0.00/0.03 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.ZJ55ZNMUig true 0.13/0.36 % Computer : n011.cluster.edu 0.13/0.36 % Model : x86_64 x86_64 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.36 % Memory : 8046.5625MB 0.13/0.36 % OS : Linux 6.8.0-71-generic 0.13/0.36 % CPULimit : 1440 0.13/0.36 % WCLimit : 180 0.13/0.36 % DateTime : Mon Jul 27 14:59:06 UTC 2026 0.13/0.36 % CPUTime : 0.13/0.36 % Running portfolio for 1440 s 0.13/0.36 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.37 % Python version: Python 3.12.3 0.13/0.37 % Running in HO mode 0.53/0.70 % Total configuration time : 828 0.53/0.70 % Estimated wc time : 1656 0.53/0.70 % Estimated cpu time (8 cpus) : 207.0 0.53/0.79 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.53/0.82 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.53/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.53/0.85 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.53/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.53/0.85 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.53/0.85 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.53/0.89 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.90 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 214.61/30.81 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 276.74/40.89 % /export/starexec/sandbox2/solver/bin/lams/15_old_s4.sh running for 30s 414.24/60.98 % /export/starexec/sandbox2/solver/bin/lams/15_lifting3.sh running for 30s 422.77/70.91 % /export/starexec/sandbox2/solver/bin/lams/33_shallow_sine.sh running for 66s 422.77/70.94 % /export/starexec/sandbox2/solver/bin/lams/40_e_lift.sh running for 80s 554.95/80.88 % /export/starexec/sandbox2/solver/bin/lams/15_lifting1.sh running for 30s 509.04/80.93 % /export/starexec/sandbox2/solver/bin/lams/8_new_cnf.sh running for 16s 632.32/86.89 % /export/starexec/sandbox2/solver/bin/lams/10_e_short2.sh running for 20s 664.54/90.96 % /export/starexec/sandbox2/solver/bin/lams/8_add_var_l_av.sh running for 16s 534.22/91.02 % /export/starexec/sandbox2/solver/bin/lams/8_new_sh_or.sh running for 16s 534.22/91.04 % /export/starexec/sandbox2/solver/bin/lams/30_old_zip1.sh running for 36s 749.59/96.87 % /export/starexec/sandbox2/solver/bin/lams/10_shallow_lift.sh running for 30s 789.92/106.92 % /export/starexec/sandbox2/solver/bin/lams/15_lcnf_noform.sh running for 30s 775.32/107.02 % /export/starexec/sandbox2/solver/bin/lams/8_sh.eqenc2.sh running for 10s 775.32/107.07 % /export/starexec/sandbox2/solver/bin/lams/8_cmb.lcnf4.sh running for 10s 840.81/110.93 % /export/starexec/sandbox2/solver/bin/lams/8_new_l_av.sh running for 24s 853.92/117.06 % /export/starexec/sandbox2/solver/bin/lams/10_forms1.sh running for 20s 835.79/117.11 % /export/starexec/sandbox2/solver/bin/lams/10_forms4.sh running for 20s 931.58/126.93 % /export/starexec/sandbox2/solver/bin/lams/15_ch_av2.sh running for 26s 932.30/127.10 % /export/starexec/sandbox2/solver/bin/lams/15_sine_deep.sh running for 44s 992.73/134.80 % /export/starexec/sandbox2/solver/bin/lams/10_shallow_sine.sh running for 30s 1009.58/136.96 % /export/starexec/sandbox2/solver/bin/lams/20_new_c.s3.sh running for 40s 941.80/137.02 % /export/starexec/sandbox2/solver/bin/lams/10_forms2.sh running for 20s 987.31/137.13 % /export/starexec/sandbox2/solver/bin/lams/8_sh.or.sh running for 24s 987.31/137.17 % /export/starexec/sandbox2/solver/bin/lams/15_combs_pe.sh running for 20s 1143.86/151.04 % /export/starexec/sandbox2/solver/bin/lams/15_b.split.li.sh running for 44s 1193.89/152.98 % /export/starexec/sandbox2/solver/bin/lams/18_sh1.sh running for 36s 1224.59/157.05 % /export/starexec/sandbox2/solver/bin/lams/8_no_ord.sh running for 10s 1187.51/157.21 % /export/starexec/sandbox2/solver/bin/lams/10_forms3.sh running for 20s 1229.20/157.62 % Solved by lams/10_forms3.sh. 1229.20/157.62 % done 53 iterations in 0.288s 1229.20/157.62 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 1229.20/157.62 % SZS output start Refutation 1229.20/157.62 thf(subst_type, type, subst: $tType). 1229.20/157.62 thf(term_type, type, term: $tType). 1229.20/157.62 thf(lam_type, type, lam: term > term). 1229.20/157.62 thf(push_type, type, push: term > subst > subst). 1229.20/157.62 thf(hoasap_type, type, hoasap: subst > term > subst > term > term). 1229.20/157.62 thf(one_type, type, one: term). 1229.20/157.62 thf(id_type, type, id: subst). 1229.20/157.62 thf(comp_type, type, comp: subst > subst > subst). 1229.20/157.62 thf(induction2_type, type, induction2: $o). 1229.20/157.62 thf(sh_type, type, sh: subst). 1229.20/157.62 thf('#sk224_type', type, '#sk224': subst > term > subst > $o). 1229.20/157.62 thf(sub_type, type, sub: term > subst > term). 1229.20/157.62 thf(hoasinduction_type, type, hoasinduction: $o). 1229.20/157.62 thf(ap_type, type, ap: term > term > term). 1229.20/157.62 thf(hoasinduction_lem1_type, type, hoasinduction_lem1: $o). 1229.20/157.62 thf(var_type, type, var: term > $o). 1229.20/157.62 thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term). 1229.20/157.62 thf('#form111_type', type, '#form111': (term > $o) > $o). 1229.20/157.62 thf(hoasinduction_lem3_type, type, hoasinduction_lem3: $o). 1229.20/157.62 thf(hoasinduction_lem2_type, type, hoasinduction_lem2: $o). 1229.20/157.62 thf('#sk71_type', type, '#sk71': (term > $o) > term). 1229.20/157.62 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o). 1229.20/157.62 thf('#form128_type', type, '#form128': (term > $o) > $o). 1229.20/157.62 thf('#form530_type', type, '#form530': $o). 1229.20/157.62 thf(hoasinduction_lthm_type, type, hoasinduction_lthm: $o). 1229.20/157.62 thf(hoasinduction_lthm, axiom, hoasinduction_lthm = 1229.20/157.62 (( induction2 ) => 1229.20/157.62 ( ( hoasinduction_lem1 ) => 1229.20/157.62 ( ( hoasinduction_lem2 ) => 1229.20/157.62 ( ( hoasinduction_lem3 ) => ( hoasinduction ) ) ) ))). 1229.20/157.62 thf('0', plain, 1229.20/157.62 (( hoasinduction_lthm ) = 1229.20/157.62 ( ( induction2 ) => 1229.20/157.62 ( ( hoasinduction_lem1 ) => 1229.20/157.62 ( ( hoasinduction_lem2 ) => 1229.20/157.62 ( ( hoasinduction_lem3 ) => ( hoasinduction ) ) ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasinduction, axiom, hoasinduction = 1229.20/157.62 (![P:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 1229.20/157.62 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 1229.20/157.62 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 1229.20/157.62 ( ( ![A:term]: ( ( hoasvar @ id @ A @ id ) => ( P @ id @ A @ id ) ) ) => 1229.20/157.62 ( ( ![A:term,B:term]: 1229.20/157.62 ( ( P @ id @ A @ id ) => 1229.20/157.62 ( ( P @ id @ B @ id ) => 1229.20/157.62 ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ) => 1229.20/157.62 ( ( ![F:( subst > term > term )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst]: 1229.20/157.62 ( ( sub @ ( F @ M @ A ) @ N ) = 1229.20/157.62 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 1229.20/157.62 ( ( ![A:term]: 1229.20/157.62 ( ( P @ id @ A @ id ) => 1229.20/157.62 ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 1229.20/157.62 ( P @ 1229.20/157.62 id @ 1229.20/157.62 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ 1229.20/157.62 id ) ) ) ) => 1229.20/157.62 ( ![A:term]: ( P @ id @ A @ id ) ) ) ) ) ) ))). 