0.00/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.09/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.s8y56W1PfI true 0.10/0.30 % Computer : n005.cluster.edu 0.10/0.30 % Model : x86_64 x86_64 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.10/0.30 % Memory : 8042.1875MB 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.10/0.30 % CPULimit : 1440 0.10/0.30 % WCLimit : 180 0.10/0.30 % DateTime : Thu Jul 4 10:50:54 EDT 2024 0.10/0.30 % CPUTime : 0.10/0.30 % Running portfolio for 1440 s 0.10/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.10/0.30 % Number of cores: 8 0.10/0.30 % Python version: Python 3.6.8 0.10/0.30 % Running in HO mode 0.15/0.53 % Total configuration time : 828 0.15/0.53 % Estimated wc time : 1656 0.15/0.53 % Estimated cpu time (8 cpus) : 207.0 1.10/0.60 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 1.10/0.61 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 1.10/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 1.10/0.62 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 1.10/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 1.10/0.62 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 1.20/0.62 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 1.20/0.62 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 1.20/0.66 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 238.91/30.66 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 248.18/31.88 % Solved by lams/40_b.comb.sh. 248.18/31.88 % done 396 iterations in 31.178s 248.18/31.88 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 248.18/31.88 % SZS output start Refutation 248.18/31.88 thf(del_type, type, del: $tType). 248.18/31.88 thf(tp__ty_2Enum_2Enum_type, type, tp__ty_2Enum_2Enum: $tType). 248.18/31.88 thf(mem_type, type, mem: $i > del > $o). 248.18/31.88 thf(ty_2Efcp_2Ecart_type, type, ty_2Efcp_2Ecart: del > del > del). 248.18/31.88 thf('#sk2_type', type, '#sk2': tp__ty_2Enum_2Enum). 248.18/31.88 thf(c_2Ebool_2ECOND_type, type, c_2Ebool_2ECOND: del > $i). 248.18/31.88 thf('#sk3_type', type, '#sk3': tp__ty_2Enum_2Enum). 248.18/31.88 thf(c_2Ewords_2Eword__add_type, type, c_2Ewords_2Eword__add: del > $i). 248.18/31.88 thf(c_2Ewords_2Eword__sub_type, type, c_2Ewords_2Eword__sub: del > $i). 248.18/31.88 thf(p_type, type, p: $i > $o). 248.18/31.88 thf(inj__ty_2Enum_2Enum_type, type, inj__ty_2Enum_2Enum: tp__ty_2Enum_2Enum > $i). 248.18/31.88 thf(c_2Ebool_2EF_type, type, c_2Ebool_2EF: $i). 248.18/31.88 thf(ap_type, type, ap: $i > $i > $i). 248.18/31.88 thf(c_2Ewords_2Eword__2comp_type, type, c_2Ewords_2Eword__2comp: del > $i). 248.18/31.88 thf(arr_type, type, arr: del > del > del). 248.18/31.88 thf('#sk4_type', type, '#sk4': del > $i > $i > $i). 248.18/31.88 thf(c_2Earithmetic_2E_3C_3D_type, type, c_2Earithmetic_2E_3C_3D: $i). 248.18/31.88 thf('#sk1_type', type, '#sk1': del). 248.18/31.88 thf(bool_type, type, bool: del). 248.18/31.88 thf(c_2Earithmetic_2E_2D_type, type, c_2Earithmetic_2E_2D: $i). 248.18/31.88 thf(c_2Ewords_2En2w_type, type, c_2Ewords_2En2w: del > $i). 248.18/31.88 thf(ty_2Enum_2Enum_type, type, ty_2Enum_2Enum: del). 248.18/31.88 thf(c_2Earithmetic_2E_2B_type, type, c_2Earithmetic_2E_2B: $i). 248.18/31.88 thf(c_2Ebool_2ET_type, type, c_2Ebool_2ET: $i). 248.18/31.88 thf(s_comb_type, type, '#S': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > (A > B) > A > C)). 248.18/31.88 thf(c_comb_type, type, '#C': !>[A:$tType, B:$tType, C:$tType]: ((A > B > C) > B > A > C)). 248.18/31.88 thf(b_comb_type, type, '#B': !>[A:$tType, B:$tType, C:$tType]: ((A > B) > (C > A) > C > B)). 248.18/31.88 thf(k_comb_type, type, '#K': !>[A:$tType, B:$tType]: (B > A > B)). 248.18/31.88 thf(i_comb_type, type, '#I': !>[A:$tType]: (A > A)). 248.18/31.88 thf(mem_c_2Earithmetic_2E_2D, axiom, 248.18/31.88 (mem @ 248.18/31.88 c_2Earithmetic_2E_2D @ 248.18/31.88 ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum ) ))). 248.18/31.88 thf(zip_derived_cl9, plain, 248.18/31.88 ( (mem @ c_2Earithmetic_2E_2D @ 248.18/31.88 (arr @ ty_2Enum_2Enum @ (arr @ ty_2Enum_2Enum @ ty_2Enum_2Enum)))), 248.18/31.88 inference('cnf', [status(esa)], [mem_c_2Earithmetic_2E_2D])). 248.18/31.88 thf(mem_c_2Earithmetic_2E_3C_3D, axiom, 248.18/31.88 (mem @ 248.18/31.88 c_2Earithmetic_2E_3C_3D @ 248.18/31.88 ( arr @ ty_2Enum_2Enum @ ( arr @ ty_2Enum_2Enum @ bool ) ))). 248.18/31.88 thf(zip_derived_cl8, plain, 248.18/31.88 ( (mem @ c_2Earithmetic_2E_3C_3D @ 248.18/31.88 (arr @ ty_2Enum_2Enum @ (arr @ ty_2Enum_2Enum @ bool)))), 248.18/31.88 inference('cnf', [status(esa)], [mem_c_2Earithmetic_2E_3C_3D])). 248.18/31.88 thf(conj_thm_2Ewords_2En2w__sub, conjecture, 248.18/31.88 (![A_27a:del,V0a:tp__ty_2Enum_2Enum,V1b:tp__ty_2Enum_2Enum]: 248.18/31.88 ( ( p @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ 248.18/31.88 ( inj__ty_2Enum_2Enum @ V0a ) ) ) => 248.18/31.88 ( ( ap @ 248.18/31.88 ( c_2Ewords_2En2w @ A_27a ) @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ 248.18/31.88 ( inj__ty_2Enum_2Enum @ V1b ) ) ) = 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ 248.18/31.88 ( c_2Ewords_2Eword__sub @ A_27a ) @ 248.18/31.88 ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ 248.18/31.88 ( ap @ ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ))). 248.18/31.88 thf(zf_stmt_0, negated_conjecture, 248.18/31.88 (~( ![A_27a:del,V0a:tp__ty_2Enum_2Enum,V1b:tp__ty_2Enum_2Enum]: 248.18/31.88 ( ( p @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V1b ) ) @ 248.18/31.88 ( inj__ty_2Enum_2Enum @ V0a ) ) ) => 248.18/31.88 ( ( ap @ 248.18/31.88 ( c_2Ewords_2En2w @ A_27a ) @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V0a ) ) @ 248.18/31.88 ( inj__ty_2Enum_2Enum @ V1b ) ) ) = 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ 248.18/31.88 ( c_2Ewords_2Eword__sub @ A_27a ) @ 248.18/31.88 ( ap @ 248.18/31.88 ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0a ) ) ) @ 248.18/31.88 ( ap @ 248.18/31.88 ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1b ) ) ) ) ) )), 248.18/31.88 inference('cnf.neg', [status(esa)], [conj_thm_2Ewords_2En2w__sub])). 248.18/31.88 thf(zip_derived_cl43, plain, 248.18/31.88 (~ (((!!) @ (^[Y0 : del]: 248.18/31.88 (((!!) @ (^[Y1 : tp__ty_2Enum_2Enum]: 248.18/31.88 (((!!) @ (^[Y2 : tp__ty_2Enum_2Enum]: 248.18/31.88 (((p @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ 248.18/31.88 c_2Earithmetic_2E_3C_3D @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y2)) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y1))) => 248.18/31.88 (((ap @ 248.18/31.88 (c_2Ewords_2En2w @ Y0) @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_2D @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y1)) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y2))) = 248.18/31.88 (ap @ 248.18/31.88 (ap @ 248.18/31.88 (c_2Ewords_2Eword__sub @ Y0) @ 248.18/31.88 (ap @ 248.18/31.88 (c_2Ewords_2En2w @ Y0) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y1))) @ 248.18/31.88 (ap @ 248.18/31.88 (c_2Ewords_2En2w @ Y0) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ Y2))))))))))))))))), 248.18/31.88 inference('cnf', [status(esa)], [zf_stmt_0])). 248.18/31.88 thf(zip_derived_cl44, plain, 248.18/31.88 (~ (((!!) @ ((('#B') @ (!!) @ 248.18/31.88 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.88 ((('#B') @ ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.88 ((('#B') @ ((('#B') @ p)) @ 248.18/31.88 ((('#B') @ ((('#C') @ ( 248.18/31.88 (('#B') @ ap @ 248.18/31.88 ((('#B') @ ( 248.18/31.88 ap @ 248.18/31.88 c_2Earithmetic_2E_3C_3D) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.88 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 c_2Ewords_2En2w)))))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 c_2Earithmetic_2E_2D) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.88 ((('#B') @ ((('#B') @ ('#B'))) @ 248.18/31.88 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 c_2Ewords_2Eword__sub)))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 c_2Ewords_2En2w)))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ c_2Ewords_2En2w)))) @ 248.18/31.88 inj__ty_2Enum_2Enum))))))))))))))), 248.18/31.88 inference('lams2combs', [status(thm)], [zip_derived_cl43])). 248.18/31.88 thf(zip_derived_cl62, plain, 248.18/31.88 (~ (((!!) @ ((('#B') @ (!!) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.88 ((('#B') @ ((('#B') @ p)) @ 248.18/31.88 ((('#B') @ ((('#C') @ ((('#B') @ ap @ 248.18/31.88 ((('#B') @ ( 248.18/31.88 ap @ 248.18/31.88 c_2Earithmetic_2E_3C_3D) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.88 ((('#B') @ ((('#B') @ (ap @ 248.18/31.88 (c_2Ewords_2En2w @ 248.18/31.88 '#sk1')))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 c_2Earithmetic_2E_2D) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ap @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 (c_2Ewords_2Eword__sub @ 248.18/31.88 '#sk1')) @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 (c_2Ewords_2En2w @ '#sk1')) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.88 ((('#B') @ (ap @ (c_2Ewords_2En2w @ '#sk1')) @ 248.18/31.88 inj__ty_2Enum_2Enum))))))))))))), 248.18/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl44])). 248.18/31.88 thf(zip_derived_cl63, plain, 248.18/31.88 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.88 ((('#B') @ p @ 248.18/31.88 ((('#C') @ ((('#B') @ ap @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 c_2Earithmetic_2E_3C_3D) @ 248.18/31.88 inj__ty_2Enum_2Enum)))) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk2'))))))) @ 248.18/31.88 ((('#S') @ ((('#B') @ (=) @ 248.18/31.88 ((('#B') @ (ap @ (c_2Ewords_2En2w @ '#sk1')) @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_2D @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk2'))) @ 248.18/31.88 inj__ty_2Enum_2Enum)))))) @ 248.18/31.88 ((('#B') @ (ap @ 248.18/31.88 (ap @ (c_2Ewords_2Eword__sub @ '#sk1') @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk2')))) @ 248.18/31.88 ((('#B') @ (ap @ (c_2Ewords_2En2w @ '#sk1')) @ 248.18/31.88 inj__ty_2Enum_2Enum))))))))))), 248.18/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl62])). 248.18/31.88 thf(zip_derived_cl64, plain, 248.18/31.88 (~ (((p @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_3C_3D @ (inj__ty_2Enum_2Enum @ '#sk3')) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk2'))) => 248.18/31.88 (((ap @ (c_2Ewords_2En2w @ '#sk1') @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ '#sk2')) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk3'))) = 248.18/31.88 (ap @ 248.18/31.88 (ap @ (c_2Ewords_2Eword__sub @ '#sk1') @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk2'))) @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk3')))))))), 248.18/31.88 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl63])). 248.18/31.88 thf(zip_derived_cl65, plain, 248.18/31.88 ( (p @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_3C_3D @ (inj__ty_2Enum_2Enum @ '#sk3')) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk2')))), 248.18/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 248.18/31.88 thf(zip_derived_cl66, plain, 248.18/31.88 (~ (((ap @ (c_2Ewords_2En2w @ '#sk1') @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ '#sk2')) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk3'))) = 248.18/31.88 (ap @ 248.18/31.88 (ap @ (c_2Ewords_2Eword__sub @ '#sk1') @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk2'))) @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk3')))))), 248.18/31.88 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl64])). 248.18/31.88 thf(zip_derived_cl67, plain, 248.18/31.88 (((ap @ (c_2Ewords_2En2w @ '#sk1') @ 248.18/31.88 (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ '#sk2')) @ 248.18/31.88 (inj__ty_2Enum_2Enum @ '#sk3'))) 248.18/31.88 != (ap @ 248.18/31.88 (ap @ (c_2Ewords_2Eword__sub @ '#sk1') @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk2'))) @ 248.18/31.88 (ap @ (c_2Ewords_2En2w @ '#sk1') @ (inj__ty_2Enum_2Enum @ '#sk3'))))), 248.18/31.88 inference('simplify nested equalities', [status(thm)], [zip_derived_cl66])). 248.18/31.88 thf(mem_c_2Ewords_2Eword__2comp, axiom, 248.18/31.88 (![A_27a:del]: 248.18/31.88 ( mem @ 248.18/31.88 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 248.18/31.88 ( arr @ 248.18/31.88 ( ty_2Efcp_2Ecart @ bool @ A_27a ) @ 248.18/31.88 ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ))). 248.18/31.88 thf(zip_derived_cl18, plain, 248.18/31.88 ( (((!!) @ (^[Y0 : del]: 248.18/31.88 (mem @ (c_2Ewords_2Eword__2comp @ Y0) @ 248.18/31.88 (arr @ (ty_2Efcp_2Ecart @ bool @ Y0) @ 248.18/31.88 (ty_2Efcp_2Ecart @ bool @ Y0))))))), 248.18/31.88 inference('cnf', [status(esa)], [mem_c_2Ewords_2Eword__2comp])). 248.18/31.88 thf(zip_derived_cl19, plain, 248.18/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ mem @ c_2Ewords_2Eword__2comp)) @ 248.18/31.88 ((('#S') @ ((('#B') @ arr @ (ty_2Efcp_2Ecart @ bool))) @ 248.18/31.88 (ty_2Efcp_2Ecart @ bool)))))))), 248.18/31.88 inference('lams2combs', [status(thm)], [zip_derived_cl18])). 248.18/31.88 thf(zip_derived_cl55, plain, 248.18/31.88 (![X2 : del]: 248.18/31.88 (mem @ (c_2Ewords_2Eword__2comp @ X2) @ 248.18/31.88 (arr @ (ty_2Efcp_2Ecart @ bool @ X2) @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.88 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 248.18/31.88 thf(ax_true_p, axiom, (p @ c_2Ebool_2ET)). 248.18/31.88 thf(zip_derived_cl4, plain, ( (p @ c_2Ebool_2ET)), 248.18/31.88 inference('cnf', [status(esa)], [ax_true_p])). 248.18/31.88 thf(mem_c_2Ebool_2ET, axiom, (mem @ c_2Ebool_2ET @ bool)). 248.18/31.88 thf(zip_derived_cl41, plain, ( (mem @ c_2Ebool_2ET @ bool)), 248.18/31.88 inference('cnf', [status(esa)], [mem_c_2Ebool_2ET])). 248.18/31.88 thf(conj_thm_2Ebool_2Ebool__case__thm, axiom, 248.18/31.88 (![A_27a:del]: 248.18/31.88 ( ( ![V0t1:$i]: 248.18/31.88 ( ( mem @ V0t1 @ A_27a ) => 248.18/31.88 ( ![V1t2:$i]: 248.18/31.88 ( ( mem @ V1t2 @ A_27a ) => 248.18/31.88 ( ( ap @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2ET ) @ V0t1 ) @ 248.18/31.88 V1t2 ) = 248.18/31.88 ( V0t1 ) ) ) ) ) ) & 248.18/31.88 ( ![V2t1:$i]: 248.18/31.88 ( ( mem @ V2t1 @ A_27a ) => 248.18/31.88 ( ![V3t2:$i]: 248.18/31.88 ( ( mem @ V3t2 @ A_27a ) => 248.18/31.88 ( ( ap @ 248.18/31.88 ( ap @ 248.18/31.88 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ c_2Ebool_2EF ) @ V2t1 ) @ 248.18/31.88 V3t2 ) = 248.18/31.88 ( V3t2 ) ) ) ) ) ) ))). 248.18/31.88 thf(zip_derived_cl37, plain, 248.18/31.88 ( (((!!) @ (^[Y0 : del]: 248.18/31.88 (((((!!) @ (^[Y1 : $i]: 248.18/31.88 (((mem @ Y1 @ Y0) => 248.18/31.88 (((!!) @ (^[Y2 : $i]: 248.18/31.88 (((mem @ Y2 @ Y0) => 248.18/31.88 (((ap @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ 248.18/31.88 (c_2Ebool_2ECOND @ Y0) @ 248.18/31.88 c_2Ebool_2ET) @ 248.18/31.88 Y1) @ 248.18/31.88 Y2) = (Y1))))))))))))) & 248.18/31.88 (((!!) @ (^[Y1 : $i]: 248.18/31.88 (((mem @ Y1 @ Y0) => 248.18/31.88 (((!!) @ (^[Y2 : $i]: 248.18/31.88 (((mem @ Y2 @ Y0) => 248.18/31.88 (((ap @ 248.18/31.88 (ap @ 248.18/31.88 (ap @ 248.18/31.88 (c_2Ebool_2ECOND @ Y0) @ 248.18/31.88 c_2Ebool_2EF) @ 248.18/31.88 Y1) @ 248.18/31.88 Y2) = (Y2))))))))))))))))))), 248.18/31.88 inference('cnf', [status(esa)], [conj_thm_2Ebool_2Ebool__case__thm])). 248.18/31.88 thf(zip_derived_cl38, plain, 248.18/31.88 ( (((!!) @ ((('#S') @ ((('#B') @ (&) @ 248.18/31.88 ((('#B') @ (!!) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.88 ((('#C') @ mem)))))) @ 248.18/31.88 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.88 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.88 ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.88 ((('#C') @ mem)))))))) @ 248.18/31.88 ((('#C') @ ((('#B') @ ('#S') @ 248.18/31.88 ((('#B') @ ((('#B') @ ('#C'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ (=))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ap @ 248.18/31.89 c_2Ebool_2ECOND)) @ 248.18/31.89 c_2Ebool_2ET)))))))))))) @ 248.18/31.89 ('#I'))))))))))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#C') @ ((('#B') @ ap @ 248.18/31.89 c_2Ebool_2ECOND)) @ 248.18/31.89 c_2Ebool_2EF)))))))))))) @ 248.18/31.89 ('#I')))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl37])). 248.18/31.89 thf(zip_derived_cl87, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2ET)))))))) @ 248.18/31.89 ('#I'))))))))))) & 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2EF)))))))) @ 248.18/31.89 ('#I')))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl38])). 248.18/31.89 thf(zip_derived_cl88, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2ET)))))))) @ 248.18/31.89 ('#I')))))))))))), 248.18/31.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 248.18/31.89 thf(zip_derived_cl90, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (((mem @ X4 @ X2) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2ET) @ 248.18/31.89 X4)))) @ 248.18/31.89 X4))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl88])). 