0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.PmjeT7fv9i true 0.15/0.36 % Computer : n007.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % WCLimit : 120 0.15/0.36 % DateTime : Tue Aug 9 07:36:42 EDT 2022 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 960 s 0.15/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.55/0.68 % Total configuration time : 828 0.55/0.68 % Estimated wc time : 1656 0.55/0.68 % Estimated cpu time (8 cpus) : 207.0 0.55/0.71 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.56/0.77 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.56/0.78 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.57/0.83 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 55.92/7.75 % Solved by lams/20_acsne_simpl.sh. 55.92/7.75 % running E: timeout 13 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.PmjeT7fv9i/e_inputa9113c --cpu-limit=11 --auto -s -p 55.92/7.75 % done 662 iterations in 6.602s 55.92/7.75 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 55.92/7.75 % SZS output start Refutation 55.92/7.75 thf(subst_type, type, subst: $tType). 55.92/7.75 thf(term_type, type, term: $tType). 55.92/7.75 thf(lamnotvar_type, type, lamnotvar: $o). 55.92/7.75 thf(hoasapinj2_type, type, hoasapinj2: $o). 55.92/7.75 thf('#sk430_type', type, '#sk430': (subst > term > term) > subst). 55.92/7.75 thf(apnotvar_type, type, apnotvar: $o). 55.92/7.75 thf(ap_type, type, ap: term > term > term). 55.92/7.75 thf(axapp_type, type, axapp: $o). 55.92/7.75 thf('#sk3185_type', type, '#sk3185': (subst > term > term) > term). 55.92/7.75 thf('#form5466_type', type, '#form5466': $o). 55.92/7.75 thf(hoaslamnotap_type, type, hoaslamnotap: $o). 55.92/7.75 thf('#sk839_type', type, '#sk839': (subst > term > subst > $o) > term). 55.92/7.75 thf(var_type, type, var: term > $o). 55.92/7.75 thf(sh_type, type, sh: subst). 55.92/7.75 thf(hoasinduction_lem1_type, type, hoasinduction_lem1: $o). 55.92/7.75 thf('#form2417_type', type, '#form2417': (subst > term > subst > $o) > $o). 55.92/7.75 thf(shinj_type, type, shinj: $o). 55.92/7.75 thf('#sk733_type', type, '#sk733': subst > term > subst > $o). 55.92/7.75 thf(hoasinduction_gthm_type, type, hoasinduction_gthm: $o). 55.92/7.75 thf(laminj_type, type, laminj: $o). 55.92/7.75 thf('#sk3410_type', type, '#sk3410': (subst > term > subst > $o) > subst > 55.92/7.75 term > term). 55.92/7.75 thf(hoasinduction_type, type, hoasinduction: $o). 55.92/7.75 thf('#form108_type', type, '#form108': (term > $o) > $o). 55.92/7.75 thf('#sk46_type', type, '#sk46': (term > $o) > term). 55.92/7.75 thf(sub_type, type, sub: term > subst > term). 55.92/7.75 thf(push_type, type, push: term > subst > subst). 55.92/7.75 thf('#sk516_type', type, '#sk516': (subst > term > term) > subst). 55.92/7.75 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o). 55.92/7.75 thf('#sk708_type', type, '#sk708': (subst > term > subst > $o) > subst). 55.92/7.75 thf(ulamvarsh_type, type, ulamvarsh: $o). 55.92/7.75 thf(hoasap_type, type, hoasap: subst > term > subst > term > term). 55.92/7.75 thf(id_type, type, id: subst). 55.92/7.75 thf(axassoc_type, type, axassoc: $o). 55.92/7.75 thf(axvarid_type, type, axvarid: $o). 55.92/7.75 thf('#sk967_type', type, '#sk967': (subst > term > subst > $o) > subst). 55.92/7.75 thf(apinj1_type, type, apinj1: $o). 55.92/7.75 thf('#sk1077_type', type, '#sk1077': (subst > term > subst > $o) > subst). 55.92/7.75 thf(axabs_type, type, axabs: $o). 55.92/7.75 thf(induction_type, type, induction: $o). 55.92/7.75 thf('#sk196_type', type, '#sk196': (term > $o) > term). 55.92/7.75 thf(lamnotap_type, type, lamnotap: $o). 55.92/7.75 thf('#sk1549_type', type, '#sk1549': (subst > term > subst > $o) > subst). 55.92/7.75 thf(substmonoid_type, type, substmonoid: $o). 55.92/7.75 thf(axidr_type, type, axidr: $o). 55.92/7.75 thf('#form3615_type', type, '#form3615': (subst > term > subst > $o) > $o). 55.92/7.75 thf(pushprop_type, type, pushprop: $o). 55.92/7.75 thf(lam_type, type, lam: term > term). 55.92/7.75 thf(apinj2_type, type, apinj2: $o). 55.92/7.75 thf(hoaslamnotvar_type, type, hoaslamnotvar: $o). 55.92/7.75 thf(one_type, type, one: term). 55.92/7.75 thf(axshiftcons_type, type, axshiftcons: $o). 55.92/7.75 thf(axvarshift_type, type, axvarshift: $o). 55.92/7.75 thf('#sk2144_type', type, '#sk2144': (subst > term > subst > $o) > subst). 55.92/7.75 thf(comp_type, type, comp: subst > subst > subst). 55.92/7.75 thf(ulamvar1_type, type, ulamvar1: $o). 55.92/7.75 thf(termmset_type, type, termmset: $o). 55.92/7.75 thf(axclos_type, type, axclos: $o). 55.92/7.75 thf(axvarcons_type, type, axvarcons: $o). 55.92/7.75 thf(induction2_type, type, induction2: $o). 55.92/7.75 thf(axidl_type, type, axidl: $o). 55.92/7.75 thf('#sk3356_type', type, '#sk3356': (subst > term > subst > $o) > term). 55.92/7.75 thf(hoasinduction_lem3_type, type, hoasinduction_lem3: $o). 55.92/7.75 thf(hoasapnotvar_type, type, hoasapnotvar: $o). 55.92/7.75 thf('#sk1760_type', type, '#sk1760': (subst > term > subst > $o) > term). 55.92/7.75 thf(hoaslaminj_type, type, hoaslaminj: $o). 55.92/7.75 thf('#form2686_type', type, '#form2686': (subst > term > subst > $o) > $o). 55.92/7.75 thf('#sk4068_type', type, '#sk4068': (subst > term > subst > $o) > term > term). 55.92/7.75 thf(induction2lem_type, type, induction2lem: $o). 55.92/7.75 thf('#l_lift30976_type', type, '#l_lift30976': term > $o). 55.92/7.75 thf('#sk1944_type', type, '#sk1944': (subst > term > subst > $o) > subst). 55.92/7.75 thf('#sk1677_type', type, '#sk1677': term). 55.92/7.75 thf(axscons_type, type, axscons: $o). 55.92/7.75 thf(hoasapinj1_type, type, hoasapinj1: $o). 55.92/7.75 thf(ulamvarind_type, type, ulamvarind: $o). 55.92/7.75 thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term). 55.92/7.75 thf('#sk467_type', type, '#sk467': (subst > term > term) > term). 55.92/7.75 thf(axmap_type, type, axmap: $o). 55.92/7.75 thf(hoasinduction_lem2_type, type, hoasinduction_lem2: $o). 55.92/7.75 thf('#sk3223_type', type, '#sk3223': (subst > term > subst > $o) > term). 55.92/7.75 thf(hoasinduction_gthm, axiom, hoasinduction_gthm = 55.92/7.75 (( axapp ) => 55.92/7.75 ( ( axvarcons ) => 55.92/7.75 ( ( axvarid ) => 55.92/7.75 ( ( axabs ) => 55.92/7.75 ( ( axclos ) => 55.92/7.75 ( ( axidl ) => 55.92/7.75 ( ( axshiftcons ) => 55.92/7.75 ( ( axassoc ) => 55.92/7.75 ( ( axmap ) => 55.92/7.75 ( ( axidr ) => 55.92/7.75 ( ( axvarshift ) => 55.92/7.75 ( ( axscons ) => 55.92/7.75 ( ( ulamvar1 ) => 55.92/7.75 ( ( ulamvarsh ) => 55.92/7.75 ( ( ulamvarind ) => 55.92/7.75 ( ( apinj1 ) => 55.92/7.75 ( ( apinj2 ) => 55.92/7.75 ( ( laminj ) => 55.92/7.75 ( ( shinj ) => 55.92/7.75 ( ( lamnotap ) => 55.92/7.75 ( ( apnotvar ) => 55.92/7.75 ( ( lamnotvar ) => 55.92/7.75 ( ( induction ) => 55.92/7.75 ( ( pushprop ) => 55.92/7.75 ( ( induction2lem ) => 55.92/7.75 ( ( induction2 ) => 55.92/7.75 ( ( substmonoid ) => 55.92/7.75 ( ( termmset ) => 55.92/7.75 ( ( hoasapinj1 ) => 55.92/7.75 ( ( hoasapinj2 ) => 55.92/7.75 ( ( hoaslaminj ) => 55.92/7.75 ( ( hoaslamnotap ) => 55.92/7.75 ( ( 55.92/7.75 hoaslamnotvar ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasapnotvar ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem1 ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem2 ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem3 ) => 55.92/7.75 ( 55.92/7.75 hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 55.92/7.75 thf('0', plain, 55.92/7.75 (( hoasinduction_gthm ) = 55.92/7.75 ( ( axapp ) => 55.92/7.75 ( ( axvarcons ) => 55.92/7.75 ( ( axvarid ) => 55.92/7.75 ( ( axabs ) => 55.92/7.75 ( ( axclos ) => 55.92/7.75 ( ( axidl ) => 55.92/7.75 ( ( axshiftcons ) => 55.92/7.75 ( ( axassoc ) => 55.92/7.75 ( ( axmap ) => 55.92/7.75 ( ( axidr ) => 55.92/7.75 ( ( axvarshift ) => 55.92/7.75 ( ( axscons ) => 55.92/7.75 ( ( ulamvar1 ) => 55.92/7.75 ( ( ulamvarsh ) => 55.92/7.75 ( ( ulamvarind ) => 55.92/7.75 ( ( apinj1 ) => 55.92/7.75 ( ( apinj2 ) => 55.92/7.75 ( ( laminj ) => 55.92/7.75 ( ( shinj ) => 55.92/7.75 ( ( lamnotap ) => 55.92/7.75 ( ( apnotvar ) => 55.92/7.75 ( ( lamnotvar ) => 55.92/7.75 ( ( induction ) => 55.92/7.75 ( ( pushprop ) => 55.92/7.75 ( ( induction2lem ) => 55.92/7.75 ( ( induction2 ) => 55.92/7.75 ( ( substmonoid ) => 55.92/7.75 ( ( termmset ) => 55.92/7.75 ( ( hoasapinj1 ) => 55.92/7.75 ( ( hoasapinj2 ) => 55.92/7.75 ( ( 55.92/7.75 hoaslaminj ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoaslamnotap ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoaslamnotvar ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasapnotvar ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem1 ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem2 ) => 55.92/7.75 ( 55.92/7.75 ( 55.92/7.75 hoasinduction_lem3 ) => 55.92/7.75 ( 55.92/7.75 hoasinduction ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 55.92/7.75 define([status(thm)])). 55.92/7.75 thf(hoasinduction, axiom, hoasinduction = 55.92/7.75 (![P:( subst > term > subst > $o )]: 55.92/7.75 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.75 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 55.92/7.75 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 55.92/7.75 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.75 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 55.92/7.75 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 55.92/7.75 ( ( ![A:term]: ( ( hoasvar @ id @ A @ id ) => ( P @ id @ A @ id ) ) ) => 55.92/7.75 ( ( ![A:term,B:term]: 55.92/7.75 ( ( P @ id @ A @ id ) => 55.92/7.75 ( ( P @ id @ B @ id ) => 55.92/7.75 ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ) => 55.92/7.75 ( ( ![F:( subst > term > term )]: 55.92/7.75 ( ( ![M:subst,A:term,N:subst]: 55.92/7.75 ( ( sub @ ( F @ M @ A ) @ N ) = 55.92/7.75 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.75 ( ( ![A:term]: 55.92/7.75 ( ( P @ id @ A @ id ) => 55.92/7.75 ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 55.92/7.75 ( P @ 55.92/7.75 id @ 55.92/7.75 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ 55.92/7.75 id ) ) ) ) => 55.92/7.75 ( ![A:term]: ( P @ id @ A @ id ) ) ) ) ) ) ))). 55.92/7.75 thf('1', plain, 55.92/7.75 (( hoasinduction ) = 55.92/7.75 ( ![X4:( subst > term > subst > $o )]: 55.92/7.75 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 55.92/7.75 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 55.92/7.75 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 55.92/7.75 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 55.92/7.75 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 55.92/7.75 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 55.92/7.75 ( ( ![X22:term]: 55.92/7.75 ( ( hoasvar @ id @ X22 @ id ) => ( X4 @ id @ X22 @ id ) ) ) => 55.92/7.75 ( ( ![X24:term,X26:term]: 55.92/7.75 ( ( X4 @ id @ X24 @ id ) => 55.92/7.75 ( ( X4 @ id @ X26 @ id ) => 55.92/7.75 ( X4 @ id @ ( hoasap @ id @ X24 @ id @ X26 ) @ id ) ) ) ) => 55.92/7.75 ( ( ![X28:( subst > term > term )]: 55.92/7.75 ( ( ![X30:subst,X32:term,X34:subst]: 55.92/7.75 ( ( sub @ ( X28 @ X30 @ X32 ) @ X34 ) = 55.92/7.75 ( X28 @ ( comp @ X30 @ X34 ) @ ( sub @ X32 @ X34 ) ) ) ) => 55.92/7.75 ( ( ![X36:term]: 55.92/7.75 ( ( X4 @ id @ X36 @ id ) => 55.92/7.75 ( X4 @ id @ ( X28 @ id @ X36 ) @ id ) ) ) => 55.92/7.75 ( X4 @ 55.92/7.75 id @ 55.92/7.75 ( hoaslam @ 55.92/7.75 id @ 55.92/7.75 ( ^[V_1:subst,V_2:term]: ( X28 @ V_1 @ V_2 ) ) ) @ 55.92/7.75 id ) ) ) ) => 55.92/7.75 ( ![X38:term]: ( X4 @ id @ X38 @ id ) ) ) ) ) ) ) )), 55.92/7.75 define([status(thm)])). 55.92/7.75 thf(hoasinduction_lem3, axiom, hoasinduction_lem3 = 55.92/7.75 (![P:( subst > term > subst > $o )]: 55.92/7.75 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.75 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 55.92/7.75 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 55.92/7.75 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.75 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 55.92/7.75 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 55.92/7.75 ( ( ![F:( subst > term > term )]: 55.92/7.75 ( ( ![M:subst,A:term,N:subst]: 55.92/7.75 ( ( sub @ ( F @ M @ A ) @ N ) = 55.92/7.75 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.75 ( ( ![A:term]: 55.92/7.75 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 55.92/7.75 ( P @ 55.92/7.75 id @ 55.92/7.75 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ) => 55.92/7.75 ( ![A:term]: 55.92/7.75 ( ( ![B:term]: 55.92/7.75 ( ( P @ id @ B @ id ) => 55.92/7.75 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ) => 55.92/7.75 ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ))). 55.92/7.75 thf('2', plain, 55.92/7.75 (( hoasinduction_lem3 ) = 55.92/7.75 ( ![X4:( subst > term > subst > $o )]: 55.92/7.75 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 55.92/7.75 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 55.92/7.75 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 55.92/7.75 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 55.92/7.75 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 55.92/7.75 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 55.92/7.75 ( ( ![X22:( subst > term > term )]: 55.92/7.75 ( ( ![X24:subst,X26:term,X28:subst]: 55.92/7.75 ( ( sub @ ( X22 @ X24 @ X26 ) @ X28 ) = 55.92/7.75 ( X22 @ ( comp @ X24 @ X28 ) @ ( sub @ X26 @ X28 ) ) ) ) => 55.92/7.76 ( ( ![X30:term]: 55.92/7.76 ( ( X4 @ id @ X30 @ id ) => 55.92/7.76 ( X4 @ id @ ( X22 @ id @ X30 ) @ id ) ) ) => 55.92/7.76 ( X4 @ 55.92/7.76 id @ 55.92/7.76 ( hoaslam @ 55.92/7.76 id @ ( ^[V_1:subst,V_2:term]: ( X22 @ V_1 @ V_2 ) ) ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( ![X32:term]: 55.92/7.76 ( ( ![X34:term]: 55.92/7.76 ( ( X4 @ id @ X34 @ id ) => 55.92/7.76 ( X4 @ id @ ( sub @ X32 @ ( push @ X34 @ id ) ) @ id ) ) ) => 55.92/7.76 ( X4 @ id @ ( lam @ X32 ) @ id ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasinduction_lem2, axiom, hoasinduction_lem2 = 55.92/7.76 (![P:( subst > term > subst > $o )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.76 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 55.92/7.76 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 55.92/7.76 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.76 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 55.92/7.76 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 55.92/7.76 ( ( ![A:term,B:term]: 55.92/7.76 ( ( P @ id @ A @ id ) => 55.92/7.76 ( ( P @ id @ B @ id ) => 55.92/7.76 ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ) => 55.92/7.76 ( ![A:term,B:term]: 55.92/7.76 ( ( P @ id @ A @ id ) => 55.92/7.76 ( ( P @ id @ B @ id ) => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ))). 55.92/7.76 thf('3', plain, 55.92/7.76 (( hoasinduction_lem2 ) = 55.92/7.76 ( ![X4:( subst > term > subst > $o )]: 55.92/7.76 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 55.92/7.76 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 55.92/7.76 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 55.92/7.76 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 55.92/7.76 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 55.92/7.76 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 55.92/7.76 ( ( ![X22:term,X24:term]: 55.92/7.76 ( ( X4 @ id @ X22 @ id ) => 55.92/7.76 ( ( X4 @ id @ X24 @ id ) => 55.92/7.76 ( X4 @ id @ ( hoasap @ id @ X22 @ id @ X24 ) @ id ) ) ) ) => 55.92/7.76 ( ![X26:term,X28:term]: 55.92/7.76 ( ( X4 @ id @ X26 @ id ) => 55.92/7.76 ( ( X4 @ id @ X28 @ id ) => 55.92/7.76 ( X4 @ id @ ( ap @ X26 @ X28 ) @ id ) ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasinduction_lem1, axiom, hoasinduction_lem1 = 55.92/7.76 (![P:( subst > term > subst > $o )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.76 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 55.92/7.76 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 55.92/7.76 ( ( ![M:subst,A:term,N:subst,K:subst]: 55.92/7.76 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 55.92/7.76 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 55.92/7.76 ( ( ![A:term]: ( ( hoasvar @ id @ A @ id ) => ( P @ id @ A @ id ) ) ) => 55.92/7.76 ( ![A:term]: ( ( var @ A ) => ( P @ id @ A @ id ) ) ) ) ) ))). 55.92/7.76 thf('4', plain, 55.92/7.76 (( hoasinduction_lem1 ) = 55.92/7.76 ( ![X4:( subst > term > subst > $o )]: 55.92/7.76 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 55.92/7.76 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 55.92/7.76 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 55.92/7.76 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 55.92/7.76 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 55.92/7.76 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 55.92/7.76 ( ( ![X22:term]: 55.92/7.76 ( ( hoasvar @ id @ X22 @ id ) => ( X4 @ id @ X22 @ id ) ) ) => 55.92/7.76 ( ![X24:term]: ( ( var @ X24 ) => ( X4 @ id @ X24 @ id ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasapnotvar, axiom, hoasapnotvar = 55.92/7.76 (![A:term,B:term]: 55.92/7.76 ( ~( hoasvar @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ))). 55.92/7.76 thf('5', plain, 55.92/7.76 (( hoasapnotvar ) = 55.92/7.76 ( ![X4:term,X6:term]: 55.92/7.76 ( ~( hoasvar @ id @ ( hoasap @ id @ X4 @ id @ X6 ) @ id ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoaslamnotvar, axiom, hoaslamnotvar = 55.92/7.76 (![F:( subst > term > term )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst]: 55.92/7.76 ( ( sub @ ( F @ M @ A ) @ N ) = 55.92/7.76 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.76 ( ~( hoasvar @ 55.92/7.76 id @ ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ))). 55.92/7.76 thf('6', plain, 55.92/7.76 (( hoaslamnotvar ) = 55.92/7.76 ( ![X4:( subst > term > term )]: 55.92/7.76 ( ( ![X6:subst,X8:term,X10:subst]: 55.92/7.76 ( ( sub @ ( X4 @ X6 @ X8 ) @ X10 ) = 55.92/7.76 ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) ) ) => 55.92/7.76 ( ~( hoasvar @ 55.92/7.76 id @ 55.92/7.76 ( hoaslam @ id @ ( ^[V_1:subst,V_2:term]: ( X4 @ V_1 @ V_2 ) ) ) @ 55.92/7.76 id ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoaslamnotap, axiom, hoaslamnotap = 55.92/7.76 (![F:( subst > term > term )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst]: 55.92/7.76 ( ( sub @ ( F @ M @ A ) @ N ) = 55.92/7.76 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.76 ( ![A:term,B:term]: 55.92/7.76 ( ( hoaslam @ id @ ( ^[M:subst,C:term]: ( F @ M @ C ) ) ) != 55.92/7.76 ( hoasap @ id @ A @ id @ B ) ) ) ))). 55.92/7.76 thf('7', plain, 55.92/7.76 (( hoaslamnotap ) = 55.92/7.76 ( ![X4:( subst > term > term )]: 55.92/7.76 ( ( ![X6:subst,X8:term,X10:subst]: 55.92/7.76 ( ( sub @ ( X4 @ X6 @ X8 ) @ X10 ) = 55.92/7.76 ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) ) ) => 55.92/7.76 ( ![X12:term,X14:term]: 55.92/7.76 ( ( hoaslam @ id @ ( ^[V_1:subst,V_2:term]: ( X4 @ V_1 @ V_2 ) ) ) != 55.92/7.76 ( hoasap @ id @ X12 @ id @ X14 ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoaslaminj, axiom, hoaslaminj = 55.92/7.76 (![F:( subst > term > term )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst]: 55.92/7.76 ( ( sub @ ( F @ M @ A ) @ N ) = 55.92/7.76 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.76 ( ![G:( subst > term > term )]: 55.92/7.76 ( ( ![M:subst,A:term,N:subst]: 55.92/7.76 ( ( sub @ ( G @ M @ A ) @ N ) = 55.92/7.76 ( G @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 55.92/7.76 ( ( ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) = 55.92/7.76 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( G @ M @ A ) ) ) ) => 55.92/7.76 ( ![M:subst,A:term]: ( ( F @ M @ A ) = ( G @ M @ A ) ) ) ) ) ) ))). 55.92/7.76 thf('8', plain, 55.92/7.76 (( hoaslaminj ) = 55.92/7.76 ( ![X4:( subst > term > term )]: 55.92/7.76 ( ( ![X6:subst,X8:term,X10:subst]: 55.92/7.76 ( ( sub @ ( X4 @ X6 @ X8 ) @ X10 ) = 55.92/7.76 ( X4 @ ( comp @ X6 @ X10 ) @ ( sub @ X8 @ X10 ) ) ) ) => 55.92/7.76 ( ![X12:( subst > term > term )]: 55.92/7.76 ( ( ![X14:subst,X16:term,X18:subst]: 55.92/7.76 ( ( sub @ ( X12 @ X14 @ X16 ) @ X18 ) = 55.92/7.76 ( X12 @ ( comp @ X14 @ X18 ) @ ( sub @ X16 @ X18 ) ) ) ) => 55.92/7.76 ( ( ( hoaslam @ 55.92/7.76 id @ ( ^[V_1:subst,V_2:term]: ( X4 @ V_1 @ V_2 ) ) ) = 55.92/7.76 ( hoaslam @ 55.92/7.76 id @ ( ^[V_3:subst,V_4:term]: ( X12 @ V_3 @ V_4 ) ) ) ) => 55.92/7.76 ( ![X20:subst,X22:term]: 55.92/7.76 ( ( X4 @ X20 @ X22 ) = ( X12 @ X20 @ X22 ) ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasapinj2, axiom, hoasapinj2 = 55.92/7.76 (![A:term,B:term,C:term,D:term]: 55.92/7.76 ( ( ( hoasap @ id @ A @ id @ C ) = ( hoasap @ id @ B @ id @ D ) ) => 55.92/7.76 ( ( C ) = ( D ) ) ))). 55.92/7.76 thf('9', plain, 55.92/7.76 (( hoasapinj2 ) = 55.92/7.76 ( ![X4:term,X6:term,X8:term,X10:term]: 55.92/7.76 ( ( ( hoasap @ id @ X4 @ id @ X8 ) = ( hoasap @ id @ X6 @ id @ X10 ) ) => 55.92/7.76 ( ( X8 ) = ( X10 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasapinj1, axiom, hoasapinj1 = 55.92/7.76 (![A:term,B:term,C:term,D:term]: 55.92/7.76 ( ( ( hoasap @ id @ A @ id @ C ) = ( hoasap @ id @ B @ id @ D ) ) => 55.92/7.76 ( ( A ) = ( B ) ) ))). 55.92/7.76 thf('10', plain, 55.92/7.76 (( hoasapinj1 ) = 55.92/7.76 ( ![X4:term,X6:term,X8:term,X10:term]: 55.92/7.76 ( ( ( hoasap @ id @ X4 @ id @ X8 ) = ( hoasap @ id @ X6 @ id @ X10 ) ) => 55.92/7.76 ( ( X4 ) = ( X6 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasvar, axiom,(( hoasvar ) = 55.92/7.76 (^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) )))). 55.92/7.76 thf('11', plain, 55.92/7.76 (( hoasvar ) = ( ^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) ) )), 55.92/7.76 inference('simplify_rw_rule', [status(thm)], [hoasvar])). 55.92/7.76 thf('12', plain, 55.92/7.76 (( hoasvar ) = 55.92/7.76 ( ^[V_1:subst,V_2:term,V_3:subst]: ( var @ ( sub @ V_2 @ V_3 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoaslam, axiom,(( hoaslam ) = 55.92/7.76 (^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) )))). 55.92/7.76 thf('13', plain, 55.92/7.76 (( hoaslam ) = 55.92/7.76 ( ^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) ) )), 55.92/7.76 inference('simplify_rw_rule', [status(thm)], [hoaslam])). 55.92/7.76 thf('14', plain, 55.92/7.76 (( hoaslam ) = 55.92/7.76 ( ^[V_1:subst,V_2:( subst > term > term )]: ( lam @ ( V_2 @ sh @ one ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(hoasap, axiom,(( hoasap ) = 55.92/7.76 (^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B )))). 55.92/7.76 thf('15', plain, 55.92/7.76 (( hoasap ) = 55.92/7.76 ( ^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B ) )), 55.92/7.76 inference('simplify_rw_rule', [status(thm)], [hoasap])). 55.92/7.76 thf('16', plain, 55.92/7.76 (( hoasap ) = 55.92/7.76 ( ^[V_1:subst,V_2:term,V_3:subst,V_4:term]: 55.92/7.76 ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(termmset, axiom, termmset = 55.92/7.76 (( ![A:term]: ( ( sub @ A @ id ) = ( A ) ) ) & 55.92/7.76 ( ![A:term,M:subst,N:subst]: 55.92/7.76 ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ) ))). 55.92/7.76 thf('17', plain, 55.92/7.76 (( termmset ) = 55.92/7.76 ( ( ![X4:term]: ( ( sub @ X4 @ id ) = ( X4 ) ) ) & 55.92/7.76 ( ![X6:term,X8:subst,X10:subst]: 55.92/7.76 ( ( sub @ ( sub @ X6 @ X8 ) @ X10 ) = 55.92/7.76 ( sub @ X6 @ ( comp @ X8 @ X10 ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(substmonoid, axiom, substmonoid = 55.92/7.76 (( ![M:subst]: ( ( comp @ M @ id ) = ( M ) ) ) & 55.92/7.76 ( ![M:subst]: ( ( comp @ id @ M ) = ( M ) ) ) & 55.92/7.76 ( ![M:subst,N:subst,K:subst]: 55.92/7.76 ( ( comp @ ( comp @ M @ N ) @ K ) = ( comp @ M @ ( comp @ N @ K ) ) ) ))). 55.92/7.76 thf('18', plain, 55.92/7.76 (( substmonoid ) = 55.92/7.76 ( ( ![X4:subst]: ( ( comp @ X4 @ id ) = ( X4 ) ) ) & 55.92/7.76 ( ![X6:subst]: ( ( comp @ id @ X6 ) = ( X6 ) ) ) & 55.92/7.76 ( ![X8:subst,X10:subst,X12:subst]: 55.92/7.76 ( ( comp @ ( comp @ X8 @ X10 ) @ X12 ) = 55.92/7.76 ( comp @ X8 @ ( comp @ X10 @ X12 ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(induction2, axiom, induction2 = 55.92/7.76 (![P:( term > $o )]: 55.92/7.76 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 55.92/7.76 ( ( ![A:term,B:term]: 55.92/7.76 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 55.92/7.76 ( ( ![A:term]: 55.92/7.76 ( ( ![B:term]: 55.92/7.76 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 55.92/7.76 ( P @ ( lam @ A ) ) ) ) => 55.92/7.76 ( ![A:term]: ( P @ A ) ) ) ) ))). 55.92/7.76 thf('19', plain, 55.92/7.76 (( induction2 ) = 55.92/7.76 ( ![X4:( term > $o )]: 55.92/7.76 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 55.92/7.76 ( ( ![X8:term,X10:term]: 55.92/7.76 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 55.92/7.76 ( ( ![X12:term]: 55.92/7.76 ( ( ![X14:term]: 55.92/7.76 ( ( X4 @ X14 ) => 55.92/7.76 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 55.92/7.76 ( X4 @ ( lam @ X12 ) ) ) ) => 55.92/7.76 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(induction2lem, axiom, induction2lem = 55.92/7.76 (![P:( term > $o )]: 55.92/7.76 ( ( ![A:term,B:term]: 55.92/7.76 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 55.92/7.76 ( ( ![A:term]: 55.92/7.76 ( ( ![B:term]: 55.92/7.76 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 55.92/7.76 ( P @ ( lam @ A ) ) ) ) => 55.92/7.76 ( ![A:term,M:subst]: 55.92/7.76 ( ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ M ) ) ) ) => 55.92/7.76 ( P @ ( sub @ A @ M ) ) ) ) ) ))). 55.92/7.76 thf('20', plain, 55.92/7.76 (( induction2lem ) = 55.92/7.76 ( ![X4:( term > $o )]: 55.92/7.76 ( ( ![X6:term,X8:term]: 55.92/7.76 ( ( X4 @ X6 ) => ( ( X4 @ X8 ) => ( X4 @ ( ap @ X6 @ X8 ) ) ) ) ) => 55.92/7.76 ( ( ![X10:term]: 55.92/7.76 ( ( ![X12:term]: 55.92/7.76 ( ( X4 @ X12 ) => 55.92/7.76 ( X4 @ ( sub @ X10 @ ( push @ X12 @ id ) ) ) ) ) => 55.92/7.76 ( X4 @ ( lam @ X10 ) ) ) ) => 55.92/7.76 ( ![X14:term,X16:subst]: 55.92/7.76 ( ( ![X18:term]: 55.92/7.76 ( ( var @ X18 ) => ( X4 @ ( sub @ X18 @ X16 ) ) ) ) => 55.92/7.76 ( X4 @ ( sub @ X14 @ X16 ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(pushprop, axiom, pushprop = 55.92/7.76 (![P:( term > $o ),A:term,M:subst]: 55.92/7.76 ( ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ M ) ) ) ) => 55.92/7.76 ( ( P @ A ) => 55.92/7.76 ( ![B:term]: ( ( var @ B ) => ( P @ ( sub @ B @ ( push @ A @ M ) ) ) ) ) ) ))). 