1229.20/157.62 thf('1', plain, 1229.20/157.62 (( hoasinduction ) = 1229.20/157.62 ( ![X4:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 1229.20/157.62 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 1229.20/157.62 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 1229.20/157.62 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 1229.20/157.62 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 1229.20/157.62 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 1229.20/157.62 ( ( ![X22:term]: 1229.20/157.62 ( ( hoasvar @ id @ X22 @ id ) => ( X4 @ id @ X22 @ id ) ) ) => 1229.20/157.62 ( ( ![X24:term,X26:term]: 1229.20/157.62 ( ( X4 @ id @ X24 @ id ) => 1229.20/157.62 ( ( X4 @ id @ X26 @ id ) => 1229.20/157.62 ( X4 @ id @ ( hoasap @ id @ X24 @ id @ X26 ) @ id ) ) ) ) => 1229.20/157.62 ( ( ![X28:( subst > term > term )]: 1229.20/157.62 ( ( ![X30:subst,X32:term,X34:subst]: 1229.20/157.62 ( ( sub @ ( X28 @ X30 @ X32 ) @ X34 ) = 1229.20/157.62 ( X28 @ ( comp @ X30 @ X34 ) @ ( sub @ X32 @ X34 ) ) ) ) => 1229.20/157.62 ( ( ![X36:term]: 1229.20/157.62 ( ( X4 @ id @ X36 @ id ) => 1229.20/157.62 ( X4 @ id @ ( X28 @ id @ X36 ) @ id ) ) ) => 1229.20/157.62 ( X4 @ 1229.20/157.62 id @ 1229.20/157.62 ( hoaslam @ 1229.20/157.62 id @ 1229.20/157.62 ( ^[V_1:subst,V_2:term]: ( X28 @ V_1 @ V_2 ) ) ) @ 1229.20/157.62 id ) ) ) ) => 1229.20/157.62 ( ![X38:term]: ( X4 @ id @ X38 @ id ) ) ) ) ) ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasinduction_lem3, axiom, hoasinduction_lem3 = 1229.20/157.62 (![P:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 1229.20/157.62 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 1229.20/157.62 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 1229.20/157.62 ( ( ![F:( subst > term > term )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst]: 1229.20/157.62 ( ( sub @ ( F @ M @ A ) @ N ) = 1229.20/157.62 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 1229.20/157.62 ( ( ![A:term]: 1229.20/157.62 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 1229.20/157.62 ( P @ 1229.20/157.62 id @ 1229.20/157.62 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ id ) ) ) ) => 1229.20/157.62 ( ![A:term]: 1229.20/157.62 ( ( ![B:term]: 1229.20/157.62 ( ( P @ id @ B @ id ) => 1229.20/157.62 ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) ) ) => 1229.20/157.62 ( P @ id @ ( lam @ A ) @ id ) ) ) ) ) ))). 1229.20/157.62 thf('2', plain, 1229.20/157.62 (( hoasinduction_lem3 ) = 1229.20/157.62 ( ![X4:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 1229.20/157.62 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 1229.20/157.62 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 1229.20/157.62 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 1229.20/157.62 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 1229.20/157.62 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 1229.20/157.62 ( ( ![X22:( subst > term > term )]: 1229.20/157.62 ( ( ![X24:subst,X26:term,X28:subst]: 1229.20/157.62 ( ( sub @ ( X22 @ X24 @ X26 ) @ X28 ) = 1229.20/157.62 ( X22 @ ( comp @ X24 @ X28 ) @ ( sub @ X26 @ X28 ) ) ) ) => 1229.20/157.62 ( ( ![X30:term]: 1229.20/157.62 ( ( X4 @ id @ X30 @ id ) => 1229.20/157.62 ( X4 @ id @ ( X22 @ id @ X30 ) @ id ) ) ) => 1229.20/157.62 ( X4 @ 1229.20/157.62 id @ 1229.20/157.62 ( hoaslam @ 1229.20/157.62 id @ ( ^[V_1:subst,V_2:term]: ( X22 @ V_1 @ V_2 ) ) ) @ 1229.20/157.62 id ) ) ) ) => 1229.20/157.62 ( ![X32:term]: 1229.20/157.62 ( ( ![X34:term]: 1229.20/157.62 ( ( X4 @ id @ X34 @ id ) => 1229.20/157.62 ( X4 @ id @ ( sub @ X32 @ ( push @ X34 @ id ) ) @ id ) ) ) => 1229.20/157.62 ( X4 @ id @ ( lam @ X32 ) @ id ) ) ) ) ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasinduction_lem2, axiom, hoasinduction_lem2 = 1229.20/157.62 (![P:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 1229.20/157.62 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 1229.20/157.62 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 1229.20/157.62 ( ( ![A:term,B:term]: 1229.20/157.62 ( ( P @ id @ A @ id ) => 1229.20/157.62 ( ( P @ id @ B @ id ) => 1229.20/157.62 ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ) => 1229.20/157.62 ( ![A:term,B:term]: 1229.20/157.62 ( ( P @ id @ A @ id ) => 1229.20/157.62 ( ( P @ id @ B @ id ) => ( P @ id @ ( ap @ A @ B ) @ id ) ) ) ) ) ) ))). 1229.20/157.62 thf('3', plain, 1229.20/157.62 (( hoasinduction_lem2 ) = 1229.20/157.62 ( ![X4:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 1229.20/157.62 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 1229.20/157.62 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 1229.20/157.62 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 1229.20/157.62 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 1229.20/157.62 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 1229.20/157.62 ( ( ![X22:term,X24:term]: 1229.20/157.62 ( ( X4 @ id @ X22 @ id ) => 1229.20/157.62 ( ( X4 @ id @ X24 @ id ) => 1229.20/157.62 ( X4 @ id @ ( hoasap @ id @ X22 @ id @ X24 ) @ id ) ) ) ) => 1229.20/157.62 ( ![X26:term,X28:term]: 1229.20/157.62 ( ( X4 @ id @ X26 @ id ) => 1229.20/157.62 ( ( X4 @ id @ X28 @ id ) => 1229.20/157.62 ( X4 @ id @ ( ap @ X26 @ X28 ) @ id ) ) ) ) ) ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasinduction_lem1, axiom, hoasinduction_lem1 = 1229.20/157.62 (![P:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 1229.20/157.62 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 1229.20/157.62 ( ( ![M:subst,A:term,N:subst,K:subst]: 1229.20/157.62 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 1229.20/157.62 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 1229.20/157.62 ( ( ![A:term]: ( ( hoasvar @ id @ A @ id ) => ( P @ id @ A @ id ) ) ) => 1229.20/157.62 ( ![A:term]: ( ( var @ A ) => ( P @ id @ A @ id ) ) ) ) ) ))). 1229.20/157.62 thf('4', plain, 1229.20/157.62 (( hoasinduction_lem1 ) = 1229.20/157.62 ( ![X4:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 1229.20/157.62 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 1229.20/157.62 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 1229.20/157.62 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 1229.20/157.62 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 1229.20/157.62 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 1229.20/157.62 ( ( ![X22:term]: 1229.20/157.62 ( ( hoasvar @ id @ X22 @ id ) => ( X4 @ id @ X22 @ id ) ) ) => 1229.20/157.62 ( ![X24:term]: ( ( var @ X24 ) => ( X4 @ id @ X24 @ id ) ) ) ) ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasvar, axiom,(( hoasvar ) = 1229.20/157.62 (^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) )))). 1229.20/157.62 thf('5', plain, 1229.20/157.62 (( hoasvar ) = ( ^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) ) )), 1229.20/157.62 inference('simplify_rw_rule', [status(thm)], [hoasvar])). 1229.20/157.62 thf('6', plain, 1229.20/157.62 (( hoasvar ) = 1229.20/157.62 ( ^[V_1:subst,V_2:term,V_3:subst]: ( var @ ( sub @ V_2 @ V_3 ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoaslam, axiom,(( hoaslam ) = 1229.20/157.62 (^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) )))). 1229.20/157.62 thf('7', plain, 1229.20/157.62 (( hoaslam ) = 1229.20/157.62 ( ^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) ) )), 1229.20/157.62 inference('simplify_rw_rule', [status(thm)], [hoaslam])). 1229.20/157.62 thf('8', plain, 1229.20/157.62 (( hoaslam ) = 1229.20/157.62 ( ^[V_1:subst,V_2:( subst > term > term )]: ( lam @ ( V_2 @ sh @ one ) ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(hoasap, axiom,(( hoasap ) = 1229.20/157.62 (^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B )))). 1229.20/157.62 thf('9', plain, 1229.20/157.62 (( hoasap ) = 1229.20/157.62 ( ^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B ) )), 1229.20/157.62 inference('simplify_rw_rule', [status(thm)], [hoasap])). 1229.20/157.62 thf('10', plain, 1229.20/157.62 (( hoasap ) = 1229.20/157.62 ( ^[V_1:subst,V_2:term,V_3:subst,V_4:term]: 1229.20/157.62 ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) )), 1229.20/157.62 define([status(thm)])). 1229.20/157.62 thf(induction2, axiom, induction2 = 1229.20/157.62 (![P:( term > $o )]: 1229.20/157.62 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 1229.20/157.62 ( ( ![A:term,B:term]: 1229.20/157.62 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 1229.20/157.62 ( ( ![A:term]: 1229.20/157.62 ( ( ![B:term]: 1229.20/157.62 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 1229.20/157.62 ( P @ ( lam @ A ) ) ) ) => 1229.20/157.62 ( ![A:term]: ( P @ A ) ) ) ) ))). 