248.18/31.89 thf(zip_derived_cl92, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (~ (mem @ X4 @ X2) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2ET) @ 248.18/31.89 X4)))) @ 248.18/31.89 X4)))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl90])). 248.18/31.89 thf(zip_derived_cl94, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 ( (((mem @ X6 @ X2) => 248.18/31.89 (((ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2ET) @ X4) @ X6) = 248.18/31.89 (X4))))) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl92])). 248.18/31.89 thf(zip_derived_cl96, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ X2) 248.18/31.89 | (((ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2ET) @ X4) @ X6) = 248.18/31.89 (X4))) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl94])). 248.18/31.89 thf(zip_derived_cl98, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ X2) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2ET) @ X4) @ 248.18/31.89 X6) = (X4)) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], [zip_derived_cl96])). 248.18/31.89 thf(conj_thm_2Ewords_2EWORD__LITERAL__ADD, axiom, 248.18/31.89 (![A_27a:del,A_27b:del]: 248.18/31.89 ( ( ![V0m:tp__ty_2Enum_2Enum,V1n:tp__ty_2Enum_2Enum]: 248.18/31.89 ( ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__add @ A_27a ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V0m ) ) ) ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27a ) @ ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) = 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__2comp @ A_27a ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27a ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ c_2Earithmetic_2E_2B @ ( inj__ty_2Enum_2Enum @ V0m ) ) @ 248.18/31.89 ( inj__ty_2Enum_2Enum @ V1n ) ) ) ) ) ) & 248.18/31.89 ( ![V2m:tp__ty_2Enum_2Enum,V3n:tp__ty_2Enum_2Enum]: 248.18/31.89 ( ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__add @ A_27b ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__2comp @ A_27b ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27b ) @ ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) = 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ebool_2ECOND @ ( ty_2Efcp_2Ecart @ bool @ A_27b ) ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ 248.18/31.89 ( inj__ty_2Enum_2Enum @ V2m ) ) ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27b ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V2m ) ) @ 248.18/31.89 ( inj__ty_2Enum_2Enum @ V3n ) ) ) ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2Eword__2comp @ A_27b ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27b ) @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ c_2Earithmetic_2E_2D @ ( inj__ty_2Enum_2Enum @ V3n ) ) @ 248.18/31.89 ( inj__ty_2Enum_2Enum @ V2m ) ) ) ) ) ) ) ))). 248.18/31.89 thf(zip_derived_cl14, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (((!!) @ (^[Y1 : del]: 248.18/31.89 (((((!!) @ (^[Y2 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((!!) @ (^[Y3 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ 248.18/31.89 Y0) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y0) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y0) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2)))) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y0) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y0) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)))) = 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y0) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y0) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 c_2Earithmetic_2E_2B @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)))))))))))) & 248.18/31.89 (((!!) @ (^[Y2 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((!!) @ (^[Y3 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y1) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2))) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y1) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)))) = 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 (ty_2Efcp_2Ecart @ 248.18/31.89 bool @ Y1)) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2))) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 c_2Earithmetic_2E_2D @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)))) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 c_2Earithmetic_2E_2D @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y3)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ 248.18/31.89 Y2)))))))))))))))))))))), 248.18/31.89 inference('cnf', [status(esa)], [conj_thm_2Ewords_2EWORD__LITERAL__ADD])). 248.18/31.89 thf(zip_derived_cl15, plain, 248.18/31.89 ( (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ (&) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ (=))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap)) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#S') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__add)))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#S') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_2B) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__add)))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ap)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ap)))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ c_2Ebool_2ECOND @ 248.18/31.89 ( 248.18/31.89 ty_2Efcp_2Ecart @ 248.18/31.89 bool))))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#C') @ ( 248.18/31.89 (('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ c_2Ewords_2En2w)))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum))))))))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl14])). 248.18/31.89 thf(zip_derived_cl133, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#B') @ (((&) @ (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ewords_2Eword__add @ 248.18/31.89 X2)) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ewords_2Eword__2comp @ 248.18/31.89 X2)) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ewords_2En2w @ 248.18/31.89 X2)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 X2)) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ewords_2En2w @ 248.18/31.89 X2)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 X2)))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_2B) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__add)))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ap)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ap)))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ c_2Ebool_2ECOND @ 248.18/31.89 ( 248.18/31.89 ty_2Efcp_2Ecart @ 248.18/31.89 bool))))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#C') @ ( 248.18/31.89 (('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2En2w)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__2comp)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ c_2Ewords_2En2w)))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum))))))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 248.18/31.89 thf(zip_derived_cl134, plain, 248.18/31.89 (![X2 : del, X4 : del]: 248.18/31.89 (((((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ 248.18/31.89 X2)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 X2)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X2)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 X2)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ X2)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ X2)))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ (c_2Ewords_2En2w @ X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2B) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))))) & 248.18/31.89 (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ 248.18/31.89 X4)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X4)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 X4)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ X4)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 (ty_2Efcp_2Ecart @ 248.18/31.89 bool @ X4))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X4)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ X4)))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum))))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl133])). 248.18/31.89 thf(zip_derived_cl136, plain, 248.18/31.89 (![X4 : del]: 248.18/31.89 (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ 248.18/31.89 X4)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X4)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ X4)) @ 248.18/31.89 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 (ty_2Efcp_2Ecart @ 248.18/31.89 bool @ X4))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ( 248.18/31.89 (('#B') @ ap @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2En2w @ 248.18/31.89 X4)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ X4)))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))) @ 248.18/31.89 inj__ty_2Enum_2Enum))))))))))))))), 248.18/31.