0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.10 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.HCioySeBAQ true 0.21/0.47 % Computer : n013.cluster.edu 0.21/0.47 % Model : x86_64 x86_64 0.21/0.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.21/0.47 % Memory : 8046.5625MB 0.21/0.47 % OS : Linux 6.8.0-71-generic 0.21/0.47 % CPULimit : 1440 0.21/0.47 % WCLimit : 180 0.21/0.47 % DateTime : Mon Jul 27 14:59:54 UTC 2026 0.21/0.47 % CPUTime : 0.21/0.47 % Running portfolio for 1440 s 0.21/0.47 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.21/0.48 % Number of cores: 8 0.21/0.48 % Python version: Python 3.12.3 0.21/0.48 % Running in HO mode 0.45/0.90 % Total configuration time : 828 0.45/0.90 % Estimated wc time : 1656 0.45/0.90 % Estimated cpu time (8 cpus) : 207.0 0.45/1.01 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 2.10/1.10 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 2.10/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 2.10/1.11 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 2.10/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 2.10/1.11 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 2.10/1.15 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 2.10/1.19 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 2.10/1.20 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 59.46/9.44 % Solved by lams/20_acsne_simpl.sh. 59.46/9.44 % done 199 iterations in 8.080s 59.46/9.44 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 59.46/9.44 % SZS output start Refutation 59.46/9.44 thf(subst_type, type, subst: $tType). 59.46/9.44 thf(term_type, type, term: $tType). 59.46/9.44 thf('#sk124_type', type, '#sk124': (term > $o) > subst > term > term). 59.46/9.44 thf(lam_type, type, lam: term > term). 59.46/9.44 thf('#sk225_type', type, '#sk225': (term > $o) > term). 59.46/9.44 thf('#sk30_type', type, '#sk30': (term > $o) > term). 59.46/9.44 thf('#sk251_type', type, '#sk251': term). 59.46/9.44 thf('#form632_type', type, '#form632': (term > $o) > $o). 59.46/9.44 thf(push_type, type, push: term > subst > subst). 59.46/9.44 thf('#form178_type', type, '#form178': (term > $o) > $o). 59.46/9.44 thf('#form234_type', type, '#form234': (term > $o) > (term > $o) > $o). 59.46/9.44 thf('#sk5_type', type, '#sk5': (term > $o) > term > $o). 59.46/9.44 thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime: 59.46/9.44 (subst > term > subst > $o) > (term > $o) > $o). 59.46/9.44 thf(hoasap_type, type, hoasap: subst > term > subst > term > term). 59.46/9.44 thf(one_type, type, one: term). 59.46/9.44 thf(id_type, type, id: subst). 