1229.20/157.62 thf('11', plain, 1229.20/157.62 (( induction2 ) = 1229.20/157.62 ( ![X4:( term > $o )]: 1229.20/157.62 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 1229.20/157.62 ( ( ![X8:term,X10:term]: 1229.20/157.62 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 1229.20/157.62 ( ( ![X12:term]: 1229.20/157.62 ( ( ![X14:term]: 1229.20/157.62 ( ( X4 @ X14 ) => 1229.20/157.62 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 1229.20/157.62 ( X4 @ ( lam @ X12 ) ) ) ) => 1229.20/157.62 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) )), 1229.20/157.62 define([status(thm)])).thf(thm, conjecture, (hoasinduction_lthm)). 1229.20/157.62 thf(zf_stmt_0, conjecture, 1229.20/157.62 (( ![X4:( term > $o )]: 1229.20/157.62 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 1229.20/157.62 ( ( ![X8:term,X10:term]: 1229.20/157.62 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 1229.20/157.62 ( ( ![X12:term]: 1229.20/157.62 ( ( ![X14:term]: 1229.20/157.62 ( ( X4 @ X14 ) => 1229.20/157.62 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 1229.20/157.62 ( X4 @ ( lam @ X12 ) ) ) ) => 1229.20/157.62 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X18:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X20:subst,X22:term,X24:subst,X26:subst]: 1229.20/157.62 ( ( X18 @ X20 @ X22 @ ( comp @ X26 @ X24 ) ) => 1229.20/157.62 ( X18 @ ( comp @ X20 @ X26 ) @ ( sub @ X22 @ X26 ) @ X24 ) ) ) => 1229.20/157.62 ( ( ![X28:subst,X30:term,X32:subst,X34:subst]: 1229.20/157.62 ( ( X18 @ ( comp @ X28 @ X34 ) @ ( sub @ X30 @ X34 ) @ X32 ) => 1229.20/157.62 ( X18 @ X28 @ X30 @ ( comp @ X34 @ X32 ) ) ) ) => 1229.20/157.62 ( ( ![X36:term]: 1229.20/157.62 ( ( var @ ( sub @ X36 @ id ) ) => ( X18 @ id @ X36 @ id ) ) ) => 1229.20/157.62 ( ![X38:term]: ( ( var @ X38 ) => ( X18 @ id @ X38 @ id ) ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X40:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X42:subst,X44:term,X46:subst,X48:subst]: 1229.20/157.62 ( ( X40 @ X42 @ X44 @ ( comp @ X48 @ X46 ) ) => 1229.20/157.62 ( X40 @ ( comp @ X42 @ X48 ) @ ( sub @ X44 @ X48 ) @ X46 ) ) ) => 1229.20/157.62 ( ( ![X50:subst,X52:term,X54:subst,X56:subst]: 1229.20/157.62 ( ( X40 @ ( comp @ X50 @ X56 ) @ ( sub @ X52 @ X56 ) @ X54 ) => 1229.20/157.62 ( X40 @ X50 @ X52 @ ( comp @ X56 @ X54 ) ) ) ) => 1229.20/157.62 ( ( ![X58:term,X60:term]: 1229.20/157.62 ( ( X40 @ id @ X58 @ id ) => 1229.20/157.62 ( ( X40 @ id @ X60 @ id ) => 1229.20/157.62 ( X40 @ id @ ( ap @ ( sub @ X58 @ id ) @ X60 ) @ id ) ) ) ) => 1229.20/157.62 ( ![X62:term,X64:term]: 1229.20/157.62 ( ( X40 @ id @ X62 @ id ) => 1229.20/157.62 ( ( X40 @ id @ X64 @ id ) => 1229.20/157.62 ( X40 @ id @ ( ap @ X62 @ X64 ) @ id ) ) ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X66:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X68:subst,X70:term,X72:subst,X74:subst]: 1229.20/157.62 ( ( X66 @ X68 @ X70 @ ( comp @ X74 @ X72 ) ) => 1229.20/157.62 ( X66 @ ( comp @ X68 @ X74 ) @ ( sub @ X70 @ X74 ) @ X72 ) ) ) => 1229.20/157.62 ( ( ![X76:subst,X78:term,X80:subst,X82:subst]: 1229.20/157.62 ( ( X66 @ ( comp @ X76 @ X82 ) @ ( sub @ X78 @ X82 ) @ X80 ) => 1229.20/157.62 ( X66 @ X76 @ X78 @ ( comp @ X82 @ X80 ) ) ) ) => 1229.20/157.62 ( ( ![X84:( subst > term > term )]: 1229.20/157.62 ( ( ![X86:subst,X88:term,X90:subst]: 1229.20/157.62 ( ( sub @ ( X84 @ X86 @ X88 ) @ X90 ) = 1229.20/157.62 ( X84 @ ( comp @ X86 @ X90 ) @ ( sub @ X88 @ X90 ) ) ) ) => 1229.20/157.62 ( ( ![X92:term]: 1229.20/157.62 ( ( X66 @ id @ X92 @ id ) => 1229.20/157.62 ( X66 @ id @ ( X84 @ id @ X92 ) @ id ) ) ) => 1229.20/157.62 ( X66 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) ) ) ) => 1229.20/157.62 ( ![X94:term]: 1229.20/157.62 ( ( ![X96:term]: 1229.20/157.62 ( ( X66 @ id @ X96 @ id ) => 1229.20/157.62 ( X66 @ 1229.20/157.62 id @ ( sub @ X94 @ ( push @ X96 @ id ) ) @ id ) ) ) => 1229.20/157.62 ( X66 @ id @ ( lam @ X94 ) @ id ) ) ) ) ) ) ) => 1229.20/157.62 ( ![X98:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X100:subst,X102:term,X104:subst,X106:subst]: 1229.20/157.62 ( ( X98 @ X100 @ X102 @ ( comp @ X106 @ X104 ) ) => 1229.20/157.62 ( X98 @ 1229.20/157.62 ( comp @ X100 @ X106 ) @ ( sub @ X102 @ X106 ) @ X104 ) ) ) => 1229.20/157.62 ( ( ![X108:subst,X110:term,X112:subst,X114:subst]: 1229.20/157.62 ( ( X98 @ 1229.20/157.62 ( comp @ X108 @ X114 ) @ ( sub @ X110 @ X114 ) @ X112 ) => 1229.20/157.62 ( X98 @ X108 @ X110 @ ( comp @ X114 @ X112 ) ) ) ) => 1229.20/157.62 ( ( ![X116:term]: 1229.20/157.62 ( ( var @ ( sub @ X116 @ id ) ) => 1229.20/157.62 ( X98 @ id @ X116 @ id ) ) ) => 1229.20/157.62 ( ( ![X118:term,X120:term]: 1229.20/157.62 ( ( X98 @ id @ X118 @ id ) => 1229.20/157.62 ( ( X98 @ id @ X120 @ id ) => 1229.20/157.62 ( X98 @ 1229.20/157.62 id @ ( ap @ ( sub @ X118 @ id ) @ X120 ) @ id ) ) ) ) => 1229.20/157.62 ( ( ![X122:( subst > term > term )]: 1229.20/157.62 ( ( ![X124:subst,X126:term,X128:subst]: 1229.20/157.62 ( ( sub @ ( X122 @ X124 @ X126 ) @ X128 ) = 1229.20/157.62 ( X122 @ 1229.20/157.62 ( comp @ X124 @ X128 ) @ ( sub @ X126 @ X128 ) ) ) ) => 1229.20/157.62 ( ( ![X130:term]: 1229.20/157.62 ( ( X98 @ id @ X130 @ id ) => 1229.20/157.62 ( X98 @ id @ ( X122 @ id @ X130 ) @ id ) ) ) => 1229.20/157.62 ( X98 @ id @ ( lam @ ( X122 @ sh @ one ) ) @ id ) ) ) ) => 1229.20/157.62 ( ![X132:term]: ( X98 @ id @ X132 @ id ) ) ) ) ) ) ) ) ) ) ))). 1229.20/157.62 thf(zf_stmt_1, negated_conjecture, 1229.20/157.62 (~( ( ![X4:( term > $o )]: 1229.20/157.62 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 1229.20/157.62 ( ( ![X8:term,X10:term]: 1229.20/157.62 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 1229.20/157.62 ( ( ![X12:term]: 1229.20/157.62 ( ( ![X14:term]: 1229.20/157.62 ( ( X4 @ X14 ) => 1229.20/157.62 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 1229.20/157.62 ( X4 @ ( lam @ X12 ) ) ) ) => 1229.20/157.62 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X18:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X20:subst,X22:term,X24:subst,X26:subst]: 1229.20/157.62 ( ( X18 @ X20 @ X22 @ ( comp @ X26 @ X24 ) ) => 1229.20/157.62 ( X18 @ ( comp @ X20 @ X26 ) @ ( sub @ X22 @ X26 ) @ X24 ) ) ) => 1229.20/157.62 ( ( ![X28:subst,X30:term,X32:subst,X34:subst]: 1229.20/157.62 ( ( X18 @ ( comp @ X28 @ X34 ) @ ( sub @ X30 @ X34 ) @ X32 ) => 1229.20/157.62 ( X18 @ X28 @ X30 @ ( comp @ X34 @ X32 ) ) ) ) => 1229.20/157.62 ( ( ![X36:term]: 1229.20/157.62 ( ( var @ ( sub @ X36 @ id ) ) => ( X18 @ id @ X36 @ id ) ) ) => 1229.20/157.62 ( ![X38:term]: ( ( var @ X38 ) => ( X18 @ id @ X38 @ id ) ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X40:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X42:subst,X44:term,X46:subst,X48:subst]: 1229.20/157.62 ( ( X40 @ X42 @ X44 @ ( comp @ X48 @ X46 ) ) => 1229.20/157.62 ( X40 @ ( comp @ X42 @ X48 ) @ ( sub @ X44 @ X48 ) @ X46 ) ) ) => 1229.20/157.62 ( ( ![X50:subst,X52:term,X54:subst,X56:subst]: 1229.20/157.62 ( ( X40 @ ( comp @ X50 @ X56 ) @ ( sub @ X52 @ X56 ) @ X54 ) => 1229.20/157.62 ( X40 @ X50 @ X52 @ ( comp @ X56 @ X54 ) ) ) ) => 1229.20/157.62 ( ( ![X58:term,X60:term]: 1229.20/157.62 ( ( X40 @ id @ X58 @ id ) => 1229.20/157.62 ( ( X40 @ id @ X60 @ id ) => 1229.20/157.62 ( X40 @ id @ ( ap @ ( sub @ X58 @ id ) @ X60 ) @ id ) ) ) ) => 1229.20/157.62 ( ![X62:term,X64:term]: 1229.20/157.62 ( ( X40 @ id @ X62 @ id ) => 1229.20/157.62 ( ( X40 @ id @ X64 @ id ) => 1229.20/157.62 ( X40 @ id @ ( ap @ X62 @ X64 ) @ id ) ) ) ) ) ) ) ) => 1229.20/157.62 ( ( ![X66:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X68:subst,X70:term,X72:subst,X74:subst]: 1229.20/157.62 ( ( X66 @ X68 @ X70 @ ( comp @ X74 @ X72 ) ) => 1229.20/157.62 ( X66 @ ( comp @ X68 @ X74 ) @ ( sub @ X70 @ X74 ) @ X72 ) ) ) => 1229.20/157.62 ( ( ![X76:subst,X78:term,X80:subst,X82:subst]: 1229.20/157.62 ( ( X66 @ 1229.20/157.62 ( comp @ X76 @ X82 ) @ ( sub @ X78 @ X82 ) @ X80 ) => 1229.20/157.62 ( X66 @ X76 @ X78 @ ( comp @ X82 @ X80 ) ) ) ) => 1229.20/157.62 ( ( ![X84:( subst > term > term )]: 1229.20/157.62 ( ( ![X86:subst,X88:term,X90:subst]: 1229.20/157.62 ( ( sub @ ( X84 @ X86 @ X88 ) @ X90 ) = 1229.20/157.62 ( X84 @ 1229.20/157.62 ( comp @ X86 @ X90 ) @ ( sub @ X88 @ X90 ) ) ) ) => 1229.20/157.62 ( ( ![X92:term]: 1229.20/157.62 ( ( X66 @ id @ X92 @ id ) => 1229.20/157.62 ( X66 @ id @ ( X84 @ id @ X92 ) @ id ) ) ) => 1229.20/157.62 ( X66 