55.92/7.76 thf('21', plain, 55.92/7.76 (( pushprop ) = 55.92/7.76 ( ![X4:( term > $o ),X6:term,X8:subst]: 55.92/7.76 ( ( ![X10:term]: ( ( var @ X10 ) => ( X4 @ ( sub @ X10 @ X8 ) ) ) ) => 55.92/7.76 ( ( X4 @ X6 ) => 55.92/7.76 ( ![X12:term]: 55.92/7.76 ( ( var @ X12 ) => ( X4 @ ( sub @ X12 @ ( push @ X6 @ X8 ) ) ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(induction, axiom, induction = 55.92/7.76 (![P:( term > $o )]: 55.92/7.76 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 55.92/7.76 ( ( ![A:term,B:term]: 55.92/7.76 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 55.92/7.76 ( ( ![A:term]: ( ( P @ A ) => ( P @ ( lam @ A ) ) ) ) => 55.92/7.76 ( ![A:term]: ( P @ A ) ) ) ) ))). 55.92/7.76 thf('22', plain, 55.92/7.76 (( induction ) = 55.92/7.76 ( ![X4:( term > $o )]: 55.92/7.76 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 55.92/7.76 ( ( ![X8:term,X10:term]: 55.92/7.76 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 55.92/7.76 ( ( ![X12:term]: ( ( X4 @ X12 ) => ( X4 @ ( lam @ X12 ) ) ) ) => 55.92/7.76 ( ![X14:term]: ( X4 @ X14 ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(lamnotvar, axiom, lamnotvar = (![A:term]: ( ~( var @ ( lam @ A ) ) ))). 55.92/7.76 thf('23', plain, 55.92/7.76 (( lamnotvar ) = ( ![X4:term]: ( ~( var @ ( lam @ X4 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(apnotvar, axiom, apnotvar = 55.92/7.76 (![A:term,B:term]: ( ~( var @ ( ap @ A @ B ) ) ))). 55.92/7.76 thf('24', plain, 55.92/7.76 (( apnotvar ) = ( ![X4:term,X6:term]: ( ~( var @ ( ap @ X4 @ X6 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(lamnotap, axiom, lamnotap = 55.92/7.76 (![A:term,B:term,C:term]: ( ( lam @ A ) != ( ap @ B @ C ) ))). 55.92/7.76 thf('25', plain, 55.92/7.76 (( lamnotap ) = 55.92/7.76 ( ![X4:term,X6:term,X8:term]: ( ( lam @ X4 ) != ( ap @ X6 @ X8 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(shinj, axiom, shinj = 55.92/7.76 (![A:term,B:term]: 55.92/7.76 ( ( ( sub @ A @ sh ) = ( sub @ B @ sh ) ) => ( ( A ) = ( B ) ) ))). 55.92/7.76 thf('26', plain, 55.92/7.76 (( shinj ) = 55.92/7.76 ( ![X4:term,X6:term]: 55.92/7.76 ( ( ( sub @ X4 @ sh ) = ( sub @ X6 @ sh ) ) => ( ( X4 ) = ( X6 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(laminj, axiom, laminj = 55.92/7.76 (![A:term,B:term]: ( ( ( lam @ A ) = ( lam @ B ) ) => ( ( A ) = ( B ) ) ))). 55.92/7.76 thf('27', plain, 55.92/7.76 (( laminj ) = 55.92/7.76 ( ![X4:term,X6:term]: 55.92/7.76 ( ( ( lam @ X4 ) = ( lam @ X6 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(apinj2, axiom, apinj2 = 55.92/7.76 (![A:term,B:term,C:term,D:term]: 55.92/7.76 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( C ) = ( D ) ) ))). 55.92/7.76 thf('28', plain, 55.92/7.76 (( apinj2 ) = 55.92/7.76 ( ![X4:term,X6:term,X8:term,X10:term]: 55.92/7.76 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X8 ) = ( X10 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(apinj1, axiom, apinj1 = 55.92/7.76 (![A:term,B:term,C:term,D:term]: 55.92/7.76 ( ( ( ap @ A @ C ) = ( ap @ B @ D ) ) => ( ( A ) = ( B ) ) ))). 55.92/7.76 thf('29', plain, 55.92/7.76 (( apinj1 ) = 55.92/7.76 ( ![X4:term,X6:term,X8:term,X10:term]: 55.92/7.76 ( ( ( ap @ X4 @ X8 ) = ( ap @ X6 @ X10 ) ) => ( ( X4 ) = ( X6 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(ulamvarind, axiom, ulamvarind = 55.92/7.76 (![P:( term > $o )]: 55.92/7.76 ( ( P @ one ) => 55.92/7.76 ( ( ![A:term]: 55.92/7.76 ( ( var @ A ) => ( ( P @ A ) => ( P @ ( sub @ A @ sh ) ) ) ) ) => 55.92/7.76 ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) ) ))). 55.92/7.76 thf('30', plain, 55.92/7.76 (( ulamvarind ) = 55.92/7.76 ( ![X4:( term > $o )]: 55.92/7.76 ( ( X4 @ one ) => 55.92/7.76 ( ( ![X6:term]: 55.92/7.76 ( ( var @ X6 ) => ( ( X4 @ X6 ) => ( X4 @ ( sub @ X6 @ sh ) ) ) ) ) => 55.92/7.76 ( ![X8:term]: ( ( var @ X8 ) => ( X4 @ X8 ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(ulamvarsh, axiom, ulamvarsh = 55.92/7.76 (![A:term]: ( ( var @ A ) => ( var @ ( sub @ A @ sh ) ) ))). 55.92/7.76 thf('31', plain, 55.92/7.76 (( ulamvarsh ) = 55.92/7.76 ( ![X4:term]: ( ( var @ X4 ) => ( var @ ( sub @ X4 @ sh ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(ulamvar1, axiom,(( ulamvar1 ) = (var @ one))). 55.92/7.76 thf('32', plain, (( ulamvar1 ) = ( var @ one )), 55.92/7.76 inference('simplify_rw_rule', [status(thm)], [ulamvar1])). 55.92/7.76 thf('33', plain, (( ulamvar1 ) = ( var @ one )), define([status(thm)])). 55.92/7.76 thf(axscons, axiom, axscons = 55.92/7.76 (![M:subst]: ( ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) = ( M ) ))). 55.92/7.76 thf('34', plain, 55.92/7.76 (( axscons ) = 55.92/7.76 ( ![X4:subst]: 55.92/7.76 ( ( push @ ( sub @ one @ X4 ) @ ( comp @ sh @ X4 ) ) = ( X4 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axvarshift, axiom, axvarshift = (( push @ one @ sh ) = ( id ))). 55.92/7.76 thf('35', plain, (( axvarshift ) = ( ( push @ one @ sh ) = ( id ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axidr, axiom, axidr = (![M:subst]: ( ( comp @ M @ id ) = ( M ) ))). 55.92/7.76 thf('36', plain, 55.92/7.76 (( axidr ) = ( ![X4:subst]: ( ( comp @ X4 @ id ) = ( X4 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axmap, axiom, axmap = 55.92/7.76 (![A:term,M:subst,N:subst]: 55.92/7.76 ( ( comp @ ( push @ A @ M ) @ N ) = 55.92/7.76 ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) ))). 55.92/7.76 thf('37', plain, 55.92/7.76 (( axmap ) = 55.92/7.76 ( ![X4:term,X6:subst,X8:subst]: 55.92/7.76 ( ( comp @ ( push @ X4 @ X6 ) @ X8 ) = 55.92/7.76 ( push @ ( sub @ X4 @ X8 ) @ ( comp @ X6 @ X8 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axassoc, axiom, axassoc = 55.92/7.76 (![M:subst,N:subst,K:subst]: 55.92/7.76 ( ( comp @ ( comp @ M @ N ) @ K ) = ( comp @ M @ ( comp @ N @ K ) ) ))). 55.92/7.76 thf('38', plain, 55.92/7.76 (( axassoc ) = 55.92/7.76 ( ![X4:subst,X6:subst,X8:subst]: 55.92/7.76 ( ( comp @ ( comp @ X4 @ X6 ) @ X8 ) = 55.92/7.76 ( comp @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axshiftcons, axiom, axshiftcons = 55.92/7.76 (![A:term,M:subst]: ( ( comp @ sh @ ( push @ A @ M ) ) = ( M ) ))). 55.92/7.76 thf('39', plain, 55.92/7.76 (( axshiftcons ) = 55.92/7.76 ( ![X4:term,X6:subst]: ( ( comp @ sh @ ( push @ X4 @ X6 ) ) = ( X6 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axidl, axiom, axidl = (![M:subst]: ( ( comp @ id @ M ) = ( M ) ))). 55.92/7.76 thf('40', plain, 55.92/7.76 (( axidl ) = ( ![X4:subst]: ( ( comp @ id @ X4 ) = ( X4 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axclos, axiom, axclos = 55.92/7.76 (![A:term,M:subst,N:subst]: 55.92/7.76 ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ))). 55.92/7.76 thf('41', plain, 55.92/7.76 (( axclos ) = 55.92/7.76 ( ![X4:term,X6:subst,X8:subst]: 55.92/7.76 ( ( sub @ ( sub @ X4 @ X6 ) @ X8 ) = ( sub @ X4 @ ( comp @ X6 @ X8 ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axabs, axiom, axabs = 55.92/7.76 (![A:term,M:subst]: 55.92/7.76 ( ( sub @ ( lam @ A ) @ M ) = 55.92/7.76 ( lam @ ( sub @ A @ ( push @ one @ ( comp @ M @ sh ) ) ) ) ))). 55.92/7.76 thf('42', plain, 55.92/7.76 (( axabs ) = 55.92/7.76 ( ![X4:term,X6:subst]: 55.92/7.76 ( ( sub @ ( lam @ X4 ) @ X6 ) = 55.92/7.76 ( lam @ ( sub @ X4 @ ( push @ one @ ( comp @ X6 @ sh ) ) ) ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axvarid, axiom, axvarid = (![A:term]: ( ( sub @ A @ id ) = ( A ) ))). 55.92/7.76 thf('43', plain, 55.92/7.76 (( axvarid ) = ( ![X4:term]: ( ( sub @ X4 @ id ) = ( X4 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axvarcons, axiom, axvarcons = 55.92/7.76 (![A:term,M:subst]: ( ( sub @ one @ ( push @ A @ M ) ) = ( A ) ))). 55.92/7.76 thf('44', plain, 55.92/7.76 (( axvarcons ) = 55.92/7.76 ( ![X4:term,X6:subst]: ( ( sub @ one @ ( push @ X4 @ X6 ) ) = ( X4 ) ) )), 55.92/7.76 define([status(thm)])). 55.92/7.76 thf(axapp, axiom, axapp = 55.92/7.76 (![A:term,B:term,M:subst]: 55.92/7.76 ( ( sub @ ( ap @ A @ B ) @ M ) = 55.92/7.76 ( ap @ ( sub @ A @ M ) @ ( sub @ B @ M ) ) ))). 55.92/7.76 thf('45', plain, 55.92/7.76 (( axapp ) = 55.92/7.76 ( ![X4:term,X6:term,X8:subst]: 55.92/7.76 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 55.92/7.76 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) )), 55.92/7.76 define([status(thm)])).thf(thm, conjecture, (hoasinduction_gthm)). 55.92/7.76 thf(zf_stmt_0, conjecture, 55.92/7.76 (( ![X4:term,X6:term,X8:subst]: 55.92/7.76 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 55.92/7.76 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 55.92/7.76 ( ( ![X10:term,X12:subst]: 55.92/7.76 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 55.92/7.76 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 55.92/7.76 ( ( ![X16:term,X18:subst]: 55.92/7.76 ( ( sub @ ( lam @ X16 ) @ X18 ) = 55.92/7.76 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 55.92/7.76 ( ( ![X20:term,X22:subst,X24:subst]: 55.92/7.76 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 55.92/7.76 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 55.92/7.76 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 55.92/7.76 ( ( ![X28:term,X30:subst]: 55.92/7.76 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 55.92/7.76 ( ( ![X32:subst,X34:subst,X36:subst]: 55.92/7.76 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 55.92/7.76 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 55.92/7.76 ( ( ![X38:term,X40:subst,X42:subst]: 55.92/7.76 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 55.92/7.76 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 55.92/7.76 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 55.92/7.76 ( ( ( push @ one @ sh ) = ( id ) ) => 55.92/7.76 ( ( ![X46:subst]: 55.92/7.76 ( ( push @ 55.92/7.76 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 55.92/7.76 ( X46 ) ) ) => 55.92/7.76 ( ( var @ one ) => 55.92/7.76 ( ( ![X48:term]: 55.92/7.76 ( ( var @ X48 ) => 55.92/7.76 ( var @ ( sub @ X48 @ sh ) ) ) ) => 55.92/7.76 ( ( ![X50:( term > $o )]: 55.92/7.76 ( ( X50 @ one ) => 55.92/7.76 ( ( ![X52:term]: 55.92/7.76 ( ( var @ X52 ) => 55.92/7.76 ( ( X50 @ X52 ) => 55.92/7.76 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 55.92/7.76 ( ![X54:term]: 55.92/7.76 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 55.92/7.76 ( ( ![X56:term,X58:term,X60:term,X62:term]: 55.92/7.76 ( ( ( ap @ X56 @ X60 ) = 55.92/7.76 ( ap @ X58 @ X62 ) ) => 55.92/7.76 ( ( X56 ) = ( X58 ) ) ) ) => 55.92/7.76 ( ( ![X64:term,X66:term,X68:term,X70:term]: 55.92/7.76 ( ( ( ap @ X64 @ X68 ) = 55.92/7.76 ( ap @ X66 @ X70 ) ) => 55.92/7.76 ( ( X68 ) = ( X70 ) ) ) ) => 55.92/7.76 ( ( ![X72:term,X74:term]: 55.92/7.76 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 55.92/7.76 ( ( X72 ) = ( X74 ) ) ) ) => 55.92/7.76 ( ( ![X76:term,X78:term]: 55.92/7.76 ( ( ( sub @ X76 @ sh ) = 55.92/7.76 ( sub @ X78 @ sh ) ) => 55.92/7.76 ( ( X76 ) = ( X78 ) ) ) ) => 55.92/7.76 ( ( ![X80:term,X82:term,X84:term]: 55.92/7.76 ( ( lam @ X80 ) != 55.92/7.76 ( ap @ X82 @ X84 ) ) ) => 55.92/7.76 ( ( ![X86:term,X88:term]: 55.92/7.76 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 55.92/7.76 ( ( ![X90:term]: 55.92/7.76 ( ~( var @ ( lam @ X90 ) ) ) ) => 55.92/7.76 ( ( ![X92:( term > $o )]: 55.92/7.76 ( ( ![X94:term]: 55.92/7.76 ( ( var @ X94 ) => 55.92/7.76 ( X92 @ X94 ) ) ) => 55.92/7.76 ( ( ![X96:term,X98:term]: 55.92/7.76 ( ( X92 @ X96 ) => 55.92/7.76 ( ( X92 @ X98 ) => 55.92/7.76 ( X92 @ 55.92/7.76 ( ap @ X96 @ X98 ) ) ) ) ) => 55.92/7.76 ( ( ![X100:term]: 55.92/7.76 ( ( X92 @ X100 ) => 55.92/7.76 ( X92 @ 55.92/7.76 ( lam @ X100 ) ) ) ) => 55.92/7.76 ( ![X102:term]: 55.92/7.76 ( X92 @ X102 ) ) ) ) ) ) => 55.92/7.76 ( ( ![X104:( term > $o ), 55.92/7.76 X106:term,X108:subst]: 55.92/7.76 ( ( ![X110:term]: 55.92/7.76 ( ( var @ X110 ) => 55.92/7.76 ( X104 @ 55.92/7.76 ( sub @ 55.92/7.76 X110 @ X108 ) ) ) ) => 55.92/7.76 ( ( X104 @ X106 ) => 55.92/7.76 ( ![X112:term]: 55.92/7.76 ( ( var @ X112 ) => 55.92/7.76 ( X104 @ 55.92/7.76 ( sub @ 55.92/7.76 X112 @ 55.92/7.76 ( push @ 55.92/7.76 X106 @ X108 ) ) ) ) ) ) ) ) => 55.92/7.76 ( ( ![X114:( term > $o )]: 55.92/7.76 ( ( ![X116:term, 55.92/7.76 X118:term]: 55.92/7.76 ( ( X114 @ X116 ) => 55.92/7.76 ( ( X114 @ X118 ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( ap @ 55.92/7.76 X116 @ X118 ) ) ) ) ) => 55.92/7.76 ( ( ![X120:term]: 55.92/7.76 ( ( ![X122:term]: 55.92/7.76 ( ( X114 @ 55.92/7.76 X122 ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X120 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X122 @ id ) ) ) ) ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( lam @ X120 ) ) ) ) => 55.92/7.76 ( ![X124:term, 55.92/7.76 X126:subst]: 55.92/7.76 ( ( ![X128:term]: 55.92/7.76 ( ( var @ X128 ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X128 @ 55.92/7.76 X126 ) ) ) ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( sub @ 55.92/7.76 X124 @ X126 ) ) ) ) ) ) ) => 55.92/7.76 ( ( ![X130:( term > $o )]: 55.92/7.76 ( ( ![X132:term]: 55.92/7.76 ( ( var @ X132 ) => 55.92/7.76 ( X130 @ X132 ) ) ) => 55.92/7.76 ( ( ![X134:term, 55.92/7.76 X136:term]: 55.92/7.76 ( ( X130 @ X134 ) => 55.92/7.76 ( ( X130 @ 55.92/7.76 X136 ) => 55.92/7.76 ( X130 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 X134 @ 55.92/7.76 X136 ) ) ) ) ) => 55.92/7.76 ( ( ![X138:term]: 55.92/7.76 ( ( ![ 55.92/7.76 X140:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 X140 ) => 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X138 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X140 @ id ) ) ) ) ) => 55.92/7.76 ( X130 @ 55.92/7.76 ( 55.92/7.76 lam @ X138 ) ) ) ) => 55.92/7.76 ( ![X142:term]: 55.92/7.76 ( X130 @ X142 ) ) ) ) ) ) => 55.92/7.76 ( ( ( ![X148:subst, 55.92/7.76 X150:subst, 55.92/7.76 X152:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 ( comp @ 55.92/7.76 X148 @ X150 ) @ 55.92/7.76 X152 ) = 55.92/7.76 ( comp @ 55.92/7.76 X148 @ 55.92/7.76 ( comp @ 55.92/7.76 X150 @ X152 ) ) ) ) & 55.92/7.76 ( ![X146:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 id @ X146 ) = 55.92/7.76 ( X146 ) ) ) & 55.92/7.76 ( ![X144:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 X144 @ id ) = 55.92/7.76 ( X144 ) ) ) ) => 55.92/7.76 ( ( ( ![X156:term, 55.92/7.76 X158:subst, 55.92/7.76 X160:subst]: 55.92/7.76 ( ( sub @ 55.92/7.76 ( sub @ 55.92/7.76 X156 @ 55.92/7.76 X158 ) @ 55.92/7.76 X160 ) = 55.92/7.76 ( sub @ 55.92/7.76 X156 @ 55.92/7.76 ( comp @ 55.92/7.76 X158 @ 55.92/7.76 X160 ) ) ) ) & 55.92/7.76 ( ![X154:term]: 55.92/7.76 ( ( sub @ 55.92/7.76 X154 @ id ) = 55.92/7.76 ( X154 ) ) ) ) => 55.92/7.76 ( ( ![X162:term, 55.92/7.76 X164:term, 55.92/7.76 X166:term, 55.92/7.76 X168:term]: 55.92/7.76 ( ( ( ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X162 @ id ) @ 55.92/7.76 X166 ) = 55.92/7.76 ( ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X164 @ id ) @ 55.92/7.76 X168 ) ) => 55.92/7.76 ( ( X162 ) = 55.92/7.76 ( X164 ) ) ) ) => 55.92/7.76 ( ( ![X170:term, 55.92/7.76 X172:term, 55.92/7.76 X174:term, 55.92/7.76 X176:term]: 55.92/7.76 ( ( ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X170 @ id ) @ 55.92/7.76 X174 ) = 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X172 @ id ) @ 55.92/7.76 X176 ) ) => 55.92/7.76 ( ( 55.92/7.76 X174 ) = 55.92/7.76 ( 55.92/7.76 X176 ) ) ) ) => 55.92/7.76 ( ( ![X178:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( ( 55.92/7.76 ![ 55.92/7.76 X180:subst, 55.92/7.76 X182:term, 55.92/7.76 X184:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 X180 @ 55.92/7.76 X182 ) @ 55.92/7.76 X184 ) = 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X180 @ 55.92/7.76 X184 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X182 @ 55.92/7.76 X184 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X186:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X188:subst, 55.92/7.76 X190:term, 55.92/7.76 X192:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 X188 @ 55.92/7.76 X190 ) @ 55.92/7.76 X192 ) = 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X188 @ 55.92/7.76 X192 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X190 @ 55.92/7.76 X192 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 sh @ one ) ) = 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 sh @ one ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X194:subst, 55.92/7.76 X196:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 X194 @ 55.92/7.76 X196 ) = 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 X194 @ 55.92/7.76 X196 ) ) ) ) ) ) ) ) => 55.92/7.76 ( ( ![ 55.92/7.76 X198:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X200:subst, 55.92/7.76 X202:term, 55.92/7.76 X204:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 X200 @ 55.92/7.76 X202 ) @ 55.92/7.76 X204 ) = 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X200 @ 55.92/7.76 X204 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X202 @ 55.92/7.76 X204 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X206:term, 55.92/7.76 X208:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 sh @ one ) ) != 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X206 @ id ) @ 55.92/7.76 X208 ) ) ) ) ) => 55.92/7.76 ( ( 55.92/7.76 ![ 55.92/7.76 X210:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X212:subst, 55.92/7.76 X214:term, 55.92/7.76 X216:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 X212 @ 55.92/7.76 X214 ) @ 55.92/7.76 X216 ) = 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X212 @ 55.92/7.76 X216 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X214 @ 55.92/7.76 X216 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ~( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X218:term, 55.92/7.76 X220:term]: 55.92/7.76 ( 55.92/7.76 ~( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X218 @ id ) @ 55.92/7.76 X220 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X222:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X224:subst, 55.92/7.76 X226:term, 55.92/7.76 X228:subst, 55.92/7.76 X230:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 X224 @ 55.92/7.76 X226 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X230 @ 55.92/7.76 X228 ) ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X224 @ 55.92/7.76 X230 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X226 @ 55.92/7.76 X230 ) @ 55.92/7.76 X228 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X232:subst, 55.92/7.76 X234:term, 55.92/7.76 X236:subst, 55.92/7.76 X238:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X232 @ 55.92/7.76 X238 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X234 @ 55.92/7.76 X238 ) @ 55.92/7.76 X236 ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 X232 @ 55.92/7.76 X234 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X238 @ 55.92/7.76 X236 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X240:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X240 @ id ) ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 id @ 55.92/7.76 X240 @ id ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X242:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ X242 ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 id @ 55.92/7.76 X242 @ id ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X244:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X246:subst, 55.92/7.76 X248:term, 55.92/7.76 X250:subst, 55.92/7.76 X252:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 X246 @ 55.92/7.76 X248 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X252 @ 55.92/7.76 X250 ) ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X246 @ 55.92/7.76 X252 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X248 @ 55.92/7.76 X252 ) @ 55.92/7.76 X250 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X254:subst, 55.92/7.76 X256:term, 55.92/7.76 X258:subst, 55.92/7.76 X260:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X254 @ 55.92/7.76 X260 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X256 @ 55.92/7.76 X260 ) @ 55.92/7.76 X258 ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 X254 @ 55.92/7.76 X256 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X260 @ 55.92/7.76 X258 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X262:term, 55.92/7.76 X264:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X262 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X264 @ id ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X262 @ id ) @ 55.92/7.76 X264 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X266:term, 55.92/7.76 X268:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X266 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X268 @ id ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 X266 @ 55.92/7.76 X268 ) @ 55.92/7.76 id ) ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X270:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X272:subst, 55.92/7.76 X274:term, 55.92/7.76 X276:subst, 55.92/7.76 X278:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 X272 @ 55.92/7.76 X274 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X278 @ 55.92/7.76 X276 ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X272 @ 55.92/7.76 X278 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X274 @ 55.92/7.76 X278 ) @ 55.92/7.76 X276 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X280:subst, 55.92/7.76 X282:term, 55.92/7.76 X284:subst, 55.92/7.76 X286:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X280 @ 55.92/7.76 X286 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X282 @ 55.92/7.76 X286 ) @ 55.92/7.76 X284 ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 X280 @ 55.92/7.76 X282 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X286 @ 55.92/7.76 X284 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X288:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X290:subst, 55.92/7.76 X292:term, 55.92/7.76 X294:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 X290 @ 55.92/7.76 X292 ) @ 55.92/7.76 X294 ) = 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X290 @ 55.92/7.76 X294 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X292 @ 55.92/7.76 X294 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X296:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 X296 @ id ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 id @ X296 ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X298:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X300:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 X300 @ id ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X298 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X300 @ id ) ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ X298 ) @ 55.92/7.76 id ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X302:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X304:subst, 55.92/7.76 X306:term, 55.92/7.76 X308:subst, 55.92/7.76 X310:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 X304 @ 55.92/7.76 X306 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X310 @ 55.92/7.76 X308 ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X304 @ 55.92/7.76 X310 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X306 @ 55.92/7.76 X310 ) @ 55.92/7.76 X308 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X312:subst, 55.92/7.76 X314:term, 55.92/7.76 X316:subst, 55.92/7.76 X318:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X312 @ 55.92/7.76 X318 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X314 @ 55.92/7.76 X318 ) @ 55.92/7.76 X316 ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 X312 @ 55.92/7.76 X314 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X318 @ 55.92/7.76 X316 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X320:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X320 @ id ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X320 @ id ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X322:term, 55.92/7.76 X324:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X322 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X324 @ id ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X322 @ id ) @ 55.92/7.76 X324 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X326:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X328:subst, 55.92/7.76 X330:term, 55.92/7.76 X332:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 X328 @ 55.92/7.76 X330 ) @ 55.92/7.76 X332 ) = 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X328 @ 55.92/7.76 X332 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X330 @ 55.92/7.76 X332 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X334:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X334 @ id ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 id @ X334 ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X336:term]: 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X336 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))). 