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl134])). 248.18/31.89 thf(zip_derived_cl138, plain, 248.18/31.89 (![X4 : del, X6 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6)))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ X4)) @ 248.18/31.89 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ap @ 248.18/31.89 ((('#S') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 (ty_2Efcp_2Ecart @ 248.18/31.89 bool @ X4))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ap @ 248.18/31.89 c_2Earithmetic_2E_3C_3D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6))))))) @ 248.18/31.89 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (ap @ c_2Earithmetic_2E_2D @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6))) @ 248.18/31.89 inj__ty_2Enum_2Enum)))))))) @ 248.18/31.89 ((('#B') @ (ap @ (c_2Ewords_2Eword__2comp @ X4)) @ 248.18/31.89 ((('#B') @ (ap @ (c_2Ewords_2En2w @ X4)) @ 248.18/31.89 ((('#C') @ ((('#B') @ ap @ 248.18/31.89 ((('#B') @ (ap @ c_2Earithmetic_2E_2D) @ 248.18/31.89 inj__ty_2Enum_2Enum)))) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6)))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl136])). 248.18/31.89 thf(zip_derived_cl140, plain, 248.18/31.89 (![X4 : del, X6 : tp__ty_2Enum_2Enum, X8 : tp__ty_2Enum_2Enum]: 248.18/31.89 (((ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ (inj__ty_2Enum_2Enum @ X6))) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ (inj__ty_2Enum_2Enum @ X8)))) = 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ (ty_2Efcp_2Ecart @ bool @ X4)) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ c_2Earithmetic_2E_3C_3D @ (inj__ty_2Enum_2Enum @ X8)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6))) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ 248.18/31.89 (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X6)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X8)))) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ 248.18/31.89 (ap @ (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X8)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6)))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl138])). 248.18/31.89 thf(zip_derived_cl142, plain, 248.18/31.89 (![X4 : del, X6 : tp__ty_2Enum_2Enum, X8 : tp__ty_2Enum_2Enum]: 248.18/31.89 ((ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ (inj__ty_2Enum_2Enum @ X6))) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ (inj__ty_2Enum_2Enum @ X8)))) 248.18/31.89 = (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ (ty_2Efcp_2Ecart @ bool @ X4)) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ c_2Earithmetic_2E_3C_3D @ (inj__ty_2Enum_2Enum @ X8)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6))) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X6)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X8)))) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2En2w @ X4) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ c_2Earithmetic_2E_2D @ (inj__ty_2Enum_2Enum @ X8)) @ 248.18/31.89 (inj__ty_2Enum_2Enum @ X6))))))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl140])). 248.18/31.89 thf(ax_thm_2Ewords_2Eword__sub__def, axiom, 248.18/31.89 (![A_27a:del,V0v:$i]: 248.18/31.89 ( ( mem @ V0v @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) => 248.18/31.89 ( ![V1w:$i]: 248.18/31.89 ( ( mem @ V1w @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) => 248.18/31.89 ( ( ap @ ( ap @ ( c_2Ewords_2Eword__sub @ A_27a ) @ V0v ) @ V1w ) = 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ ( c_2Ewords_2Eword__add @ A_27a ) @ V0v ) @ 248.18/31.89 ( ap @ ( c_2Ewords_2Eword__2comp @ A_27a ) @ V1w ) ) ) ) ) ))). 248.18/31.89 thf(zip_derived_cl21, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (((!!) @ (^[Y1 : $i]: 248.18/31.89 (((mem @ Y1 @ (ty_2Efcp_2Ecart @ bool @ Y0)) => 248.18/31.89 (((!!) @ (^[Y2 : $i]: 248.18/31.89 (((mem @ Y2 @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool @ Y0)) => 248.18/31.89 (((ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__sub @ Y0) @ 248.18/31.89 Y1) @ 248.18/31.89 Y2) = (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__add @ Y0) @ 248.18/31.89 Y1) @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ewords_2Eword__2comp @ 248.18/31.89 Y0) @ 248.18/31.89 Y2)))))))))))))))))), 248.18/31.89 inference('cnf', [status(esa)], [ax_thm_2Ewords_2Eword__sub__def])). 248.18/31.89 thf(zip_derived_cl22, plain, 248.18/31.89 ( (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#C') @ mem)) @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#C') @ mem)) @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__sub)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ewords_2Eword__add)))))))) @ 248.18/31.89 ((('#B') @ ap @ c_2Ewords_2Eword__2comp))))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl21])). 248.18/31.89 thf(zip_derived_cl74, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (ty_2Efcp_2Ecart @ bool @ X2))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool @ X2))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__sub @ X2)))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X2)))))) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 248.18/31.89 thf(zip_derived_cl75, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (((mem @ X4 @ (ty_2Efcp_2Ecart @ bool @ X2)) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool @ X2))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__sub @ X2) @ X4)))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X2) @ X4)) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl74])). 248.18/31.89 thf(zip_derived_cl76, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (~ (mem @ X4 @ (ty_2Efcp_2Ecart @ bool @ X2)) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool @ X2))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__sub @ X2) @ X4)))) @ 248.18/31.89 ((('#B') @ (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X2) @ X4)) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2)))))))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl75])). 248.18/31.89 thf(zip_derived_cl77, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 ( (((mem @ X6 @ (ty_2Efcp_2Ecart @ bool @ X2)) => 248.18/31.89 (((ap @ (ap @ (c_2Ewords_2Eword__sub @ X2) @ X4) @ X6) = (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X2) @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2) @ X6)))))) 248.18/31.89 | ~ (mem @ X4 @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl76])). 248.18/31.89 thf(zip_derived_cl78, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ (ty_2Efcp_2Ecart @ bool @ X2)) 248.18/31.89 | (((ap @ (ap @ (c_2Ewords_2Eword__sub @ X2) @ X4) @ X6) = (ap @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__add @ X2) @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2) @ X6)))) 248.18/31.89 | ~ (mem @ X4 @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])). 248.18/31.89 thf(zip_derived_cl79, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ (ty_2Efcp_2Ecart @ bool @ X2)) 248.18/31.89 | ((ap @ (ap @ (c_2Ewords_2Eword__sub @ X2) @ X4) @ X6) 248.18/31.89 = (ap @ (ap @ (c_2Ewords_2Eword__add @ X2) @ X4) @ 248.18/31.89 (ap @ (c_2Ewords_2Eword__2comp @ X2) @ X6))) 248.18/31.89 | ~ (mem @ X4 @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], [zip_derived_cl78])). 248.18/31.89 thf(mem_c_2Ewords_2En2w, axiom, 248.18/31.89 (![A_27a:del]: 248.18/31.89 ( mem @ 248.18/31.89 ( c_2Ewords_2En2w @ A_27a ) @ 248.18/31.89 ( arr @ ty_2Enum_2Enum @ ( ty_2Efcp_2Ecart @ bool @ A_27a ) ) ))). 248.18/31.89 thf(zip_derived_cl27, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (mem @ (c_2Ewords_2En2w @ Y0) @ 248.18/31.89 (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ Y0))))))), 248.18/31.89 inference('cnf', [status(esa)], [mem_c_2Ewords_2En2w])). 248.18/31.89 thf(zip_derived_cl28, plain, 248.18/31.89 ( (((!!) @ ((('#S') @ ((('#B') @ mem @ c_2Ewords_2En2w)) @ 248.18/31.89 ((('#B') @ (arr @ ty_2Enum_2Enum) @ (ty_2Efcp_2Ecart @ bool)))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl27])). 