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) ) ) ) => 1229.20/157.62 ( ![X94:term]: 1229.20/157.62 ( ( ![X96:term]: 1229.20/157.62 ( ( X66 @ id @ X96 @ id ) => 1229.20/157.62 ( X66 @ 1229.20/157.62 id @ ( sub @ X94 @ ( push @ X96 @ id ) ) @ id ) ) ) => 1229.20/157.62 ( X66 @ id @ ( lam @ X94 ) @ id ) ) ) ) ) ) ) => 1229.20/157.62 ( ![X98:( subst > term > subst > $o )]: 1229.20/157.62 ( ( ![X100:subst,X102:term,X104:subst,X106:subst]: 1229.20/157.62 ( ( X98 @ X100 @ X102 @ ( comp @ X106 @ X104 ) ) => 1229.20/157.62 ( X98 @ 1229.20/157.62 ( comp @ X100 @ X106 ) @ ( sub @ X102 @ X106 ) @ X104 ) ) ) => 1229.20/157.62 ( ( ![X108:subst,X110:term,X112:subst,X114:subst]: 1229.20/157.62 ( ( X98 @ 1229.20/157.62 ( comp @ X108 @ X114 ) @ ( sub @ X110 @ X114 ) @ X112 ) => 1229.20/157.62 ( X98 @ X108 @ X110 @ ( comp @ X114 @ X112 ) ) ) ) => 1229.20/157.62 ( ( ![X116:term]: 1229.20/157.62 ( ( var @ ( sub @ X116 @ id ) ) => 1229.20/157.62 ( X98 @ id @ X116 @ id ) ) ) => 1229.20/157.62 ( ( ![X118:term,X120:term]: 1229.20/157.62 ( ( X98 @ id @ X118 @ id ) => 1229.20/157.62 ( ( X98 @ id @ X120 @ id ) => 1229.20/157.62 ( X98 @ 1229.20/157.62 id @ ( ap @ ( sub @ X118 @ id ) @ X120 ) @ id ) ) ) ) => 1229.20/157.62 ( ( ![X122:( subst > term > term )]: 1229.20/157.62 ( ( ![X124:subst,X126:term,X128:subst]: 1229.20/157.62 ( ( sub @ ( X122 @ X124 @ X126 ) @ X128 ) = 1229.20/157.62 ( X122 @ 1229.20/157.62 ( comp @ X124 @ X128 ) @ 1229.20/157.62 ( sub @ X126 @ X128 ) ) ) ) => 1229.20/157.62 ( ( ![X130:term]: 1229.20/157.62 ( ( X98 @ id @ X130 @ id ) => 1229.20/157.62 ( X98 @ id @ ( X122 @ id @ X130 ) @ id ) ) ) => 1229.20/157.62 ( X98 @ id @ ( lam @ ( X122 @ sh @ one ) ) @ id ) ) ) ) => 1229.20/157.62 ( ![X132:term]: ( X98 @ id @ X132 @ id ) ) ) ) ) ) ) ) ) ) ) )), 1229.20/157.62 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 1229.20/157.62 thf(zip_derived_cl0, plain, 1229.20/157.62 (~ (((((!!) @ (^[Y0 : term > $o]: 1229.20/157.62 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : term]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ Y1) => 1229.20/157.62 (((Y0 @ Y2) => (Y0 @ 1229.20/157.62 (ap @ Y1 @ Y2)))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : term]: 1229.20/157.62 (((((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ Y2) => (Y0 @ 1229.20/157.62 (sub @ Y1 @ 1229.20/157.62 (push @ Y2 @ id)))))))) => 1229.20/157.62 (Y0 @ (lam @ Y1))))))) => 1229.20/157.62 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (((Y0 @ 1229.20/157.62 Y1 @ Y2 @ 1229.20/157.62 (comp @ 1229.20/157.62 Y4 @ Y3)) => 1229.20/157.62 (Y0 @ 1229.20/157.62 (comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 (sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (Y0 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3) => 1229.20/157.62 (Y0 @ 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y4 @ Y3)))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : term]: 1229.20/157.62 (((var @ (sub @ Y1 @ id)) => (Y0 @ 1229.20/157.62 id @ Y1 @ id)))))) => 1229.20/157.62 (((!!) @ (^[Y1 : term]: 1229.20/157.62 (((var @ Y1) => (Y0 @ id @ Y1 @ id))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (Y0 @ 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y4 @ Y3)) => 1229.20/157.62 (Y0 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (Y0 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3) => 1229.20/157.62 (Y0 @ 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y4 @ Y3)))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : term]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ id @ Y1 @ 1229.20/157.62 id) => 1229.20/157.62 (((Y0 @ id @ Y2 @ 1229.20/157.62 id) => (Y0 @ id @ 1229.20/157.62 (ap @ 1229.20/157.62 (sub @ Y1 @ id) @ 1229.20/157.62 Y2) @ 1229.20/157.62 id))))))))))) => 1229.20/157.62 (((!!) @ (^[Y1 : term]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ id @ Y1 @ 1229.20/157.62 id) => 1229.20/157.62 (((Y0 @ id @ Y2 @ 1229.20/157.62 id) => (Y0 @ id @ 1229.20/157.62 (ap @ Y1 @ Y2) @ 1229.20/157.62 id)))))))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (Y0 @ 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y4 @ Y3)) => 1229.20/157.62 (Y0 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (( 1229.20/157.62 (!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (Y0 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y1 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 Y3) => 1229.20/157.62 (Y0 @ 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y4 @ Y3)))))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.62 (((((!!) @ (^[Y2 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y3 : term]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.62 (sub @ 1229.20/157.62 ( 1229.20/157.62 Y1 @ 1229.20/157.62 Y2 @ Y3) @ 1229.20/157.62 Y4) = 1229.20/157.62 (Y1 @ 1229.20/157.62 ( 1229.20/157.62 comp @ 1229.20/157.62 Y2 @ Y4) @ 1229.20/157.62 ( 1229.20/157.62 sub @ 1229.20/157.62 Y3 @ Y4))))))))))))) => 1229.20/157.62 (((((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ id @ 1229.20/157.62 Y2 @ id) => 1229.20/157.62 (Y0 @ id @ 1229.20/157.62 (Y1 @ id @ Y2) @ 1229.20/157.62 id)))))) => 1229.20/157.62 (Y0 @ id @ 1229.20/157.62 (lam @ (Y1 @ sh @ one)) @ 1229.20/157.62 id)))))))) => 1229.20/157.62 (((!!) @ (^[Y1 : term]: 1229.20/157.62 (((((!!) @ (^[Y2 : term]: 1229.20/157.62 (((Y0 @ id @ Y2 @ 1229.20/157.62 id) => (Y0 @ 1229.20/157.62 id @ 1229.20/157.62 (sub @ Y1 @ 1229.20/157.62 (push @ Y2 @ id)) @ 1229.20/157.62 id)))))) => 1229.20/157.62 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 1229.20/157.62 (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.62 (((((!!) @ (^[Y1 : subst]: 1229.20/157.62 (((!!) @ (^[Y2 : term]: 1229.20/157.62 (((!!) @ (^[Y3 : subst]: 1229.20/157.62 (((!!) @ ( 1229.20/157.62 ^[Y4 : subst]: 1229.20/157.62 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (( 1229.20/157.63 (!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ (sub @ Y1 @ id)) => 1229.20/157.63 (Y0 @ id @ Y1 @ id)))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ 1229.20/157.63 id) => 1229.20/157.63 (((Y0 @ id @ 1229.20/157.63 Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ 1229.20/157.63 id) @ 1229.20/157.63 Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y3 : term]: 1229.20/157.63 (( 1229.20/157.63 (!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 id @ Y2 @ 1229.20/157.63 id) => 1229.20/157.63 (Y0 @ 1229.20/157.63 id @ 1229.20/157.63 (Y1 @ 1229.20/157.63 id @ Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ 1229.20/157.63 id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))), 1229.20/157.63 inference('cnf', [status(esa)], [zf_stmt_1])). 1229.20/157.63 thf(zip_derived_cl2, plain, 1229.20/157.63 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ Y2 @ 1229.20/157.63 Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ (sub @ Y1 @ id)) => (Y0 @ 1229.20/157.63 id @ Y1 @ id)))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ Y1) => (Y0 @ id @ Y1 @ id))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ id) @ 1229.20/157.63 Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (ap @ Y1 @ Y2) @ id)))))))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ (^[Y3 : term]: 1229.20/157.63 (( 1229.20/157.63 (!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ 1229.20/157.63 id @ 1229.20/157.63 (Y1 @ id @ Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (sub @ Y1 @ 1229.20/157.63 (push @ Y2 @ id)) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 1229.20/157.63 (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ (sub @ Y1 @ id)) => 1229.20/157.63 (Y0 @ id @ Y1 @ id)))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ 1229.20/157.63 id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ 1229.20/157.63 id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ id) @ 1229.20/157.63 Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y3 : term]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ 1229.20/157.63 Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (Y1 @ id @ 1229.20/157.63 Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ 1229.20/157.63 id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))), 1229.20/157.