59.46/9.44 thf(comp_type, type, comp: subst > subst > subst). 59.46/9.44 thf(induction2_type, type, induction2: $o). 59.46/9.44 thf(axvarid_type, type, axvarid: $o). 59.46/9.44 thf(sh_type, type, sh: subst). 59.46/9.44 thf(hoasinduction_lthm_3_type, type, hoasinduction_lthm_3: $o). 59.46/9.44 thf('#l_lift5217_type', type, '#l_lift5217': term > $o). 59.46/9.44 thf('#sk417_type', type, '#sk417': (term > $o) > term > term). 59.46/9.44 thf('#form922_type', type, '#form922': $o). 59.46/9.44 thf(sub_type, type, sub: term > subst > term). 59.46/9.44 thf(hoasinduction_type, type, hoasinduction: $o). 59.46/9.44 thf(ap_type, type, ap: term > term > term). 59.46/9.44 thf('#sk31_type', type, '#sk31': subst > term > subst > $o). 59.46/9.44 thf(hoasinduction_lem3v2a_type, type, hoasinduction_lem3v2a: $o). 59.46/9.44 thf(var_type, type, var: term > $o). 59.46/9.44 thf('#sk372_type', type, '#sk372': (subst > term > term) > subst). 59.46/9.44 thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term). 59.46/9.44 thf('#sk500_type', type, '#sk500': (subst > term > term) > term). 59.46/9.44 thf('#sk405_type', type, '#sk405': (subst > term > term) > term). 59.46/9.44 thf(hoasinduction_lem0_type, type, hoasinduction_lem0: $o). 59.46/9.44 thf(hoasvar_type, type, hoasvar: subst > term > subst > $o). 59.46/9.44 thf('#sk294_type', type, '#sk294': (term > $o) > (term > $o) > term). 59.46/9.44 thf('#sk135_type', type, '#sk135': (term > $o) > term). 59.46/9.44 thf('#sk103_type', type, '#sk103': (term > $o) > term). 59.46/9.44 thf('#sk428_type', type, '#sk428': (subst > term > term) > subst). 59.46/9.44 thf(hoasinduction_lthm_3, axiom, hoasinduction_lthm_3 = 59.46/9.44 (( hoasinduction_lem0 ) => 59.46/9.44 ( ( induction2 ) => 59.46/9.44 ( ( axvarid ) => ( ( hoasinduction_lem3v2a ) => ( hoasinduction ) ) ) ))). 59.46/9.44 thf('0', plain, 59.46/9.44 (( hoasinduction_lthm_3 ) = 59.46/9.44 ( ( hoasinduction_lem0 ) => 59.46/9.44 ( ( induction2 ) => 59.46/9.44 ( ( axvarid ) => ( ( hoasinduction_lem3v2a ) => ( hoasinduction ) ) ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasinduction, axiom, hoasinduction = 59.46/9.44 (![P:( subst > term > subst > $o )]: 59.46/9.44 ( ( ![M:subst,A:term,N:subst,K:subst]: 59.46/9.44 ( ( P @ M @ A @ ( comp @ K @ N ) ) => 59.46/9.44 ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) => 59.46/9.44 ( ( ![M:subst,A:term,N:subst,K:subst]: 59.46/9.44 ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) => 59.46/9.44 ( P @ M @ A @ ( comp @ K @ N ) ) ) ) => 59.46/9.44 ( ( ![A:term]: ( ( hoasvar @ id @ A @ id ) => ( P @ id @ A @ id ) ) ) => 59.46/9.44 ( ( ![A:term,B:term]: 59.46/9.44 ( ( P @ id @ A @ id ) => 59.46/9.44 ( ( P @ id @ B @ id ) => 59.46/9.44 ( P @ id @ ( hoasap @ id @ A @ id @ B ) @ id ) ) ) ) => 59.46/9.44 ( ( ![F:( subst > term > term )]: 59.46/9.44 ( ( ![M:subst,A:term,N:subst]: 59.46/9.44 ( ( sub @ ( F @ M @ A ) @ N ) = 59.46/9.44 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 59.46/9.44 ( ( ![A:term]: 59.46/9.44 ( ( P @ id @ A @ id ) => 59.46/9.44 ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 59.46/9.44 ( P @ 59.46/9.44 id @ 59.46/9.44 ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ 59.46/9.44 id ) ) ) ) => 59.46/9.44 ( ![A:term]: ( P @ id @ A @ id ) ) ) ) ) ) ))). 59.46/9.44 thf('1', plain, 59.46/9.44 (( hoasinduction ) = 59.46/9.44 ( ![X4:( subst > term > subst > $o )]: 59.46/9.44 ( ( ![X6:subst,X8:term,X10:subst,X12:subst]: 59.46/9.44 ( ( X4 @ X6 @ X8 @ ( comp @ X12 @ X10 ) ) => 59.46/9.44 ( X4 @ ( comp @ X6 @ X12 ) @ ( sub @ X8 @ X12 ) @ X10 ) ) ) => 59.46/9.44 ( ( ![X14:subst,X16:term,X18:subst,X20:subst]: 59.46/9.44 ( ( X4 @ ( comp @ X14 @ X20 ) @ ( sub @ X16 @ X20 ) @ X18 ) => 59.46/9.44 ( X4 @ X14 @ X16 @ ( comp @ X20 @ X18 ) ) ) ) => 59.46/9.44 ( ( ![X22:term]: 59.46/9.44 ( ( hoasvar @ id @ X22 @ id ) => ( X4 @ id @ X22 @ id ) ) ) => 59.46/9.44 ( ( ![X24:term,X26:term]: 59.46/9.44 ( ( X4 @ id @ X24 @ id ) => 59.46/9.44 ( ( X4 @ id @ X26 @ id ) => 59.46/9.44 ( X4 @ id @ ( hoasap @ id @ X24 @ id @ X26 ) @ id ) ) ) ) => 59.46/9.44 ( ( ![X28:( subst > term > term )]: 59.46/9.44 ( ( ![X30:subst,X32:term,X34:subst]: 59.46/9.44 ( ( sub @ ( X28 @ X30 @ X32 ) @ X34 ) = 59.46/9.44 ( X28 @ ( comp @ X30 @ X34 ) @ ( sub @ X32 @ X34 ) ) ) ) => 59.46/9.44 ( ( ![X36:term]: 59.46/9.44 ( ( X4 @ id @ X36 @ id ) => 59.46/9.44 ( X4 @ id @ ( X28 @ id @ X36 ) @ id ) ) ) => 59.46/9.44 ( X4 @ 59.46/9.44 id @ 59.46/9.44 ( hoaslam @ 59.46/9.44 id @ 59.46/9.44 ( ^[V_1:subst,V_2:term]: ( X28 @ V_1 @ V_2 ) ) ) @ 59.46/9.44 id ) ) ) ) => 59.46/9.44 ( ![X38:term]: ( X4 @ id @ X38 @ id ) ) ) ) ) ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasinduction_lem3v2a, axiom, hoasinduction_lem3v2a = 59.46/9.44 (![P:( subst > term > subst > $o ),Q:( term > $o )]: 59.46/9.44 ( ( ![F:( subst > term > term )]: 59.46/9.44 ( ( ![M:subst,A:term,N:subst]: 59.46/9.44 ( ( sub @ ( F @ M @ A ) @ N ) = 59.46/9.44 ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) => 59.46/9.44 ( ( ![A:term]: 59.46/9.44 ( ( P @ id @ A @ id ) => ( P @ id @ ( F @ id @ A ) @ id ) ) ) => 59.46/9.44 ( P @ 59.46/9.44 id @ ( hoaslam @ id @ ( ^[M:subst,A:term]: ( F @ M @ A ) ) ) @ 59.46/9.44 id ) ) ) ) => 59.46/9.44 ( ( hoasinduction_p_and_p_prime @ P @ Q ) => 59.46/9.44 ( ![A:term]: 59.46/9.44 ( ( ![B:term]: 59.46/9.44 ( ( Q @ B ) => ( Q @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 59.46/9.44 ( Q @ ( lam @ A ) ) ) ) ) ))). 