55.92/7.76 thf(zf_stmt_1, negated_conjecture, 55.92/7.76 (~( ( ![X4:term,X6:term,X8:subst]: 55.92/7.76 ( ( sub @ ( ap @ X4 @ X6 ) @ X8 ) = 55.92/7.76 ( ap @ ( sub @ X4 @ X8 ) @ ( sub @ X6 @ X8 ) ) ) ) => 55.92/7.76 ( ( ![X10:term,X12:subst]: 55.92/7.76 ( ( sub @ one @ ( push @ X10 @ X12 ) ) = ( X10 ) ) ) => 55.92/7.76 ( ( ![X14:term]: ( ( sub @ X14 @ id ) = ( X14 ) ) ) => 55.92/7.76 ( ( ![X16:term,X18:subst]: 55.92/7.76 ( ( sub @ ( lam @ X16 ) @ X18 ) = 55.92/7.76 ( lam @ ( sub @ X16 @ ( push @ one @ ( comp @ X18 @ sh ) ) ) ) ) ) => 55.92/7.76 ( ( ![X20:term,X22:subst,X24:subst]: 55.92/7.76 ( ( sub @ ( sub @ X20 @ X22 ) @ X24 ) = 55.92/7.76 ( sub @ X20 @ ( comp @ X22 @ X24 ) ) ) ) => 55.92/7.76 ( ( ![X26:subst]: ( ( comp @ id @ X26 ) = ( X26 ) ) ) => 55.92/7.76 ( ( ![X28:term,X30:subst]: 55.92/7.76 ( ( comp @ sh @ ( push @ X28 @ X30 ) ) = ( X30 ) ) ) => 55.92/7.76 ( ( ![X32:subst,X34:subst,X36:subst]: 55.92/7.76 ( ( comp @ ( comp @ X32 @ X34 ) @ X36 ) = 55.92/7.76 ( comp @ X32 @ ( comp @ X34 @ X36 ) ) ) ) => 55.92/7.76 ( ( ![X38:term,X40:subst,X42:subst]: 55.92/7.76 ( ( comp @ ( push @ X38 @ X40 ) @ X42 ) = 55.92/7.76 ( push @ ( sub @ X38 @ X42 ) @ ( comp @ X40 @ X42 ) ) ) ) => 55.92/7.76 ( ( ![X44:subst]: ( ( comp @ X44 @ id ) = ( X44 ) ) ) => 55.92/7.76 ( ( ( push @ one @ sh ) = ( id ) ) => 55.92/7.76 ( ( ![X46:subst]: 55.92/7.76 ( ( push @ 55.92/7.76 ( sub @ one @ X46 ) @ ( comp @ sh @ X46 ) ) = 55.92/7.76 ( X46 ) ) ) => 55.92/7.76 ( ( var @ one ) => 55.92/7.76 ( ( ![X48:term]: 55.92/7.76 ( ( var @ X48 ) => 55.92/7.76 ( var @ ( sub @ X48 @ sh ) ) ) ) => 55.92/7.76 ( ( ![X50:( term > $o )]: 55.92/7.76 ( ( X50 @ one ) => 55.92/7.76 ( ( ![X52:term]: 55.92/7.76 ( ( var @ X52 ) => 55.92/7.76 ( ( X50 @ X52 ) => 55.92/7.76 ( X50 @ ( sub @ X52 @ sh ) ) ) ) ) => 55.92/7.76 ( ![X54:term]: 55.92/7.76 ( ( var @ X54 ) => ( X50 @ X54 ) ) ) ) ) ) => 55.92/7.76 ( ( ![X56:term,X58:term,X60:term,X62:term]: 55.92/7.76 ( ( ( ap @ X56 @ X60 ) = 55.92/7.76 ( ap @ X58 @ X62 ) ) => 55.92/7.76 ( ( X56 ) = ( X58 ) ) ) ) => 55.92/7.76 ( ( ![X64:term,X66:term,X68:term,X70:term]: 55.92/7.76 ( ( ( ap @ X64 @ X68 ) = 55.92/7.76 ( ap @ X66 @ X70 ) ) => 55.92/7.76 ( ( X68 ) = ( X70 ) ) ) ) => 55.92/7.76 ( ( ![X72:term,X74:term]: 55.92/7.76 ( ( ( lam @ X72 ) = ( lam @ X74 ) ) => 55.92/7.76 ( ( X72 ) = ( X74 ) ) ) ) => 55.92/7.76 ( ( ![X76:term,X78:term]: 55.92/7.76 ( ( ( sub @ X76 @ sh ) = 55.92/7.76 ( sub @ X78 @ sh ) ) => 55.92/7.76 ( ( X76 ) = ( X78 ) ) ) ) => 55.92/7.76 ( ( ![X80:term,X82:term,X84:term]: 55.92/7.76 ( ( lam @ X80 ) != 55.92/7.76 ( ap @ X82 @ X84 ) ) ) => 55.92/7.76 ( ( ![X86:term,X88:term]: 55.92/7.76 ( ~( var @ ( ap @ X86 @ X88 ) ) ) ) => 55.92/7.76 ( ( ![X90:term]: 55.92/7.76 ( ~( var @ ( lam @ X90 ) ) ) ) => 55.92/7.76 ( ( ![X92:( term > $o )]: 55.92/7.76 ( ( ![X94:term]: 55.92/7.76 ( ( var @ X94 ) => 55.92/7.76 ( X92 @ X94 ) ) ) => 55.92/7.76 ( ( ![X96:term,X98:term]: 55.92/7.76 ( ( X92 @ X96 ) => 55.92/7.76 ( ( X92 @ X98 ) => 55.92/7.76 ( X92 @ 55.92/7.76 ( ap @ 55.92/7.76 X96 @ X98 ) ) ) ) ) => 55.92/7.76 ( ( ![X100:term]: 55.92/7.76 ( ( X92 @ X100 ) => 55.92/7.76 ( X92 @ 55.92/7.76 ( lam @ X100 ) ) ) ) => 55.92/7.76 ( ![X102:term]: 55.92/7.76 ( X92 @ X102 ) ) ) ) ) ) => 55.92/7.76 ( ( ![X104:( term > $o ), 55.92/7.76 X106:term,X108:subst]: 55.92/7.76 ( ( ![X110:term]: 55.92/7.76 ( ( var @ X110 ) => 55.92/7.76 ( X104 @ 55.92/7.76 ( sub @ 55.92/7.76 X110 @ X108 ) ) ) ) => 55.92/7.76 ( ( X104 @ X106 ) => 55.92/7.76 ( ![X112:term]: 55.92/7.76 ( ( var @ X112 ) => 55.92/7.76 ( X104 @ 55.92/7.76 ( sub @ 55.92/7.76 X112 @ 55.92/7.76 ( push @ 55.92/7.76 X106 @ 55.92/7.76 X108 ) ) ) ) ) ) ) ) => 55.92/7.76 ( ( ![X114:( term > $o )]: 55.92/7.76 ( ( ![X116:term, 55.92/7.76 X118:term]: 55.92/7.76 ( ( X114 @ X116 ) => 55.92/7.76 ( ( X114 @ X118 ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( ap @ 55.92/7.76 X116 @ 55.92/7.76 X118 ) ) ) ) ) => 55.92/7.76 ( ( ![X120:term]: 55.92/7.76 ( ( ![X122:term]: 55.92/7.76 ( ( 55.92/7.76 X114 @ 55.92/7.76 X122 ) => 55.92/7.76 ( 55.92/7.76 X114 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X120 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X122 @ id ) ) ) ) ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( lam @ 55.92/7.76 X120 ) ) ) ) => 55.92/7.76 ( ![X124:term, 55.92/7.76 X126:subst]: 55.92/7.76 ( ( ![X128:term]: 55.92/7.76 ( ( 55.92/7.76 var @ 55.92/7.76 X128 ) => 55.92/7.76 ( 55.92/7.76 X114 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X128 @ 55.92/7.76 X126 ) ) ) ) => 55.92/7.76 ( X114 @ 55.92/7.76 ( sub @ 55.92/7.76 X124 @ 55.92/7.76 X126 ) ) ) ) ) ) ) => 55.92/7.76 ( ( ![X130:( term > $o )]: 55.92/7.76 ( ( ![X132:term]: 55.92/7.76 ( ( var @ X132 ) => 55.92/7.76 ( X130 @ X132 ) ) ) => 55.92/7.76 ( ( ![X134:term, 55.92/7.76 X136:term]: 55.92/7.76 ( ( X130 @ 55.92/7.76 X134 ) => 55.92/7.76 ( ( 55.92/7.76 X130 @ 55.92/7.76 X136 ) => 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 X134 @ 55.92/7.76 X136 ) ) ) ) ) => 55.92/7.76 ( ( ![X138:term]: 55.92/7.76 ( ( 55.92/7.76 ![ 55.92/7.76 X140:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 X140 ) => 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X138 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X140 @ id ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 X130 @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 X138 ) ) ) ) => 55.92/7.76 ( ![X142:term]: 55.92/7.76 ( X130 @ 55.92/7.76 X142 ) ) ) ) ) ) => 55.92/7.76 ( ( ( ![X148:subst, 55.92/7.76 X150:subst, 55.92/7.76 X152:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 ( comp @ 55.92/7.76 X148 @ 55.92/7.76 X150 ) @ 55.92/7.76 X152 ) = 55.92/7.76 ( comp @ 55.92/7.76 X148 @ 55.92/7.76 ( comp @ 55.92/7.76 X150 @ 55.92/7.76 X152 ) ) ) ) & 55.92/7.76 ( ![X146:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 id @ X146 ) = 55.92/7.76 ( X146 ) ) ) & 55.92/7.76 ( ![X144:subst]: 55.92/7.76 ( ( comp @ 55.92/7.76 X144 @ id ) = 55.92/7.76 ( X144 ) ) ) ) => 55.92/7.76 ( ( ( ![X156:term, 55.92/7.76 X158:subst, 55.92/7.76 X160:subst]: 55.92/7.76 ( ( sub @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X156 @ 55.92/7.76 X158 ) @ 55.92/7.76 X160 ) = 55.92/7.76 ( sub @ 55.92/7.76 X156 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X158 @ 55.92/7.76 X160 ) ) ) ) & 55.92/7.76 ( ![X154:term]: 55.92/7.76 ( ( sub @ 55.92/7.76 X154 @ id ) = 55.92/7.76 ( X154 ) ) ) ) => 55.92/7.76 ( ( ![X162:term, 55.92/7.76 X164:term, 55.92/7.76 X166:term, 55.92/7.76 X168:term]: 55.92/7.76 ( ( ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X162 @ id ) @ 55.92/7.76 X166 ) = 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X164 @ id ) @ 55.92/7.76 X168 ) ) => 55.92/7.76 ( ( 55.92/7.76 X162 ) = 55.92/7.76 ( 55.92/7.76 X164 ) ) ) ) => 55.92/7.76 ( ( ![X170:term, 55.92/7.76 X172:term, 55.92/7.76 X174:term, 55.92/7.76 X176:term]: 55.92/7.76 ( ( 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X170 @ id ) @ 55.92/7.76 X174 ) = 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X172 @ id ) @ 55.92/7.76 X176 ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X174 ) = 55.92/7.76 ( 55.92/7.76 X176 ) ) ) ) => 55.92/7.76 ( ( ![ 55.92/7.76 X178:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X180:subst, 55.92/7.76 X182:term, 55.92/7.76 X184:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 X180 @ 55.92/7.76 X182 ) @ 55.92/7.76 X184 ) = 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X180 @ 55.92/7.76 X184 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X182 @ 55.92/7.76 X184 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X186:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X188:subst, 55.92/7.76 X190:term, 55.92/7.76 X192:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 X188 @ 55.92/7.76 X190 ) @ 55.92/7.76 X192 ) = 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X188 @ 55.92/7.76 X192 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X190 @ 55.92/7.76 X192 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 sh @ one ) ) = 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 sh @ one ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X194:subst, 55.92/7.76 X196:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X178 @ 55.92/7.76 X194 @ 55.92/7.76 X196 ) = 55.92/7.76 ( 55.92/7.76 X186 @ 55.92/7.76 X194 @ 55.92/7.76 X196 ) ) ) ) ) ) ) ) => 55.92/7.76 ( ( 55.92/7.76 ![ 55.92/7.76 X198:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X200:subst, 55.92/7.76 X202:term, 55.92/7.76 X204:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 X200 @ 55.92/7.76 X202 ) @ 55.92/7.76 X204 ) = 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X200 @ 55.92/7.76 X204 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X202 @ 55.92/7.76 X204 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X206:term, 55.92/7.76 X208:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X198 @ 55.92/7.76 sh @ one ) ) != 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X206 @ id ) @ 55.92/7.76 X208 ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X210:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X212:subst, 55.92/7.76 X214:term, 55.92/7.76 X216:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 X212 @ 55.92/7.76 X214 ) @ 55.92/7.76 X216 ) = 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X212 @ 55.92/7.76 X216 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X214 @ 55.92/7.76 X216 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ~ 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X210 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X218:term, 55.92/7.76 X220:term]: 55.92/7.76 ( 55.92/7.76 ~ 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X218 @ id ) @ 55.92/7.76 X220 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X222:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > 55.92/7.76 $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X224:subst, 55.92/7.76 X226:term, 55.92/7.76 X228:subst, 55.92/7.76 X230:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 X224 @ 55.92/7.76 X226 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X230 @ 55.92/7.76 X228 ) ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X224 @ 55.92/7.76 X230 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X226 @ 55.92/7.76 X230 ) @ 55.92/7.76 X228 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X232:subst, 55.92/7.76 X234:term, 55.92/7.76 X236:subst, 55.92/7.76 X238:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X232 @ 55.92/7.76 X238 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X234 @ 55.92/7.76 X238 ) @ 55.92/7.76 X236 ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 X232 @ 55.92/7.76 X234 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X238 @ 55.92/7.76 X236 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X240:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X240 @ id ) ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 id @ 55.92/7.76 X240 @ id ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X242:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 X242 ) => 55.92/7.76 ( 55.92/7.76 X222 @ 55.92/7.76 id @ 55.92/7.76 X242 @ id ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X244:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > 55.92/7.76 $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X246:subst, 55.92/7.76 X248:term, 55.92/7.76 X250:subst, 55.92/7.76 X252:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 X246 @ 55.92/7.76 X248 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X252 @ 55.92/7.76 X250 ) ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X246 @ 55.92/7.76 X252 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X248 @ 55.92/7.76 X252 ) @ 55.92/7.76 X250 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X254:subst, 55.92/7.76 X256:term, 55.92/7.76 X258:subst, 55.92/7.76 X260:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X254 @ 55.92/7.76 X260 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X256 @ 55.92/7.76 X260 ) @ 55.92/7.76 X258 ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 X254 @ 55.92/7.76 X256 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X260 @ 55.92/7.76 X258 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X262:term, 55.92/7.76 X264:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X262 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X264 @ id ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X262 @ id ) @ 55.92/7.76 X264 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X266:term, 55.92/7.76 X268:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X266 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 X268 @ id ) => 55.92/7.76 ( 55.92/7.76 X244 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 X266 @ 55.92/7.76 X268 ) @ 55.92/7.76 id ) ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X270:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > 55.92/7.76 $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X272:subst, 55.92/7.76 X274:term, 55.92/7.76 X276:subst, 55.92/7.76 X278:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 X272 @ 55.92/7.76 X274 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X278 @ 55.92/7.76 X276 ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X272 @ 55.92/7.76 X278 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X274 @ 55.92/7.76 X278 ) @ 55.92/7.76 X276 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X280:subst, 55.92/7.76 X282:term, 55.92/7.76 X284:subst, 55.92/7.76 X286:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X280 @ 55.92/7.76 X286 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X282 @ 55.92/7.76 X286 ) @ 55.92/7.76 X284 ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 X280 @ 55.92/7.76 X282 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X286 @ 55.92/7.76 X284 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X288:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X290:subst, 55.92/7.76 X292:term, 55.92/7.76 X294:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 X290 @ 55.92/7.76 X292 ) @ 55.92/7.76 X294 ) = 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X290 @ 55.92/7.76 X294 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X292 @ 55.92/7.76 X294 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X296:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 X296 @ id ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 id @ X296 ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X288 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X298:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X300:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 X300 @ id ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X298 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 X300 @ id ) ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X270 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 X298 ) @ 55.92/7.76 id ) ) ) ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X302:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > 55.92/7.76 $o )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X304:subst, 55.92/7.76 X306:term, 55.92/7.76 X308:subst, 55.92/7.76 X310:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 X304 @ 55.92/7.76 X306 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X310 @ 55.92/7.76 X308 ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X304 @ 55.92/7.76 X310 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X306 @ 55.92/7.76 X310 ) @ 55.92/7.76 X308 ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X312:subst, 55.92/7.76 X314:term, 55.92/7.76 X316:subst, 55.92/7.76 X318:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X312 @ 55.92/7.76 X318 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X314 @ 55.92/7.76 X318 ) @ 55.92/7.76 X316 ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 X312 @ 55.92/7.76 X314 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X318 @ 55.92/7.76 X316 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X320:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X320 @ id ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X320 @ id ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X322:term, 55.92/7.76 X324:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X322 @ id ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X324 @ id ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X322 @ id ) @ 55.92/7.76 X324 ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X326:( 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 term )]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X328:subst, 55.92/7.76 X330:term, 55.92/7.76 X332:subst]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 X328 @ 55.92/7.76 X330 ) @ 55.92/7.76 X332 ) = 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 X328 @ 55.92/7.76 X332 ) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 X330 @ 55.92/7.76 X332 ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X334:term]: 55.92/7.76 ( 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X334 @ id ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 id @ X334 ) @ 55.92/7.76 id ) ) ) => 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 X326 @ 55.92/7.76 sh @ one ) ) @ 55.92/7.76 id ) ) ) ) => 55.92/7.76 ( 55.92/7.76 ![ 55.92/7.76 X336:term]: 55.92/7.76 ( 55.92/7.76 X302 @ 55.92/7.76 id @ 55.92/7.76 X336 @ id ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )), 55.92/7.76 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 55.92/7.76 thf(zip_derived_cl0, plain, 55.92/7.76 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((sub @ (ap @ Y0 @ Y1) @ Y2) = 55.92/7.76 (ap @ (sub @ Y0 @ Y2) @ 55.92/7.76 (sub @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((sub @ (lam @ Y0) @ Y1) = (lam @ 55.92/7.76 (sub @ Y0 @ 55.92/7.76 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((sub @ 55.92/7.76 (sub @ Y0 @ Y1) @ 55.92/7.76 Y2) = (sub @ Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((comp @ sh @ 55.92/7.76 (push @ Y0 @ Y1)) = (Y1))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (comp @ Y0 @ Y1) @ 55.92/7.76 Y2) = (comp @ 55.92/7.76 Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (push @ Y0 @ 55.92/7.76 Y1) @ 55.92/7.76 Y2) = (push @ 55.92/7.76 (sub @ Y0 @ Y2) @ 55.92/7.76 (comp @ Y1 @ 55.92/7.76 Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((push @ one @ sh) = (id))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((push @ (sub @ one @ Y0) @ 55.92/7.76 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.76 (((var @ one) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((var @ Y0) => (var @ 55.92/7.76 (sub @ Y0 @ sh))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((Y0 @ one) => 55.92/7.76 (((((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 (sub @ 55.92/7.76 Y1 @ sh))))))))) => 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 Y0) = 55.92/7.76 (lam @ 55.92/7.76 Y1))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 sh) = 55.92/7.76 (sub @ 55.92/7.76 Y1 @ sh))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 Y0) != 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (((~) @ ( 55.92/7.76 var @ 55.92/7.76 (ap @ 55.92/7.76 Y0 @ Y1)))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((~) @ ( 55.92/7.76 var @ 55.92/7.76 (lam @ Y0))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y1 @ Y2))))))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ Y2))))))))))))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term > $o]: 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (comp @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (comp @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (( 55.92/7.76 (comp @ 55.92/7.76 id @ 55.92/7.76 Y0) = 55.92/7.76 (Y0)))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (( 55.92/7.76 (comp @ 55.92/7.76 Y0 @ 55.92/7.76 id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) = 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2 @ 55.92/7.76 Y3) = 55.92/7.76 (Y1 @ 55.92/7.76 Y2 @ Y3))))))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) != 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2)))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y1) @ id)))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id)) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2) @ id))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 id)))))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 id @ Y2) @ 55.92/7.76 id)))))) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id)))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 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55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2) @ id))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 id @ Y2) @ 55.92/7.76 id)))))) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id)))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.76 inference('cnf', [status(esa)], [zf_stmt_1])). 55.92/7.76 thf(zip_derived_cl2, plain, 55.92/7.76 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((sub @ one @ (push @ Y0 @ Y1)) = (Y0))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((sub @ (lam @ Y0) @ Y1) = (lam @ 55.92/7.76 (sub @ Y0 @ 55.92/7.76 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((sub @ 55.92/7.76 (sub @ Y0 @ Y1) @ Y2) = 55.92/7.76 (sub @ Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((comp @ sh @ (push @ Y0 @ Y1)) = 55.92/7.76 (Y1))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (comp @ Y0 @ Y1) @ 55.92/7.76 Y2) = (comp @ 55.92/7.76 Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (push @ Y0 @ Y1) @ 55.92/7.76 Y2) = (push @ 55.92/7.76 (sub @ Y0 @ Y2) @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((push @ one @ sh) = (id))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((push @ (sub @ one @ Y0) @ 55.92/7.76 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.76 (((var @ one) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((var @ Y0) => (var @ 55.92/7.76 (sub @ Y0 @ sh))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((Y0 @ one) => 55.92/7.76 (((((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ 55.92/7.76 Y1) => 55.92/7.76 (((Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 (sub @ 55.92/7.76 Y1 @ sh))))))))) => 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((( 55.92/7.76 (lam @ 55.92/7.76 Y0) = 55.92/7.76 (lam @ Y1))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 sh) = 55.92/7.76 (sub @ 55.92/7.76 Y1 @ sh))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 Y0) != 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (((~) @ ( 55.92/7.76 var @ 55.92/7.76 (ap @ Y0 @ 55.92/7.76 Y1)))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((~) @ ( 55.92/7.76 var @ 55.92/7.76 (lam @ Y0))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y1 @ Y2))))))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ Y2))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (comp @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (comp @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 id @ Y0) = 55.92/7.76 (Y0)))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 Y0 @ id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) = 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2 @ 55.92/7.76 Y3) = 55.92/7.76 (Y1 @ 55.92/7.76 Y2 @ Y3))))))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) != 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2)))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y1) @ id)))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id)) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2) @ id))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 id)))))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 id @ Y2) @ 55.92/7.76 id)))))) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id)))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)) @ 55.92/7.76 id)))))) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ Y1) @ 55.92/7.76 id))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id)) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2) @ id))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 id @ Y2) @ 55.92/7.76 id)))))) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id)))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.76 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 55.92/7.76 thf(zip_derived_cl5, plain, 55.92/7.76 (~ (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((sub @ (lam @ Y0) @ Y1) = (lam @ 55.92/7.76 (sub @ Y0 @ 55.92/7.76 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((sub @ (sub @ Y0 @ Y1) @ 55.92/7.76 Y2) = (sub @ Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((comp @ sh @ (push @ Y0 @ Y1)) = 55.92/7.76 (Y1))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (comp @ Y0 @ Y1) @ 55.92/7.76 Y2) = (comp @ Y0 @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : subst]: 55.92/7.76 (((!!) @ (^[Y2 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 (push @ Y0 @ Y1) @ 55.92/7.76 Y2) = (push @ 55.92/7.76 (sub @ Y0 @ Y2) @ 55.92/7.76 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.76 (((((push @ one @ sh) = (id))) => 55.92/7.76 (((((!!) @ (^[Y0 : subst]: 55.92/7.76 (((push @ (sub @ one @ Y0) @ 55.92/7.76 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.76 (((var @ one) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((var @ Y0) => (var @ 55.92/7.76 (sub @ Y0 @ sh))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((Y0 @ one) => 55.92/7.76 (((((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ Y1) => 55.92/7.76 (((Y0 @ Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 (sub @ Y1 @ 55.92/7.76 sh))))))))) => 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((var @ Y1) => 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 Y0 @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((((lam @ 55.92/7.76 Y0) = 55.92/7.76 (lam @ Y1))) => 55.92/7.76 (((Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (((( 55.92/7.76 (sub @ 55.92/7.76 Y0 @ sh) = 55.92/7.76 (sub @ 55.92/7.76 Y1 @ sh))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 Y0) != 55.92/7.76 (ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((!!) @ (^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y0 @ Y1)))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term]: 55.92/7.76 (((~) @ (var @ 55.92/7.76 ( 55.92/7.76 lam @ Y0))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y1 @ Y2))))))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y2))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ Y2))))))))))))))))) => 55.92/7.76 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ Y1)))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2)))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ 55.92/7.76 ( 55.92/7.76 push @ 55.92/7.76 Y2 @ id)))))))) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 lam @ Y1))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (Y0 @ Y1))))))))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (comp @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (comp @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 id @ Y0) = 55.92/7.76 (Y0)))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : subst]: 55.92/7.76 (((comp @ 55.92/7.76 Y0 @ id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ Y1) @ 55.92/7.76 Y2) = 55.92/7.76 (sub @ 55.92/7.76 Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y2))))))))))))) & 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (((sub @ 55.92/7.76 Y0 @ id) = 55.92/7.76 (Y0)))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (((!