (=) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ 135.73/20.25 c_2Einteger__word_2Ei2w)) @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ c_2Ewords_2En2w)) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl65])). 135.73/20.25 thf(zip_derived_cl97, plain, 135.73/20.25 (~ (((ap @ (c_2Einteger__word_2Ei2w @ '#sk2') @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = 135.73/20.25 (ap @ (c_2Ewords_2En2w @ '#sk2') @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))), 135.73/20.25 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])). 135.73/20.25 thf(zip_derived_cl98, plain, 135.73/20.25 (((ap @ (c_2Einteger__word_2Ei2w @ '#sk2') @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) 135.73/20.25 != (ap @ (c_2Ewords_2En2w @ '#sk2') @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))), 135.73/20.25 inference('simplify nested equalities', [status(thm)], [zip_derived_cl97])). 135.73/20.25 thf(mem_c_2Ewords_2En2w, axiom, 135.73/20.25 (![A_27a:del]: 135.73/20.25 ( mem @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ))). 135.73/20.25 thf(zip_derived_cl61, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : del]: 135.73/20.25 (mem @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ Y0))))))), 135.73/20.25 inference('cnf', [status(esa)], [mem_c_2Ewords_2En2w])). 135.73/20.25 thf(zip_derived_cl62, plain, 135.73/20.25 ( (((!!) @ ((('#S') @ ((('#B') @ mem @ c_2Ewords_2En2w)) @ 135.73/20.25 ((('#B') @ (arr @ ty_2Enum_2Enum) @ (ty_2Efcp_2Ecart @ bool)))))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl61])). 135.73/20.25 thf(zip_derived_cl86, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 (mem @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ X2)))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl62])). 135.73/20.25 thf(mem_c_2Einteger_2Eint__lt, axiom, 135.73/20.25 (mem @ 135.73/20.25 c_2Einteger_2Eint__lt @ 135.73/20.25 ( arr @ ty_2Einteger_2Eint @ ( arr @ ty_2Einteger_2Eint @ bool ) ))). 135.73/20.25 thf(zip_derived_cl30, plain, 135.73/20.25 ( (mem @ c_2Einteger_2Eint__lt @ 135.73/20.25 (arr @ ty_2Einteger_2Eint @ (arr @ ty_2Einteger_2Eint @ bool)))), 135.73/20.25 inference('cnf', [status(esa)], [mem_c_2Einteger_2Eint__lt])). 135.73/20.25 thf(mem_c_2Ebool_2EF, axiom, (mem @ c_2Ebool_2EF @ bool)). 135.73/20.25 thf(zip_derived_cl26, plain, ( (mem @ c_2Ebool_2EF @ bool)), 135.73/20.25 inference('cnf', [status(esa)], [mem_c_2Ebool_2EF])). 135.73/20.25 thf(conj_thm_2Ewords_2EWORD__NEG__0, axiom, 135.73/20.25 (![A_27a:del]: 135.73/20.25 ( ( ap @ 135.73/20.25 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) = 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ))). 135.73/20.25 thf(zip_derived_cl24, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : del]: 135.73/20.25 (((ap @ (c_2Ewords_2Eword__2comp @ Y0) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = 135.73/20.25 (ap @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))), 135.73/20.25 inference('cnf', [status(esa)], [conj_thm_2Ewords_2EWORD__NEG__0])). 135.73/20.25 thf(zip_derived_cl25, plain, 135.73/20.25 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 135.73/20.25 ((('#S') @ ((('#B') @ ap @ 135.73/20.25 c_2Ewords_2Eword__2comp)) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ c_2Ewords_2En2w)) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ c_2Ewords_2En2w)) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl24])). 135.73/20.25 thf(zip_derived_cl109, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 (((ap @ (c_2Ewords_2Eword__2comp @ X2) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) = 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])). 135.73/20.25 thf(zip_derived_cl110, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 ((ap @ (c_2Ewords_2Eword__2comp @ X2) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))) 135.73/20.25 = (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))), 135.73/20.25 inference('simplify nested equalities', [status(thm)], 135.73/20.25 [zip_derived_cl109])). 135.73/20.25 thf(ax_false_p, axiom, (~( p @ c_2Ebool_2EF ))). 135.73/20.25 thf(zip_derived_cl29, plain, (~ (p @ c_2Ebool_2EF)), 135.73/20.25 inference('cnf', [status(esa)], [ax_false_p])). 135.73/20.25 thf(stp_inj_mem_ty_2Enum_2Enum, axiom, 135.73/20.25 (![X:tp__ty_2Enum_2Enum]: 135.73/20.25 ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ))). 135.73/20.25 thf(zip_derived_cl21, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : tp__ty_2Enum_2Enum]: 135.73/20.25 (mem @ (inj__ty_2Enum_2Enum @ Y0) @ ty_2Enum_2Enum))))), 135.73/20.25 inference('cnf', [status(esa)], [stp_inj_mem_ty_2Enum_2Enum])). 135.73/20.25 thf(zip_derived_cl22, plain, 135.73/20.25 ( (((!!) @ ((('#C') @ ((('#B') @ mem @ inj__ty_2Enum_2Enum)) @ 135.73/20.25 ty_2Enum_2Enum))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl21])). 135.73/20.25 thf(zip_derived_cl80, plain, 135.73/20.25 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.25 (mem @ (inj__ty_2Enum_2Enum @ X2) @ ty_2Enum_2Enum)), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 135.73/20.25 thf(stp_inj_surj_ty_2Enum_2Enum, axiom, 135.73/20.25 (![X:tp__ty_2Enum_2Enum]: 135.73/20.25 ( ( surj__ty_2Enum_2Enum @ ( inj__ty_2Enum_2Enum @ X ) ) = ( X ) ))). 135.73/20.25 thf(zip_derived_cl48, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : tp__ty_2Enum_2Enum]: 135.73/20.25 (((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ Y0)) = 135.73/20.25 (Y0))))))), 135.73/20.25 inference('cnf', [status(esa)], [stp_inj_surj_ty_2Enum_2Enum])). 135.73/20.25 thf(zip_derived_cl49, plain, 135.73/20.25 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 135.73/20.25 ((('#B') @ surj__ty_2Enum_2Enum @ 135.73/20.25 inj__ty_2Enum_2Enum)))) @ 135.73/20.25 ('#I')))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl48])). 135.73/20.25 thf(zip_derived_cl83, plain, 135.73/20.25 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.25 (((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X2)) = (X2)))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 135.73/20.25 thf(zip_derived_cl84, plain, 135.73/20.25 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.25 ((surj__ty_2Enum_2Enum @ (inj__ty_2Enum_2Enum @ X2)) = (X2))), 135.73/20.25 inference('simplify nested equalities', [status(thm)], [zip_derived_cl83])). 135.73/20.25 thf(mem_c_2Einteger_2Eint__neg, axiom, 135.73/20.25 (mem @ 135.73/20.25 c_2Einteger_2Eint__neg @ ( arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint ))). 135.73/20.25 thf(zip_derived_cl39, plain, 135.73/20.25 ( (mem @ c_2Einteger_2Eint__neg @ 135.73/20.25 (arr @ ty_2Einteger_2Eint @ ty_2Einteger_2Eint))), 135.73/20.25 inference('cnf', [status(esa)], [mem_c_2Einteger_2Eint__neg])). 135.73/20.25 thf(ax_thm_2Einteger__word_2Ei2w__def, axiom, 135.73/20.25 (![A_27a:del,V0i:tp__ty_2Einteger_2Eint]: 135.73/20.25 ( ( ap @ 135.73/20.25 ( c_2Einteger__word_2Ei2w @ A_27a ) @ 135.73/20.25 ( inj__ty_2Einteger_2Eint @ V0i ) ) = 135.73/20.25 ( ap @ 135.73/20.25 ( ap @ 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) @ 135.73/20.25 ( ap @ 135.73/20.25 ( ap @ c_2Einteger_2Eint__lt @ ( inj__ty_2Einteger_2Eint @ V0i ) ) @ 135.73/20.25 ( ap @ 135.73/20.25 c_2Einteger_2Eint__of__num @ 135.73/20.25 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) @ 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( ap @ 135.73/20.25 c_2Einteger_2ENum @ 135.73/20.25 ( ap @ 135.73/20.25 c_2Einteger_2Eint__neg @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ) ) @ 135.73/20.25 ( ap @ 135.73/20.25 ( c_2Ewords_2En2w @ A_27a ) @ 135.73/20.25 ( ap @ c_2Einteger_2ENum @ ( inj__ty_2Einteger_2Eint @ V0i ) ) ) ) ))). 