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 1229.20/157.63 thf(zip_derived_cl4, plain, 1229.20/157.63 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ Y2 @ 1229.20/157.63 Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ id) @ Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (ap @ Y1 @ Y2) @ id)))))))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ (^[Y3 : term]: 1229.20/157.63 (( 1229.20/157.63 (!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (Y1 @ id @ Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (sub @ Y1 @ 1229.20/157.63 (push @ Y2 @ id)) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 1229.20/157.63 (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ (sub @ Y1 @ id)) => (Y0 @ 1229.20/157.63 id @ Y1 @ id)))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ 1229.20/157.63 id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ id) @ 1229.20/157.63 Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y3 : term]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ 1229.20/157.63 Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (Y1 @ id @ Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ 1229.20/157.63 id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))))), 1229.20/157.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 1229.20/157.63 thf(zip_derived_cl6, plain, 1229.20/157.63 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ Y2 @ 1229.20/157.63 Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ (^[Y3 : term]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (Y1 @ id @ Y2) @ id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ id) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (sub @ Y1 @ 1229.20/157.63 (push @ Y2 @ id)) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ (lam @ Y1) @ id))))))))))))))) => 1229.20/157.63 (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ Y2 @ 1229.20/157.63 Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((Y0 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 (sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ Y2 @ 1229.20/157.63 (comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((var @ (sub @ Y1 @ id)) => (Y0 @ 1229.20/157.63 id @ Y1 @ id)))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : term]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y1 @ id) => 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ id @ 1229.20/157.63 (ap @ 1229.20/157.63 (sub @ Y1 @ id) @ 1229.20/157.63 Y2) @ 1229.20/157.63 id))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ (^[Y3 : term]: 1229.20/157.63 (( 1229.20/157.63 (!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (sub @ 1229.20/157.63 ( 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ Y3) @ 1229.20/157.63 Y4) = 1229.20/157.63 (Y1 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y3 @ Y4))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y2 : term]: 1229.20/157.63 (((Y0 @ id @ Y2 @ 1229.20/157.63 id) => (Y0 @ 1229.20/157.63 id @ 1229.20/157.63 (Y1 @ id @ Y2) @ 1229.20/157.63 id)))))) => 1229.20/157.63 (Y0 @ id @ 1229.20/157.63 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 1229.20/157.63 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))), 1229.20/157.63 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 1229.20/157.63 thf(zip_derived_cl7, plain, 1229.20/157.63 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ (^[Y4 : subst]: 1229.20/157.63 ( 1229.20/157.63 ( 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)) => 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst]: 1229.20/157.63 (((!!) @ (^[Y2 : term]: 1229.20/157.63 (((!!) @ (^[Y3 : subst]: 1229.20/157.63 (((!!) @ (^[Y4 : subst]: 1229.20/157.63 (( 1229.20/157.63 (Y0 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y1 @ Y4) @ 1229.20/157.63 ( 1229.20/157.63 sub @ 1229.20/157.63 Y2 @ Y4) @ 1229.20/157.63 Y3) => 1229.20/157.63 (Y0 @ 1229.20/157.63 Y1 @ 1229.20/157.63 Y2 @ 1229.20/157.63 ( 1229.20/157.63 comp @ 1229.20/157.63 Y4 @ Y3)))))))))))))))) => 1229.20/157.63 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.63 (((((!!) @ (^[Y2 : subst]: 1229.20/157.63 (((!!) @ (^[Y3 : term]: 1229.20/157.63 (((!!) @ ( 1229.20/157.63 ^[Y4 : subst]: 1229.20/157.63 (((sub @ 1229.20/157.64 ( 1229.20/157.64 Y1 @ 1229.20/157.64 Y2 @ Y3) @ 1229.20/157.64 Y4) = 1229.20/157.64 (Y1 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y2 @ Y4) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y3 @ Y4))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ id @ Y2 @ id) => 1229.20/157.64 (Y0 @ id @ 1229.20/157.64 (Y1 @ id @ Y2) @ id)))))) => 1229.20/157.64 (Y0 @ id @ (lam @ (Y1 @ sh @ one)) @ 1229.20/157.64 id)))))))) => 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ id @ Y2 @ id) => 1229.20/157.64 (Y0 @ id @ 1229.20/157.64 (sub @ Y1 @ 1229.20/157.64 (push @ Y2 @ id)) @ 1229.20/157.64 id)))))) => 1229.20/157.64 (Y0 @ id @ (lam @ Y1) @ id)))))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 1229.20/157.64 thf(zip_derived_cl126, plain, 1229.20/157.64 (![X2 : subst > term > subst > $o]: 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((X2 @ Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 (X2 @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((X2 @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => (X2 @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ 1229.20/157.64 Y2) @ 1229.20/157.64 Y3) = 1229.20/157.64 (Y0 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y1 @ Y3) @ 1229.20/157.64 (sub @ 1229.20/157.64 Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ id @ Y1 @ id) => (X2 @ 1229.20/157.64 id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 (X2 @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 (X2 @ id @ (lam @ Y0) @ id))))))))))))), 1229.20/157.64 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl7])). 1229.20/157.64 thf(zip_derived_cl127, plain, 1229.20/157.64 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ 1229.20/157.64 Y3) @ 1229.20/157.64 (sub @ Y2 @ 1229.20/157.64 Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ 1229.20/157.64 id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id))))))))))))), 1229.20/157.64 inference('triggered_bool_instantiation', [status(thm)], 1229.20/157.64 [zip_derived_cl126])). 1229.20/157.64 thf(zip_derived_cl183, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ 1229.20/157.64 Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ 1229.20/157.64 Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ 1229.20/157.64 id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl127])). 1229.20/157.64 thf(zip_derived_cl8, plain, 1229.20/157.64 (~ (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((!!) @ (^[Y4 : subst]: 1229.20/157.64 (( 1229.20/157.64 (Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 Y2 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y4 @ Y3)) => 1229.20/157.64 (Y0 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y1 @ Y4) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y2 @ Y4) @ 1229.20/157.64 Y3))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((!!) @ ( 1229.20/157.64 ^[Y4 : subst]: 1229.20/157.64 (((Y0 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y1 @ Y4) @ 1229.20/157.64 (sub @ Y2 @ 1229.20/157.64 Y4) @ 1229.20/157.64 Y3) => 1229.20/157.64 (Y0 @ Y1 @ 1229.20/157.64 Y2 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y4 @ Y3)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((var @ (sub @ Y1 @ id)) => (Y0 @ id @ 1229.20/157.64 Y1 @ id)))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ id @ Y1 @ id) => 1229.20/157.64 (((Y0 @ id @ Y2 @ id) => 1229.20/157.64 (Y0 @ id @ 1229.20/157.64 (ap @ 1229.20/157.64 (sub @ Y1 @ id) @ Y2) @ 1229.20/157.64 id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : term]: 1229.20/157.64 (( 1229.20/157.64 (!!) @ ( 1229.20/157.64 ^[Y4 : subst]: 1229.20/157.64 (( 1229.20/157.64 (sub @ 1229.20/157.64 ( 1229.20/157.64 Y1 @ 1229.20/157.64 Y2 @ Y3) @ 1229.20/157.64 Y4) = 1229.20/157.64 (Y1 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y2 @ Y4) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y3 @ Y4))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ id @ Y2 @ 1229.20/157.64 id) => (Y0 @ id @ 1229.20/157.64 (Y1 @ id @ Y2) @ 1229.20/157.64 id)))))) => 1229.20/157.64 (Y0 @ id @ 1229.20/157.64 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 1229.20/157.64 thf(zip_derived_cl40, plain, 1229.20/157.64 (~ (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ 1229.20/157.64 id)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (( 1229.20/157.64 (sub @ 1229.20/157.64 ( 1229.20/157.64 Y0 @ 1229.20/157.64 Y1 @ Y2) @ 1229.20/157.64 Y3) = 1229.20/157.64 (Y0 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y1 @ Y3) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ 1229.20/157.64 id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))))))))))), 1229.20/157.64 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl8])). 