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y0) = 55.92/7.76 (Y1))))))))))))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y2) = 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y3))) => 55.92/7.76 (( 55.92/7.76 (Y2) = 55.92/7.76 (Y3))))))))))))))))) => 55.92/7.76 (((((!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ Y3) @ 55.92/7.76 Y4) = 55.92/7.76 (Y1 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y3 @ Y4))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) = 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y1 @ 55.92/7.76 sh @ one)))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y2 @ 55.92/7.76 Y3) = 55.92/7.76 (Y1 @ 55.92/7.76 Y2 @ Y3))))))))))))))))))))) => 55.92/7.76 (((( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) != 55.92/7.76 (ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2)))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > term]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (sub @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 Y3) = 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y3) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y3))))))))))))) => 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 lam @ 55.92/7.76 ( 55.92/7.76 Y0 @ 55.92/7.76 sh @ one)) @ 55.92/7.76 id))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (~) @ ( 55.92/7.76 var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y0 @ id) @ 55.92/7.76 Y1) @ id)))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id)) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id)))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (var @ 55.92/7.76 Y1) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ id))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3) => 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y1 @ id) @ 55.92/7.76 Y2) @ id))))))))))) => 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y1 @ 55.92/7.76 id) => 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 Y2 @ 55.92/7.76 id) => 55.92/7.76 (Y0 @ 55.92/7.76 id @ 55.92/7.76 ( 55.92/7.76 ap @ 55.92/7.76 Y1 @ Y2) @ 55.92/7.76 id)))))))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y0 : 55.92/7.76 subst > 55.92/7.76 term > 55.92/7.76 subst > $o]: 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 Y1 @ 55.92/7.76 Y2 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y4 @ Y3)) => 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.76 Y1 @ Y4) @ 55.92/7.76 ( 55.92/7.76 sub @ 55.92/7.76 Y2 @ Y4) @ 55.92/7.76 Y3))))))))))))))) => 55.92/7.76 (( 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y1 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y2 : term]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y3 : subst]: 55.92/7.76 (( 55.92/7.76 (!!) @ ( 55.92/7.76 ^[Y4 : subst]: 55.92/7.76 (( 55.92/7.76 (Y0 @ 55.92/7.76 ( 55.92/7.76 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 55.92/7.77 thf(zip_derived_cl9, plain, 55.92/7.77 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((sub @ (lam @ Y0) @ Y1) = (lam @ 55.92/7.77 (sub @ Y0 @ 55.92/7.77 (push @ one @ (comp @ Y1 @ sh)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((sub @ (sub @ Y0 @ Y1) @ 55.92/7.77 Y2) = (sub @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((comp @ sh @ (push @ Y0 @ Y1)) = 55.92/7.77 (Y1))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (comp @ Y0 @ Y1) @ 55.92/7.77 Y2) = (comp @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (push @ Y0 @ Y1) @ 55.92/7.77 Y2) = (push @ 55.92/7.77 (sub @ Y0 @ Y2) @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.77 (((((push @ one @ sh) = (id))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((push @ (sub @ one @ Y0) @ 55.92/7.77 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.77 (((var @ one) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((var @ Y0) => (var @ 55.92/7.77 (sub @ Y0 @ sh))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((Y0 @ one) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (((Y0 @ Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 (sub @ Y1 @ sh))))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((lam @ Y0) = 55.92/7.77 (lam @ Y1))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((sub @ 55.92/7.77 Y0 @ sh) = 55.92/7.77 (sub @ 55.92/7.77 Y1 @ sh))) => 55.92/7.77 (((Y0) = 55.92/7.77 (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 Y0) != 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y0 @ Y1)))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((~) @ (var @ 55.92/7.77 (lam @ Y0))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y1 @ Y2))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ Y2))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 id @ 55.92/7.77 Y0) = 55.92/7.77 (Y0)))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((sub @ Y0 @ 55.92/7.77 id) = (Y0)))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) = 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2 @ 55.92/7.77 Y3) = 55.92/7.77 (Y1 @ 55.92/7.77 Y2 @ Y3))))))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) != 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2)))))))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y1) @ id)))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 id)))))))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 55.92/7.77 thf(zip_derived_cl14, plain, 55.92/7.77 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((sub @ (sub @ Y0 @ Y1) @ Y2) = 55.92/7.77 (sub @ Y0 @ (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (comp @ Y0 @ Y1) @ Y2) = 55.92/7.77 (comp @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (push @ Y0 @ Y1) @ 55.92/7.77 Y2) = (push @ 55.92/7.77 (sub @ Y0 @ Y2) @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.77 (((((push @ one @ sh) = (id))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((push @ (sub @ one @ Y0) @ 55.92/7.77 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.77 (((var @ one) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((var @ Y0) => (var @ 55.92/7.77 (sub @ Y0 @ sh))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((Y0 @ one) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (((Y0 @ Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 (sub @ Y1 @ sh))))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((lam @ Y0) = 55.92/7.77 (lam @ Y1))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((sub @ Y0 @ 55.92/7.77 sh) = 55.92/7.77 (sub @ Y1 @ 55.92/7.77 sh))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 Y0) != 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((~) @ ( 55.92/7.77 var @ 55.92/7.77 (ap @ 55.92/7.77 Y0 @ Y1)))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((~) @ (var @ 55.92/7.77 (lam @ Y0))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y1 @ Y2))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ Y2))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 id @ 55.92/7.77 Y0) = 55.92/7.77 (Y0)))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > term > term]: 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) = 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2 @ 55.92/7.77 Y3) = 55.92/7.77 (Y1 @ 55.92/7.77 Y2 @ Y3))))))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) != 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2)))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y1) @ id)))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 id)))))))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 55.92/7.77 thf(zip_derived_cl20, plain, 55.92/7.77 (~ (((((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (comp @ Y0 @ Y1) @ Y2) = 55.92/7.77 (comp @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (push @ Y0 @ Y1) @ Y2) = 55.92/7.77 (push @ 55.92/7.77 (sub @ Y0 @ Y2) @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.77 (((((push @ one @ sh) = (id))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((push @ (sub @ one @ Y0) @ 55.92/7.77 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.77 (((var @ one) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((Y0 @ one) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (((Y0 @ Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 (sub @ Y1 @ sh))))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => (Y0 @ 55.92/7.77 Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((lam @ Y0) = 55.92/7.77 (lam @ Y1))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((sub @ Y0 @ 55.92/7.77 sh) = (sub @ 55.92/7.77 Y1 @ sh))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (((lam @ 55.92/7.77 Y0) != 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((~) @ ( 55.92/7.77 var @ 55.92/7.77 (ap @ Y0 @ 55.92/7.77 Y1)))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((~) @ (var @ 55.92/7.77 (lam @ Y0))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 (lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y1 @ Y2))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ Y2))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 id @ Y0) = 55.92/7.77 (Y0)))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 Y0 @ id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : subst > 55.92/7.77 term > term]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) = 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2 @ 55.92/7.77 Y3) = 55.92/7.77 (Y1 @ 55.92/7.77 Y2 @ Y3))))))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > term > term]: 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) != 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2)))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y1) @ id)))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 id)))))))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl14])). 55.92/7.77 thf(zip_derived_cl24, plain, 55.92/7.77 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((comp @ sh @ (push @ Y0 @ Y1)) = (Y1))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ (comp @ Y0 @ Y1) @ 55.92/7.77 Y2) = (comp @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 (push @ Y0 @ Y1) @ Y2) = 55.92/7.77 (push @ (sub @ Y0 @ Y2) @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.77 (((((push @ one @ sh) = (id))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((push @ (sub @ one @ Y0) @ 55.92/7.77 (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.77 (((var @ one) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((Y0 @ one) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (((Y0 @ Y1) => (Y0 @ 55.92/7.77 (sub @ Y1 @ sh))))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => (Y0 @ 55.92/7.77 Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((lam @ Y0) = 55.92/7.77 (lam @ Y1))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((sub @ Y0 @ 55.92/7.77 sh) = (sub @ 55.92/7.77 Y1 @ sh))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (((lam @ 55.92/7.77 Y0) != 55.92/7.77 (ap @ Y1 @ 55.92/7.77 Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((~) @ ( 55.92/7.77 var @ 55.92/7.77 (ap @ Y0 @ Y1)))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((Y0 @ Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 (lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y1 @ Y2))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 (lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ Y2))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 id @ Y0) = 55.92/7.77 (Y0)))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ 55.92/7.77 Y0 @ id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : term]: 55.92/7.77 (((sub @ 55.92/7.77 Y0 @ id) = 55.92/7.77 (Y0)))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) = 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2 @ 55.92/7.77 Y3) = 55.92/7.77 (Y1 @ 55.92/7.77 Y2 @ Y3))))))))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : subst > 55.92/7.77 term > term]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) != 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2)))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > term > term]: 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y1) @ id)))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id))))))))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 id)))))))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.77 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 55.92/7.77 thf(zip_derived_cl29, plain, 55.92/7.77 (~ (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ (comp @ Y0 @ Y1) @ 55.92/7.77 Y2) = (comp @ Y0 @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : subst]: 55.92/7.77 (((!!) @ (^[Y2 : subst]: 55.92/7.77 (((comp @ (push @ Y0 @ Y1) @ 55.92/7.77 Y2) = (push @ 55.92/7.77 (sub @ Y0 @ Y2) @ 55.92/7.77 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.77 (((((push @ one @ sh) = (id))) => 55.92/7.77 (((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 55.92/7.77 (Y0)))))) => 55.92/7.77 (((var @ one) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((Y0 @ one) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => 55.92/7.77 (((Y0 @ Y1) => (Y0 @ 55.92/7.77 (sub @ Y1 @ sh))))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (((( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 Y0 @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((lam @ Y0) = (lam @ 55.92/7.77 Y1))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((((sub @ Y0 @ sh) = 55.92/7.77 (sub @ Y1 @ sh))) => 55.92/7.77 (((Y0) = (Y1))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ (^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 Y0) != 55.92/7.77 (ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((~) @ (var @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y0 @ Y1)))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (((var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((!!) @ (^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y1 @ Y2))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ (^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 (lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y2))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ Y2))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ Y1)))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2)))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)))))))) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 lam @ Y1))))))) => 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (Y0 @ Y1))))))))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : subst]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (comp @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (comp @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ id @ 55.92/7.77 Y0) = (Y0)))))) & 55.92/7.77 (((!!) @ (^[Y0 : subst]: 55.92/7.77 (((comp @ Y0 @ 55.92/7.77 id) = (Y0)))))))) => 55.92/7.77 (((((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ Y1) @ 55.92/7.77 Y2) = 55.92/7.77 (sub @ 55.92/7.77 Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y2))))))))))))) & 55.92/7.77 (((!!) @ (^[Y0 : term]: 55.92/7.77 (((sub @ Y0 @ 55.92/7.77 id) = (Y0)))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y0) = 55.92/7.77 (Y1))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y2) = 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y3))) => 55.92/7.77 (( 55.92/7.77 (Y2) = 55.92/7.77 (Y3))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) = 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y2 @ 55.92/7.77 Y3) = 55.92/7.77 (Y1 @ 55.92/7.77 Y2 @ Y3))))))))))))))))))))) => 55.92/7.77 (((((!!) @ (^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) != 55.92/7.77 (ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2)))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : subst > 55.92/7.77 term > term]: 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 Y3) = 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y3) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y3))))))))))))) => 55.92/7.77 (((~) @ ( 55.92/7.77 var @ 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y0 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : term]: 55.92/7.77 (((!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (~) @ ( 55.92/7.77 var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y0 @ id) @ 55.92/7.77 Y1) @ id)))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id)) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id)))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (var @ 55.92/7.77 Y1) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ id))))))))))))))) => 55.92/7.77 (((((!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ id) @ 55.92/7.77 Y2) @ id))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y1 @ 55.92/7.77 id) => 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 ap @ 55.92/7.77 Y1 @ Y2) @ 55.92/7.77 id)))))))))))))))))))) => 55.92/7.77 (((( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : 55.92/7.77 subst > 55.92/7.77 term > term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (sub @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ Y3) @ 55.92/7.77 Y4) = 55.92/7.77 (Y1 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y3 @ Y4))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 id @ Y2) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ 55.92/7.77 ( 55.92/7.77 Y1 @ 55.92/7.77 sh @ one)) @ 55.92/7.77 id)))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : term]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 Y2 @ 55.92/7.77 id) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y1 @ 55.92/7.77 ( 55.92/7.77 push @ 55.92/7.77 Y2 @ id)) @ 55.92/7.77 id)))))) => 55.92/7.77 (Y0 @ 55.92/7.77 id @ 55.92/7.77 ( 55.92/7.77 lam @ Y1) @ 55.92/7.77 id))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y0 : 55.92/7.77 subst > 55.92/7.77 term > 55.92/7.77 subst > $o]: 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)) => 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y1 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y2 : term]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y3 : subst]: 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.77 ^[Y4 : subst]: 55.92/7.77 (( 55.92/7.77 (Y0 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y1 @ Y4) @ 55.92/7.77 ( 55.92/7.77 sub @ 55.92/7.77 Y2 @ Y4) @ 55.92/7.77 Y3) => 55.92/7.77 (Y0 @ 55.92/7.77 Y1 @ 55.92/7.77 Y2 @ 55.92/7.77 ( 55.92/7.77 comp @ 55.92/7.77 Y4 @ Y3)))))))))))))))) => 55.92/7.77 (( 55.92/7.77 (( 55.92/7.77 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 55.92/7.78 thf(zip_derived_cl34, plain, 55.92/7.78 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ (^[Y2 : subst]: 55.92/7.78 (((comp @ (push @ Y0 @ Y1) @ 55.92/7.78 Y2) = (push @ 55.92/7.78 (sub @ Y0 @ Y2) @ 55.92/7.78 (comp @ Y1 @ Y2))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.78 (((((push @ one @ sh) = (id))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 55.92/7.78 (Y0)))))) => 55.92/7.78 (((var @ one) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (((((ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (((Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (((( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ 55.92/7.78 Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = 55.92/7.78 (sub @ Y1 @ sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 Y0) != 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ 55.92/7.78 (ap @ Y0 @ 55.92/7.78 Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (comp @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ 55.92/7.78 Y0) = (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ 55.92/7.78 id) = (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ 55.92/7.78 id) = (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > term > term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 id)))))))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ Y1) @ 55.92/7.78 id))))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 55.92/7.78 thf(zip_derived_cl39, plain, 55.92/7.78 (~ (((((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))) => 55.92/7.78 (((((push @ one @ sh) = (id))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = 55.92/7.78 (Y0)))))) => 55.92/7.78 (((var @ one) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (((((ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (((Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = 55.92/7.78 (sub @ Y1 @ sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((lam @ 55.92/7.78 Y0) != 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ 55.92/7.78 (ap @ Y0 @ Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (comp @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ Y0) = 55.92/7.78 (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ id) = 55.92/7.78 (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ 55.92/7.78 id) = (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > term > term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 id)))))))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ Y1) @ 55.92/7.78 id))))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])). 55.92/7.78 thf(zip_derived_cl44, plain, 55.92/7.78 (~ (((((push @ one @ sh) = (id))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.78 (((var @ one) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = 55.92/7.78 (sub @ Y1 @ sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((lam @ 55.92/7.78 Y0) != 55.92/7.78 (ap @ Y1 @ 55.92/7.78 Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ 55.92/7.78 (ap @ Y0 @ Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (((Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (comp @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ Y0) = 55.92/7.78 (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ id) = 55.92/7.78 (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ id) = 55.92/7.78 (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > term > term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 id)))))))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ Y1) @ 55.92/7.78 id))))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 55.92/7.78 thf(zip_derived_cl49, plain, 55.92/7.78 (~ (((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((push @ (sub @ one @ Y0) @ (comp @ sh @ Y0)) = (Y0)))))) => 55.92/7.78 (((var @ one) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (((( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = (sub @ 55.92/7.78 Y1 @ sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((lam @ Y0) != 55.92/7.78 (ap @ Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ 55.92/7.78 (ap @ Y0 @ Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (((Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (comp @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ Y0) = 55.92/7.78 (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ id) = 55.92/7.78 (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ id) = 55.92/7.78 (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > term > term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 (Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 (Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((~) @ ( 55.92/7.78 var @ 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 id)))))))))))))))))))) => 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y0 : subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ Y1) @ 55.92/7.78 id))))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y0 : subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 55.92/7.78 thf(zip_derived_cl55, plain, 55.92/7.78 (~ (((var @ one) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (((((ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (((Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (((( 55.92/7.78 (ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = (sub @ 55.92/7.78 Y1 @ sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((lam @ Y0) != 55.92/7.78 (ap @ Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ 55.92/7.78 (ap @ Y0 @ Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ 55.92/7.78 Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (((Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (sub @ 55.92/7.78 Y1 @ Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (comp @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (lam @ 55.92/7.78 (Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 (Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((~) @ ( 55.92/7.78 var @ 55.92/7.78 (sub @ 55.92/7.78 (lam @ 55.92/7.78 (Y0 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (~) @ ( 55.92/7.78 var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 id)))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ Y1) @ 55.92/7.78 id))))))))))))))) => 55.92/7.78 (((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 id @ Y2) @ 55.92/7.78 id)))))) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)) @ 55.92/7.78 id)))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.78 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl49])). 