135.73/20.25 thf(zip_derived_cl15, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : del]: 135.73/20.25 (((!!) @ (^[Y1 : tp__ty_2Einteger_2Eint]: 135.73/20.25 (((ap @ (c_2Einteger__word_2Ei2w @ Y0) @ 135.73/20.25 (inj__ty_2Einteger_2Eint @ Y1)) = (ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ 135.73/20.25 (c_2Ebool_2ECOND @ 135.73/20.25 (ty_2Efcp_2Ecart @ bool @ Y0)) @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.25 (inj__ty_2Einteger_2Eint @ Y1)) @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) @ 135.73/20.25 (ap @ (c_2Ewords_2Eword__2comp @ Y0) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ 135.73/20.25 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.25 (inj__ty_2Einteger_2Eint @ Y1)))))) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ Y0) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ 135.73/20.25 (inj__ty_2Einteger_2Eint @ Y1))))))))))))), 135.73/20.25 inference('cnf', [status(esa)], [ax_thm_2Einteger__word_2Ei2w__def])). 135.73/20.25 thf(zip_derived_cl16, plain, 135.73/20.25 ( (((!!) @ ((('#B') @ (!!) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 c_2Einteger__word_2Ei2w)))) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.25 ((('#C') @ ((('#B') @ ( 135.73/20.25 '#B') @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 ((('#B') @ c_2Ebool_2ECOND @ 135.73/20.25 (ty_2Efcp_2Ecart @ 135.73/20.25 bool))))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ 135.73/20.25 ((('#B') @ ( 135.73/20.25 ap @ 135.73/20.25 c_2Einteger_2Eint__lt) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))) @ 135.73/20.25 (ap @ 135.73/20.25 c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ 135.73/20.25 fo__c_2Enum_2E0)))))))))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 c_2Ewords_2Eword__2comp)))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 c_2Ewords_2En2w)))) @ 135.73/20.25 ((('#B') @ (ap @ c_2Einteger_2ENum) @ 135.73/20.25 ((('#B') @ (ap @ 135.73/20.25 c_2Einteger_2Eint__neg) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))))))))))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ap @ c_2Ewords_2En2w)))) @ 135.73/20.25 ((('#B') @ (ap @ c_2Einteger_2ENum) @ 135.73/20.25 inj__ty_2Einteger_2Eint))))))))))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl15])). 135.73/20.25 thf(zip_derived_cl133, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 135.73/20.25 ((('#B') @ (ap @ (c_2Einteger__word_2Ei2w @ X2)) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ap @ 135.73/20.25 ((('#S') @ ((('#B') @ ap @ 135.73/20.25 ((('#B') @ (ap @ 135.73/20.25 (c_2Ebool_2ECOND @ 135.73/20.25 (ty_2Efcp_2Ecart @ 135.73/20.25 bool @ X2))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ 135.73/20.25 ((('#B') @ ( 135.73/20.25 ap @ 135.73/20.25 c_2Einteger_2Eint__lt) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))) @ 135.73/20.25 (ap @ 135.73/20.25 c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ 135.73/20.25 fo__c_2Enum_2E0)))))))) @ 135.73/20.25 ((('#B') @ (ap @ 135.73/20.25 (c_2Ewords_2Eword__2comp @ X2)) @ 135.73/20.25 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X2)) @ 135.73/20.25 ((('#B') @ (ap @ c_2Einteger_2ENum) @ 135.73/20.25 ((('#B') @ (ap @ 135.73/20.25 c_2Einteger_2Eint__neg) @ 135.73/20.25 inj__ty_2Einteger_2Eint)))))))))))) @ 135.73/20.25 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X2)) @ 135.73/20.25 ((('#B') @ (ap @ c_2Einteger_2ENum) @ 135.73/20.25 inj__ty_2Einteger_2Eint))))))))))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 135.73/20.25 thf(zip_derived_cl134, plain, 135.73/20.25 (![X2 : del, X4 : tp__ty_2Einteger_2Eint]: 135.73/20.25 (((ap @ (c_2Einteger__word_2Ei2w @ X2) @ 135.73/20.25 (inj__ty_2Einteger_2Eint @ X4)) = (ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ (ty_2Efcp_2Ecart @ bool @ X2)) @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ c_2Einteger_2Eint__lt @ (inj__ty_2Einteger_2Eint @ X4)) @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) @ 135.73/20.25 (ap @ (c_2Ewords_2Eword__2comp @ X2) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ 135.73/20.25 (ap @ c_2Einteger_2Eint__neg @ (inj__ty_2Einteger_2Eint @ X4)))))) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ (inj__ty_2Einteger_2Eint @ X4))))))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl133])). 135.73/20.25 thf(zip_derived_cl135, plain, 135.73/20.25 (![X2 : del, X4 : tp__ty_2Einteger_2Eint]: 135.73/20.25 ((ap @ (c_2Einteger__word_2Ei2w @ X2) @ (inj__ty_2Einteger_2Eint @ X4)) 135.73/20.25 = (ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ (ty_2Efcp_2Ecart @ bool @ X2)) @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ c_2Einteger_2Eint__lt @ (inj__ty_2Einteger_2Eint @ X4)) @ 135.73/20.25 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.25 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) @ 135.73/20.25 (ap @ (c_2Ewords_2Eword__2comp @ X2) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ 135.73/20.25 (ap @ c_2Einteger_2Eint__neg @ (inj__ty_2Einteger_2Eint @ X4)))))) @ 135.73/20.25 (ap @ (c_2Ewords_2En2w @ X2) @ 135.73/20.25 (ap @ c_2Einteger_2ENum @ (inj__ty_2Einteger_2Eint @ X4)))))), 135.73/20.25 inference('simplify nested equalities', [status(thm)], 135.73/20.25 [zip_derived_cl134])). 135.73/20.25 thf(conj_thm_2Ebool_2Ebool__case__thm, axiom, 135.73/20.25 (![A_27a:del]: 135.73/20.25 ( ( ![V2t1:$i]: 135.73/20.25 ( ( mem @ V2t1 @ A_27a ) => 135.73/20.25 ( ![V3t2:$i]: 135.73/20.25 ( ( mem @ V3t2 @ A_27a ) => 135.73/20.25 ( ( ap @ 135.73/20.25 ( ap @ 135.73/20.25 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ 135.73/20.25 V3t2 ) = 135.73/20.25 ( V3t2 ) ) ) ) ) ) & 135.73/20.25 ( ![V0t1:$i]: 135.73/20.25 ( ( mem @ V0t1 @ A_27a ) => 135.73/20.25 ( ![V1t2:$i]: 135.73/20.25 ( ( mem @ V1t2 @ A_27a ) => 135.73/20.25 ( ( ap @ 135.73/20.25 ( ap @ 135.73/20.25 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ 135.73/20.25 V1t2 ) = 135.73/20.25 ( V0t1 ) ) ) ) ) ) ))). 135.73/20.25 thf(zip_derived_cl52, plain, 135.73/20.25 ( (((!!) @ (^[Y0 : del]: 135.73/20.25 (((((!!) @ (^[Y1 : $i]: 135.73/20.25 (((mem @ Y1 @ Y0) => 135.73/20.25 (((!!) @ (^[Y2 : $i]: 135.73/20.25 (((mem @ Y2 @ Y0) => 135.73/20.25 (((ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ 135.73/20.25 (c_2Ebool_2ECOND @ Y0) @ 135.73/20.25 c_2Ebool_2EF) @ 135.73/20.25 Y1) @ 135.73/20.25 Y2) = (Y2))))))))))))) & 135.73/20.25 (((!!) @ (^[Y1 : $i]: 135.73/20.25 (((mem @ Y1 @ Y0) => 135.73/20.25 (((!!) @ (^[Y2 : $i]: 135.73/20.25 (((mem @ Y2 @ Y0) => 135.73/20.25 (((ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ 135.73/20.25 (c_2Ebool_2ECOND @ Y0) @ 135.73/20.25 c_2Ebool_2ET) @ 135.73/20.25 Y1) @ 135.73/20.25 Y2) = (Y1))))))))))))))))))), 135.73/20.25 inference('cnf', [status(esa)], [conj_thm_2Ebool_2Ebool__case__thm])). 135.73/20.25 thf(zip_derived_cl53, plain, 135.73/20.25 ( (((!!) @ ((('#S') @ ((('#B') @ (&) @ 135.73/20.25 ((('#B') @ (!!) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.25 ((('#C') @ mem)))))) @ 135.73/20.25 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.25 ((('#C') @ mem)))))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.25 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.25 ((('#B') @ ((('#B') @ ( 135.73/20.25 (('#B') @ (=))))) @ 135.73/20.25 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 ((('#C') @ ( 135.73/20.25 (('#B') @ ap @ 135.73/20.25 c_2Ebool_2ECOND)) @ 135.73/20.25 c_2Ebool_2EF)))))))))))) @ 135.73/20.25 ('#I'))))))))))))) @ 135.73/20.25 ((('#B') @ (!!) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.25 ((('#C') @ mem)))))) @ 135.73/20.25 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.25 ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.25 ((('#C') @ mem)))))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ ('#C'))) @ 135.73/20.25 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 135.73/20.25 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 ((('#C') @ ((('#B') @ ap @ 135.73/20.25 c_2Ebool_2ECOND)) @ 135.73/20.25 c_2Ebool_2ET)))))))))))) @ 135.73/20.25 ('#I')))))))))))))))), 135.73/20.25 inference('lams2combs', [status(thm)], [zip_derived_cl52])). 135.73/20.25 thf(zip_derived_cl147, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.25 ((('#B') @ (!!) @ 135.73/20.25 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.25 ((('#C') @ mem @ X2)))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=))) @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.25 c_2Ebool_2EF)))))))) @ 135.73/20.25 ('#I'))))))))))) & 135.73/20.25 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.25 ((('#B') @ (!!) @ 135.73/20.25 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.25 ((('#C') @ mem @ X2)))))) @ 135.73/20.25 ((('#S') @ ((('#B') @ ('#C') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=))) @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.25 c_2Ebool_2ET)))))))) @ 135.73/20.25 ('#I')))))))))))))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 135.73/20.25 thf(zip_derived_cl148, plain, 135.73/20.25 (![X2 : del]: 135.73/20.25 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.25 ((('#B') @ (!!) @ 135.73/20.25 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.25 ((('#C') @ mem @ X2)))))) @ 135.73/20.25 ((('#C') @ ((('#B') @ ('#S') @ 135.73/20.25 ((('#B') @ ((('#B') @ (=))) @ 135.73/20.25 ((('#B') @ ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.25 c_2Ebool_2EF)))))))) @ 135.73/20.25 ('#I')))))))))))), 135.73/20.25 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 135.73/20.25 thf(zip_derived_cl150, plain, 135.73/20.25 (![X2 : del, X4 : $i]: 135.73/20.25 (((mem @ X4 @ X2) => 135.73/20.25 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.25 ((('#S') @ ((('#B') @ (=) @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ 135.73/20.25 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.25 c_2Ebool_2EF) @ 135.73/20.25 X4)))) @ 135.73/20.25 ('#I')))))))))), 135.73/20.25 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl148])). 135.73/20.25 thf(zip_derived_cl152, plain, 135.73/20.25 (![X2 : del, X4 : $i]: 135.73/20.25 (~ (mem @ X4 @ X2) 135.73/20.25 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.25 ((('#S') @ ((('#B') @ (=) @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.26 c_2Ebool_2EF) @ 135.73/20.26 X4)))) @ 135.73/20.26 ('#I'))))))))), 135.73/20.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 135.73/20.26 thf(zip_derived_cl154, plain, 135.73/20.26 (![X2 : del, X4 : $i, X6 : $i]: 135.73/20.26 ( (((mem @ X6 @ X2) => 135.73/20.26 (((ap @ 135.73/20.26 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ X6) = 135.73/20.26 (X6))))) 135.73/20.26 | ~ (mem @ X4 @ X2))), 135.73/20.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl152])). 135.73/20.26 thf(zip_derived_cl156, plain, 135.73/20.26 (![X2 : del, X4 : $i, X6 : $i]: 135.73/20.26 (~ (mem @ X6 @ X2) 135.73/20.26 | (((ap @ 135.73/20.26 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ X6) = 135.73/20.26 (X6))) 135.73/20.26 | ~ (mem @ X4 @ X2))), 135.73/20.26 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 135.73/20.26 thf(zip_derived_cl158, plain, 135.73/20.26 (![X2 : del, X4 : $i, X6 : $i]: 135.73/20.26 (~ (mem @ X6 @ X2) 135.73/20.26 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ 135.73/20.26 X6) = (X6)) 135.73/20.26 | ~ (mem @ X4 @ X2))), 135.73/20.26 inference('simplify nested equalities', [status(thm)], 135.73/20.26 [zip_derived_cl156])). 135.73/20.26 thf(conj_thm_2Einteger_2EINT__LT__CALCULATE, axiom, 135.73/20.26 (![V0n:tp__ty_2Enum_2Enum,V1m:tp__ty_2Enum_2Enum]: 135.73/20.26 ( ( ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ 135.73/20.26 ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) <=> 135.73/20.26 ( ( ( V1m ) != ( fo__c_2Enum_2E0 ) ) | 135.73/20.26 ( ( V0n ) != ( fo__c_2Enum_2E0 ) ) ) ) & 135.73/20.26 ( ( $false ) <=> 135.73/20.26 ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) & 135.73/20.26 ( ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V1m ) ) @ 135.73/20.26 ( inj__ty_2Enum_2Enum @ V0n ) ) ) <=> 135.73/20.26 ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ) ) & 135.73/20.26 ( ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) @ 135.73/20.26 ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) <=> 135.73/20.26 ( p @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ c_2Eprim__rec_2E_3C @ ( inj__ty_2Enum_2Enum @ V0n ) ) @ 135.73/20.26 ( inj__ty_2Enum_2Enum @ V1m ) ) ) ) ))). 135.73/20.26 thf(zip_derived_cl31, plain, 135.73/20.26 ( (((!!) @ (^[Y0 : tp__ty_2Enum_2Enum]: 135.73/20.26 (((!!) @ (^[Y1 : tp__ty_2Enum_2Enum]: 135.73/20.26 (((((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1)))) <=> 135.73/20.26 (((((Y1) != (fo__c_2Enum_2E0))) | 135.73/20.26 (((Y0) != (fo__c_2Enum_2E0))))))) & 135.73/20.26 ((($false) <=> (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Eprim__rec_2E_3C @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1)))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Eprim__rec_2E_3C @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y0)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ Y1)))))))))))))), 135.73/20.26 inference('cnf', [status(esa)], [conj_thm_2Einteger_2EINT__LT__CALCULATE])). 135.73/20.26 thf(zip_derived_cl32, plain, 135.73/20.26 ( (((!!) @ ((('#B') @ (!!) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ (( 135.73/20.26 ('#B') @ ( 135.73/20.26 &))) @ 135.73/20.26 ((('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#S') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 <=>))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ p)) @ 135.73/20.26 ((('#C') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ap @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__lt) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__neg) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))) @ 135.73/20.26 (( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#C') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 |) @ 135.73/20.26 ((('#C') @ ( 135.73/20.26 !=) @ 135.73/20.26 fo__c_2Enum_2E0)))))) @ 135.73/20.26 ((('#C') @ ( 135.73/20.26 !