248.18/31.89 thf(zip_derived_cl48, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (mem @ (c_2Ewords_2En2w @ X2) @ 248.18/31.89 (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 248.18/31.89 thf(conj_thm_2Ebool_2ECOND__CONG, axiom, 248.18/31.89 (![A_27a:del,V0P:$i]: 248.18/31.89 ( ( mem @ V0P @ bool ) => 248.18/31.89 ( ![V1Q:$i]: 248.18/31.89 ( ( mem @ V1Q @ bool ) => 248.18/31.89 ( ![V2x:$i]: 248.18/31.89 ( ( mem @ V2x @ A_27a ) => 248.18/31.89 ( ![V3x_27:$i]: 248.18/31.89 ( ( mem @ V3x_27 @ A_27a ) => 248.18/31.89 ( ![V4y:$i]: 248.18/31.89 ( ( mem @ V4y @ A_27a ) => 248.18/31.89 ( ![V5y_27:$i]: 248.18/31.89 ( ( mem @ V5y_27 @ A_27a ) => 248.18/31.89 ( ( ( ( p @ V0P ) <=> ( p @ V1Q ) ) & 248.18/31.89 ( ( p @ V1Q ) => ( ( V2x ) = ( V3x_27 ) ) ) & 248.18/31.89 ( ( ~( p @ V1Q ) ) => ( ( V4y ) = ( V5y_27 ) ) ) ) => 248.18/31.89 ( ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V0P ) @ 248.18/31.89 V2x ) @ 248.18/31.89 V4y ) = 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ 248.18/31.89 ( ap @ ( c_2Ebool_2ECOND @ A_27a ) @ V1Q ) @ 248.18/31.89 V3x_27 ) @ 248.18/31.89 V5y_27 ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 248.18/31.89 thf(zip_derived_cl23, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (((!!) @ (^[Y1 : $i]: 248.18/31.89 (((mem @ Y1 @ bool) => 248.18/31.89 (((!!) @ (^[Y2 : $i]: 248.18/31.89 (((mem @ Y2 @ bool) => 248.18/31.89 (((!!) @ (^[Y3 : $i]: 248.18/31.89 (((mem @ Y3 @ 248.18/31.89 Y0) => 248.18/31.89 (((!!) @ ( 248.18/31.89 ^[Y4 : $i]: 248.18/31.89 (((mem @ 248.18/31.89 Y4 @ Y0) => 248.18/31.89 (((!!) @ ( 248.18/31.89 ^[Y5 : $i]: 248.18/31.89 (( 248.18/31.89 (mem @ 248.18/31.89 Y5 @ 248.18/31.89 Y0) => 248.18/31.89 (( 248.18/31.89 (!!) @ ( 248.18/31.89 ^[Y6 : $i]: 248.18/31.89 (( 248.18/31.89 (mem @ 248.18/31.89 Y6 @ 248.18/31.89 Y0) => 248.18/31.89 (( 248.18/31.89 (( 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 (p @ 248.18/31.89 Y1) <=> 248.18/31.89 (p @ Y2))) & 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 (p @ 248.18/31.89 Y2) => 248.18/31.89 (( 248.18/31.89 (Y3) = 248.18/31.89 (Y4))))) & 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 (( 248.18/31.89 (~) @ ( 248.18/31.89 p @ Y2))) => 248.18/31.89 (( 248.18/31.89 (Y5) = 248.18/31.89 (Y6))))))) => 248.18/31.89 (( 248.18/31.89 (ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ebool_2ECOND @ 248.18/31.89 Y0) @ Y1) @ 248.18/31.89 Y3) @ 248.18/31.89 Y5) = 248.18/31.89 (ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ebool_2ECOND @ 248.18/31.89 Y0) @ Y2) @ 248.18/31.89 Y4) @ Y6))))))))))))))))))))))))))))))))))))))), 248.18/31.89 inference('cnf', [status(esa)], [conj_thm_2Ebool_2ECOND__CONG])). 248.18/31.89 thf(zip_derived_cl24, plain, 248.18/31.89 ( (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ bool)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ bool)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ (!!))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 !!))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 =>))) @ 248.18/31.89 ((('#C') @ mem)))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ (!!))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>))))))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#C'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#C'))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 &))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 <=>) @ p)))) @ 248.18/31.89 p)))))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ p)))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ~) @ p)))))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#C'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ('#B'))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C'))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B'))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap)))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap)) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 c_2Ebool_2ECOND)))))))))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ap)))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 c_2Ebool_2ECOND))))))))))))))))))))))))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl23])). 248.18/31.89 thf(zip_derived_cl143, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ bool)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 !!))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#S') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ (!!))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>))))))))))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C'))) @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#C'))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 &))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 <=>) @ p)))) @ 248.18/31.89 p)))))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ p)))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))))))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ~) @ p)))))))) @ 248.18/31.89 (=))))))))))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ('#C'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B'))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ebool_2ECOND @ 248.18/31.89 X2)))))))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2))))))))))))))))))))))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl24])). 248.18/31.89 thf(zip_derived_cl144, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (((mem @ X4 @ bool) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 (( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 !!))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))))) @ 248.18/31.89 ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>))))))))) @ 248.18/31.89 ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B'))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))) @ 248.18/31.89 (( 248.18/31.89 ('#S') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 &) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (<=>) @ ( 248.18/31.89 p @ X4))) @ 248.18/31.89 p)))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ p)))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ~) @ p)))))))) @ 248.18/31.89 (=))))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 (( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ebool_2ECOND @ 248.18/31.89 X2) @ X4)))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2))))))))))))))))))))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl143])). 248.18/31.89 thf(zip_derived_cl145, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (~ (mem @ X4 @ bool) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ bool)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 !!))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#S'))))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ (=>))))))))) @ 248.18/31.89 ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#C'))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B'))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#S') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 &) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (<=>) @ ( 248.18/31.89 p @ X4))) @ 248.18/31.89 p)))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>) @ p)))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))))) @ 248.18/31.89 ((('#C') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ~) @ p)))))))) @ 248.18/31.89 (=))))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 =))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 ap @ 248.18/31.89 ( 248.18/31.89 c_2Ebool_2ECOND @ 248.18/31.89 X2) @ X4)))))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ap)) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2)))))))))))))))))))))))))))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl144])). 248.18/31.89 thf(zip_derived_cl146, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 ( (((mem @ X6 @ bool) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (&) @ ( 248.18/31.89 ( 248.18/31.89 (p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (=>) @ ( 248.18/31.89 p @ X6))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 (=>) @ ( 248.18/31.89 ( 248.18/31.89 (~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 =))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 X2) @ 248.18/31.89 X4)))))))))))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))))))) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl145])). 