1229.20/157.64 thf(zip_derived_cl41, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ Y2)))))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 1229.20/157.64 thf(zip_derived_cl184, plain, 1229.20/157.64 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id))))))))))), 1229.20/157.64 inference('clc', [status(thm)], [zip_derived_cl183, zip_derived_cl41])). 1229.20/157.64 thf(zip_derived_cl185, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ 1229.20/157.64 Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ 1229.20/157.64 id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 1229.20/157.64 thf(zip_derived_cl42, plain, 1229.20/157.64 (~ (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ 1229.20/157.64 Y1 @ Y2) @ 1229.20/157.64 Y3) = 1229.20/157.64 (Y0 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y1 @ Y3) @ 1229.20/157.64 (sub @ 1229.20/157.64 Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 1229.20/157.64 thf(zip_derived_cl43, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2))))))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 1229.20/157.64 thf(zip_derived_cl186, plain, 1229.20/157.64 ( (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.64 id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id))))))))), 1229.20/157.64 inference('clc', [status(thm)], [zip_derived_cl185, zip_derived_cl43])). 1229.20/157.64 thf(zip_derived_cl187, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])). 1229.20/157.64 thf(zip_derived_cl44, plain, 1229.20/157.64 (~ (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ 1229.20/157.64 Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ 1229.20/157.64 Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ 1229.20/157.64 Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ 1229.20/157.64 id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 1229.20/157.64 thf(zip_derived_cl46, plain, 1229.20/157.64 (~ (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ 1229.20/157.64 Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ 1229.20/157.64 id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 1229.20/157.64 thf(zip_derived_cl48, plain, 1229.20/157.64 (~ (((((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 1229.20/157.64 thf(zip_derived_cl49, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : subst > term > term]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((sub @ 1229.20/157.64 (Y0 @ Y1 @ Y2) @ 1229.20/157.64 Y3) = (Y0 @ 1229.20/157.64 (comp @ Y1 @ Y3) @ 1229.20/157.64 (sub @ Y2 @ Y3))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.64 id @ (Y0 @ id @ Y1) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ (Y0 @ sh @ one)) @ id))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 1229.20/157.64 thf(zip_derived_cl188, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.64 id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id))))))), 1229.20/157.64 inference('clc', [status(thm)], [zip_derived_cl187, zip_derived_cl49])). 1229.20/157.64 thf(zip_derived_cl189, plain, 1229.20/157.64 ((~ ('#form530') 1229.20/157.64 | (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))))), 1229.20/157.64 define([status(thm)])). 1229.20/157.64 thf(zip_derived_cl1, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : term > $o]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ Y1) => 1229.20/157.64 (((Y0 @ Y2) => (Y0 @ 1229.20/157.64 (ap @ Y1 @ Y2)))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((((!!) @ (^[Y2 : term]: 1229.20/157.64 (((Y0 @ Y2) => (Y0 @ 1229.20/157.64 (sub @ Y1 @ 1229.20/157.64 (push @ Y2 @ id)))))))) => 1229.20/157.64 (Y0 @ (lam @ Y1))))))) => 1229.20/157.64 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 1229.20/157.64 thf(zip_derived_cl9, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y1) => (X2 @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ Y0))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: (X2 @ Y0))))))))))), 1229.20/157.64 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 1229.20/157.64 thf(zip_derived_cl52, plain, 1229.20/157.64 ( (((((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))))))))), 1229.20/157.64 inference('triggered_bool_instantiation', [status(thm)], 1229.20/157.64 [zip_derived_cl9])). 1229.20/157.64 thf(zip_derived_cl76, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id)))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 1229.20/157.64 thf(zip_derived_cl9, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y1) => (X2 @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ Y0))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: (X2 @ Y0))))))))))), 1229.20/157.64 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 1229.20/157.64 thf(zip_derived_cl10, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y1) => (X2 @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ Y0))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 1229.20/157.64 thf(zip_derived_cl11, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y1) => (X2 @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ Y0))))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 1229.20/157.64 thf(zip_derived_cl12, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y1) => (X2 @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ Y0))))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])). 1229.20/157.64 thf(zip_derived_cl17, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (~ (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((X2 @ Y0) => (X2 @ 1229.20/157.64 (sub @ ('#sk71' @ X2) @ (push @ Y0 @ id)))))))) => 1229.20/157.64 (X2 @ (lam @ ('#sk71' @ X2))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 1229.20/157.64 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl12])). 1229.20/157.64 thf(zip_derived_cl18, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 ( (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((X2 @ Y0) => (X2 @ 1229.20/157.64 (sub @ ('#sk71' @ X2) @ (push @ Y0 @ id)))))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 1229.20/157.64 thf(zip_derived_cl20, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 ( ('#form111' @ X2) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))))), 1229.20/157.64 define([status(thm)])). 1229.20/157.64 thf(zip_derived_cl77, plain, 1229.20/157.64 ((~ ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))))))))), 1229.20/157.64 inference('renaming', [status(thm)], [zip_derived_cl76, zip_derived_cl20])). 1229.20/157.64 thf(zip_derived_cl78, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.64 id @ (ap @ Y0 @ Y1) @ id))))))))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))))) 1229.20/157.64 | ~ ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl77])). 1229.20/157.64 thf(zip_derived_cl18, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 ( (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((X2 @ Y0) => (X2 @ 1229.20/157.64 (sub @ ('#sk71' @ X2) @ (push @ Y0 @ id)))))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl17])). 1229.20/157.64 thf(zip_derived_cl20, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 ( ('#form111' @ X2) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))))), 1229.20/157.64 define([status(thm)])). 