59.46/9.44 thf('2', plain, 59.46/9.44 (( hoasinduction_lem3v2a ) = 59.46/9.44 ( ![X4:( subst > term > subst > $o ),X6:( term > $o )]: 59.46/9.44 ( ( ![X8:( subst > term > term )]: 59.46/9.44 ( ( ![X10:subst,X12:term,X14:subst]: 59.46/9.44 ( ( sub @ ( X8 @ X10 @ X12 ) @ X14 ) = 59.46/9.44 ( X8 @ ( comp @ X10 @ X14 ) @ ( sub @ X12 @ X14 ) ) ) ) => 59.46/9.44 ( ( ![X16:term]: 59.46/9.44 ( ( X4 @ id @ X16 @ id ) => 59.46/9.44 ( X4 @ id @ ( X8 @ id @ X16 ) @ id ) ) ) => 59.46/9.44 ( X4 @ 59.46/9.44 id @ 59.46/9.44 ( hoaslam @ 59.46/9.44 id @ ( ^[V_1:subst,V_2:term]: ( X8 @ V_1 @ V_2 ) ) ) @ 59.46/9.44 id ) ) ) ) => 59.46/9.44 ( ( hoasinduction_p_and_p_prime @ X4 @ X6 ) => 59.46/9.44 ( ![X18:term]: 59.46/9.44 ( ( ![X20:term]: 59.46/9.44 ( ( X6 @ X20 ) => 59.46/9.44 ( X6 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) ) ) => 59.46/9.44 ( X6 @ ( lam @ X18 ) ) ) ) ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasinduction_lem0, axiom, hoasinduction_lem0 = 59.46/9.44 (![P:( subst > term > subst > $o )]: 59.46/9.44 ( ?[Q:( term > $o )]: ( hoasinduction_p_and_p_prime @ P @ Q ) ))). 59.46/9.44 thf('3', plain, 59.46/9.44 (( hoasinduction_lem0 ) = 59.46/9.44 ( ![X4:( subst > term > subst > $o )]: 59.46/9.44 ( ?[X6:( term > $o )]: ( hoasinduction_p_and_p_prime @ X4 @ X6 ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasinduction_p_and_p_prime, axiom,(( hoasinduction_p_and_p_prime ) = 59.46/9.44 (^[P:( subst > term > subst > $o ),Q:( term > $o )]: 59.46/9.44 ( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) )))). 59.46/9.44 thf('4', plain, 59.46/9.44 (( hoasinduction_p_and_p_prime ) = 59.46/9.44 ( ^[P:( subst > term > subst > $o ),Q:( term > $o )]: 59.46/9.44 ( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) )), 59.46/9.44 inference('simplify_rw_rule', [status(thm)], 59.46/9.44 [hoasinduction_p_and_p_prime])). 59.46/9.44 thf('5', plain, 59.46/9.44 (( hoasinduction_p_and_p_prime ) = 59.46/9.44 ( ^[V_1:( subst > term > subst > $o ),V_2:( term > $o )]: 59.46/9.44 ( ![X4:term]: ( ( V_2 @ X4 ) <=> ( V_1 @ id @ X4 @ id ) ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasvar, axiom,(( hoasvar ) = 59.46/9.44 (^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) )))). 59.46/9.44 thf('6', plain, 59.46/9.44 (( hoasvar ) = ( ^[M:subst,A:term,N:subst]: ( var @ ( sub @ A @ N ) ) )), 59.46/9.44 inference('simplify_rw_rule', [status(thm)], [hoasvar])). 