248.18/31.89 thf(zip_derived_cl147, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ bool) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 '#S'))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#C') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (&) @ ( 248.18/31.89 ( 248.18/31.89 (p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))))))) @ 248.18/31.89 ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 ('#B') @ ( 248.18/31.89 ( 248.18/31.89 (=>) @ ( 248.18/31.89 p @ X6))))) @ 248.18/31.89 ( 248.18/31.89 =))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ( 248.18/31.89 (=>) @ ( 248.18/31.89 ( 248.18/31.89 (~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 '#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 =))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 X2) @ 248.18/31.89 X4)))))))))))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))))) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl146])). 248.18/31.89 thf(zip_derived_cl148, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i]: 248.18/31.89 ( (((mem @ X8 @ X2) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ((&) @ ( 248.18/31.89 ((p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ((=>) @ ( 248.18/31.89 p @ X6))) @ 248.18/31.89 ((($i) = 248.18/31.89 (X8))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ((=>) @ ( 248.18/31.89 ((~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 X2) @ 248.18/31.89 X4) @ 248.18/31.89 X8)))))))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))))) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl147])). 248.18/31.89 thf(zip_derived_cl149, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i]: 248.18/31.89 (~ (mem @ X8 @ X2) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (( 248.18/31.89 ('#B') @ ( 248.18/31.89 =>))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ((&) @ ( 248.18/31.89 ((p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))))) @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 ((=>) @ ( 248.18/31.89 p @ X6))) @ 248.18/31.89 ((($i) = 248.18/31.89 (X8))))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ( 248.18/31.89 ((=>) @ ( 248.18/31.89 ((~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))))) @ 248.18/31.89 ((('#B') @ ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (c_2Ebool_2ECOND @ 248.18/31.89 X2) @ 248.18/31.89 X4) @ 248.18/31.89 X8)))))))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6)))))))))))))))))))) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl148])). 248.18/31.89 thf(zip_derived_cl150, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 248.18/31.89 ( (((mem @ X10 @ X2) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (((((p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))) & 248.18/31.89 (((p @ 248.18/31.89 X6) => 248.18/31.89 (( 248.18/31.89 (X8) = 248.18/31.89 (X10))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (((=>) @ ( 248.18/31.89 ((~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 X4) @ 248.18/31.89 X8)))))) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))))))) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl149])). 248.18/31.89 thf(zip_derived_cl151, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i]: 248.18/31.89 (~ (mem @ X10 @ X2) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (((((p @ 248.18/31.89 X4) <=> 248.18/31.89 (p @ X6))) & 248.18/31.89 (((p @ 248.18/31.89 X6) => 248.18/31.89 (( 248.18/31.89 (X8) = 248.18/31.89 (X10))))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (((=>) @ ( 248.18/31.89 ((~) @ ( 248.18/31.89 p @ X6))))))) @ 248.18/31.89 (=))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 X4) @ 248.18/31.89 X8)))))) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))))) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl150])). 248.18/31.89 thf(zip_derived_cl152, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 248.18/31.89 ( (((mem @ X12 @ X2) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#B') @ (((((p @ X4) <=> (p @ X6))) & 248.18/31.89 (((p @ X6) => 248.18/31.89 (((X8) = (X10))))))) @ 248.18/31.89 ((('#B') @ (((=>) @ (((~) @ (p @ X6))))) @ 248.18/31.89 ((($i) = (X12))))))))) @ 248.18/31.89 ((('#B') @ ((($i) = (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ 248.18/31.89 X12))) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))))) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl151])). 248.18/31.89 thf(zip_derived_cl153, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i]: 248.18/31.89 (~ (mem @ X12 @ X2) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#B') @ (((((p @ X4) <=> (p @ X6))) & 248.18/31.89 (((p @ X6) => 248.18/31.89 (((X8) = (X10))))))) @ 248.18/31.89 ((('#B') @ (((=>) @ (((~) @ (p @ X6))))) @ 248.18/31.89 ((($i) = (X12))))))))) @ 248.18/31.89 ((('#B') @ ((($i) = (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ 248.18/31.89 X12))) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10)))))))))) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl152])). 248.18/31.89 thf(zip_derived_cl154, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 ( (((mem @ X14 @ X2) => 248.18/31.89 (((((((p @ X4) <=> (p @ X6))) & 248.18/31.89 (((p @ X6) => (((X8) = (X10))))) & 248.18/31.89 (((((~) @ (p @ X6))) => (((X12) = (X14))))))) => 248.18/31.89 (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 248.18/31.89 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))))))) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl153])). 248.18/31.89 thf(zip_derived_cl155, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (mem @ X14 @ X2) 248.18/31.89 | (((((((p @ X4) <=> (p @ X6))) & 248.18/31.89 (((p @ X6) => (((X8) = (X10))))) & 248.18/31.89 (((((~) @ (p @ X6))) => (((X12) = (X14))))))) => 248.18/31.89 (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 248.18/31.89 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))))) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 248.18/31.89 thf(zip_derived_cl156, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (((((p @ X4) <=> (p @ X6))) & (((p @ X6) => (((X8) = (X10))))) & 248.18/31.89 (((((~) @ (p @ X6))) => (((X12) = (X14))))))) 248.18/31.89 | (((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) = 248.18/31.89 (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14))) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl155])). 248.18/31.89 thf(zip_derived_cl157, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (((((p @ X4) <=> (p @ X6))) & (((p @ X6) => (((X8) = (X10))))) & 248.18/31.89 (((((~) @ (p @ X6))) => (((X12) = (X14))))))) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl156])). 248.18/31.89 thf(zip_derived_cl158, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (((p @ X4) <=> (p @ X6))) 248.18/31.89 | ~ (((p @ X6) => (((X8) = (X10))))) 248.18/31.89 | ~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)))), 248.18/31.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl157])). 248.18/31.89 thf(zip_derived_cl159, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (((p @ X4) != (p @ X6)) 248.18/31.89 | ~ (((p @ X6) => (((X8) = (X10))))) 248.18/31.89 | ~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl158])). 248.18/31.89 thf(zip_derived_cl161, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (((X8) = (X10))) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 248.18/31.89 | ((p @ X4) != (p @ X6)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 248.18/31.89 thf(zip_derived_cl165, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (((X8) != (X10)) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 248.18/31.89 | ((p @ X4) != (p @ X6)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl161])). 248.18/31.89 thf(zip_derived_cl167, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (((X12) = (X14))) 248.18/31.89 | ((p @ X4) != (p @ X6)) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ((X8) != (X10)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])). 248.18/31.89 thf(zip_derived_cl169, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (((X12) != (X14)) 248.18/31.89 | ((p @ X4) != (p @ X6)) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ((X8) != (X10)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl167])). 248.18/31.89 thf(stp_inj_mem_ty_2Enum_2Enum, axiom, 248.18/31.89 (![X:tp__ty_2Enum_2Enum]: 248.18/31.89 ( mem @ ( inj__ty_2Enum_2Enum @ X ) @ ty_2Enum_2Enum ))). 248.18/31.89 thf(zip_derived_cl25, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : tp__ty_2Enum_2Enum]: 248.18/31.89 (mem @ (inj__ty_2Enum_2Enum @ Y0) @ ty_2Enum_2Enum))))), 248.18/31.89 inference('cnf', [status(esa)], [stp_inj_mem_ty_2Enum_2Enum])). 