=) @ 135.73/20.26 fo__c_2Enum_2E0)))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ (( 135.73/20.26 (<=>) @ ( 135.73/20.26 $false))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ p)) @ 135.73/20.26 ((('#C') @ ((('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__lt) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__neg) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ (<=>))) @ 135.73/20.26 ((('#B') @ ((('#B') @ p)) @ 135.73/20.26 ((('#B') @ ((('#C') @ ( 135.73/20.26 (('#B') @ ap @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Eprim__rec_2E_3C) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ p)) @ 135.73/20.26 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__lt) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__neg) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))) @ 135.73/20.26 ((('#B') @ (ap @ c_2Einteger_2Eint__neg) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ (<=>))) @ 135.73/20.26 ((('#B') @ ((('#B') @ p)) @ 135.73/20.26 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__lt) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ p)) @ 135.73/20.26 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 ((('#B') @ (ap @ c_2Eprim__rec_2E_3C) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))) @ 135.73/20.26 inj__ty_2Enum_2Enum))))))))))))), 135.73/20.26 inference('lams2combs', [status(thm)], [zip_derived_cl31])). 135.73/20.26 thf(zip_derived_cl160, plain, 135.73/20.26 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.26 (((!!) @ ((('#S') @ ((('#S') @ ((('#S') @ ((('#B') @ (&) @ 135.73/20.26 ((('#S') @ ((('#B') @ ( 135.73/20.26 <=>) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 (( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ 135.73/20.26 ( 135.73/20.26 inj__ty_2Enum_2Enum @ 135.73/20.26 X2))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.26 ((('#C') @ ((('#B') @ ( 135.73/20.26 |) @ 135.73/20.26 (( 135.73/20.26 ('#C') @ ( 135.73/20.26 !=) @ 135.73/20.26 fo__c_2Enum_2E0)))) @ 135.73/20.26 (((X2) != 135.73/20.26 (fo__c_2Enum_2E0))))))))) @ 135.73/20.26 ((('#B') @ (((<=>) @ ($false))) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 (ap @ 135.73/20.26 c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ 135.73/20.26 X2)))) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__neg) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ (<=>) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 ((('#C') @ ((('#B') @ ap @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ap @ 135.73/20.26 c_2Eprim__rec_2E_3C) @ 135.73/20.26 inj__ty_2Enum_2Enum)))) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))))))) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))))) @ 135.73/20.26 ((('#B') @ (ap @ c_2Einteger_2Eint__neg) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ (<=>) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2)))) @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 c_2Einteger_2Eint__of__num) @ 135.73/20.26 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.26 ((('#B') @ p @ 135.73/20.26 ((('#B') @ (ap @ 135.73/20.26 (ap @ c_2Eprim__rec_2E_3C @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 inj__ty_2Enum_2Enum))))))))))), 135.73/20.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 135.73/20.26 thf(zip_derived_cl161, plain, 135.73/20.26 (![X2 : tp__ty_2Enum_2Enum, X4 : tp__ty_2Enum_2Enum]: 135.73/20.26 (((((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4)))) <=> 135.73/20.26 (((((X4) != (fo__c_2Enum_2E0))) | (((X2) != (fo__c_2Enum_2E0))))))) & 135.73/20.26 ((($false) <=> (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X4)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4)))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X2)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X4)))))))), 135.73/20.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl160])). 135.73/20.26 thf(zip_derived_cl162, plain, 135.73/20.26 (![X2 : tp__ty_2Enum_2Enum, X4 : tp__ty_2Enum_2Enum]: 135.73/20.26 (((((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4)))) <=> 135.73/20.26 (((((X4) != (fo__c_2Enum_2E0))) | (((X2) != (fo__c_2Enum_2E0))))))) & 135.73/20.26 (((~) @ (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X4))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X4)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X2))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4))))))) & 135.73/20.26 (((p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4)))) <=> 135.73/20.26 (p @ 135.73/20.26 (ap @ (ap @ c_2Eprim__rec_2E_3C @ (inj__ty_2Enum_2Enum @ X2)) @ 135.73/20.26 (inj__ty_2Enum_2Enum @ X4)))))))), 135.73/20.26 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl161])). 135.73/20.26 thf(zip_derived_cl164, plain, 135.73/20.26 (![X2 : tp__ty_2Enum_2Enum, X4 : tp__ty_2Enum_2Enum]: 135.73/20.26 ~ (p @ 135.73/20.26 (ap @ 135.73/20.26 (ap @ c_2Einteger_2Eint__lt @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2))) @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X4)))))), 135.73/20.26 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl162])). 135.73/20.26 thf(mem_c_2Einteger_2Eint__of__num, axiom, 135.73/20.26 (mem @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint ))). 135.73/20.26 thf(zip_derived_cl14, plain, 135.73/20.26 ( (mem @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (arr @ ty_2Enum_2Enum @ ty_2Einteger_2Eint))), 135.73/20.26 inference('cnf', [status(esa)], [mem_c_2Einteger_2Eint__of__num])). 135.73/20.26 thf(mem_c_2Einteger_2ENum, axiom, 135.73/20.26 (mem @ c_2Einteger_2ENum @ ( arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum ))). 135.73/20.26 thf(zip_derived_cl60, plain, 135.73/20.26 ( (mem @ c_2Einteger_2ENum @ (arr @ ty_2Einteger_2Eint @ ty_2Enum_2Enum))), 135.73/20.26 inference('cnf', [status(esa)], [mem_c_2Einteger_2ENum])). 135.73/20.26 thf(conj_thm_2Einteger_2EINT__NEG__0, axiom, 135.73/20.26 (( surj__ty_2Einteger_2Eint @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__neg @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ 135.73/20.26 ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ) ) = 135.73/20.26 ( surj__ty_2Einteger_2Eint @ 135.73/20.26 ( ap @ 135.73/20.26 c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0 ) ) ))). 135.73/20.26 thf(zip_derived_cl13, plain, 135.73/20.26 (((surj__ty_2Einteger_2Eint @ 135.73/20.26 (ap @ c_2Einteger_2Eint__neg @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0)))) 135.73/20.26 = (surj__ty_2Einteger_2Eint @ 135.73/20.26 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.26 (inj__ty_2Enum_2Enum @ fo__c_2Enum_2E0))))), 135.73/20.26 inference('cnf', [status(esa)], [conj_thm_2Einteger_2EINT__NEG__0])). 135.73/20.26 thf(conj_thm_2Ebool_2ECOND__CONG, axiom, 135.73/20.26 (![A_27a:del,V0P:$i]: 135.73/20.26 ( ( mem @ V0P @ bool ) => 135.73/20.26 ( ![V1Q:$i]: 135.73/20.26 ( ( mem @ V1Q @ bool ) => 135.73/20.26 ( ![V2x:$i]: 135.73/20.26 ( ( mem @ V2x @ A_27a ) => 135.73/20.26 ( ![V3x_27:$i]: 135.73/20.26 ( ( mem @ V3x_27 @ A_27a ) => 135.73/20.26 ( ![V4y:$i]: 135.73/20.26 ( ( mem @ V4y @ A_27a ) => 135.73/20.26 ( ![V5y_27:$i]: 135.73/20.26 ( ( mem @ V5y_27 @ A_27a ) => 135.73/20.26 ( ( ( ( ~( p @ V1Q ) ) => ( ( V4y ) = ( V5y_27 ) ) ) & 135.73/20.26 ( ( p @ V1Q ) => ( ( V2x ) = ( V3x_27 ) ) ) & 135.73/20.26 ( ( p @ V0P ) <=> ( p @ V1Q ) ) ) => 135.73/20.26 ( ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ 135.73/20.26 V2x ) @ 135.73/20.26 V4y ) = 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ 135.73/20.26 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ 135.73/20.26 V3x_27 ) @ 135.73/20.26 V5y_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 135.73/20.26 thf(zip_derived_cl33, plain, 135.73/20.26 ( (((!!) @ (^[Y0 : del]: 135.73/20.26 (((!!) @ (^[Y1 : $i]: 135.73/20.26 (((mem @ Y1 @ bool) => 135.73/20.26 (((!!) @ (^[Y2 : $i]: 135.73/20.26 (((mem @ Y2 @ bool) => 135.73/20.26 (((!!) @ (^[Y3 : $i]: 135.73/20.26 (((mem @ Y3 @ 