1229.20/157.64 thf(zip_derived_cl21, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 (~ ('#form111' @ X2) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((X2 @ Y0) => (X2 @ 1229.20/157.64 (sub @ ('#sk71' @ X2) @ (push @ Y0 @ id)))))))))), 1229.20/157.64 inference('renaming', [status(thm)], [zip_derived_cl18, zip_derived_cl20])). 1229.20/157.64 thf(zip_derived_cl23, plain, 1229.20/157.64 (![X2 : term > $o]: 1229.20/157.64 ( ('#form128' @ X2) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((X2 @ Y0) => 1229.20/157.64 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.64 define([status(thm)])). 1229.20/157.64 thf(zip_derived_cl79, plain, 1229.20/157.64 ((~ ('#form128' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | ~ ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))))))), 1229.20/157.64 inference('renaming', [status(thm)], [zip_derived_cl78, zip_derived_cl23])). 1229.20/157.64 thf(zip_derived_cl80, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.64 id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))) 1229.20/157.64 | (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))) 1229.20/157.64 | ~ ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | ~ ('#form128' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 1229.20/157.64 thf(zip_derived_cl50, plain, 1229.20/157.64 (~ (((!!) @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 1229.20/157.64 thf(zip_derived_cl81, plain, 1229.20/157.64 ((~ ('#form128' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | ~ ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.64 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.64 ('#sk224' @ id @ 1229.20/157.64 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.64 ('#sk224' @ id @ (lam @ Y0) @ id)))))))), 1229.20/157.64 inference('clc', [status(thm)], [zip_derived_cl80, zip_derived_cl50])). 1229.20/157.64 thf(zip_derived_cl3, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((!!) @ (^[Y4 : subst]: 1229.20/157.64 ( 1229.20/157.64 ( 1229.20/157.64 (Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 Y2 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y4 @ Y3)) => 1229.20/157.64 (Y0 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y1 @ Y4) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y2 @ Y4) @ 1229.20/157.64 Y3))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : subst]: 1229.20/157.64 (((!!) @ (^[Y2 : term]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((!!) @ (^[Y4 : subst]: 1229.20/157.64 (( 1229.20/157.64 (Y0 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y1 @ Y4) @ 1229.20/157.64 ( 1229.20/157.64 sub @ 1229.20/157.64 Y2 @ Y4) @ 1229.20/157.64 Y3) => 1229.20/157.64 (Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 Y2 @ 1229.20/157.64 ( 1229.20/157.64 comp @ 1229.20/157.64 Y4 @ Y3)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y1 : term]: 1229.20/157.64 (((var @ (sub @ Y1 @ id)) => (Y0 @ id @ 1229.20/157.64 Y1 @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((var @ Y1) => (Y0 @ id @ Y1 @ id)))))))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 1229.20/157.64 thf(zip_derived_cl58, plain, 1229.20/157.64 (![X2 : subst > term > subst > $o]: 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((X2 @ Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 (X2 @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 (((X2 @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => (X2 @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => (X2 @ id @ Y0 @ id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ id @ Y0 @ id))))))))))))), 1229.20/157.64 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])). 1229.20/157.64 thf(zip_derived_cl59, plain, 1229.20/157.64 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ 1229.20/157.64 id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ Y0) => ('#sk224' @ id @ Y0 @ id))))))))))))), 1229.20/157.64 inference('triggered_bool_instantiation', [status(thm)], 1229.20/157.64 [zip_derived_cl58])). 1229.20/157.64 thf(zip_derived_cl86, plain, 1229.20/157.64 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2))))))))))))))) 1229.20/157.64 | (((((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ 1229.20/157.64 (comp @ Y0 @ Y3) @ 1229.20/157.64 (sub @ Y1 @ Y3) @ 1229.20/157.64 Y2) => 1229.20/157.64 ('#sk224' @ 1229.20/157.64 Y0 @ Y1 @ 1229.20/157.64 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.64 (((((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ 1229.20/157.64 id)))))) => 1229.20/157.64 (((!!) @ (^[Y0 : term]: 1229.20/157.64 (((var @ Y0) => ('#sk224' @ id @ Y0 @ id)))))))))))), 1229.20/157.64 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl59])). 1229.20/157.64 thf(zip_derived_cl41, plain, 1229.20/157.64 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.64 (((!!) @ (^[Y1 : term]: 1229.20/157.64 (((!!) @ (^[Y2 : subst]: 1229.20/157.64 (((!!) @ (^[Y3 : subst]: 1229.20/157.64 ((('#sk224' @ Y0 @ 1229.20/157.64 Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)) => 1229.20/157.65 ('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ Y2)))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 1229.20/157.65 thf(zip_derived_cl87, plain, 1229.20/157.65 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id))))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl86, zip_derived_cl41])). 1229.20/157.65 thf(zip_derived_cl88, plain, 1229.20/157.65 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) 1229.20/157.65 | (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ Y0) => ('#sk224' @ id @ Y0 @ id)))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 1229.20/157.65 thf(zip_derived_cl43, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2))))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 1229.20/157.65 thf(zip_derived_cl89, plain, 1229.20/157.65 ( (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl88, zip_derived_cl43])). 1229.20/157.65 thf(zip_derived_cl90, plain, 1229.20/157.65 ((~ (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id)))))) 1229.20/157.65 | (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id)))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl89])). 1229.20/157.65 thf(zip_derived_cl45, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((var @ (sub @ Y0 @ id)) => ('#sk224' @ id @ Y0 @ id))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl44])). 1229.20/157.65 thf(zip_derived_cl91, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl90, zip_derived_cl45])). 1229.20/157.65 thf(zip_derived_cl91, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk224' @ id @ Y0 @ id))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl90, zip_derived_cl45])). 1229.20/157.65 thf(zip_derived_cl92, plain, 1229.20/157.65 (![X2 : term > $o]: 1229.20/157.65 (~ ('#form111' @ X2) 1229.20/157.65 | (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))))), 1229.20/157.65 define([status(thm)])). 1229.20/157.65 thf(zip_derived_cl20, plain, 1229.20/157.65 (![X2 : term > $o]: 1229.20/157.65 ( ('#form111' @ X2) 1229.20/157.65 | ~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))))), 1229.20/157.65 define([status(thm)])). 1229.20/157.65 thf(zip_derived_cl93, plain, 1229.20/157.65 ( ('#form111' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))), 1229.20/157.65 inference('renaming', [status(thm)], 1229.20/157.65 [zip_derived_cl91, zip_derived_cl92, zip_derived_cl20])). 1229.20/157.65 thf(zip_derived_cl97, plain, 1229.20/157.65 ((~ ('#form128' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id))) 1229.20/157.65 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.65 ('#sk224' @ id @ (lam @ Y0) @ id)))))))), 1229.20/157.65 inference('demod', [status(thm)], [zip_derived_cl81, zip_derived_cl93])). 