248.18/31.89 thf(zip_derived_cl26, plain, 248.18/31.89 ( (((!!) @ ((('#C') @ ((('#B') @ mem @ inj__ty_2Enum_2Enum)) @ 248.18/31.89 ty_2Enum_2Enum))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl25])). 248.18/31.89 thf(zip_derived_cl47, plain, 248.18/31.89 (![X2 : tp__ty_2Enum_2Enum]: 248.18/31.89 (mem @ (inj__ty_2Enum_2Enum @ X2) @ ty_2Enum_2Enum)), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl26])). 248.18/31.89 thf(zip_derived_cl166, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (p @ X6) 248.18/31.89 | ((p @ X4) != (p @ X6)) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ((X8) != (X10)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl165])). 248.18/31.89 thf(zip_derived_cl168, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 (~ (p @ X6) 248.18/31.89 | ~ (p @ X4) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ((X8) != (X10)))), 248.18/31.89 inference('local_rewriting', [status(thm)], [zip_derived_cl166])). 248.18/31.89 thf(zip_derived_cl55, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (mem @ (c_2Ewords_2Eword__2comp @ X2) @ 248.18/31.89 (arr @ (ty_2Efcp_2Ecart @ bool @ X2) @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 248.18/31.89 thf(ap_tp, axiom, 248.18/31.89 (![A:del,B:del,F:$i]: 248.18/31.89 ( ( mem @ F @ ( arr @ A @ B ) ) => 248.18/31.89 ( ![X:$i]: ( ( mem @ X @ A ) => ( mem @ ( ap @ F @ X ) @ B ) ) ) ))). 248.18/31.89 thf(zip_derived_cl0, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (((!!) @ (^[Y1 : del]: 248.18/31.89 (((!!) @ (^[Y2 : $i]: 248.18/31.89 (((mem @ Y2 @ (arr @ Y0 @ Y1)) => 248.18/31.89 (((!!) @ (^[Y3 : $i]: 248.18/31.89 (((mem @ Y3 @ Y0) => 248.18/31.89 (mem @ 248.18/31.89 (ap @ Y2 @ Y3) @ 248.18/31.89 Y1)))))))))))))))))), 248.18/31.89 inference('cnf', [status(esa)], [ap_tp])). 248.18/31.89 thf(zip_derived_cl1, plain, 248.18/31.89 ( (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#C') @ mem)))) @ 248.18/31.89 arr)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ mem)) @ ap))))))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl0])). 248.18/31.89 thf(zip_derived_cl49, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#C') @ mem)) @ (arr @ X2))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ mem)) @ ap))))))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 248.18/31.89 thf(zip_derived_cl50, plain, 248.18/31.89 (![X2 : del, X4 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (arr @ X2 @ X4))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ mem)) @ ap)))) @ 248.18/31.89 X4))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl49])). 248.18/31.89 thf(zip_derived_cl51, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i]: 248.18/31.89 (((mem @ X6 @ (arr @ X2 @ X4)) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ mem @ (ap @ X6))) @ X4))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl50])). 248.18/31.89 thf(zip_derived_cl52, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#C') @ ((('#B') @ mem @ (ap @ X6))) @ X4)))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 248.18/31.89 thf(zip_derived_cl53, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 ( (((mem @ X8 @ X2) => (mem @ (ap @ X6 @ X8) @ X4))) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl52])). 248.18/31.89 thf(zip_derived_cl54, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (mem @ X8 @ X2) 248.18/31.89 | (mem @ (ap @ X6 @ X8) @ X4) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 248.18/31.89 thf(zip_derived_cl228, plain, 248.18/31.89 (![X0 : del, X1 : del, X2 : $i]: 248.18/31.89 (~ (mem @ X2 @ 248.18/31.89 (arr @ 248.18/31.89 (arr @ (ty_2Efcp_2Ecart @ bool @ X0) @ 248.18/31.89 (ty_2Efcp_2Ecart @ bool @ X0)) @ 248.18/31.89 X1)) 248.18/31.89 | (mem @ (ap @ X2 @ (c_2Ewords_2Eword__2comp @ X0)) @ X1))), 248.18/31.89 inference('sup-', [status(thm)], [zip_derived_cl55, zip_derived_cl54])). 248.18/31.89 thf(zip_derived_cl48, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (mem @ (c_2Ewords_2En2w @ X2) @ 248.18/31.89 (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ X2)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 248.18/31.89 thf(zip_derived_cl54, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (mem @ X8 @ X2) 248.18/31.89 | (mem @ (ap @ X6 @ X8) @ X4) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 248.18/31.89 thf(zip_derived_cl222, plain, 248.18/31.89 (![X0 : del, X1 : del, X2 : $i]: 248.18/31.89 (~ (mem @ X2 @ 248.18/31.89 (arr @ (arr @ ty_2Enum_2Enum @ (ty_2Efcp_2Ecart @ bool @ X0)) @ X1)) 248.18/31.89 | (mem @ (ap @ X2 @ (c_2Ewords_2En2w @ X0)) @ X1))), 248.18/31.89 inference('sup-', [status(thm)], [zip_derived_cl48, zip_derived_cl54])). 248.18/31.89 thf(mem_c_2Ebool_2EF, axiom, (mem @ c_2Ebool_2EF @ bool)). 248.18/31.89 thf(zip_derived_cl42, plain, ( (mem @ c_2Ebool_2EF @ bool)), 248.18/31.89 inference('cnf', [status(esa)], [mem_c_2Ebool_2EF])). 248.18/31.89 thf(ax_false_p, axiom, (~( p @ c_2Ebool_2EF ))). 248.18/31.89 thf(zip_derived_cl20, plain, (~ (p @ c_2Ebool_2EF)), 248.18/31.89 inference('cnf', [status(esa)], [ax_false_p])). 248.18/31.89 thf(funcext, axiom, 248.18/31.89 (![A:del,B:del,F:$i]: 248.18/31.89 ( ( mem @ F @ ( arr @ A @ B ) ) => 248.18/31.89 ( ![G:$i]: 248.18/31.89 ( ( mem @ G @ ( arr @ A @ B ) ) => 248.18/31.89 ( ( ![X:$i]: 248.18/31.89 ( ( mem @ X @ A ) => ( ( ap @ F @ X ) = ( ap @ G @ X ) ) ) ) => 248.18/31.89 ( ( F ) = ( G ) ) ) ) ) ))). 248.18/31.89 thf(zip_derived_cl2, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (((!!) @ (^[Y1 : del]: 248.18/31.89 (((!!) @ (^[Y2 : $i]: 248.18/31.89 (((mem @ Y2 @ (arr @ Y0 @ Y1)) => 248.18/31.89 (((!!) @ (^[Y3 : $i]: 248.18/31.89 (((mem @ Y3 @ 248.18/31.89 (arr @ Y0 @ Y1)) => 248.18/31.89 (((((!!) @ ( 248.18/31.89 ^[Y4 : $i]: 248.18/31.89 (((mem @ 248.18/31.89 Y4 @ Y0) => 248.18/31.89 (((ap @ 248.18/31.89 Y2 @ 248.18/31.89 Y4) = 248.18/31.89 (ap @ 248.18/31.89 Y3 @ Y4)))))))) => 248.18/31.89 (((Y2) = (Y3)))))))))))))))))))))), 248.18/31.89 inference('cnf', [status(esa)], [funcext])). 248.18/31.89 thf(zip_derived_cl3, plain, 248.18/31.89 ( (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#C') @ mem)))) @ 248.18/31.89 arr)))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (!!))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#C') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#B'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#C') @ mem)))) @ 248.18/31.89 arr)))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ ('#S'))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ (=>))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#B') @ ( 248.18/31.89 !!))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=>))) @ 248.18/31.89 ((('#C') @ mem)))))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ( 248.18/31.89 '#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=))) @ 248.18/31.89 ap)))))) @ 248.18/31.89 ap)))))))))))) @ 248.18/31.89 (=)))))))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl2])). 248.18/31.89 thf(zip_derived_cl100, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#B') @ (!!) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#C') @ mem)) @ (arr @ X2))))))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#C') @ mem)) @ 248.18/31.89 (arr @ X2))))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 (( 248.18/31.89 ('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 '#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=))) @ 248.18/31.89 ap)))))) @ 248.18/31.89 ap)))))))))) @ 248.18/31.89 (=)))))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 248.18/31.89 thf(zip_derived_cl101, plain, 248.18/31.89 (![X2 : del, X4 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (arr @ X2 @ X4))))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (arr @ X2 @ X4))))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=>))) @ 248.18/31.89 ((('#B') @ ((('#B') @ (!!))) @ 248.18/31.89 ((('#B') @ ((('#B') @ ((('#S') @ ( 248.18/31.89 (('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#B') @ 248.18/31.89 ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ( 248.18/31.89 (('#B') @ (=))) @ 248.18/31.89 ap)))))) @ 248.18/31.89 ap)))))))))) @ 248.18/31.89 (=)))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 248.18/31.89 thf(zip_derived_cl102, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i]: 248.18/31.89 (((mem @ X6 @ (arr @ X2 @ X4)) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (arr @ X2 @ X4))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =) @ (ap @ X6))))) @ 248.18/31.89 ap)))))))) @ 248.18/31.89 ((($i) = (X6)))))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl101])). 