135.73/20.26 Y0) => 135.73/20.26 (((!!) @ ( 135.73/20.26 ^[Y4 : $i]: 135.73/20.26 (((mem @ 135.73/20.26 Y4 @ Y0) => 135.73/20.26 (((!!) @ ( 135.73/20.26 ^[Y5 : $i]: 135.73/20.26 (( 135.73/20.26 (mem @ 135.73/20.26 Y5 @ 135.73/20.26 Y0) => 135.73/20.26 (( 135.73/20.26 (!!) @ ( 135.73/20.26 ^[Y6 : $i]: 135.73/20.26 (( 135.73/20.26 (mem @ 135.73/20.26 Y6 @ 135.73/20.26 Y0) => 135.73/20.26 (( 135.73/20.26 (( 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 (( 135.73/20.26 (~) @ ( 135.73/20.26 p @ Y2))) => 135.73/20.26 (( 135.73/20.26 (Y5) = 135.73/20.26 (Y6))))) & 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 (p @ 135.73/20.26 Y2) => 135.73/20.26 (( 135.73/20.26 (Y3) = 135.73/20.26 (Y4))))) & 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 (p @ 135.73/20.26 Y1) <=> 135.73/20.26 (p @ Y2))))) => 135.73/20.26 (( 135.73/20.26 (ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 c_2Ebool_2ECOND @ 135.73/20.26 Y0) @ Y1) @ 135.73/20.26 Y3) @ 135.73/20.26 Y5) = 135.73/20.26 (ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 c_2Ebool_2ECOND @ 135.73/20.26 Y0) @ Y2) @ 135.73/20.26 Y4) @ Y6))))))))))))))))))))))))))))))))))))))), 135.73/20.26 inference('cnf', [status(esa)], [conj_thm_2Ebool_2ECOND__CONG])). 135.73/20.26 thf(zip_derived_cl34, plain, 135.73/20.26 ( (((!!) @ ((('#B') @ (!!) @ 135.73/20.26 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.26 ((('#C') @ mem @ bool)))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.26 ((('#C') @ mem @ bool)))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.26 ((('#C') @ mem)))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.26 ((('#C') @ mem)))))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 !!))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 =>))) @ 135.73/20.26 ((('#C') @ mem)))))))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ (!!))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 '#S') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ (=>))) @ 135.73/20.26 ((('#C') @ mem)))))))))))))))) @ 135.73/20.26 ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.26 '#S') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#S'))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#S'))))) @ 135.73/20.26 (( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#S'))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#S'))))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>))))))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#S') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#S') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 &))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ~) @ p)))))))) @ 135.73/20.26 ( 135.73/20.26 =))))))))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>) @ p)))))) @ 135.73/20.26 ( 135.73/20.26 =))))))))))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 <=>) @ p)))) @ 135.73/20.26 p)))))))))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#C') @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 '#B'))) @ 135.73/20.26 ((('#B') @ (( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ('#B'))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#C'))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#B'))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ap)))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ap)) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ap @ 135.73/20.26 c_2Ebool_2ECOND)))))))))))))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ap)))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 c_2Ebool_2ECOND))))))))))))))))))))))))))))))))))))), 135.73/20.26 inference('lams2combs', [status(thm)], [zip_derived_cl33])). 135.73/20.26 thf(zip_derived_cl170, plain, 135.73/20.26 (![X2 : del]: 135.73/20.26 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 135.73/20.26 ((('#B') @ (!!) @ 135.73/20.26 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.26 ((('#C') @ mem @ bool)))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ((('#C') @ mem @ 135.73/20.26 X2)))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ((('#C') @ mem @ 135.73/20.26 X2)))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 !!))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#S') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ mem @ 135.73/20.26 X2)))))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ (!!))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ((('#C') @ mem @ 135.73/20.26 X2)))))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 '#S'))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#S'))))) @ 135.73/20.26 ((('#B') @ (( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#S'))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#S'))))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =>))))))))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#S') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 &))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ~) @ p)))))))) @ 135.73/20.26 ( 135.73/20.26 =))))))))))))) @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#C') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>) @ p)))))) @ 135.73/20.26 ( 135.73/20.26 =))))))))))))))) @ 135.73/20.26 ((('#C') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 (( 135.73/20.26 ('#B') @ ( 135.73/20.26 <=>) @ p)))) @ 135.73/20.26 p)))))))))))))))) @ 135.73/20.26 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.26 ((('#B') @ ('#C') @ 135.73/20.26 ((('#B') @ (( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B'))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ('#C'))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#B'))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ap)) @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 ( 135.73/20.26 ap @ 135.73/20.26 ( 135.73/20.26 c_2Ebool_2ECOND @ 135.73/20.26 X2)))))))))))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.26 ((('#B') @ ap @ 135.73/20.26 (ap @ (c_2Ebool_2ECOND @ X2))))))))))))))))))))))))))))))))))), 135.73/20.26 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 135.73/20.26 thf(zip_derived_cl171, plain, 135.73/20.26 (![X2 : del, X4 : $i]: 135.73/20.26 (((mem @ X4 @ bool) => 135.73/20.26 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 135.73/20.26 ((('#B') @ (!!) @ 135.73/20.26 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.26 ((('#C') @ mem @ X2)))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ((('#C') @ mem @ 135.73/20.26 X2)))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 (( 135.73/20.26 ('#C') @ mem @ 135.73/20.26 X2)))))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 !!))))