59.46/9.44 thf('7', plain, 59.46/9.44 (( hoasvar ) = 59.46/9.44 ( ^[V_1:subst,V_2:term,V_3:subst]: ( var @ ( sub @ V_2 @ V_3 ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoaslam, axiom,(( hoaslam ) = 59.46/9.44 (^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) )))). 59.46/9.44 thf('8', plain, 59.46/9.44 (( hoaslam ) = 59.46/9.44 ( ^[M:subst,F:( subst > term > term )]: ( lam @ ( F @ sh @ one ) ) )), 59.46/9.44 inference('simplify_rw_rule', [status(thm)], [hoaslam])). 59.46/9.44 thf('9', plain, 59.46/9.44 (( hoaslam ) = 59.46/9.44 ( ^[V_1:subst,V_2:( subst > term > term )]: ( lam @ ( V_2 @ sh @ one ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(hoasap, axiom,(( hoasap ) = 59.46/9.44 (^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B )))). 59.46/9.44 thf('10', plain, 59.46/9.44 (( hoasap ) = 59.46/9.44 ( ^[M:subst,A:term,N:subst,B:term]: ( ap @ ( sub @ A @ N ) @ B ) )), 59.46/9.44 inference('simplify_rw_rule', [status(thm)], [hoasap])). 59.46/9.44 thf('11', plain, 59.46/9.44 (( hoasap ) = 59.46/9.44 ( ^[V_1:subst,V_2:term,V_3:subst,V_4:term]: 59.46/9.44 ( ap @ ( sub @ V_2 @ V_3 ) @ V_4 ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(induction2, axiom, induction2 = 59.46/9.44 (![P:( term > $o )]: 59.46/9.44 ( ( ![A:term]: ( ( var @ A ) => ( P @ A ) ) ) => 59.46/9.44 ( ( ![A:term,B:term]: 59.46/9.44 ( ( P @ A ) => ( ( P @ B ) => ( P @ ( ap @ A @ B ) ) ) ) ) => 59.46/9.44 ( ( ![A:term]: 59.46/9.44 ( ( ![B:term]: 59.46/9.44 ( ( P @ B ) => ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) => 59.46/9.44 ( P @ ( lam @ A ) ) ) ) => 59.46/9.44 ( ![A:term]: ( P @ A ) ) ) ) ))). 59.46/9.44 thf('12', plain, 59.46/9.44 (( induction2 ) = 59.46/9.44 ( ![X4:( term > $o )]: 59.46/9.44 ( ( ![X6:term]: ( ( var @ X6 ) => ( X4 @ X6 ) ) ) => 59.46/9.44 ( ( ![X8:term,X10:term]: 59.46/9.44 ( ( X4 @ X8 ) => ( ( X4 @ X10 ) => ( X4 @ ( ap @ X8 @ X10 ) ) ) ) ) => 59.46/9.44 ( ( ![X12:term]: 59.46/9.44 ( ( ![X14:term]: 59.46/9.44 ( ( X4 @ X14 ) => 59.46/9.44 ( X4 @ ( sub @ X12 @ ( push @ X14 @ id ) ) ) ) ) => 59.46/9.44 ( X4 @ ( lam @ X12 ) ) ) ) => 59.46/9.44 ( ![X16:term]: ( X4 @ X16 ) ) ) ) ) )), 59.46/9.44 define([status(thm)])). 59.46/9.44 thf(axvarid, axiom, axvarid = (![A:term]: ( ( sub @ A @ id ) = ( A ) ))). 59.46/9.44 thf('13', plain, 59.46/9.44 (( axvarid ) = ( ![X4:term]: ( ( sub @ X4 @ id ) = ( X4 ) ) )), 59.46/9.44 define([status(thm)])).thf(thm, conjecture, (hoasinduction_lthm_3)). 59.46/9.44 thf(zf_stmt_0, conjecture, 59.46/9.44 (( ![X4:( subst > term > subst > $o )]: 59.46/9.44 ( ?