55.92/7.78 thf(zip_derived_cl59, plain, 55.92/7.78 (~ (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (var @ (sub @ Y0 @ sh))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((Y0 @ one) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (((Y0 @ Y1) => (Y0 @ 55.92/7.78 (sub @ Y1 @ sh))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (((((ap @ Y0 @ 55.92/7.78 Y2) = (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (((Y0) = (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((!!) @ (^[Y3 : term]: 55.92/7.78 (((((ap @ 55.92/7.78 Y0 @ Y2) = 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y3))) => 55.92/7.78 (((Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((((sub @ Y0 @ sh) = (sub @ Y1 @ 55.92/7.78 sh))) => 55.92/7.78 (((Y0) = (Y1))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (((lam @ Y0) != 55.92/7.78 (ap @ Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => (Y0 @ 55.92/7.78 Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((Y0 @ Y1) => 55.92/7.78 (Y0 @ (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : subst]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y1 @ Y2))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ (^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y2))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (sub @ Y1 @ 55.92/7.78 Y2))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((var @ Y1) => 55.92/7.78 (Y0 @ Y1)))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (((Y0 @ 55.92/7.78 Y1) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 (ap @ 55.92/7.78 Y1 @ Y2)))))))))))) => 55.92/7.78 (((((!!) @ (^[Y1 : term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ 55.92/7.78 ( 55.92/7.78 push @ 55.92/7.78 Y2 @ id)))))))) => 55.92/7.78 (Y0 @ 55.92/7.78 (lam @ Y1))))))) => 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (Y0 @ Y1))))))))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : subst]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (((comp @ 55.92/7.78 (comp @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (comp @ 55.92/7.78 Y0 @ 55.92/7.78 (comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.78 (((!!) @ (^[Y0 : subst]: 55.92/7.78 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.78 (((((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ Y1) @ 55.92/7.78 Y2) = 55.92/7.78 (sub @ 55.92/7.78 Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y2))))))))))))) & 55.92/7.78 (((!!) @ (^[Y0 : term]: 55.92/7.78 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y0) = 55.92/7.78 (Y1))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ (^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y2) = 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y3))) => 55.92/7.78 (( 55.92/7.78 (Y2) = 55.92/7.78 (Y3))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ (^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ (^[Y1 : 55.92/7.78 subst > 55.92/7.78 term > term]: 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ Y3) @ 55.92/7.78 Y4) = 55.92/7.78 (Y1 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y3 @ Y4))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) = 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y1 @ 55.92/7.78 sh @ one)))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y2 @ 55.92/7.78 Y3) = 55.92/7.78 (Y1 @ 55.92/7.78 Y2 @ Y3))))))))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (lam @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 sh @ one)) != 55.92/7.78 (ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2)))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 Y0 @ 55.92/7.78 Y1 @ Y2) @ 55.92/7.78 Y3) = 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y3) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y3))))))))))))) => 55.92/7.78 (((~) @ ( 55.92/7.78 var @ 55.92/7.78 (sub @ 55.92/7.78 (lam @ 55.92/7.78 (Y0 @ sh @ 55.92/7.78 one)) @ 55.92/7.78 id))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : term]: 55.92/7.78 (((!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (((~) @ ( 55.92/7.78 var @ 55.92/7.78 (sub @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y0 @ id) @ 55.92/7.78 Y1) @ id)))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : subst > 55.92/7.78 term > 55.92/7.78 subst > $o]: 55.92/7.78 (((((!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id)) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id)))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (var @ 55.92/7.78 Y1) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ id))))))))))))))) => 55.92/7.78 (((((!!) @ (^[Y0 : 55.92/7.78 subst > 55.92/7.78 term > subst > $o]: 55.92/7.78 (((( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)) => 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y3 : subst]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y4 : subst]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y1 @ Y4) @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y2 @ Y4) @ 55.92/7.78 Y3) => 55.92/7.78 (Y0 @ 55.92/7.78 Y1 @ 55.92/7.78 Y2 @ 55.92/7.78 ( 55.92/7.78 comp @ 55.92/7.78 Y4 @ Y3)))))))))))))))) => 55.92/7.78 (( 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y2 @ 55.92/7.78 id) => 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 ( 55.92/7.78 ap @ 55.92/7.78 ( 55.92/7.78 sub @ 55.92/7.78 Y1 @ id) @ 55.92/7.78 Y2) @ id))))))))))) => 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y1 : term]: 55.92/7.78 (( 55.92/7.78 (!!) @ ( 55.92/7.78 ^[Y2 : term]: 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.78 Y1 @ 55.92/7.78 id) => 55.92/7.78 (( 55.92/7.78 (Y0 @ 55.92/7.78 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 id)))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : 55.92/7.79 subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ Y1) @ 55.92/7.79 id))))))))))))))) => 55.92/7.79 (((!!) @ (^[Y0 : 55.92/7.79 subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl55])). 55.92/7.79 thf(zip_derived_cl62, plain, 55.92/7.79 (~ (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((Y0 @ one) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => 55.92/7.79 (((Y0 @ Y1) => (Y0 @ (sub @ Y1 @ sh))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((!!) @ (^[Y3 : term]: 55.92/7.79 (((((ap @ Y0 @ 55.92/7.79 Y2) = (ap @ 55.92/7.79 Y1 @ Y3))) => 55.92/7.79 (((Y0) = (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((!!) @ (^[Y3 : term]: 55.92/7.79 (((((ap @ Y0 @ 55.92/7.79 Y2) = (ap @ 55.92/7.79 Y1 @ Y3))) => 55.92/7.79 (((Y2) = (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((sub @ Y0 @ sh) = (sub @ Y1 @ 55.92/7.79 sh))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((lam @ Y0) != (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((Y0 @ Y1) => (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (((Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y1 @ Y2))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((Y0 @ Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ Y1 @ 55.92/7.79 (push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ Y2))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => 55.92/7.79 (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : subst]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (((comp @ 55.92/7.79 (comp @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (comp @ 55.92/7.79 Y0 @ 55.92/7.79 (comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (((sub @ 55.92/7.79 (sub @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (sub @ 55.92/7.79 Y0 @ 55.92/7.79 (comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : term]: 55.92/7.79 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y0) = 55.92/7.79 (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y2) = 55.92/7.79 (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) = 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2 @ 55.92/7.79 Y3) = 55.92/7.79 (Y1 @ 55.92/7.79 Y2 @ Y3))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) != 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2)))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((~) @ (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (((~) @ ( 55.92/7.79 var @ 55.92/7.79 (sub @ 55.92/7.79 (ap @ 55.92/7.79 (sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y1) @ 55.92/7.79 id)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y1) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 id)))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : 55.92/7.79 subst > 55.92/7.79 term > subst > $o]: 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ Y1) @ 55.92/7.79 id))))))))))))))) => 55.92/7.79 (((!!) @ (^[Y0 : 55.92/7.79 subst > 55.92/7.79 term > subst > $o]: 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 55.92/7.79 thf(zip_derived_cl65, plain, 55.92/7.79 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((!!) @ (^[Y3 : term]: 55.92/7.79 (((((ap @ Y0 @ Y2) = 55.92/7.79 (ap @ Y1 @ Y3))) => 55.92/7.79 (((Y0) = (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((!!) @ (^[Y3 : term]: 55.92/7.79 (((((ap @ Y0 @ 55.92/7.79 Y2) = (ap @ 55.92/7.79 Y1 @ Y3))) => 55.92/7.79 (((Y2) = (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((lam @ Y0) != (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((Y0 @ Y1) => (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y1 @ Y2))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ Y2))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ 55.92/7.79 Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : subst]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (comp @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (comp @ 55.92/7.79 Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (((sub @ 55.92/7.79 (sub @ Y0 @ 55.92/7.79 Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (sub @ Y0 @ 55.92/7.79 (comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : term]: 55.92/7.79 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y0) = 55.92/7.79 (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y2) = 55.92/7.79 (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : 55.92/7.79 subst > term > term]: 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (lam @ 55.92/7.79 (Y0 @ 55.92/7.79 sh @ one)) = 55.92/7.79 (lam @ 55.92/7.79 (Y1 @ 55.92/7.79 sh @ one)))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2 @ 55.92/7.79 Y3) = 55.92/7.79 (Y1 @ 55.92/7.79 Y2 @ Y3))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) != 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2)))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((~) @ (var @ 55.92/7.79 (sub @ 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (~) @ ( 55.92/7.79 var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y1) @ id)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y1) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 id)))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ Y1) @ 55.92/7.79 id))))))))))))))) => 55.92/7.79 (((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 55.92/7.79 thf(zip_derived_cl69, plain, 55.92/7.79 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((!!) @ (^[Y3 : term]: 55.92/7.79 (((((ap @ Y0 @ Y2) = 55.92/7.79 (ap @ Y1 @ Y3))) => 55.92/7.79 (((Y2) = (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((lam @ Y0) != (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ Y1 @ 55.92/7.79 Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((Y0 @ Y1) => (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (((var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y1 @ Y2))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ 55.92/7.79 Y1 @ Y2))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ 55.92/7.79 Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((Y0 @ Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ Y1 @ 55.92/7.79 (push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : subst]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (comp @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (comp @ 55.92/7.79 Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (sub @ 55.92/7.79 Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : term]: 55.92/7.79 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y0) = 55.92/7.79 (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y2) = 55.92/7.79 (Y3))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : subst > 55.92/7.79 term > term]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (lam @ 55.92/7.79 (Y0 @ 55.92/7.79 sh @ one)) = 55.92/7.79 (lam @ 55.92/7.79 (Y1 @ 55.92/7.79 sh @ one)))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2 @ 55.92/7.79 Y3) = 55.92/7.79 (Y1 @ 55.92/7.79 Y2 @ Y3))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (lam @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 sh @ one)) != 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2)))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 55.92/7.79 (((((!!) @ (^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y0 @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 Y3) = 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y3) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y3))))))))))))) => 55.92/7.79 (((~) @ (var @ 55.92/7.79 (sub @ 55.92/7.79 (lam @ 55.92/7.79 (Y0 @ sh @ 55.92/7.79 one)) @ 55.92/7.79 id))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (~) @ ( 55.92/7.79 var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y1) @ id)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y1) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 Y1 @ Y2) @ 55.92/7.79 id)))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ Y1) @ 55.92/7.79 id))))))))))))))) => 55.92/7.79 (((!!) @ (^[Y0 : subst > 55.92/7.79 term > 55.92/7.79 subst > $o]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3))))))))))))))) => 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y1 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y4 @ Y3)))))))))))))))) => 55.92/7.79 (((( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id)) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ 55.92/7.79 id) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y2) @ id))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : 55.92/7.79 subst > 55.92/7.79 term > term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y4 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 Y2 @ Y3) @ 55.92/7.79 Y4) = 55.92/7.79 (Y1 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y2 @ Y4) @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y4))))))))))))) => 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y2 @ 55.92/7.79 id) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 id @ Y2) @ 55.92/7.79 id)))))) => 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 ( 55.92/7.79 lam @ 55.92/7.79 ( 55.92/7.79 Y1 @ 55.92/7.79 sh @ one)) @ 55.92/7.79 id)))))))) => 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y1 : term]: 55.92/7.79 (Y0 @ 55.92/7.79 id @ 55.92/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 55.92/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl65])). 55.92/7.79 thf(zip_derived_cl73, plain, 55.92/7.79 (~ (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((lam @ Y0) = (lam @ Y1))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 55.92/7.79 (((Y0) = (Y1))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((lam @ Y0) != (ap @ Y1 @ 55.92/7.79 Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((Y0 @ Y1) => (Y0 @ 55.92/7.79 (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (((var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ Y3 @ 55.92/7.79 Y2))))))) => 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (((var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ 55.92/7.79 Y3 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y1 @ Y2))))))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ Y1) => 55.92/7.79 (((Y0 @ Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ Y1 @ 55.92/7.79 Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((((!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (var @ 55.92/7.79 Y3) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y3 @ Y2))))))) => 55.92/7.79 (Y0 @ 55.92/7.79 (sub @ Y1 @ 55.92/7.79 Y2))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term > $o]: 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (((Y0 @ 55.92/7.79 Y1) => 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 (ap @ 55.92/7.79 Y1 @ Y2)))))))))))) => 55.92/7.79 (((((!!) @ (^[Y1 : term]: 55.92/7.79 (((((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (Y0 @ 55.92/7.79 Y2) => 55.92/7.79 (Y0 @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ 55.92/7.79 ( 55.92/7.79 push @ 55.92/7.79 Y2 @ id)))))))) => 55.92/7.79 (Y0 @ (lam @ Y1))))))) => 55.92/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : subst]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (((comp @ 55.92/7.79 (comp @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (comp @ 55.92/7.79 Y0 @ 55.92/7.79 (comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ id @ Y0) = (Y0)))))) & 55.92/7.79 (((!!) @ (^[Y0 : subst]: 55.92/7.79 (((comp @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : subst]: 55.92/7.79 (((!!) @ (^[Y2 : subst]: 55.92/7.79 (( 55.92/7.79 (sub @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ Y1) @ 55.92/7.79 Y2) = 55.92/7.79 (sub @ 55.92/7.79 Y0 @ 55.92/7.79 ( 55.92/7.79 comp @ 55.92/7.79 Y1 @ Y2))))))))))))) & 55.92/7.79 (((!!) @ (^[Y0 : term]: 55.92/7.79 (((sub @ Y0 @ id) = (Y0)))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 55.92/7.79 (((!!) @ (^[Y2 : term]: 55.92/7.79 (( 55.92/7.79 (!!) @ ( 55.92/7.79 ^[Y3 : term]: 55.92/7.79 (( 55.92/7.79 (( 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y0 @ id) @ 55.92/7.79 Y2) = 55.92/7.79 (ap @ 55.92/7.79 ( 55.92/7.79 sub @ 55.92/7.79 Y1 @ id) @ 55.92/7.79 Y3))) => 55.92/7.79 (( 55.92/7.79 (Y0) = 55.92/7.79 (Y1))))))))))))))))) => 55.92/7.79 (((((!!) @ (^[Y0 : term]: 55.92/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y2) = 56.27/7.79 (Y3))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : subst > 56.27/7.79 term > term]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (((((lam @ 56.27/7.79 (Y0 @ 56.27/7.79 sh @ one)) = 56.27/7.79 (lam @ 56.27/7.79 (Y1 @ 56.27/7.79 sh @ one)))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y2 @ 56.27/7.79 Y3) = 56.27/7.79 (Y1 @ 56.27/7.79 Y2 @ Y3))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (lam @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 sh @ one)) != 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2)))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((~) @ (var @ 56.27/7.79 (sub @ 56.27/7.79 (lam @ 56.27/7.79 (Y0 @ sh @ 56.27/7.79 one)) @ 56.27/7.79 id))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ ( 56.27/7.79 var @ 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y1) @ id)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((var @ 56.27/7.79 (sub @ 56.27/7.79 Y1 @ id)) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ Y1 @ 56.27/7.79 id)))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y1) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ Y1 @ 56.27/7.79 id))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 id)))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > 56.27/7.79 term > subst > $o]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > 56.27/7.79 term > term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y2 @ id)) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ Y1) @ 56.27/7.79 id))))))))))))))) => 56.27/7.79 (((!!) @ (^[Y0 : subst > 56.27/7.79 term > subst > $o]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id)) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))) => 56.27/7.79 (((( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > 56.27/7.79 term > term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])). 56.27/7.79 thf(zip_derived_cl78, plain, 56.27/7.79 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((((sub @ Y0 @ sh) = (sub @ Y1 @ sh))) => 56.27/7.79 (((Y0) = (Y1))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((Y0 @ Y1) => (Y0 @ 56.27/7.79 (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ (^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y2))))))) => 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y3 @ 56.27/7.79 (push @ 56.27/7.79 Y1 @ Y2))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 (push @ 56.27/7.79 Y2 @ id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y2))))))) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ 56.27/7.79 Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ 56.27/7.79 Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y2 @ id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : subst]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((comp @ 56.27/7.79 (comp @ 56.27/7.79 Y0 @ Y1) @ 56.27/7.79 Y2) = 56.27/7.79 (comp @ 56.27/7.79 Y0 @ 56.27/7.79 (comp @ 56.27/7.79 Y1 @ Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: 56.27/7.79 (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: 56.27/7.79 (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((sub @ 56.27/7.79 (sub @ 56.27/7.79 Y0 @ Y1) @ 56.27/7.79 Y2) = 56.27/7.79 (sub @ 56.27/7.79 Y0 @ 56.27/7.79 (comp @ 56.27/7.79 Y1 @ Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : term]: 56.27/7.79 (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y0) = 56.27/7.79 (Y1))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y2) = 56.27/7.79 (Y3))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (((((lam @ 56.27/7.79 (Y0 @ sh @ 56.27/7.79 one)) = 56.27/7.79 (lam @ 56.27/7.79 (Y1 @ sh @ 56.27/7.79 one)))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y2 @ 56.27/7.79 Y3) = 56.27/7.79 (Y1 @ 56.27/7.79 Y2 @ Y3))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((lam @ 56.27/7.79 (Y0 @ 56.27/7.79 sh @ one)) != 56.27/7.79 (ap @ 56.27/7.79 (sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2)))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((~) @ (var @ 56.27/7.79 (sub @ 56.27/7.79 (lam @ 56.27/7.79 (Y0 @ sh @ one)) @ 56.27/7.79 id))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ ( 56.27/7.79 var @ 56.27/7.79 (sub @ 56.27/7.79 (ap @ 56.27/7.79 (sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y1) @ 56.27/7.79 id)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((var @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 id)) => 56.27/7.79 (Y0 @ id @ 56.27/7.79 Y1 @ id)))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y1) => 56.27/7.79 (Y0 @ id @ 56.27/7.79 Y1 @ id))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 id)))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > 56.27/7.79 term > term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y2 @ id)) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ Y1) @ 56.27/7.79 id))))))))))))))) => 56.27/7.79 (((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id)) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (((( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > 56.27/7.79 term > term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 56.27/7.79 thf(zip_derived_cl84, plain, 56.27/7.79 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((lam @ Y0) != (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ (^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y2))))))) => 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((!!) @ (^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y1 @ Y2))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 (push @ Y2 @ 56.27/7.79 id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ 56.27/7.79 Y3 @ Y2))))))) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ 56.27/7.79 Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ 56.27/7.79 Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ 56.27/7.79 Y1 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y2 @ id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : subst]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((comp @ 56.27/7.79 (comp @ Y0 @ 56.27/7.79 Y1) @ 56.27/7.79 Y2) = (comp @ 56.27/7.79 Y0 @ 56.27/7.79 (comp @ Y1 @ 56.27/7.79 Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((sub @ 56.27/7.79 (sub @ Y0 @ 56.27/7.79 Y1) @ 56.27/7.79 Y2) = 56.27/7.79 (sub @ Y0 @ 56.27/7.79 (comp @ 56.27/7.79 Y1 @ Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y0) = 56.27/7.79 (Y1))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y2) = 56.27/7.79 (Y3))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (((((lam @ 56.27/7.79 (Y0 @ sh @ one)) = 56.27/7.79 (lam @ 56.27/7.79 (Y1 @ sh @ one)))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y2 @ 56.27/7.79 Y3) = 56.27/7.79 (Y1 @ 56.27/7.79 Y2 @ Y3))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((lam @ 56.27/7.79 (Y0 @ sh @ 56.27/7.79 one)) != 56.27/7.79 (ap @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 id) @ 56.27/7.79 Y2)))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((~) @ (var @ 56.27/7.79 (sub @ 56.27/7.79 (lam @ 56.27/7.79 (Y0 @ sh @ one)) @ 56.27/7.79 id))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ ( 56.27/7.79 var @ 56.27/7.79 (sub @ 56.27/7.79 (ap @ 56.27/7.79 (sub @ Y0 @ 56.27/7.79 id) @ 56.27/7.79 Y1) @ 56.27/7.79 id)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id)) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y1) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 id)))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > term > term]: 56.27/7.79 (((( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 (lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y2 @ id)) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 (lam @ Y1) @ 56.27/7.79 id))))))))))))))) => 56.27/7.79 (((!!) @ (^[Y0 : subst > term > 56.27/7.79 subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (((var @ 56.27/7.79 (sub @ 56.27/7.79 Y1 @ id)) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ Y1 @ 56.27/7.79 id)))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ 56.27/7.79 id) => 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2) @ id))))))))))) => 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y1 : 56.27/7.79 subst > 56.27/7.79 term > term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y2 @ 56.27/7.79 id) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 id @ Y2) @ 56.27/7.79 id)))))) => 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 ( 56.27/7.79 lam @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 sh @ one)) @ 56.27/7.79 id)))))))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y1 : term]: 56.27/7.79 (Y0 @ 56.27/7.79 id @ 56.27/7.79 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.79 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 56.27/7.79 thf(zip_derived_cl92, plain, 56.27/7.79 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: (((~) @ (var @ (ap @ Y0 @ Y1)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ (^[Y3 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ 56.27/7.79 Y3 @ Y2))))))) => 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((!!) @ (^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ 56.27/7.79 ( 56.27/7.79 push @ 56.27/7.79 Y1 @ Y2))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 (push @ Y2 @ id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (((var @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y3 @ 56.27/7.79 Y2))))))) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y1) => 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (((((!!) @ (^[Y2 : term]: 56.27/7.79 (((Y0 @ Y2) => 56.27/7.79 (Y0 @ 56.27/7.79 (sub @ Y1 @ 56.27/7.79 (push @ 56.27/7.79 Y2 @ id)))))))) => 56.27/7.79 (Y0 @ (lam @ Y1))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : subst]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((comp @ 56.27/7.79 (comp @ Y0 @ Y1) @ 56.27/7.79 Y2) = (comp @ 56.27/7.79 Y0 @ 56.27/7.79 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.79 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : subst]: 56.27/7.79 (((sub @ 56.27/7.79 (sub @ Y0 @ Y1) @ 56.27/7.79 Y2) = (sub @ 56.27/7.79 Y0 @ 56.27/7.79 (comp @ Y1 @ 56.27/7.79 Y2))))))))))))) & 56.27/7.79 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (((( 56.27/7.79 (ap @ 56.27/7.79 (sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 (sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y0) = 56.27/7.79 (Y1))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (( 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y2) = 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y3))) => 56.27/7.79 (( 56.27/7.79 (Y2) = 56.27/7.79 (Y3))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y2 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ Y3) @ 56.27/7.79 Y4) = 56.27/7.79 (Y1 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y3 @ Y4))))))))))))) => 56.27/7.79 (((((lam @ 56.27/7.79 (Y0 @ sh @ one)) = 56.27/7.79 (lam @ 56.27/7.79 (Y1 @ sh @ one)))) => 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : term]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y2 @ 56.27/7.79 Y3) = 56.27/7.79 (Y1 @ 56.27/7.79 Y2 @ Y3))))))))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((!!) @ (^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (lam @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 sh @ one)) != 56.27/7.79 (ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y1 @ id) @ 56.27/7.79 Y2)))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (sub @ 56.27/7.79 ( 56.27/7.79 Y0 @ 56.27/7.79 Y1 @ Y2) @ 56.27/7.79 Y3) = 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y3) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y3))))))))))))) => 56.27/7.79 (((~) @ (var @ 56.27/7.79 (sub @ 56.27/7.79 (lam @ 56.27/7.79 (Y0 @ sh @ one)) @ 56.27/7.79 id))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : term]: 56.27/7.79 (((!!) @ (^[Y1 : term]: 56.27/7.79 (((~) @ (var @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 ( 56.27/7.79 ap @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y0 @ id) @ 56.27/7.79 Y1) @ id)))))))))) => 56.27/7.79 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)) => 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : subst]: 56.27/7.79 (((!!) @ ( 56.27/7.79 ^[Y2 : term]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y3 : subst]: 56.27/7.79 (( 56.27/7.79 (!!) @ ( 56.27/7.79 ^[Y4 : subst]: 56.27/7.79 (( 56.27/7.79 (Y0 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y1 @ Y4) @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.79 Y2 @ Y4) @ 56.27/7.79 Y3) => 56.27/7.79 (Y0 @ 56.27/7.79 Y1 @ 56.27/7.79 Y2 @ 56.27/7.79 ( 56.27/7.79 comp @ 56.27/7.79 Y4 @ Y3)))))))))))))))) => 56.27/7.79 (((((!!) @ (^[Y1 : term]: 56.27/7.79 (( 56.27/7.79 (var @ 56.27/7.79 ( 56.27/7.79 sub @ 56.27/7.80 Y1 @ id)) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (var @ 56.27/7.80 Y1) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > 56.27/7.80 subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > 56.27/7.80 subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id)) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : 56.27/7.80 subst > 56.27/7.80 term > term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl84])). 56.27/7.80 thf(zip_derived_cl102, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term]: (((~) @ (var @ (lam @ Y0))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ 56.27/7.80 Y2))))))) => 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ 56.27/7.80 Y3 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y1 @ Y2))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y2))))))) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ 56.27/7.80 id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ 56.27/7.80 (comp @ Y0 @ Y1) @ 56.27/7.80 Y2) = (comp @ 56.27/7.80 Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ 56.27/7.80 Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y0) = 56.27/7.80 (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((( 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ 56.27/7.80 (Y0 @ sh @ one)) = 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (lam @ (Y0 @ sh @ one)) @ 56.27/7.80 id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id)) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y1) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > 56.27/7.80 term > term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (var @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id)) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : 56.27/7.80 subst > term > term]: 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl92])). 56.27/7.80 thf(zip_derived_cl113, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((Y0 @ Y1) => (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ Y2))))))) => 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ 56.27/7.80 (push @ 56.27/7.80 Y1 @ Y2))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y2))))))) => 56.27/7.80 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ 56.27/7.80 (comp @ Y0 @ Y1) @ 56.27/7.80 Y2) = (comp @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y0) = 56.27/7.80 (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ 56.27/7.80 (Y0 @ sh @ one)) = 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ 56.27/7.80 sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (lam @ (Y0 @ sh @ one)) @ 56.27/7.80 id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id)) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y1) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > 56.27/7.80 term > term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (var @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id)) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y1 : term]: 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 56.27/7.80 thf(zip_derived_cl122, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ Y2))))))) => 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ 56.27/7.80 (push @ Y1 @ 56.27/7.80 Y2))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ 56.27/7.80 Y3 @ Y2))))))) => 56.27/7.80 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ 56.27/7.80 (comp @ Y0 @ Y1) @ 56.27/7.80 Y2) = (comp @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y0) = 56.27/7.80 (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ 56.27/7.80 (Y0 @ sh @ one)) = 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ 56.27/7.80 one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (lam @ (Y0 @ sh @ one)) @ 56.27/7.80 id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y0 @ 56.27/7.80 id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > term > term]: 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id)) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > 56.27/7.80 term > term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 56.27/7.80 thf(zip_derived_cl126, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((((!!) @ (^[Y3 : term]: 56.27/7.80 (((var @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 (sub @ Y3 @ 56.27/7.80 Y2))))))) => 56.27/7.80 (Y0 @ (sub @ Y1 @ Y2))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ 56.27/7.80 (comp @ Y0 @ Y1) @ Y2) = 56.27/7.80 (comp @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((( 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y0) = 56.27/7.80 (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ 56.27/7.80 (Y0 @ sh @ one)) = 56.27/7.80 (lam @ (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id)) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > 56.27/7.80 term > term]: 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl122])). 56.27/7.80 thf(zip_derived_cl130, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y1) => 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ Y2) => (Y0 @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ Y2 @ id)))))))) => 56.27/7.80 (Y0 @ (lam @ Y1))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ 56.27/7.80 (comp @ Y0 @ Y1) @ Y2) = 56.27/7.80 (comp @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (sub @ Y0 @ Y1) @ Y2) = 56.27/7.80 (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y0) = 56.27/7.80 (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((( 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (( 56.27/7.80 (Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = 56.27/7.80 (lam @ (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 Y2 @ Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y1 @ id) => 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y1 @ id) => 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ 56.27/7.80 one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ 56.27/7.80 id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : 56.27/7.80 subst > term > term]: 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (( 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 56.27/7.80 thf(zip_derived_cl135, plain, 56.27/7.80 (~ (((((((!!) @ (^[Y0 : subst]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((comp @ (comp @ Y0 @ Y1) @ 56.27/7.80 Y2) = (comp @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0)))))) & 56.27/7.80 (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ 56.27/7.80 id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y0) = (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ 56.27/7.80 Y0 @ id) @ 56.27/7.80 Y2) = 56.27/7.80 (ap @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y2) = 56.27/7.80 (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = 56.27/7.80 (lam @ (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (((Y0 @ Y2 @ 56.27/7.80 Y3) = (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ (lam @ (Y0 @ sh @ one)) @ 56.27/7.80 id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ 56.27/7.80 id @ Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ 56.27/7.80 one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (lam @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ id @ 56.27/7.80 Y1 @ id)))))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 56.27/7.80 thf(zip_derived_cl142, plain, 56.27/7.80 (~ (((((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((sub @ (sub @ Y0 @ Y1) @ 56.27/7.80 Y2) = (sub @ Y0 @ 56.27/7.80 (comp @ Y1 @ Y2))))))))))))) & 56.27/7.80 (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y0) = (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ 56.27/7.80 id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y2) = (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = 56.27/7.80 (lam @ (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y0 @ id) @ Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ 56.27/7.80 id @ Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y2 @ id) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (sub @ Y1 @ 56.27/7.80 (push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y1 @ id) => 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > 56.27/7.80 term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ 56.27/7.80 one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ id @ Y1 @ 56.27/7.80 id)))))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 56.27/7.80 thf(zip_derived_cl154, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y0) = (Y1))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y2) = (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = 56.27/7.80 (lam @ (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y2 @ 56.27/7.80 Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ 56.27/7.80 (sub @ Y1 @ id) @ Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ (sub @ Y0 @ id) @ 56.27/7.80 Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ 56.27/7.80 id @ Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y2 @ id) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (Y1 @ id @ 56.27/7.80 Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ 56.27/7.80 one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 56.27/7.80 thf(zip_derived_cl167, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((((ap @ 56.27/7.80 (sub @ Y0 @ id) @ 56.27/7.80 Y2) = (ap @ 56.27/7.80 (sub @ Y1 @ id) @ 56.27/7.80 Y3))) => 56.27/7.80 (((Y2) = (Y3))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ Y1 @ 56.27/7.80 Y3) @ 56.27/7.80 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = (lam @ 56.27/7.80 (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 Y2 @ Y3) = 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ 56.27/7.80 (Y0 @ sh @ one)) != 56.27/7.80 (ap @ (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 Y3) = 56.27/7.80 (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ 56.27/7.80 Y2 @ Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ (sub @ Y0 @ id) @ Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ id @ 56.27/7.80 Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y1 @ id) => 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ 56.27/7.80 id))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((Y0 @ id @ 56.27/7.80 Y1 @ id) => 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (ap @ 56.27/7.80 Y1 @ Y2) @ 56.27/7.80 id)))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ 56.27/7.80 ( 56.27/7.80 push @ 56.27/7.80 Y2 @ id)) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ Y1) @ id))))))))))))))) => 56.27/7.80 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ 56.27/7.80 (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y1 @ 56.27/7.80 id) => 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 ( 56.27/7.80 ap @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y1 @ id) @ 56.27/7.80 Y2) @ id))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : term]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (sub @ 56.27/7.80 ( 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((!!) @ ( 56.27/7.80 ^[Y2 : term]: 56.27/7.80 (((Y0 @ 56.27/7.80 id @ Y2 @ 56.27/7.80 id) => 56.27/7.80 (Y0 @ 56.27/7.80 id @ 56.27/7.80 (Y1 @ 56.27/7.80 id @ Y2) @ 56.27/7.80 id)))))) => 56.27/7.80 (Y0 @ id @ 56.27/7.80 (lam @ 56.27/7.80 (Y1 @ sh @ one)) @ 56.27/7.80 id)))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))))))))))), 56.27/7.80 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl154])). 56.27/7.80 thf(zip_derived_cl186, plain, 56.27/7.80 (~ (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y1 @ 56.27/7.80 Y2 @ Y3) @ 56.27/7.80 Y4) = 56.27/7.80 (Y1 @ 56.27/7.80 (comp @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 (sub @ 56.27/7.80 Y3 @ Y4))))))))))))) => 56.27/7.80 (((((lam @ (Y0 @ sh @ one)) = (lam @ 56.27/7.80 (Y1 @ sh @ one)))) => 56.27/7.80 (((!!) @ (^[Y2 : subst]: 56.27/7.80 (((!!) @ (^[Y3 : term]: 56.27/7.80 (((Y0 @ Y2 @ 56.27/7.80 Y3) = (Y1 @ 56.27/7.80 Y2 @ Y3))))))))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ Y1 @ 56.27/7.80 Y3) @ 56.27/7.80 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((lam @ (Y0 @ sh @ one)) != 56.27/7.80 (ap @ (sub @ Y1 @ id) @ 56.27/7.80 Y2)))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (((sub @ 56.27/7.80 (Y0 @ Y1 @ 56.27/7.80 Y2) @ 56.27/7.80 Y3) = (Y0 @ 56.27/7.80 (comp @ 56.27/7.80 Y1 @ Y3) @ 56.27/7.80 (sub @ Y2 @ 56.27/7.80 Y3))))))))))))) => 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : term]: 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((~) @ (var @ 56.27/7.80 (sub @ 56.27/7.80 (ap @ (sub @ Y0 @ id) @ Y1) @ 56.27/7.80 id)))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ (sub @ Y1 @ id)) => 56.27/7.80 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.80 (((!!) @ (^[Y1 : term]: 56.27/7.80 (((var @ Y1) => (Y0 @ id @ 56.27/7.80 Y1 @ id))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ (^[Y3 : subst]: 56.27/7.80 (( 56.27/7.80 (!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y4 @ Y3)) => 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3))))))))))))))) => 56.27/7.80 (((((!!) @ (^[Y1 : subst]: 56.27/7.80 (((!!) @ (^[Y2 : term]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y3 : subst]: 56.27/7.80 (((!!) @ ( 56.27/7.80 ^[Y4 : subst]: 56.27/7.80 (( 56.27/7.80 (Y0 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.80 Y1 @ Y4) @ 56.27/7.80 ( 56.27/7.80 sub @ 56.27/7.80 Y2 @ Y4) @ 56.27/7.80 Y3) => 56.27/7.80 (Y0 @ 56.27/7.80 Y1 @ 56.27/7.80 Y2 @ 56.27/7.80 ( 56.27/7.80 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y1 @ id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ 56.27/7.81 Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y1 @ id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ 56.27/7.81 id @ Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 (sub @ 56.27/7.81 Y1 @ 56.27/7.81 ( 56.27/7.81 push @ 56.27/7.81 Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ 56.27/7.81 id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ 56.27/7.81 (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ 56.27/7.81 id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 id @ Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 (ap @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ ( 56.27/7.81 ^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ 56.27/7.81 Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ 56.27/7.81 (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl167])). 56.27/7.81 thf(zip_derived_cl203, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((lam @ (Y0 @ sh @ one)) != 56.27/7.81 (ap @ (sub @ Y1 @ id) @ Y2)))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((~) @ (var @ (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((~) @ (var @ 56.27/7.81 (sub @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ 56.27/7.81 id)))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ Y1) => (Y0 @ id @ Y1 @ 56.27/7.81 id))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ Y2) @ 56.27/7.81 id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ 56.27/7.81 id @ Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 (Y1 @ 56.27/7.81 id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ 56.27/7.81 Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ 56.27/7.81 id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y1 @ id) => 56.27/7.81 (((Y0 @ 56.27/7.81 id @ Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 (ap @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ 56.27/7.81 (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])). 56.27/7.81 thf(zip_derived_cl220, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((~) @ (var @ (sub @ (lam @ (Y0 @ sh @ one)) @ id))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((~) @ (var @ 56.27/7.81 (sub @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id)))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ Y1) => (Y0 @ id @ Y1 @ 56.27/7.81 id))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (ap @ Y1 @ Y2) @ 56.27/7.81 id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ 56.27/7.81 Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ 56.27/7.81 id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y1 @ id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ 56.27/7.81 Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl203])). 56.27/7.81 thf(zip_derived_cl239, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((~) @ (var @ 56.27/7.81 (sub @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id)))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ 56.27/7.81 id @ Y1 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ Y1) => (Y0 @ id @ Y1 @ id))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ Y2) @ 56.27/7.81 id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ 56.27/7.81 id @ Y2 @ 56.27/7.81 id) => 56.27/7.81 (Y0 @ 56.27/7.81 id @ 56.27/7.81 (Y1 @ 56.27/7.81 id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl220])). 56.27/7.81 thf(zip_derived_cl252, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ 56.27/7.81 id @ Y1 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ Y1) => (Y0 @ id @ Y1 @ id))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ Y2) @ id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => 56.27/7.81 (Y0 @ id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ 56.27/7.81 Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl239])). 56.27/7.81 thf(zip_derived_cl266, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ Y2) @ id)))))))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ 56.27/7.81 id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ 56.27/7.81 id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ 56.27/7.81 Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl252])). 56.27/7.81 thf(zip_derived_cl281, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ 56.27/7.81 id @ Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ 56.27/7.81 id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])). 56.27/7.81 thf(zip_derived_cl292, plain, 56.27/7.81 (~ (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 (comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ id @ 56.27/7.81 Y1 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ 56.27/7.81 (sub @ Y1 @ id) @ Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (( 56.27/7.81 (!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ 56.27/7.81 id) => (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl281])). 56.27/7.81 thf(zip_derived_cl307, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 ('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => ('#sk733' @ id @ Y0 @ 56.27/7.81 id)))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (( 56.27/7.81 (sub @ 56.27/7.81 ( 56.27/7.81 Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl292])). 56.27/7.81 thf(zip_derived_cl317, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => ('#sk733' @ id @ Y0 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])). 56.27/7.81 thf(zip_derived_cl325, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => ('#sk733' @ id @ Y0 @ id)))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (Y0 @ id @ Y1) @ 56.27/7.81 id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl317])). 56.27/7.81 thf(zip_derived_cl333, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (Y0 @ id @ Y1) @ 56.27/7.81 id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 56.27/7.81 thf(zip_derived_cl344, plain, 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl333])). 56.27/7.81 thf(zip_derived_cl357, plain, 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl344])). 56.27/7.81 thf(zip_derived_cl369, plain, (~ ('#sk733' @ id @ '#sk1677' @ id)), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl357])). 56.27/7.81 thf(zip_derived_cl134, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : term > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ Y1) => 56.27/7.81 (((Y0 @ Y2) => (Y0 @ 56.27/7.81 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ Y2) => (Y0 @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)))))))) => 56.27/7.81 (Y0 @ (lam @ Y1))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 56.27/7.81 thf(zip_derived_cl140, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0))))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl134])). 56.27/7.81 thf(zip_derived_cl149, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 56.27/7.81 thf(zip_derived_cl160, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((var @ ('#sk46' @ X2)) => (X2 @ ('#sk46' @ X2)))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 56.27/7.81 thf(zip_derived_cl177, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( (var @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 56.27/7.81 thf(zip_derived_cl195, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))) 56.27/7.81 | (var @ ('#sk46' @ X2)))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])). 56.27/7.81 thf(zip_derived_cl129, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : term > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ Y1) => 56.27/7.81 (((Y0 @ Y2) => (Y0 @ 56.27/7.81 (ap @ Y1 @ Y2)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ Y2) => (Y0 @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)))))))) => 56.27/7.81 (Y0 @ (lam @ Y1))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((((!!) @ (^[Y3 : term]: 56.27/7.81 (((var @ Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 (sub @ Y3 @ Y2))))))) => 56.27/7.81 (Y0 @ (sub @ Y1 @ Y2)))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl126])). 