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 =>) @ 135.73/20.26 ((('#C') @ mem @ 135.73/20.26 X2)))))))))))) @ 135.73/20.26 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 '#S'))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#S'))))) @ 135.73/20.26 ((('#B') @ ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#S'))))))) @ 135.73/20.26 ((('#B') @ (( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 =>))))))))) @ 135.73/20.26 ((('#S') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 '#C'))))) @ 135.73/20.26 ((('#B') @ ( 135.73/20.26 (('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))))))) @ 135.73/20.26 (( 135.73/20.26 ('#S') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#B') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C') @ 135.73/20.26 ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 ( 135.73/20.26 ('#B') @ ( 135.73/20.26 '#C'))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ~) @ p)))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>) @ p)))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((<=>) @ ( 135.73/20.27 p @ X4))) @ 135.73/20.27 p)))))))))))))) @ 135.73/20.27 ((('#B') @ ((('#C') @ ((('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#B'))) @ 135.73/20.27 (( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ap @ 135.73/20.27 ( 135.73/20.27 ap @ 135.73/20.27 ( 135.73/20.27 ap @ 135.73/20.27 ( 135.73/20.27 c_2Ebool_2ECOND @ 135.73/20.27 X2) @ X4)))))))))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2))))))))))))))))))))))))))))))))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl170])). 135.73/20.27 thf(zip_derived_cl172, plain, 135.73/20.27 (![X2 : del, X4 : $i]: 135.73/20.27 (~ (mem @ X4 @ bool) 135.73/20.27 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ mem @ 135.73/20.27 X2)))))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (( 135.73/20.27 ('#B') @ ( 135.73/20.27 !!))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#S') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 '#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#S'))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#S'))))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ (=>))))))))) @ 135.73/20.27 ((('#S') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C'))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#S') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ~) @ p)))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>) @ p)))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((<=>) @ ( 135.73/20.27 p @ X4))) @ 135.73/20.27 p)))))))))))))) @ 135.73/20.27 ((('#B') @ ((('#C') @ ((('#B') @ ( 135.73/20.27 '#B') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#B'))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 =))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ap @ 135.73/20.27 ( 135.73/20.27 ap @ 135.73/20.27 ( 135.73/20.27 ap @ 135.73/20.27 ( 135.73/20.27 c_2Ebool_2ECOND @ 135.73/20.27 X2) @ X4)))))))))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ap)) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2)))))))))))))))))))))))))))))))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl171])). 135.73/20.27 thf(zip_derived_cl173, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i]: 135.73/20.27 ( (((mem @ X6 @ bool) => 135.73/20.27 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ mem @ 135.73/20.27 X2)))))))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#S'))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 p @ X6))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ 135.73/20.27 X6))))))))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ ('#C') @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 '#B'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 =))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (c_2Ebool_2ECOND @ 135.73/20.27 X2) @ 135.73/20.27 X4)))))))))))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))))))) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl172])). 135.73/20.27 thf(zip_derived_cl174, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i]: 135.73/20.27 (~ (mem @ X6 @ bool) 135.73/20.27 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#C') @ mem @ 135.73/20.27 X2)))))))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#S'))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 =>))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C'))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#C') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 p @ X6))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ 135.73/20.27 X6))))))))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ ('#C') @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 '#B'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ( 135.73/20.27 =))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (c_2Ebool_2ECOND @ 135.73/20.27 X2) @ 135.73/20.27 X4)))))))))))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))))) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl173])). 135.73/20.27 thf(zip_derived_cl175, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i]: 135.73/20.27 ( (((mem @ X8 @ X2) => 135.73/20.27 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#C') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((=>) @ ( 135.73/20.27 p @ X6))) @ 135.73/20.27 ((($i) = 135.73/20.27 (X8))))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))))))) @ 135.73/20.27 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ (=) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (c_2Ebool_2ECOND @ 135.73/20.27 X2) @ 135.73/20.27 X4) @ 135.73/20.27 X8)))))))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl174])). 135.73/20.27 thf(zip_derived_cl176, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i]: 135.73/20.27 (~ (mem @ X8 @ X2) 135.73/20.27 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 135.73/20.27 =>) @ 135.73/20.27 ((('#C') @ mem @ 135.73/20.27 X2)))))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (( 135.73/20.27 ('#B') @ ( 135.73/20.27 =>))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C'))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 (('#C') @ ( 135.73/20.27 (('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))))) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((=>) @ ( 135.73/20.27 p @ X6))) @ 135.73/20.27 ((($i) = 135.73/20.27 (X8))))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))))))) @ 135.73/20.27 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ (=) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (c_2Ebool_2ECOND @ 135.73/20.27 X2) @ 135.73/20.27 X4) @ 135.73/20.27 X8)))))))) @ 135.73/20.27 ((('#B') @ ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl175])). 135.73/20.27 thf(zip_derived_cl177, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 135.73/20.27 ( (((mem @ X10 @ X2) => 135.73/20.27 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 (( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))) @ 135.73/20.27 (((p @ X6) => 135.73/20.27 (((X8) = (X10))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ (=) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.27 X4) @ 135.73/20.27 X8)))))) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))))))) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl176])). 135.73/20.27 thf(zip_derived_cl178, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 135.73/20.27 (~ (mem @ X10 @ X2) 135.73/20.27 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.27 ((('#C') @ ((('#B') @ ( 135.73/20.27 '#C') @ 135.73/20.27 (( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 &))) @ 135.73/20.27 ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 ('#B') @ ( 135.73/20.27 ( 135.73/20.27 (=>) @ ( 135.73/20.27 ( 135.73/20.27 (~) @ ( 135.73/20.27 p @ X6))))))) @ 135.73/20.27 ( 135.73/20.27 =))))))) @ 135.73/20.27 (((p @ X6) => 135.73/20.27 (((X8) = (X10))))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ (=) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ 135.73/20.27 X4) @ 135.73/20.27 X8)))))) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))))) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 135.73/20.27 thf(zip_derived_cl179, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 135.73/20.27 ( (((mem @ X12 @ X2) => 135.73/20.27 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ ((('#C') @ ((('#B') @ ( 135.73/20.27 &) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((=>) @ ( 135.73/20.27 ((~) @ (p @ X6))))) @ 135.73/20.27 ((($i) = (X12))))))) @ 135.73/20.27 (((p @ X6) => 135.73/20.27 (((X8) = (X10))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))) @ 135.73/20.27 ((('#B') @ ((($i) = (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ 135.73/20.27 X12))) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl178])). 