248.18/31.89 thf(zip_derived_cl103, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ (arr @ X2 @ X4))))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =>) @ 248.18/31.89 ((('#C') @ mem @ 248.18/31.89 X2)))))) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ ( 248.18/31.89 =) @ ( 248.18/31.89 ap @ X6))))) @ 248.18/31.89 ap)))))))) @ 248.18/31.89 ((($i) = (X6))))))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 248.18/31.89 thf(zip_derived_cl104, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 ( (((mem @ X8 @ (arr @ X2 @ X4)) => 248.18/31.89 (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ (ap @ X6))) @ (ap @ X8))))))) => 248.18/31.89 (((X6) = (X8))))))) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 248.18/31.89 thf(zip_derived_cl105, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (mem @ X8 @ (arr @ X2 @ X4)) 248.18/31.89 | (((((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ (ap @ X6))) @ (ap @ X8))))))) => 248.18/31.89 (((X6) = (X8))))) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl104])). 248.18/31.89 thf(zip_derived_cl106, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ (ap @ X6))) @ (ap @ X8))))))) 248.18/31.89 | (((X6) = (X8))) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl105])). 248.18/31.89 thf(zip_derived_cl107, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ (ap @ X6))) @ (ap @ X8))))))) 248.18/31.89 | ((X6) = (X8)) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl106])). 248.18/31.89 thf(zip_derived_cl108, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (((mem @ ('#sk4' @ X2 @ X6 @ X8) @ X2) => 248.18/31.89 (((ap @ X6 @ ('#sk4' @ X2 @ X6 @ X8)) = (ap @ X8 @ 248.18/31.89 ('#sk4' @ X2 @ X6 @ X8)))))) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ((X6) = (X8)))), 248.18/31.89 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 248.18/31.89 thf(zip_derived_cl109, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 ( (mem @ ('#sk4' @ X2 @ X6 @ X8) @ X2) 248.18/31.89 | ((X6) = (X8)) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 248.18/31.89 thf(zip_derived_cl89, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#B') @ (!!) @ 248.18/31.89 ((('#B') @ ((('#S') @ ((('#B') @ (=>) @ 248.18/31.89 ((('#C') @ mem @ X2)))))) @ 248.18/31.89 ((('#C') @ ((('#B') @ ('#S') @ 248.18/31.89 ((('#B') @ ((('#B') @ (=))) @ 248.18/31.89 ((('#B') @ ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2EF)))))))) @ 248.18/31.89 ('#I')))))))))))), 248.18/31.89 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl87])). 248.18/31.89 thf(zip_derived_cl91, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (((mem @ X4 @ X2) => 248.18/31.89 (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2EF) @ 248.18/31.89 X4)))) @ 248.18/31.89 ('#I')))))))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])). 248.18/31.89 thf(zip_derived_cl93, plain, 248.18/31.89 (![X2 : del, X4 : $i]: 248.18/31.89 (~ (mem @ X4 @ X2) 248.18/31.89 | (((!!) @ ((('#S') @ ((('#B') @ (=>) @ ((('#C') @ mem @ X2)))) @ 248.18/31.89 ((('#S') @ ((('#B') @ (=) @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ 248.18/31.89 (ap @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 c_2Ebool_2EF) @ 248.18/31.89 X4)))) @ 248.18/31.89 ('#I'))))))))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl91])). 248.18/31.89 thf(zip_derived_cl95, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 ( (((mem @ X6 @ X2) => 248.18/31.89 (((ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ X6) = 248.18/31.89 (X6))))) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 248.18/31.89 thf(zip_derived_cl97, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ X2) 248.18/31.89 | (((ap @ 248.18/31.89 (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ X6) = 248.18/31.89 (X6))) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])). 248.18/31.89 thf(zip_derived_cl99, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i]: 248.18/31.89 (~ (mem @ X6 @ X2) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ c_2Ebool_2EF) @ X4) @ 248.18/31.89 X6) = (X6)) 248.18/31.89 | ~ (mem @ X4 @ X2))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], [zip_derived_cl97])). 248.18/31.89 thf(zip_derived_cl110, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (((ap @ X6 @ ('#sk4' @ X2 @ X6 @ X8)) = (ap @ X8 @ 248.18/31.89 ('#sk4' @ X2 @ X6 @ X8)))) 248.18/31.89 | ((X6) = (X8)) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 248.18/31.89 thf(zip_derived_cl111, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (((ap @ X6 @ ('#sk4' @ X2 @ X6 @ X8)) 248.18/31.89 != (ap @ X8 @ ('#sk4' @ X2 @ X6 @ X8))) 248.18/31.89 | ((X6) = (X8)) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)) 248.18/31.89 | ~ (mem @ X8 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl110])). 248.18/31.89 thf(zip_derived_cl160, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 ( (p @ X6) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (((((~) @ (p @ X6))) => (((X12) = (X14))))) 248.18/31.89 | ((p @ X4) != (p @ X6)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 248.18/31.89 thf(zip_derived_cl162, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 ( (p @ X6) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (((((~) @ ($false))) => (((X12) = (X14))))) 248.18/31.89 | (p @ X4))), 248.18/31.89 inference('local_rewriting', [status(thm)], [zip_derived_cl160])). 248.18/31.89 thf(zip_derived_cl163, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 ( (p @ X6) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ~ (((X12) = (X14))) 248.18/31.89 | (p @ X4))), 248.18/31.89 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl162])). 248.18/31.89 thf(zip_derived_cl164, plain, 248.18/31.89 (![X2 : del, X4 : $i, X6 : $i, X8 : $i, X10 : $i, X12 : $i, X14 : $i]: 248.18/31.89 ( (p @ X6) 248.18/31.89 | ((ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X4) @ X8) @ X12) 248.18/31.89 = (ap @ (ap @ (ap @ (c_2Ebool_2ECOND @ X2) @ X6) @ X10) @ X14)) 248.18/31.89 | ~ (mem @ X4 @ bool) 248.18/31.89 | ~ (mem @ X6 @ bool) 248.18/31.89 | ~ (mem @ X8 @ X2) 248.18/31.89 | ~ (mem @ X10 @ X2) 248.18/31.89 | ~ (mem @ X12 @ X2) 248.18/31.89 | ~ (mem @ X14 @ X2) 248.18/31.89 | ((X12) != (X14)) 248.18/31.89 | (p @ X4))), 248.18/31.89 inference('simplify nested equalities', [status(thm)], 248.18/31.89 [zip_derived_cl163])). 248.18/31.89 thf(mem_c_2Ebool_2ECOND, axiom, 248.18/31.89 (![A_27a:del]: 248.18/31.89 ( mem @ 248.18/31.89 ( c_2Ebool_2ECOND @ A_27a ) @ 248.18/31.89 ( arr @ bool @ ( arr @ A_27a @ ( arr @ A_27a @ A_27a ) ) ) ))). 248.18/31.89 thf(zip_derived_cl39, plain, 248.18/31.89 ( (((!!) @ (^[Y0 : del]: 248.18/31.89 (mem @ (c_2Ebool_2ECOND @ Y0) @ 248.18/31.89 (arr @ bool @ (arr @ Y0 @ (arr @ Y0 @ Y0)))))))), 248.18/31.89 inference('cnf', [status(esa)], [mem_c_2Ebool_2ECOND])). 248.18/31.89 thf(zip_derived_cl40, plain, 248.18/31.89 ( (((!!) @ ((('#S') @ ((('#B') @ mem @ c_2Ebool_2ECOND)) @ 248.18/31.89 ((('#B') @ (arr @ bool) @ 248.18/31.89 ((('#S') @ arr @ ((('#S') @ arr @ ('#I')))))))))))), 248.18/31.89 inference('lams2combs', [status(thm)], [zip_derived_cl39])). 248.18/31.89 thf(zip_derived_cl56, plain, 248.18/31.89 (![X2 : del]: 248.18/31.89 (mem @ (c_2Ebool_2ECOND @ X2) @ 248.18/31.89 (arr @ bool @ (arr @ X2 @ (arr @ X2 @ X2))))), 248.18/31.89 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 248.18/31.89 thf(zip_derived_cl54, plain, 248.18/31.89 (![X2 : del, X4 : del, X6 : $i, X8 : $i]: 248.18/31.89 (~ (mem @ X8 @ X2) 248.18/31.89 | (mem @ (ap @ X6 @ X8) @ X4) 248.18/31.89 | ~ (mem @ X6 @ (arr @ X2 @ X4)))), 248.18/31.89 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl53])). 248.18/31.89 thf(zip_derived_cl12284, plain, ($false), 248.18/31.89 inference('eprover', [status(thm)], 248.18/31.89 [zip_derived_cl9, zip_derived_cl8, zip_derived_cl65, 248.18/31.89 zip_derived_cl67, zip_derived_cl55, zip_derived_cl4, 248.18/31.89 zip_derived_cl41, zip_derived_cl98, zip_derived_cl142, 248.18/31.89 zip_derived_cl79, zip_derived_cl48, zip_derived_cl169, 248.18/31.89 zip_derived_cl47, zip_derived_cl168, zip_derived_cl228, 248.18/31.89 zip_derived_cl222, zip_derived_cl42, zip_derived_cl20, 248.18/31.89 zip_derived_cl109, zip_derived_cl99, zip_derived_cl111, 248.18/31.89 zip_derived_cl164, zip_derived_cl56, zip_derived_cl54])). 248.18/31.89 248.18/31.89 % SZS output end Refutation 248.18/31.89 248.18/31.89 248.18/31.89 % Terminating... 248.75/32.01 % Runner terminated. 248.75/32.02 % Zipperpin 1.5 exiting 248.75/32.02 EOF