56.27/7.81 thf(zip_derived_cl133, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((var @ Y2) => (X2 @ 56.27/7.81 (sub @ Y2 @ Y1))))))) => 56.27/7.81 (X2 @ (sub @ Y0 @ Y1))))))))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl129])). 56.27/7.81 thf(zip_derived_cl139, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((var @ Y2) => (X2 @ 56.27/7.81 (sub @ Y2 @ Y1))))))) => 56.27/7.81 (X2 @ (sub @ Y0 @ Y1)))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])). 56.27/7.81 thf(zip_derived_cl146, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( ('#form108' @ X2) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl212, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ (^[Y0 : term]: (X2 @ Y0))) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl195, zip_derived_cl146])). 56.27/7.81 thf(zip_derived_cl229, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ X2) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 56.27/7.81 inference('ho_norm', [status(thm)], [zip_derived_cl212])). 56.27/7.81 thf(zip_derived_cl230, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl229])). 56.27/7.81 thf(zip_derived_cl244, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ Y0) => (X2 @ 56.27/7.81 (sub @ ('#sk196' @ X2) @ (push @ Y0 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ ('#sk196' @ X2))))) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl230])). 56.27/7.81 thf(zip_derived_cl256, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (X2 @ (lam @ ('#sk196' @ X2))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])). 56.27/7.81 thf(zip_derived_cl271, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 ( (X2 @ X4) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | ~ (X2 @ (lam @ ('#sk196' @ X2))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl256])). 56.27/7.81 thf(zip_derived_cl332, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => ('#sk733' @ id @ Y0 @ id))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])). 56.27/7.81 thf(zip_derived_cl342, plain, 56.27/7.81 (![X2 : term]: (((var @ (sub @ X2 @ id)) => ('#sk733' @ id @ X2 @ id)))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl332])). 56.27/7.81 thf(zip_derived_cl354, plain, 56.27/7.81 (![X2 : term]: (~ (var @ (sub @ X2 @ id)) | ('#sk733' @ id @ X2 @ id))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl342])). 56.27/7.81 thf(zip_derived_cl8, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 56.27/7.81 thf(zip_derived_cl12, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 56.27/7.81 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 56.27/7.81 thf(zip_derived_cl501, plain, 56.27/7.81 (![X2 : term]: (~ (var @ X2) | ('#sk733' @ id @ X2 @ id))), 56.27/7.81 inference('demod', [status(thm)], [zip_derived_cl354, zip_derived_cl17])). 56.27/7.81 thf(zip_derived_cl356, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => ('#sk733' @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (Y0 @ sh @ one)) @ id))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl344])). 56.27/7.81 thf(zip_derived_cl368, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ (X2 @ Y0 @ Y1) @ Y2) = 56.27/7.81 (X2 @ (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id)))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl356])). 56.27/7.81 thf(zip_derived_cl379, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ (X2 @ Y0 @ Y1) @ Y2) = 56.27/7.81 (X2 @ (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl368])). 56.27/7.81 thf(zip_derived_cl387, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((sub @ (X2 @ ('#sk430' @ X2) @ Y0) @ 56.27/7.81 Y1) = (X2 @ 56.27/7.81 (comp @ ('#sk430' @ X2) @ Y1) @ 56.27/7.81 (sub @ Y0 @ Y1)))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl379])). 56.27/7.81 thf(zip_derived_cl394, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ 56.27/7.81 Y0) = (X2 @ (comp @ ('#sk430' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ Y0))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl387])). 56.27/7.81 thf(zip_derived_cl404, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ (((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ 56.27/7.81 ('#sk516' @ X2)) = (X2 @ 56.27/7.81 (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl394])). 56.27/7.81 thf(zip_derived_cl416, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ ('#sk516' @ X2)) 56.27/7.81 != (X2 @ (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2)))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) => 56.27/7.81 ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], 56.27/7.81 [zip_derived_cl404])). 56.27/7.81 thf(zip_derived_cl417, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ Y0) @ id)))))) 56.27/7.81 | ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id) 56.27/7.81 | ((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ ('#sk516' @ X2)) 56.27/7.81 != (X2 @ (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2)))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl416])). 56.27/7.81 thf(zip_derived_cl424, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ ((('#sk733' @ id @ ('#sk3185' @ X2) @ id) => ('#sk733' @ id @ 56.27/7.81 (X2 @ id @ ('#sk3185' @ X2)) @ id))) 56.27/7.81 | ((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ ('#sk516' @ X2)) 56.27/7.81 != (X2 @ (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2)))) 56.27/7.81 | ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl417])). 56.27/7.81 thf(zip_derived_cl431, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 ( ('#sk733' @ id @ ('#sk3185' @ X2) @ id) 56.27/7.81 | ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id) 56.27/7.81 | ((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ ('#sk516' @ X2)) 56.27/7.81 != (X2 @ (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2)))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl424])). 56.27/7.81 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 56.27/7.81 thf(zip_derived_cl178, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl160])). 56.27/7.81 thf(zip_derived_cl196, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl178])). 56.27/7.81 thf(zip_derived_cl146, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( ('#form108' @ X2) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl213, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ (^[Y0 : term]: (X2 @ Y0))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl196, zip_derived_cl146])). 56.27/7.81 thf(zip_derived_cl231, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ X2) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 56.27/7.81 inference('ho_norm', [status(thm)], [zip_derived_cl213])). 56.27/7.81 thf(zip_derived_cl232, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y1) => (X2 @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ Y0))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])). 56.27/7.81 thf(zip_derived_cl245, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ Y0) => (X2 @ 56.27/7.81 (sub @ ('#sk196' @ X2) @ (push @ Y0 @ id)))))))) => 56.27/7.81 (X2 @ (lam @ ('#sk196' @ X2))))) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl232])). 56.27/7.81 thf(zip_derived_cl258, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ (X2 @ (lam @ ('#sk196' @ X2))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl245])). 56.27/7.81 thf(zip_derived_cl273, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 ( (X2 @ X4) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | ~ (X2 @ (lam @ ('#sk196' @ X2))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl258])). 56.27/7.81 thf(zip_derived_cl255, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ Y0) => (X2 @ 56.27/7.81 (sub @ ('#sk196' @ X2) @ (push @ Y0 @ id)))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])). 56.27/7.81 thf(zip_derived_cl270, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 ( (((X2 @ X4) => (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))))) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl255])). 56.27/7.81 thf(zip_derived_cl283, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 (~ (X2 @ X4) 56.27/7.81 | (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl270])). 56.27/7.81 thf(zip_derived_cl295, plain, 56.27/7.81 (![X2 : term > $o, X4 : term, X6 : term]: 56.27/7.81 ( (X2 @ X6) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | (var @ ('#sk46' @ X2)) 56.27/7.81 | (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))) 56.27/7.81 | ~ (X2 @ X4))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl283])). 56.27/7.81 thf(zip_derived_cl308, plain, 56.27/7.81 (![X0 : term > $o, X1 : term]: 56.27/7.81 (~ (X0 @ X1) 56.27/7.81 | ~ ('#form108' @ X0) 56.27/7.81 | (var @ ('#sk46' @ X0)) 56.27/7.81 | (X0 @ (sub @ ('#sk196' @ X0) @ (push @ X1 @ id))))), 56.27/7.81 inference('condensation', [status(thm)], [zip_derived_cl295])). 56.27/7.81 thf(zip_derived_cl43, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: (((comp @ Y0 @ id) = (Y0))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl39])). 56.27/7.81 thf(zip_derived_cl47, plain, (![X2 : subst]: (((comp @ X2 @ id) = (X2)))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 56.27/7.81 thf(zip_derived_cl52, plain, (![X2 : subst]: ((comp @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl47])). 56.27/7.81 thf(zip_derived_cl291, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 ( 56.27/7.81 ( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : term]: 56.27/7.81 (((!!) @ ( 56.27/7.81 ^[Y4 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ( 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ Y3) @ 56.27/7.81 Y4) = 56.27/7.81 (Y1 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y3 @ Y4))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (Y1 @ id @ Y2) @ id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ 56.27/7.81 id)))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (sub @ Y1 @ 56.27/7.81 (push @ Y2 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (Y0 @ id @ (lam @ Y1) @ id)))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl281])). 56.27/7.81 thf(zip_derived_cl303, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 (X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id))))))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl291])). 56.27/7.81 thf(zip_derived_cl315, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 (X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl303])). 56.27/7.81 thf(zip_derived_cl322, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ Y0 @ 56.27/7.81 (comp @ Y2 @ Y1)) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl315])). 56.27/7.81 thf(zip_derived_cl329, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ 56.27/7.81 ('#sk839' @ X2) @ (comp @ Y1 @ Y0)) => 56.27/7.81 (X2 @ (comp @ ('#sk708' @ X2) @ Y1) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ Y1) @ Y0))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl322])). 56.27/7.81 thf(zip_derived_cl339, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ Y0 @ ('#sk967' @ X2))) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ Y0) @ ('#sk967' @ X2))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl329])). 56.27/7.81 thf(zip_derived_cl351, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl339])). 56.27/7.81 thf(zip_derived_cl363, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl351])). 56.27/7.81 thf(zip_derived_cl375, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl363])). 56.27/7.81 thf(zip_derived_cl384, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ ('#sk1549' @ X2) @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 Y0 @ (comp @ Y2 @ Y1))))))))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl375])). 56.27/7.81 thf(zip_derived_cl392, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y1) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y1) @ Y0) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ (comp @ Y1 @ Y0)))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl384])). 56.27/7.81 thf(zip_derived_cl402, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y0) @ ('#sk1944' @ X2)) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ Y0 @ ('#sk1944' @ X2)))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl392])). 56.27/7.81 thf(zip_derived_cl414, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl402])). 56.27/7.81 thf(zip_derived_cl265, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 ( 56.27/7.81 ( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ (sub @ Y1 @ id)) => (Y0 @ id @ 56.27/7.81 Y1 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl252])). 56.27/7.81 thf(zip_derived_cl279, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 (X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id))))))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl265])). 56.27/7.81 thf(zip_derived_cl289, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 (X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl279])). 56.27/7.81 thf(zip_derived_cl301, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ Y0 @ 56.27/7.81 (comp @ Y2 @ Y1)) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl289])). 56.27/7.81 thf(zip_derived_cl313, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ 56.27/7.81 ('#sk839' @ X2) @ (comp @ Y1 @ Y0)) => 56.27/7.81 (X2 @ (comp @ ('#sk708' @ X2) @ Y1) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ Y1) @ Y0))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl301])). 56.27/7.81 thf(zip_derived_cl320, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ Y0 @ ('#sk967' @ X2))) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ Y0) @ ('#sk967' @ X2))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl313])). 56.27/7.81 thf(zip_derived_cl327, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) => (X2 @ 56.27/7.81 (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl320])). 56.27/7.81 thf(zip_derived_cl337, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl327])). 56.27/7.81 thf(zip_derived_cl348, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])). 56.27/7.81 thf(zip_derived_cl360, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ ('#sk1549' @ X2) @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 Y0 @ (comp @ Y2 @ Y1))))))))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl348])). 56.27/7.81 thf(zip_derived_cl372, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y1) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y1) @ Y0) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ (comp @ Y1 @ Y0)))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl360])). 56.27/7.81 thf(zip_derived_cl381, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y0) @ ('#sk1944' @ X2)) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ Y0 @ ('#sk1944' @ X2)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl372])). 56.27/7.81 thf(zip_derived_cl389, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl381])). 56.27/7.81 thf(zip_derived_cl389, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl381])). 56.27/7.81 thf(zip_derived_cl397, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form2417' @ X2) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id)))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl399, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form2417' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl389, zip_derived_cl397])). 56.27/7.81 thf(zip_derived_cl407, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form2686' @ X2) 56.27/7.81 | ~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl422, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl414, zip_derived_cl407])). 56.27/7.81 thf(zip_derived_cl429, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl422])). 56.27/7.81 thf(zip_derived_cl437, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl429])). 56.27/7.81 thf(zip_derived_cl444, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl437])). 56.27/7.81 thf(zip_derived_cl364, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ 56.27/7.81 Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ 56.27/7.81 Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ Y2) @ 56.27/7.81 Y3) = 56.27/7.81 (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ 56.27/7.81 Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ 56.27/7.81 id @ (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ 56.27/7.81 id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl351])). 56.27/7.81 thf(zip_derived_cl376, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])). 56.27/7.81 thf(zip_derived_cl385, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ ('#sk1549' @ X2) @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 Y0 @ (comp @ Y2 @ Y1))))))))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl376])). 56.27/7.81 thf(zip_derived_cl393, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y1) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y1) @ Y0) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ (comp @ Y1 @ Y0)))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl385])). 56.27/7.81 thf(zip_derived_cl403, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((X2 @ (comp @ ('#sk1549' @ X2) @ Y0) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ Y0) @ ('#sk1944' @ X2)) => 56.27/7.81 (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ Y0 @ ('#sk1944' @ X2)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl393])). 56.27/7.81 thf(zip_derived_cl415, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl403])). 56.27/7.81 thf(zip_derived_cl407, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form2686' @ X2) 56.27/7.81 | ~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl423, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ 56.27/7.81 Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ 56.27/7.81 Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ 56.27/7.81 Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl415, zip_derived_cl407])). 56.27/7.81 thf(zip_derived_cl430, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((!!) @ (^[Y0 : subst > term > term]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 (Y0 @ Y1 @ Y2) @ 56.27/7.81 Y3) = (Y0 @ 56.27/7.81 (comp @ Y1 @ Y3) @ 56.27/7.81 (sub @ Y2 @ Y3))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (Y0 @ id @ Y1) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl423])). 56.27/7.81 thf(zip_derived_cl438, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl430])). 56.27/7.81 thf(zip_derived_cl445, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form3615' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl455, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form3615' @ X2) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl444, zip_derived_cl445])). 56.27/7.81 thf(zip_derived_cl466, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl455])). 56.27/7.81 thf(zip_derived_cl479, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 ( (((X2 @ id @ X4 @ id) => (X2 @ id @ ('#sk3410' @ X2 @ id @ X4) @ id))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl466])). 56.27/7.81 thf(zip_derived_cl491, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 (~ (X2 @ id @ X4 @ id) 56.27/7.81 | (X2 @ id @ ('#sk3410' @ X2 @ id @ X4) @ id) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl479])). 56.27/7.81 thf(zip_derived_cl432, plain, 56.27/7.81 (![X2 : subst > term > term]: 56.27/7.81 (~ ('#sk733' @ id @ (X2 @ id @ ('#sk3185' @ X2)) @ id) 56.27/7.81 | ('#sk733' @ id @ (lam @ (X2 @ sh @ one)) @ id) 56.27/7.81 | ((sub @ (X2 @ ('#sk430' @ X2) @ ('#sk467' @ X2)) @ ('#sk516' @ X2)) 56.27/7.81 != (X2 @ (comp @ ('#sk430' @ X2) @ ('#sk516' @ X2)) @ 56.27/7.81 (sub @ ('#sk467' @ X2) @ ('#sk516' @ X2)))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl424])). 56.27/7.81 thf(zip_derived_cl438, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl430])). 56.27/7.81 thf(zip_derived_cl445, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form3615' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl447, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl438, zip_derived_cl445])). 56.27/7.81 thf(zip_derived_cl457, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl447])). 56.27/7.81 thf(zip_derived_cl469, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 ('#sk3410' @ X2 @ id @ Y0) @ id)))))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])). 56.27/7.81 thf(zip_derived_cl481, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 ( (((X2 @ id @ X4 @ id) => (X2 @ id @ ('#sk3410' @ X2 @ id @ X4) @ id))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl469])). 56.27/7.81 thf(zip_derived_cl493, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 (~ (X2 @ id @ X4 @ id) 56.27/7.81 | (X2 @ id @ ('#sk3410' @ X2 @ id @ X4) @ id) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl481])). 56.27/7.81 thf(zip_derived_cl23, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: (((comp @ id @ Y0) = (Y0))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 56.27/7.81 thf(zip_derived_cl27, plain, (![X2 : subst]: (((comp @ id @ X2) = (X2)))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl23])). 56.27/7.81 thf(zip_derived_cl31, plain, (![X2 : subst]: ((comp @ id @ X2) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl27])). 56.27/7.81 thf(zip_derived_cl467, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl455])). 56.27/7.81 thf(zip_derived_cl443, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl437])). 56.27/7.81 thf(zip_derived_cl445, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form3615' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl454, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form3615' @ X2) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl443, zip_derived_cl445])). 56.27/7.81 thf(zip_derived_cl465, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ Y0) @ Y1) = 56.27/7.81 ('#sk3410' @ X2 @ (comp @ X4 @ Y1) @ 56.27/7.81 (sub @ Y0 @ Y1)))))))))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl454])). 56.27/7.81 thf(zip_derived_cl478, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term]: 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ Y0) = 56.27/7.81 ('#sk3410' @ X2 @ (comp @ X4 @ Y0) @ (sub @ X6 @ Y0))))))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl465])). 56.27/7.81 thf(zip_derived_cl490, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term, X8 : subst]: 56.27/7.81 ( (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ X8) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ X4 @ X8) @ (sub @ X6 @ X8)))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl478])). 56.27/7.81 thf(zip_derived_cl498, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term, X8 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ X8) 56.27/7.81 = ('#sk3410' @ X2 @ (comp @ X4 @ X8) @ (sub @ X6 @ X8))) 56.27/7.81 | (X2 @ ('#sk708' @ X2) @ ('#sk839' @ X2) @ 56.27/7.81 (comp @ ('#sk1077' @ X2) @ ('#sk967' @ X2))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], 56.27/7.81 [zip_derived_cl490])). 56.27/7.81 thf(zip_derived_cl257, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ Y0) => (X2 @ 56.27/7.81 (sub @ ('#sk196' @ X2) @ (push @ Y0 @ id)))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl245])). 56.27/7.81 thf(zip_derived_cl272, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 ( (((X2 @ X4) => (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))))) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl257])). 56.27/7.81 thf(zip_derived_cl284, plain, 56.27/7.81 (![X2 : term > $o, X4 : term]: 56.27/7.81 (~ (X2 @ X4) 56.27/7.81 | (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | ~ ('#form108' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl272])). 56.27/7.81 thf(zip_derived_cl296, plain, 56.27/7.81 (![X2 : term > $o, X4 : term, X6 : term]: 56.27/7.81 ( (X2 @ X6) 56.27/7.81 | ~ ('#form108' @ X2) 56.27/7.81 | ~ (X2 @ ('#sk46' @ X2)) 56.27/7.81 | (X2 @ (sub @ ('#sk196' @ X2) @ (push @ X4 @ id))) 56.27/7.81 | ~ (X2 @ X4))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl284])). 56.27/7.81 thf(zip_derived_cl309, plain, 56.27/7.81 (![X0 : term > $o, X1 : term]: 56.27/7.81 (~ (X0 @ X1) 56.27/7.81 | ~ ('#form108' @ X0) 56.27/7.81 | ~ (X0 @ ('#sk46' @ X0)) 56.27/7.81 | (X0 @ (sub @ ('#sk196' @ X0) @ (push @ X1 @ id))))), 56.27/7.81 inference('condensation', [status(thm)], [zip_derived_cl296])). 56.27/7.81 thf(zip_derived_cl280, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 ( 56.27/7.81 ( 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)) => 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((!!) @ (^[Y4 : subst]: 56.27/7.81 (( 56.27/7.81 (Y0 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y1 @ Y4) @ 56.27/7.81 ( 56.27/7.81 sub @ 56.27/7.81 Y2 @ Y4) @ 56.27/7.81 Y3) => 56.27/7.81 (Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 Y2 @ 56.27/7.81 ( 56.27/7.81 comp @ 56.27/7.81 Y4 @ Y3)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ (sub @ Y1 @ id) @ 56.27/7.81 Y2) @ 56.27/7.81 id))))))))))) => 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : term]: 56.27/7.81 (((Y0 @ id @ Y1 @ id) => 56.27/7.81 (((Y0 @ id @ Y2 @ id) => 56.27/7.81 (Y0 @ id @ 56.27/7.81 (ap @ Y1 @ Y2) @ id))))))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl266])). 56.27/7.81 thf(zip_derived_cl290, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 (X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 (((X2 @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => (X2 @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (ap @ Y0 @ Y1) @ id)))))))))))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl280])). 