[X6:( term > $o )]: 59.46/9.44 ( ![X8:term]: ( ( X6 @ X8 ) <=> ( X4 @ id @ X8 @ id ) ) ) ) ) => 59.46/9.44 ( ( ![X10:( term > $o )]: 59.46/9.44 ( ( ![X12:term]: ( ( var @ X12 ) => ( X10 @ X12 ) ) ) => 59.46/9.44 ( ( ![X14:term,X16:term]: 59.46/9.44 ( ( X10 @ X14 ) => 59.46/9.44 ( ( X10 @ X16 ) => ( X10 @ ( ap @ X14 @ X16 ) ) ) ) ) => 59.46/9.44 ( ( ![X18:term]: 59.46/9.44 ( ( ![X20:term]: 59.46/9.44 ( ( X10 @ X20 ) => 59.46/9.44 ( X10 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) ) ) => 59.46/9.44 ( X10 @ ( lam @ X18 ) ) ) ) => 59.46/9.44 ( ![X22:term]: ( X10 @ X22 ) ) ) ) ) ) => 59.46/9.44 ( ( ![X24:term]: ( ( sub @ X24 @ id ) = ( X24 ) ) ) => 59.46/9.44 ( ( ![X26:( subst > term > subst > $o ),X28:( term > $o )]: 59.46/9.44 ( ( ![X30:( subst > term > term )]: 59.46/9.44 ( ( ![X32:subst,X34:term,X36:subst]: 59.46/9.44 ( ( sub @ ( X30 @ X32 @ X34 ) @ X36 ) = 59.46/9.44 ( X30 @ ( comp @ X32 @ X36 ) @ ( sub @ X34 @ X36 ) ) ) ) => 59.46/9.44 ( ( ![X38:term]: 59.46/9.44 ( ( X26 @ id @ X38 @ id ) => 59.46/9.44 ( X26 @ id @ ( X30 @ id @ X38 ) @ id ) ) ) => 59.46/9.44 ( X26 @ id @ ( lam @ ( X30 @ sh @ one ) ) @ id ) ) ) ) => 59.46/9.44 ( ( ![X40:term]: ( ( X28 @ X40 ) <=> ( X26 @ id @ X40 @ id ) ) ) => 59.46/9.44 ( ![X42:term]: 59.46/9.44 ( ( ![X44:term]: 59.46/9.44 ( ( X28 @ X44 ) => 59.46/9.44 ( X28 @ ( sub @ X42 @ ( push @ X44 @ id ) ) ) ) ) => 59.46/9.44 ( X28 @ ( lam @ X42 ) ) ) ) ) ) ) => 59.46/9.44 ( ![X46:( subst > term > subst > $o )]: 59.46/9.44 ( ( ![X48:subst,X50:term,X52:subst,X54:subst]: 59.46/9.44 ( ( X46 @ X48 @ X50 @ ( comp @ X54 @ X52 ) ) => 59.46/9.44 ( X46 @ ( comp @ X48 @ X54 ) @ ( sub @ X50 @ X54 ) @ X52 ) ) ) => 59.46/9.44 ( ( ![X56:subst,X58:term,X60:subst,X62:subst]: 59.46/9.44 ( ( X46 @ ( comp @ X56 @ X62 ) @ ( sub @ X58 @ X62 ) @ X60 ) => 59.46/9.44 ( X46 @ X56 @ X58 @ ( comp @ X62 @ X60 ) ) ) ) => 59.46/9.44 ( ( ![X64:term]: 59.46/9.44 ( ( var @ ( sub @ X64 @ id ) ) => ( X46 @ id @ X64 @ id ) ) ) => 59.46/9.44 ( ( ![X66:term,X68:term]: 59.46/9.44 ( ( X46 @ id @ X66 @ id ) => 59.46/9.44 ( ( X46 @ id @ X68 @ id ) => 59.46/9.44 ( X46 @ id @ ( ap @ ( sub @ X66 @ id ) @ X68 ) @ id ) ) ) ) => 59.46/9.44 ( ( ![X70:( subst > term > term )]: 59.46/9.44 ( ( ![X72:subst,X74:term,X76:subst]: 59.46/9.44 ( ( sub @ ( X70 @ X72 @ X74 ) @ X76 ) = 59.46/9.44 ( X70 @ 59.46/9.44 ( comp @ X72 @ X76 ) @ ( sub @ X74 @ X76 ) ) ) ) => 59.46/9.44 ( ( ![X78:term]: 59.46/9.44 ( ( X46 @ id @ X78 @ id ) => 59.46/9.44 ( X46 @ id @ ( X70 @ id @ X78 ) @ id ) ) ) => 59.46/9.44 ( X46 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) ) ) => 59.46/9.44 ( ![X80:term]: ( X46 @ id @ X80 @ id ) ) ) ) ) ) ) ) ) ) ))). 