135.73/20.27 thf(zip_derived_cl180, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 135.73/20.27 (~ (mem @ X12 @ X2) 135.73/20.27 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.27 ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ ((('#C') @ ((('#B') @ ( 135.73/20.27 &) @ 135.73/20.27 ((('#B') @ ( 135.73/20.27 ((=>) @ ( 135.73/20.27 ((~) @ (p @ X6))))) @ 135.73/20.27 ((($i) = (X12))))))) @ 135.73/20.27 (((p @ X6) => 135.73/20.27 (((X8) = (X10))))))) @ 135.73/20.27 (((p @ X4) <=> (p @ X6))))))) @ 135.73/20.27 ((('#B') @ ((($i) = (ap @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ 135.73/20.27 X12))) @ 135.73/20.27 (ap @ 135.73/20.27 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl179])). 135.73/20.27 thf(zip_derived_cl181, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 ( (((mem @ X14 @ X2) => 135.73/20.27 (((((((((~) @ (p @ X6))) => (((X12) = (X14))))) & 135.73/20.27 (((p @ X6) => (((X8) = (X10))))) & (((p @ X4) <=> (p @ X6))))) => 135.73/20.27 (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 135.73/20.27 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))))))) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl180])). 135.73/20.27 thf(zip_derived_cl182, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (mem @ X14 @ X2) 135.73/20.27 | (((((((((~) @ (p @ X6))) => (((X12) = (X14))))) & 135.73/20.27 (((p @ X6) => (((X8) = (X10))))) & (((p @ X4) <=> (p @ X6))))) => 135.73/20.27 (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 135.73/20.27 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))))) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl181])). 135.73/20.27 thf(zip_derived_cl183, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((((((~) @ (p @ X6))) => (((X12) = (X14))))) & 135.73/20.27 (((p @ X6) => (((X8) = (X10))))) & (((p @ X4) <=> (p @ X6))))) 135.73/20.27 | (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 135.73/20.27 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X14 @ X2))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl182])). 135.73/20.27 thf(zip_derived_cl184, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((((((~) @ (p @ X6))) => (((X12) = (X14))))) & 135.73/20.27 (((p @ X6) => (((X8) = (X10))))) & (((p @ X4) <=> (p @ X6))))) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X14 @ X2))), 135.73/20.27 inference('simplify nested equalities', [status(thm)], 135.73/20.27 [zip_derived_cl183])). 135.73/20.27 thf(zip_derived_cl185, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 135.73/20.27 | ~ (((p @ X6) => (((X8) = (X10))))) 135.73/20.27 | ~ (((p @ X4) <=> (p @ X6))) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)))), 135.73/20.27 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl184])). 135.73/20.27 thf(zip_derived_cl186, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 135.73/20.27 | ~ (((p @ X6) => (((X8) = (X10))))) 135.73/20.27 | ((p @ X4) != (p @ X6)) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)))), 135.73/20.27 inference('simplify nested equalities', [status(thm)], 135.73/20.27 [zip_derived_cl185])). 135.73/20.27 thf(zip_derived_cl188, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((X12) = (X14))) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ((p @ X4) != (p @ X6)) 135.73/20.27 | ~ (((p @ X6) => (((X8) = (X10))))))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])). 135.73/20.27 thf(zip_derived_cl192, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (((X12) != (X14)) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ((p @ X4) != (p @ X6)) 135.73/20.27 | ~ (((p @ X6) => (((X8) = (X10))))))), 135.73/20.27 inference('simplify nested equalities', [status(thm)], 135.73/20.27 [zip_derived_cl188])). 135.73/20.27 thf(zip_derived_cl194, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (~ (((X8) = (X10))) 135.73/20.27 | ((p @ X4) != (p @ X6)) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 135.73/20.27 | ((X12) != (X14)))), 135.73/20.27 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl192])). 135.73/20.27 thf(zip_derived_cl196, plain, 135.73/20.27 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 135.73/20.27 (((X8) != (X10)) 135.73/20.27 | ((p @ X4) != (p @ X6)) 135.73/20.27 | ~ (mem @ X14 @ X2) 135.73/20.27 | ~ (mem @ X12 @ X2) 135.73/20.27 | ~ (mem @ X10 @ X2) 135.73/20.27 | ~ (mem @ X8 @ X2) 135.73/20.27 | ~ (mem @ X6 @ bool) 135.73/20.27 | ~ (mem @ X4 @ bool) 135.73/20.27 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 135.73/20.27 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 135.73/20.27 | ((X12) != (X14)))), 135.73/20.27 inference('simplify nested equalities', [status(thm)], 135.73/20.27 [zip_derived_cl194])). 135.73/20.27 thf(ap_tp, axiom, 135.73/20.27 (![A:del,B:del,F:$i]: 135.73/20.27 ( ( mem @ F @ ( arr @ A @ B ) ) => 135.73/20.27 ( ![X:$i]: ( ( mem @ X @ A ) => ( mem @ ( ap @ F @ X ) @ B ) ) ) ))). 135.73/20.27 thf(zip_derived_cl2, plain, 135.73/20.27 ( (((!!) @ (^[Y0 : del]: 135.73/20.27 (((!!) @ (^[Y1 : del]: 135.73/20.27 (((!!) @ (^[Y2 : $i]: 135.73/20.27 (((mem @ Y2 @ (arr @ Y0 @ Y1)) => 135.73/20.27 (((!!) @ (^[Y3 : $i]: 135.73/20.27 (((mem @ Y3 @ Y0) => 135.73/20.27 (mem @ 135.73/20.27 (ap @ Y2 @ Y3) @ 135.73/20.27 Y1)))))))))))))))))), 135.73/20.27 inference('cnf', [status(esa)], [ap_tp])). 135.73/20.27 thf(zip_derived_cl3, plain, 135.73/20.27 ( (((!!) @ ((('#B') @ (!!) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ ('#S'))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#C') @ mem)))) @ 135.73/20.27 arr)))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ ('#B') @ 135.73/20.27 ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.27 ((('#C') @ mem)))))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.27 ((('#B') @ ((('#B') @ mem)) @ ap))))))))))))))))))), 135.73/20.27 inference('lams2combs', [status(thm)], [zip_derived_cl2])). 135.73/20.27 thf(zip_derived_cl91, plain, 135.73/20.27 (![X2 : del]: 135.73/20.27 (((!!) @ ((('#B') @ (!!) @ 135.73/20.27 ((('#S') @ ((('#B') @ ('#S') @ 135.73/20.27 ((('#B') @ ((('#B') @ (=>))) @ 135.73/20.27 ((('#B') @ ((('#C') @ mem)) @ (arr @ X2))))))) @ 135.73/20.27 ((('#B') @ ((('#B') @ (!!))) @ 135.73/20.27 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.27 ((('#C') @ mem @ X2)))))))) @ 135.73/20.27 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.27 ((('#B') @ ((('#B') @ mem)) @ ap))))))))))))))))), 135.73/20.27 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 135.73/20.27 thf(zip_derived_cl92, plain, 135.73/20.28 (![X2 : del, X4 : del]: 135.73/20.28 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.28 ((('#C') @ mem @ (arr @ X2 @ X4))))) @ 135.73/20.28 ((('#B') @ (!!) @ 135.73/20.28 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.28 ((('#C') @ mem @ X2)))))) @ 135.73/20.28 ((('#C') @ ((('#B') @ ('#C') @ 135.73/20.28 ((('#B') @ ((('#B') @ mem)) @ ap)))) @ 135.73/20.28 X4))))))))))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl91])). 