56.27/7.81 thf(zip_derived_cl305, plain, 56.27/7.81 ( (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 ('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id)))))))))))))))))), 56.27/7.81 inference('triggered_bool_instantiation', [status(thm)], 56.27/7.81 [zip_derived_cl290])). 56.27/7.81 thf(zip_derived_cl577, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)) => 56.27/7.81 ('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])). 56.27/7.81 thf(zip_derived_cl578, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 ('#sk708' @ '#sk733') @ Y0 @ 56.27/7.81 (comp @ Y2 @ Y1)) => 56.27/7.81 ('#sk733' @ 56.27/7.81 (comp @ 56.27/7.81 ('#sk708' @ '#sk733') @ Y2) @ 56.27/7.81 (sub @ Y0 @ Y2) @ Y1)))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl577])). 56.27/7.81 thf(zip_derived_cl579, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 ((('#sk733' @ ('#sk708' @ '#sk733') @ 56.27/7.81 ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ Y1 @ Y0)) => ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ Y1) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ Y1) @ Y0))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl578])). 56.27/7.81 thf(zip_derived_cl580, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 ((('#sk733' @ ('#sk708' @ '#sk733') @ 56.27/7.81 ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ Y0 @ ('#sk967' @ '#sk733'))) => ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ Y0) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ Y0) @ 56.27/7.81 ('#sk967' @ '#sk733'))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl579])). 56.27/7.81 thf(zip_derived_cl581, plain, 56.27/7.81 ((~ ((('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) => 56.27/7.81 ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl580])). 56.27/7.81 thf(zip_derived_cl582, plain, 56.27/7.81 (( ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl581])). 56.27/7.81 thf(zip_derived_cl584, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl582])). 56.27/7.81 thf(zip_derived_cl584, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl582])). 56.27/7.81 thf(zip_derived_cl586, plain, 56.27/7.81 (( ('#form5466') 56.27/7.81 | ~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl588, plain, 56.27/7.81 ((~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl584, zip_derived_cl586])). 56.27/7.81 thf(zip_derived_cl590, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466'))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])). 56.27/7.81 thf(zip_derived_cl590, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466'))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])). 56.27/7.81 thf(zip_derived_cl593, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl146, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( ('#form108' @ X2) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl595, plain, 56.27/7.81 (( ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl590, zip_derived_cl593, zip_derived_cl146])). 56.27/7.81 thf(zip_derived_cl598, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ ('#sk3223' @ '#sk733') @ id) @ Y0) @ id)))))))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl595])). 56.27/7.81 thf(zip_derived_cl602, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ 56.27/7.81 id @ 56.27/7.81 (ap @ (sub @ ('#sk3223' @ '#sk733') @ id) @ 56.27/7.81 ('#sk3356' @ '#sk733')) @ 56.27/7.81 id))))) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl598])). 56.27/7.81 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 56.27/7.81 thf(zip_derived_cl607, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id))))) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('demod', [status(thm)], [zip_derived_cl602, zip_derived_cl17])). 56.27/7.81 thf(zip_derived_cl608, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl607])). 56.27/7.81 thf(zip_derived_cl13007, plain, 56.27/7.81 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl470, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (X2 @ id @ (lam @ ('#sk3410' @ X2 @ sh @ one)) @ id) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])). 56.27/7.81 thf(zip_derived_cl407, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( ('#form2686' @ X2) 56.27/7.81 | ~ (((X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 ('#sk1944' @ X2)) => (X2 @ ('#sk1549' @ X2) @ 56.27/7.81 ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl408, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (X2 @ (comp @ ('#sk1549' @ X2) @ ('#sk2144' @ X2)) @ 56.27/7.81 (sub @ ('#sk1760' @ X2) @ ('#sk2144' @ X2)) @ ('#sk1944' @ X2)) 56.27/7.81 | ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl407])). 56.27/7.81 thf(zip_derived_cl456, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((sub @ 56.27/7.81 ('#sk3410' @ X2 @ Y0 @ Y1) @ 56.27/7.81 Y2) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ Y0 @ Y2) @ 56.27/7.81 (sub @ Y1 @ Y2))))))))))))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl447])). 56.27/7.81 thf(zip_derived_cl468, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst]: 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ Y0) @ Y1) = 56.27/7.81 ('#sk3410' @ X2 @ (comp @ X4 @ Y1) @ 56.27/7.81 (sub @ Y0 @ Y1)))))))))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl456])). 56.27/7.81 thf(zip_derived_cl480, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term]: 56.27/7.81 ( (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ Y0) = 56.27/7.81 ('#sk3410' @ X2 @ (comp @ X4 @ Y0) @ (sub @ X6 @ Y0))))))) 56.27/7.81 | ~ ('#form2686' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl468])). 56.27/7.81 thf(zip_derived_cl492, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term, X8 : subst]: 56.27/7.81 ( (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ X8) = ('#sk3410' @ X2 @ 56.27/7.81 (comp @ X4 @ X8) @ (sub @ X6 @ X8)))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl480])). 56.27/7.81 thf(zip_derived_cl499, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : subst, X6 : term, X8 : subst]: 56.27/7.81 (((sub @ ('#sk3410' @ X2 @ X4 @ X6) @ X8) 56.27/7.81 = ('#sk3410' @ X2 @ (comp @ X4 @ X8) @ (sub @ X6 @ X8))) 56.27/7.81 | ('#form3615' @ X2) 56.27/7.81 | ~ (X2 @ (comp @ ('#sk708' @ X2) @ ('#sk1077' @ X2)) @ 56.27/7.81 (sub @ ('#sk839' @ X2) @ ('#sk1077' @ X2)) @ ('#sk967' @ X2)) 56.27/7.81 | ~ ('#form2686' @ X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], 56.27/7.81 [zip_derived_cl492])). 56.27/7.81 thf(zip_derived_cl445, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ ('#form3615' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 56.27/7.81 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ Y0) @ id)))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl446, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 ( (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 (sub @ X4 @ (push @ Y0 @ id)) @ id)))))) => 56.27/7.81 (X2 @ id @ (lam @ X4) @ id))) 56.27/7.81 | ~ ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl445])). 56.27/7.81 thf(zip_derived_cl458, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 (~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((X2 @ id @ Y0 @ id) => (X2 @ id @ 56.27/7.81 (sub @ X4 @ (push @ Y0 @ id)) @ id)))))) 56.27/7.81 | (X2 @ id @ (lam @ X4) @ id) 56.27/7.81 | ~ ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl446])). 56.27/7.81 thf(zip_derived_cl471, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 (~ (((X2 @ id @ ('#sk4068' @ X2 @ X4) @ id) => (X2 @ id @ 56.27/7.81 (sub @ X4 @ (push @ ('#sk4068' @ X2 @ X4) @ id)) @ id))) 56.27/7.81 | ~ ('#form3615' @ X2) 56.27/7.81 | (X2 @ id @ (lam @ X4) @ id))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl458])). 56.27/7.81 thf(zip_derived_cl482, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 ( (X2 @ id @ ('#sk4068' @ X2 @ X4) @ id) 56.27/7.81 | (X2 @ id @ (lam @ X4) @ id) 56.27/7.81 | ~ ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])). 56.27/7.81 thf(zip_derived_cl343, plain, 56.27/7.81 ( (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id)))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl333])). 56.27/7.81 thf(zip_derived_cl355, plain, 56.27/7.81 (![X2 : term]: 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ X2 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ X2 @ id) @ Y0) @ id))))))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl343])). 56.27/7.81 thf(zip_derived_cl367, plain, 56.27/7.81 (![X2 : term, X4 : term]: 56.27/7.81 ((('#sk733' @ id @ X2 @ id) => 56.27/7.81 ((('#sk733' @ id @ X4 @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ X2 @ id) @ X4) @ id)))))), 56.27/7.81 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl355])). 56.27/7.81 thf(zip_derived_cl378, plain, 56.27/7.81 (![X2 : term, X4 : term]: 56.27/7.81 (~ ('#sk733' @ id @ X2 @ id) 56.27/7.81 | ((('#sk733' @ id @ X4 @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ X2 @ id) @ X4) @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl367])). 56.27/7.81 thf(zip_derived_cl386, plain, 56.27/7.81 (![X2 : term, X4 : term]: 56.27/7.81 (~ ('#sk733' @ id @ X4 @ id) 56.27/7.81 | ('#sk733' @ id @ (ap @ (sub @ X2 @ id) @ X4) @ id) 56.27/7.81 | ~ ('#sk733' @ id @ X2 @ id))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl378])). 56.27/7.81 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 56.27/7.81 thf(zip_derived_cl510, plain, 56.27/7.81 (![X2 : term, X4 : term]: 56.27/7.81 (~ ('#sk733' @ id @ X4 @ id) 56.27/7.81 | ('#sk733' @ id @ (ap @ X2 @ X4) @ id) 56.27/7.81 | ~ ('#sk733' @ id @ X2 @ id))), 56.27/7.81 inference('demod', [status(thm)], [zip_derived_cl386, zip_derived_cl17])). 56.27/7.81 thf(zip_derived_cl483, plain, 56.27/7.81 (![X2 : subst > term > subst > $o, X4 : term]: 56.27/7.81 (~ (X2 @ id @ (sub @ X4 @ (push @ ('#sk4068' @ X2 @ X4) @ id)) @ id) 56.27/7.81 | (X2 @ id @ (lam @ X4) @ id) 56.27/7.81 | ~ ('#form3615' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])). 56.27/7.81 thf(zip_derived_cl409, plain, 56.27/7.81 (![X2 : subst > term > subst > $o]: 56.27/7.81 (~ (X2 @ ('#sk1549' @ X2) @ ('#sk1760' @ X2) @ 56.27/7.81 (comp @ ('#sk2144' @ X2) @ ('#sk1944' @ X2))) 56.27/7.81 | ('#form2686' @ X2))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl407])). 56.27/7.81 thf(zip_derived_cl608, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl607])). 56.27/7.81 thf(zip_derived_cl13007, plain, 56.27/7.81 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl13008, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ '#l_lift30976'))), 56.27/7.81 inference('lambda_lifting', [status(thm)], 56.27/7.81 [zip_derived_cl608, zip_derived_cl13007])). 56.27/7.81 thf(zip_derived_cl583, plain, 56.27/7.81 ((~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | (((((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) => 56.27/7.81 (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ 56.27/7.81 id))))))))))))))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl581])). 56.27/7.81 thf(zip_derived_cl585, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => ('#sk733' @ 56.27/7.81 Y0 @ Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl583])). 56.27/7.81 thf(zip_derived_cl586, plain, 56.27/7.81 (( ('#form5466') 56.27/7.81 | ~ (((!!) @ (^[Y0 : subst]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((!!) @ (^[Y2 : subst]: 56.27/7.81 (((!!) @ (^[Y3 : subst]: 56.27/7.81 ((('#sk733' @ 56.27/7.81 (comp @ Y0 @ Y3) @ 56.27/7.81 (sub @ Y1 @ Y3) @ 56.27/7.81 Y2) => 56.27/7.81 ('#sk733' @ Y0 @ 56.27/7.81 Y1 @ 56.27/7.81 (comp @ Y3 @ Y2)))))))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl589, plain, 56.27/7.81 ((~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | (((((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 56.27/7.81 (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl585, zip_derived_cl586])). 56.27/7.81 thf(zip_derived_cl592, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ ('#form5466'))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl589])). 56.27/7.81 thf(zip_derived_cl593, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 (~ ('#form108' @ X2) 56.27/7.81 | (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl146, plain, 56.27/7.81 (![X2 : term > $o]: 56.27/7.81 ( ('#form108' @ X2) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 (((X2 @ Y0) => 56.27/7.81 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl597, plain, 56.27/7.81 (( ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ (((!!) @ (^[Y0 : term]: 56.27/7.81 (((!!) @ (^[Y1 : term]: 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => 56.27/7.81 ((('#sk733' @ id @ Y1 @ id) => 56.27/7.81 ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))))), 56.27/7.81 inference('renaming', [status(thm)], 56.27/7.81 [zip_derived_cl592, zip_derived_cl593, zip_derived_cl146])). 56.27/7.81 thf(zip_derived_cl601, plain, 56.27/7.81 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.81 ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ Y0 @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ (sub @ ('#sk3223' @ '#sk733') @ id) @ Y0) @ id)))))))) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl597])). 56.27/7.81 thf(zip_derived_cl606, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ 56.27/7.81 id @ 56.27/7.81 (ap @ (sub @ ('#sk3223' @ '#sk733') @ id) @ 56.27/7.81 ('#sk3356' @ '#sk733')) @ 56.27/7.81 id))))) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))), 56.27/7.81 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl601])). 56.27/7.81 thf(zip_derived_cl17, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 56.27/7.81 inference('simplify nested equalities', [status(thm)], [zip_derived_cl12])). 56.27/7.81 thf(zip_derived_cl611, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) => 56.27/7.81 ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ 56.27/7.81 id @ (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id))))) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))), 56.27/7.81 inference('demod', [status(thm)], [zip_derived_cl606, zip_derived_cl17])). 56.27/7.81 thf(zip_derived_cl612, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl611])). 56.27/7.81 thf(zip_derived_cl13007, plain, 56.27/7.81 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl13009, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3223' @ '#sk733') @ id) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ '#l_lift30976'))), 56.27/7.81 inference('lambda_lifting', [status(thm)], 56.27/7.81 [zip_derived_cl612, zip_derived_cl13007])). 56.27/7.81 thf(zip_derived_cl609, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id))) 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl607])). 56.27/7.81 thf(zip_derived_cl614, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])). 56.27/7.81 thf(zip_derived_cl13007, plain, 56.27/7.81 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl13010, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) 56.27/7.81 | ('#form108' @ '#l_lift30976') 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lambda_lifting', [status(thm)], 56.27/7.81 [zip_derived_cl614, zip_derived_cl13007])). 56.27/7.81 thf(zip_derived_cl613, plain, 56.27/7.81 ((~ ((('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) => ('#sk733' @ id @ 56.27/7.81 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id))) 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl611])). 56.27/7.81 thf(zip_derived_cl616, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl613])). 56.27/7.81 thf(zip_derived_cl13007, plain, 56.27/7.81 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.81 define([status(thm)])). 56.27/7.81 thf(zip_derived_cl13012, plain, 56.27/7.81 (( ('#sk733' @ id @ ('#sk3356' @ '#sk733') @ id) 56.27/7.81 | ('#form108' @ '#l_lift30976') 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ~ ('#sk733' @ 56.27/7.81 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.81 ('#sk967' @ '#sk733')))), 56.27/7.81 inference('lambda_lifting', [status(thm)], 56.27/7.81 [zip_derived_cl616, zip_derived_cl13007])). 56.27/7.81 thf(zip_derived_cl615, plain, 56.27/7.81 ((~ ('#sk733' @ id @ 56.27/7.81 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id) 56.27/7.81 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.81 | ~ ('#form5466') 56.27/7.81 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.81 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.81 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])). 56.27/7.82 thf(zip_derived_cl13007, plain, 56.27/7.82 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.82 define([status(thm)])). 56.27/7.82 thf(zip_derived_cl13011, plain, 56.27/7.82 ((~ ('#sk733' @ id @ 56.27/7.82 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id) 56.27/7.82 | ('#form108' @ '#l_lift30976') 56.27/7.82 | ~ ('#form5466') 56.27/7.82 | ('#sk733' @ ('#sk708' @ '#sk733') @ ('#sk839' @ '#sk733') @ 56.27/7.82 (comp @ ('#sk1077' @ '#sk733') @ ('#sk967' @ '#sk733'))))), 56.27/7.82 inference('lambda_lifting', [status(thm)], 56.27/7.82 [zip_derived_cl615, zip_derived_cl13007])). 56.27/7.82 thf(zip_derived_cl316, plain, 56.27/7.82 ( (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : term]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 (((!!) @ (^[Y3 : subst]: 56.27/7.82 ((('#sk733' @ Y0 @ 56.27/7.82 Y1 @ 56.27/7.82 (comp @ Y3 @ Y2)) => 56.27/7.82 ('#sk733' @ 56.27/7.82 (comp @ Y0 @ Y3) @ 56.27/7.82 (sub @ Y1 @ Y3) @ Y2)))))))))))))))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl307])). 56.27/7.82 thf(zip_derived_cl323, plain, 56.27/7.82 (![X2 : subst]: 56.27/7.82 (((!!) @ (^[Y0 : term]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 ((('#sk733' @ X2 @ Y0 @ 56.27/7.82 (comp @ Y2 @ Y1)) => 56.27/7.82 ('#sk733' @ (comp @ X2 @ Y2) @ 56.27/7.82 (sub @ Y0 @ Y2) @ Y1))))))))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl316])). 56.27/7.82 thf(zip_derived_cl330, plain, 56.27/7.82 (![X2 : subst, X4 : term]: 56.27/7.82 (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 ((('#sk733' @ X2 @ X4 @ (comp @ Y1 @ Y0)) => 56.27/7.82 ('#sk733' @ (comp @ X2 @ Y1) @ 56.27/7.82 (sub @ X4 @ Y1) @ Y0)))))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl323])). 56.27/7.82 thf(zip_derived_cl340, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst]: 56.27/7.82 (((!!) @ (^[Y0 : subst]: 56.27/7.82 ((('#sk733' @ X2 @ X4 @ (comp @ Y0 @ X6)) => ('#sk733' @ 56.27/7.82 (comp @ X2 @ Y0) @ (sub @ X4 @ Y0) @ X6))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl330])). 56.27/7.82 thf(zip_derived_cl352, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst, X8 : subst]: 56.27/7.82 ((('#sk733' @ X2 @ X4 @ (comp @ X8 @ X6)) => ('#sk733' @ 56.27/7.82 (comp @ X2 @ X8) @ (sub @ X4 @ X8) @ X6)))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl340])). 56.27/7.82 thf(zip_derived_cl365, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst, X8 : subst]: 56.27/7.82 (~ ('#sk733' @ X2 @ X4 @ (comp @ X8 @ X6)) 56.27/7.82 | ('#sk733' @ (comp @ X2 @ X8) @ (sub @ X4 @ X8) @ X6))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl352])). 56.27/7.82 thf(zip_derived_cl586, plain, 56.27/7.82 (( ('#form5466') 56.27/7.82 | ~ (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : term]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 (((!!) @ (^[Y3 : subst]: 56.27/7.82 ((('#sk733' @ 56.27/7.82 (comp @ Y0 @ Y3) @ 56.27/7.82 (sub @ Y1 @ Y3) @ 56.27/7.82 Y2) => 56.27/7.82 ('#sk733' @ Y0 @ 56.27/7.82 Y1 @ 56.27/7.82 (comp @ Y3 @ Y2)))))))))))))))))), 56.27/7.82 define([status(thm)])). 56.27/7.82 thf(zip_derived_cl587, plain, 56.27/7.82 ((~ (((!!) @ (^[Y0 : term]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 ((('#sk733' @ 56.27/7.82 (comp @ 56.27/7.82 ('#sk1549' @ '#sk733') @ Y2) @ 56.27/7.82 (sub @ Y0 @ Y2) @ Y1) => 56.27/7.82 ('#sk733' @ 56.27/7.82 ('#sk1549' @ '#sk733') @ Y0 @ 56.27/7.82 (comp @ Y2 @ Y1))))))))))))) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl586])). 56.27/7.82 thf(zip_derived_cl591, plain, 56.27/7.82 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 ((('#sk733' @ 56.27/7.82 (comp @ ('#sk1549' @ '#sk733') @ Y1) @ 56.27/7.82 (sub @ ('#sk1760' @ '#sk733') @ Y1) @ 56.27/7.82 Y0) => ('#sk733' @ 56.27/7.82 ('#sk1549' @ '#sk733') @ 56.27/7.82 ('#sk1760' @ '#sk733') @ (comp @ Y1 @ Y0)))))))))) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl587])). 56.27/7.82 thf(zip_derived_cl596, plain, 56.27/7.82 ((~ (((!!) @ (^[Y0 : subst]: 56.27/7.82 ((('#sk733' @ (comp @ ('#sk1549' @ '#sk733') @ Y0) @ 56.27/7.82 (sub @ ('#sk1760' @ '#sk733') @ Y0) @ 56.27/7.82 ('#sk1944' @ '#sk733')) => ('#sk733' @ 56.27/7.82 ('#sk1549' @ '#sk733') @ ('#sk1760' @ '#sk733') @ 56.27/7.82 (comp @ Y0 @ ('#sk1944' @ '#sk733')))))))) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl591])). 56.27/7.82 thf(zip_derived_cl600, plain, 56.27/7.82 ((~ ((('#sk733' @ 56.27/7.82 (comp @ ('#sk1549' @ '#sk733') @ ('#sk2144' @ '#sk733')) @ 56.27/7.82 (sub @ ('#sk1760' @ '#sk733') @ ('#sk2144' @ '#sk733')) @ 56.27/7.82 ('#sk1944' @ '#sk733')) => ('#sk733' @ ('#sk1549' @ '#sk733') @ 56.27/7.82 ('#sk1760' @ '#sk733') @ 56.27/7.82 (comp @ ('#sk2144' @ '#sk733') @ ('#sk1944' @ '#sk733'))))) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl596])). 56.27/7.82 thf(zip_derived_cl604, plain, 56.27/7.82 (( ('#sk733' @ 56.27/7.82 (comp @ ('#sk1549' @ '#sk733') @ ('#sk2144' @ '#sk733')) @ 56.27/7.82 (sub @ ('#sk1760' @ '#sk733') @ ('#sk2144' @ '#sk733')) @ 56.27/7.82 ('#sk1944' @ '#sk733')) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 56.27/7.82 thf(zip_derived_cl617, plain, 56.27/7.82 ((~ ('#sk733' @ id @ 56.27/7.82 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id) 56.27/7.82 | ('#form108' @ (^[Y0 : term]: ('#sk733' @ id @ Y0 @ id))) 56.27/7.82 | ~ ('#form5466') 56.27/7.82 | ~ ('#sk733' @ 56.27/7.82 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.82 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.82 ('#sk967' @ '#sk733')))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl613])). 56.27/7.82 thf(zip_derived_cl13007, plain, 56.27/7.82 (![X1 : term]: (('#l_lift30976' @ X1) = ('#sk733' @ id @ X1 @ id))), 56.27/7.82 define([status(thm)])). 56.27/7.82 thf(zip_derived_cl13013, plain, 56.27/7.82 ((~ ('#sk733' @ id @ 56.27/7.82 (ap @ ('#sk3223' @ '#sk733') @ ('#sk3356' @ '#sk733')) @ id) 56.27/7.82 | ('#form108' @ '#l_lift30976') 56.27/7.82 | ~ ('#form5466') 56.27/7.82 | ~ ('#sk733' @ 56.27/7.82 (comp @ ('#sk708' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.82 (sub @ ('#sk839' @ '#sk733') @ ('#sk1077' @ '#sk733')) @ 56.27/7.82 ('#sk967' @ '#sk733')))), 56.27/7.82 inference('lambda_lifting', [status(thm)], 56.27/7.82 [zip_derived_cl617, zip_derived_cl13007])). 56.27/7.82 thf(zip_derived_cl605, plain, 56.27/7.82 ((~ ('#sk733' @ ('#sk1549' @ '#sk733') @ ('#sk1760' @ '#sk733') @ 56.27/7.82 (comp @ ('#sk2144' @ '#sk733') @ ('#sk1944' @ '#sk733'))) 56.27/7.82 | ('#form5466'))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl600])). 56.27/7.82 thf(zip_derived_cl324, plain, 56.27/7.82 ( (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : term]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 (((!!) @ (^[Y3 : subst]: 56.27/7.82 ((('#sk733' @ 56.27/7.82 (comp @ Y0 @ Y3) @ 56.27/7.82 (sub @ Y1 @ Y3) @ 56.27/7.82 Y2) => ('#sk733' @ 56.27/7.82 Y0 @ Y1 @ 56.27/7.82 (comp @ Y3 @ Y2))))))))))))))))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl317])). 56.27/7.82 thf(zip_derived_cl331, plain, 56.27/7.82 (![X2 : subst]: 56.27/7.82 (((!!) @ (^[Y0 : term]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 (((!!) @ (^[Y2 : subst]: 56.27/7.82 ((('#sk733' @ (comp @ X2 @ Y2) @ 56.27/7.82 (sub @ Y0 @ Y2) @ Y1) => 56.27/7.82 ('#sk733' @ X2 @ Y0 @ 56.27/7.82 (comp @ Y2 @ Y1)))))))))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl324])). 56.27/7.82 thf(zip_derived_cl341, plain, 56.27/7.82 (![X2 : subst, X4 : term]: 56.27/7.82 (((!!) @ (^[Y0 : subst]: 56.27/7.82 (((!!) @ (^[Y1 : subst]: 56.27/7.82 ((('#sk733' @ (comp @ X2 @ Y1) @ 56.27/7.82 (sub @ X4 @ Y1) @ Y0) => ('#sk733' @ X2 @ 56.27/7.82 X4 @ (comp @ Y1 @ Y0))))))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl331])). 56.27/7.82 thf(zip_derived_cl353, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst]: 56.27/7.82 (((!!) @ (^[Y0 : subst]: 56.27/7.82 ((('#sk733' @ (comp @ X2 @ Y0) @ (sub @ X4 @ Y0) @ X6) => 56.27/7.82 ('#sk733' @ X2 @ X4 @ (comp @ Y0 @ X6)))))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl341])). 56.27/7.82 thf(zip_derived_cl366, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst, X8 : subst]: 56.27/7.82 ((('#sk733' @ (comp @ X2 @ X8) @ (sub @ X4 @ X8) @ X6) => 56.27/7.82 ('#sk733' @ X2 @ X4 @ (comp @ X8 @ X6))))), 56.27/7.82 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl353])). 56.27/7.82 thf(zip_derived_cl377, plain, 56.27/7.82 (![X2 : subst, X4 : term, X6 : subst, X8 : subst]: 56.27/7.82 (~ ('#sk733' @ (comp @ X2 @ X8) @ (sub @ X4 @ X8) @ X6) 56.27/7.82 | ('#sk733' @ X2 @ X4 @ (comp @ X8 @ X6)))), 56.27/7.82 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl366])). 56.27/7.82 thf(zip_derived_cl13021, plain, ($false), 56.27/7.82 inference('eprover', [status(thm)], 56.27/7.82 [zip_derived_cl369, zip_derived_cl271, zip_derived_cl501, 56.27/7.82 zip_derived_cl431, zip_derived_cl17, zip_derived_cl273, 56.27/7.82 zip_derived_cl308, zip_derived_cl52, zip_derived_cl491, 56.27/7.82 zip_derived_cl432, zip_derived_cl493, zip_derived_cl31, 56.27/7.82 zip_derived_cl467, zip_derived_cl498, zip_derived_cl309, 56.27/7.82 zip_derived_cl13007, zip_derived_cl470, zip_derived_cl408, 56.27/7.82 zip_derived_cl499, zip_derived_cl482, zip_derived_cl510, 56.27/7.82 zip_derived_cl483, zip_derived_cl409, zip_derived_cl13008, 56.27/7.82 zip_derived_cl13009, zip_derived_cl13010, 56.27/7.82 zip_derived_cl13012, zip_derived_cl13011, zip_derived_cl365, 56.27/7.82 zip_derived_cl604, zip_derived_cl13013, zip_derived_cl605, 56.27/7.82 zip_derived_cl377])). 56.27/7.82 56.27/7.82 % SZS output end Refutation 56.27/7.82 56.27/7.82 56.27/7.82 % Terminating... 56.70/7.94 % Runner terminated. 56.70/7.94 % Zipperpin 1.5 exiting 56.70/7.94 EOF