1229.20/157.65 thf(zip_derived_cl5, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 1229.20/157.65 (((((!!) @ (^[Y1 : subst]: 1229.20/157.65 (((!!) @ (^[Y2 : term]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 (((!!) @ (^[Y4 : subst]: 1229.20/157.65 ( 1229.20/157.65 ( 1229.20/157.65 (Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 Y2 @ 1229.20/157.65 ( 1229.20/157.65 comp @ 1229.20/157.65 Y4 @ Y3)) => 1229.20/157.65 (Y0 @ 1229.20/157.65 ( 1229.20/157.65 comp @ 1229.20/157.65 Y1 @ Y4) @ 1229.20/157.65 ( 1229.20/157.65 sub @ 1229.20/157.65 Y2 @ Y4) @ 1229.20/157.65 Y3))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y1 : subst]: 1229.20/157.65 (((!!) @ (^[Y2 : term]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 (((!!) @ (^[Y4 : subst]: 1229.20/157.65 (( 1229.20/157.65 (Y0 @ 1229.20/157.65 ( 1229.20/157.65 comp @ 1229.20/157.65 Y1 @ Y4) @ 1229.20/157.65 ( 1229.20/157.65 sub @ 1229.20/157.65 Y2 @ Y4) @ 1229.20/157.65 Y3) => 1229.20/157.65 (Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 Y2 @ 1229.20/157.65 ( 1229.20/157.65 comp @ 1229.20/157.65 Y4 @ Y3)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : term]: 1229.20/157.65 (((Y0 @ id @ Y1 @ id) => 1229.20/157.65 (((Y0 @ id @ Y2 @ id) => 1229.20/157.65 (Y0 @ id @ 1229.20/157.65 (ap @ (sub @ Y1 @ id) @ 1229.20/157.65 Y2) @ 1229.20/157.65 id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : term]: 1229.20/157.65 (((Y0 @ id @ Y1 @ id) => 1229.20/157.65 (((Y0 @ id @ Y2 @ id) => 1229.20/157.65 (Y0 @ id @ 1229.20/157.65 (ap @ Y1 @ Y2) @ id))))))))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])). 1229.20/157.65 thf(zip_derived_cl100, plain, 1229.20/157.65 (![X2 : subst > term > subst > $o]: 1229.20/157.65 (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 (((X2 @ Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)) => 1229.20/157.65 (X2 @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 (((X2 @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => (X2 @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((X2 @ id @ Y0 @ id) => 1229.20/157.65 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 1229.20/157.65 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((X2 @ id @ Y0 @ id) => 1229.20/157.65 (((X2 @ id @ Y1 @ id) => (X2 @ id @ 1229.20/157.65 (ap @ Y0 @ Y1) @ id)))))))))))))))))), 1229.20/157.65 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])). 1229.20/157.65 thf(zip_derived_cl101, plain, 1229.20/157.65 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)) => 1229.20/157.65 ('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => 1229.20/157.65 ('#sk224' @ Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id)))))))))))))))))), 1229.20/157.65 inference('triggered_bool_instantiation', [status(thm)], 1229.20/157.65 [zip_derived_cl100])). 1229.20/157.65 thf(zip_derived_cl114, plain, 1229.20/157.65 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)) => 1229.20/157.65 ('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2))))))))))))))) 1229.20/157.65 | (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => 1229.20/157.65 ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ 1229.20/157.65 id))))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl101])). 1229.20/157.65 thf(zip_derived_cl41, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ Y0 @ 1229.20/157.65 Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)) => 1229.20/157.65 ('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ Y2)))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])). 1229.20/157.65 thf(zip_derived_cl115, plain, 1229.20/157.65 ( (((((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) => 1229.20/157.65 (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id)))))))))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl114, zip_derived_cl41])). 1229.20/157.65 thf(zip_derived_cl116, plain, 1229.20/157.65 ((~ (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2)))))))))))))))) 1229.20/157.65 | (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 1229.20/157.65 thf(zip_derived_cl43, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : subst]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((!!) @ (^[Y2 : subst]: 1229.20/157.65 (((!!) @ (^[Y3 : subst]: 1229.20/157.65 ((('#sk224' @ 1229.20/157.65 (comp @ Y0 @ Y3) @ 1229.20/157.65 (sub @ Y1 @ Y3) @ 1229.20/157.65 Y2) => ('#sk224' @ 1229.20/157.65 Y0 @ Y1 @ 1229.20/157.65 (comp @ Y3 @ Y2))))))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 1229.20/157.65 thf(zip_derived_cl117, plain, 1229.20/157.65 ( (((((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 1229.20/157.65 (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ Y0 @ Y1) @ id)))))))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl116, zip_derived_cl43])). 1229.20/157.65 thf(zip_derived_cl118, plain, 1229.20/157.65 ((~ (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) 1229.20/157.65 | (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ (ap @ Y0 @ Y1) @ id))))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl117])). 1229.20/157.65 thf(zip_derived_cl47, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id)))))))))))), 1229.20/157.65 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl46])). 1229.20/157.65 thf(zip_derived_cl119, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ Y0 @ Y1) @ id)))))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl47])). 1229.20/157.65 thf(zip_derived_cl119, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y0 @ id) => 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (ap @ Y0 @ Y1) @ id)))))))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl118, zip_derived_cl47])). 1229.20/157.65 thf(zip_derived_cl120, plain, 1229.20/157.65 (![X2 : term > $o]: 1229.20/157.65 (~ ('#form128' @ X2) 1229.20/157.65 | (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((X2 @ Y0) => 1229.20/157.65 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.65 define([status(thm)])). 1229.20/157.65 thf(zip_derived_cl23, plain, 1229.20/157.65 (![X2 : term > $o]: 1229.20/157.65 ( ('#form128' @ X2) 1229.20/157.65 | ~ (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((!!) @ (^[Y1 : term]: 1229.20/157.65 (((X2 @ Y0) => 1229.20/157.65 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))))), 1229.20/157.65 define([status(thm)])). 1229.20/157.65 thf(zip_derived_cl121, plain, 1229.20/157.65 ( ('#form128' @ (^[Y0 : term]: ('#sk224' @ id @ Y0 @ id)))), 1229.20/157.65 inference('renaming', [status(thm)], 1229.20/157.65 [zip_derived_cl119, zip_derived_cl120, zip_derived_cl23])). 1229.20/157.65 thf(zip_derived_cl123, plain, 1229.20/157.65 (~ (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.65 ('#sk224' @ id @ (lam @ Y0) @ id))))))), 1229.20/157.65 inference('demod', [status(thm)], [zip_derived_cl97, zip_derived_cl121])). 1229.20/157.65 thf(zip_derived_cl191, plain, (~ ('#form530')), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl189, zip_derived_cl123])). 1229.20/157.65 thf(zip_derived_cl188, plain, 1229.20/157.65 ( (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => ('#sk224' @ 1229.20/157.65 id @ (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.65 ('#sk224' @ id @ (lam @ Y0) @ id))))))), 1229.20/157.65 inference('clc', [status(thm)], [zip_derived_cl187, zip_derived_cl49])). 1229.20/157.65 thf(zip_derived_cl189, plain, 1229.20/157.65 ((~ ('#form530') 1229.20/157.65 | (((!!) @ (^[Y0 : term]: 1229.20/157.65 (((((!!) @ (^[Y1 : term]: 1229.20/157.65 ((('#sk224' @ id @ Y1 @ id) => 1229.20/157.65 ('#sk224' @ id @ 1229.20/157.65 (sub @ Y0 @ (push @ Y1 @ id)) @ id)))))) => 1229.20/157.65 ('#sk224' @ id @ (lam @ Y0) @ id)))))))), 1229.20/157.65 define([status(thm)])). 1229.20/157.65 thf(zip_derived_cl190, plain, ( ('#form530')), 1229.20/157.65 inference('renaming', [status(thm)], 1229.20/157.65 [zip_derived_cl188, zip_derived_cl189])). 1229.20/157.65 thf(zip_derived_cl199, plain, ($false), 1229.20/157.65 inference('demod', [status(thm)], [zip_derived_cl191, zip_derived_cl190])). 1229.20/157.65 1229.20/157.65 % SZS output end Refutation 1229.20/157.65 1229.20/157.65 1229.20/157.65 % /export/starexec/sandbox2/solver/bin/lams/8_lcnf_new_simp.sh running for 16s 1229.20/157.65 % Terminating... 1129.68/157.72 % Runner terminated. 1129.68/157.74 % Zipperpin 1.5 exiting 1129.68/157.76 EOF