135.73/20.28 thf(zip_derived_cl93, plain, 135.73/20.28 (![X2 : del, X4 : del, X6 : $i]: 135.73/20.28 (((mem @ X6 @ (arr @ X2 @ X4)) => 135.73/20.28 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.28 ((('#C') @ ((('#B') @ mem @ (ap @ X6))) @ X4))))))))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])). 135.73/20.28 thf(zip_derived_cl94, plain, 135.73/20.28 (![X2 : del, X4 : del, X6 : $i]: 135.73/20.28 (~ (mem @ X6 @ (arr @ X2 @ X4)) 135.73/20.28 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 135.73/20.28 ((('#C') @ ((('#B') @ mem @ (ap @ X6))) @ X4)))))))), 135.73/20.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl93])). 135.73/20.28 thf(zip_derived_cl95, plain, 135.73/20.28 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 135.73/20.28 ( (((mem @ X8 @ X2) => (mem @ (ap @ X6 @ X8) @ X4))) 135.73/20.28 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 135.73/20.28 thf(zip_derived_cl96, plain, 135.73/20.28 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 135.73/20.28 (~ (mem @ X8 @ X2) 135.73/20.28 | (mem @ (ap @ X6 @ X8) @ X4) 135.73/20.28 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 135.73/20.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 135.73/20.28 thf(conj_thm_2Einteger_2ENUM__OF__INT, axiom, 135.73/20.28 (![V0n:tp__ty_2Enum_2Enum]: 135.73/20.28 ( ( surj__ty_2Enum_2Enum @ 135.73/20.28 ( ap @ 135.73/20.28 c_2Einteger_2ENum @ 135.73/20.28 ( ap @ c_2Einteger_2Eint__of__num @ ( inj__ty_2Enum_2Enum @ V0n ) ) ) ) = 135.73/20.28 ( V0n ) ))). 135.73/20.28 thf(zip_derived_cl5, plain, 135.73/20.28 ( (((!!) @ (^[Y0 : tp__ty_2Enum_2Enum]: 135.73/20.28 (((surj__ty_2Enum_2Enum @ 135.73/20.28 (ap @ c_2Einteger_2ENum @ 135.73/20.28 (ap @ c_2Einteger_2Eint__of__num @ 135.73/20.28 (inj__ty_2Enum_2Enum @ Y0)))) = 135.73/20.28 (Y0))))))), 135.73/20.28 inference('cnf', [status(esa)], [conj_thm_2Einteger_2ENUM__OF__INT])). 135.73/20.28 thf(zip_derived_cl6, plain, 135.73/20.28 ( (((!!) @ ((('#S') @ ((('#B') @ (=) @ 135.73/20.28 ((('#B') @ surj__ty_2Enum_2Enum @ 135.73/20.28 ((('#B') @ (ap @ c_2Einteger_2ENum) @ 135.73/20.28 ((('#B') @ (ap @ c_2Einteger_2Eint__of__num) @ 135.73/20.28 inj__ty_2Enum_2Enum)))))))) @ 135.73/20.28 ('#I')))))), 135.73/20.28 inference('lams2combs', [status(thm)], [zip_derived_cl5])). 135.73/20.28 thf(zip_derived_cl106, plain, 135.73/20.28 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.28 (((surj__ty_2Enum_2Enum @ 135.73/20.28 (ap @ c_2Einteger_2ENum @ 135.73/20.28 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) = 135.73/20.28 (X2)))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])). 135.73/20.28 thf(zip_derived_cl107, plain, 135.73/20.28 (![X2 : tp__ty_2Enum_2Enum]: 135.73/20.28 ((surj__ty_2Enum_2Enum @ 135.73/20.28 (ap @ c_2Einteger_2ENum @ 135.73/20.28 (ap @ c_2Einteger_2Eint__of__num @ (inj__ty_2Enum_2Enum @ X2)))) 135.73/20.28 = (X2))), 135.73/20.28 inference('simplify nested equalities', [status(thm)], 135.73/20.28 [zip_derived_cl106])). 135.73/20.28 thf(stp_iso_mem_ty_2Einteger_2Eint, axiom, 135.73/20.28 (![X:$i]: 135.73/20.28 ( ( mem @ X @ ty_2Einteger_2Eint ) => 135.73/20.28 ( ( X ) = ( inj__ty_2Einteger_2Eint @ ( surj__ty_2Einteger_2Eint @ X ) ) ) ))). 135.73/20.28 thf(zip_derived_cl63, plain, 135.73/20.28 ( (((!!) @ (^[Y0 : $i]: 135.73/20.28 (((mem @ Y0 @ ty_2Einteger_2Eint) => 135.73/20.28 (((Y0) = (inj__ty_2Einteger_2Eint @ 135.73/20.28 (surj__ty_2Einteger_2Eint @ Y0)))))))))), 135.73/20.28 inference('cnf', [status(esa)], [stp_iso_mem_ty_2Einteger_2Eint])). 135.73/20.28 thf(zip_derived_cl64, plain, 135.73/20.28 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 135.73/20.28 ((('#C') @ mem @ ty_2Einteger_2Eint)))) @ 135.73/20.28 ((('#S') @ (=) @ 135.73/20.28 ((('#B') @ inj__ty_2Einteger_2Eint @ 135.73/20.28 surj__ty_2Einteger_2Eint))))))))), 135.73/20.28 inference('lams2combs', [status(thm)], [zip_derived_cl63])). 135.73/20.28 thf(zip_derived_cl102, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (((mem @ X2 @ ty_2Einteger_2Eint) => 135.73/20.28 (((X2) = (inj__ty_2Einteger_2Eint @ 135.73/20.28 (surj__ty_2Einteger_2Eint @ X2))))))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 135.73/20.28 thf(zip_derived_cl103, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (~ (mem @ X2 @ ty_2Einteger_2Eint) 135.73/20.28 | (((X2) = (inj__ty_2Einteger_2Eint @ 135.73/20.28 (surj__ty_2Einteger_2Eint @ X2)))))), 135.73/20.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 135.73/20.28 thf(zip_derived_cl104, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (~ (mem @ X2 @ ty_2Einteger_2Eint) 135.73/20.28 | ((X2) = (inj__ty_2Einteger_2Eint @ (surj__ty_2Einteger_2Eint @ X2))))), 135.73/20.28 inference('simplify nested equalities', [status(thm)], 135.73/20.28 [zip_derived_cl103])). 135.73/20.28 thf(stp_iso_mem_ty_2Enum_2Enum, axiom, 135.73/20.28 (![X:$i]: 135.73/20.28 ( ( mem @ X @ ty_2Enum_2Enum ) => 135.73/20.28 ( ( X ) = ( inj__ty_2Enum_2Enum @ ( surj__ty_2Enum_2Enum @ X ) ) ) ))). 135.73/20.28 thf(zip_derived_cl37, plain, 135.73/20.28 ( (((!!) @ (^[Y0 : $i]: 135.73/20.28 (((mem @ Y0 @ ty_2Enum_2Enum) => 135.73/20.28 (((Y0) = (inj__ty_2Enum_2Enum @ 135.73/20.28 (surj__ty_2Enum_2Enum @ Y0)))))))))), 135.73/20.28 inference('cnf', [status(esa)], [stp_iso_mem_ty_2Enum_2Enum])). 135.73/20.28 thf(zip_derived_cl38, plain, 135.73/20.28 ( (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ ty_2Enum_2Enum)))) @ 135.73/20.28 ((('#S') @ (=) @ 135.73/20.28 ((('#B') @ inj__ty_2Enum_2Enum @ surj__ty_2Enum_2Enum))))))))), 135.73/20.28 inference('lams2combs', [status(thm)], [zip_derived_cl37])). 135.73/20.28 thf(zip_derived_cl99, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (((mem @ X2 @ ty_2Enum_2Enum) => 135.73/20.28 (((X2) = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X2))))))), 135.73/20.28 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 135.73/20.28 thf(zip_derived_cl100, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (~ (mem @ X2 @ ty_2Enum_2Enum) 135.73/20.28 | (((X2) = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X2)))))), 135.73/20.28 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 135.73/20.28 thf(zip_derived_cl101, plain, 135.73/20.28 (![X2 : $i]: 135.73/20.28 (~ (mem @ X2 @ ty_2Enum_2Enum) 135.73/20.28 | ((X2) = (inj__ty_2Enum_2Enum @ (surj__ty_2Enum_2Enum @ X2))))), 135.73/20.28 inference('simplify nested equalities', [status(thm)], 135.73/20.28 [zip_derived_cl100])). 135.73/20.28 thf(zip_derived_cl6854, plain, ($false), 135.73/20.28 inference('eprover', [status(thm)], 135.73/20.28 [zip_derived_cl98, zip_derived_cl86, zip_derived_cl30, 135.73/20.28 zip_derived_cl26, zip_derived_cl110, zip_derived_cl29, 135.73/20.28 zip_derived_cl80, zip_derived_cl84, zip_derived_cl39, 135.73/20.28 zip_derived_cl135, zip_derived_cl158, zip_derived_cl164, 135.73/20.28 zip_derived_cl14, zip_derived_cl60, zip_derived_cl13, 135.73/20.28 zip_derived_cl196, zip_derived_cl96, zip_derived_cl107, 135.73/20.28 zip_derived_cl104, zip_derived_cl101])). 135.73/20.28 135.73/20.28 % SZS output end Refutation 135.73/20.28 135.73/20.28 135.73/20.28 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 135.73/20.28 % Terminating... 21.65/20.37 % Runner terminated. 21.65/20.43 % Zipperpin 1.5 exiting 21.65/20.47 EOF