59.46/9.44 thf(zf_stmt_1, negated_conjecture, 59.46/9.44 (~( ( ![X4:( subst > term > subst > $o )]: 59.46/9.44 ( ?[X6:( term > $o )]: 59.46/9.44 ( ![X8:term]: ( ( X6 @ X8 ) <=> ( X4 @ id @ X8 @ id ) ) ) ) ) => 59.46/9.44 ( ( ![X10:( term > $o )]: 59.46/9.44 ( ( ![X12:term]: ( ( var @ X12 ) => ( X10 @ X12 ) ) ) => 59.46/9.44 ( ( ![X14:term,X16:term]: 59.46/9.44 ( ( X10 @ X14 ) => 59.46/9.44 ( ( X10 @ X16 ) => ( X10 @ ( ap @ X14 @ X16 ) ) ) ) ) => 59.46/9.44 ( ( ![X18:term]: 59.46/9.44 ( ( ![X20:term]: 59.46/9.44 ( ( X10 @ X20 ) => 59.46/9.44 ( X10 @ ( sub @ X18 @ ( push @ X20 @ id ) ) ) ) ) => 59.46/9.44 ( X10 @ ( lam @ X18 ) ) ) ) => 59.46/9.44 ( ![X22:term]: ( X10 @ X22 ) ) ) ) ) ) => 59.46/9.44 ( ( ![X24:term]: ( ( sub @ X24 @ id ) = ( X24 ) ) ) => 59.46/9.44 ( ( ![X26:( subst > term > subst > $o ),X28:( term > $o )]: 59.46/9.44 ( ( ![X30:( subst > term > term )]: 59.46/9.44 ( ( ![X32:subst,X34:term,X36:subst]: 59.46/9.44 ( ( sub @ ( X30 @ X32 @ X34 ) @ X36 ) = 59.46/9.44 ( X30 @ ( comp @ X32 @ X36 ) @ ( sub @ X34 @ X36 ) ) ) ) => 59.46/9.44 ( ( ![X38:term]: 59.46/9.44 ( ( X26 @ id @ X38 @ id ) => 59.46/9.44 ( X26 @ id @ ( X30 @ id @ X38 ) @ id ) ) ) => 59.46/9.44 ( X26 @ id @ ( lam @ ( X30 @ sh @ one ) ) @ id ) ) ) ) => 59.46/9.44 ( ( ![X40:term]: 59.46/9.44 ( ( X28 @ X40 ) <=> ( X26 @ id @ X40 @ id ) ) ) => 59.46/9.44 ( ![X42:term]: 59.46/9.44 ( ( ![X44:term]: 59.46/9.44 ( ( X28 @ X44 ) => 59.46/9.44 ( X28 @ ( sub @ X42 @ ( push @ X44 @ id ) ) ) ) ) => 59.46/9.44 ( X28 @ ( lam @ X42 ) ) ) ) ) ) ) => 59.46/9.44 ( ![X46:( subst > term > subst > $o )]: 59.46/9.44 ( ( ![X48:subst,X50:term,X52:subst,X54:subst]: 59.46/9.44 ( ( X46 @ X48 @ X50 @ ( comp @ X54 @ X52 ) ) => 59.46/9.44 ( X46 @ ( comp @ X48 @ X54 ) @ ( sub @ X50 @ X54 ) @ X52 ) ) ) => 59.46/9.44 ( ( ![X56:subst,X58:term,X60:subst,X62:subst]: 59.46/9.44 ( ( X46 @ 59.46/9.44 ( comp @ X56 @ X62 ) @ ( sub @ X58 @ X62 ) @ X60 ) => 59.46/9.44 ( X46 @ X56 @ X58 @ ( comp @ X62 @ X60 ) ) ) ) => 59.46/9.44 ( ( ![X64:term]: 59.46/9.44 ( ( var @ ( sub @ X64 @ id ) ) => 59.46/9.44 ( X46 @ id @ X64 @ id ) ) ) => 59.46/9.44 ( ( ![X66:term,X68:term]: 59.46/9.44 ( ( X46 @ id @ X66 @ id ) => 59.46/9.44 ( ( X46 @ id @ X68 @ id ) => 59.46/9.44 ( X46 @ 59.46/9.44 id @ ( ap @ ( sub @ X66 @ id ) @ X68 ) @ id ) ) ) ) => 59.46/9.44 ( ( ![X70:( subst > term > term )]: 59.46/9.44 ( ( ![X72:subst,X74:term,X76:subst]: 59.46/9.44 ( ( sub @ ( X70 @ X72 @ X74 ) @ X76 ) = 59.46/9.44 ( X70 @ 59.46/9.44 ( comp @ X72 @ X76 ) @ ( sub @ X74 @ X76 ) ) ) ) => 59.46/9.44 ( ( ![X78:term]: 59.46/9.44 ( ( X46 @ id @ X78 @ id ) => 59.46/9.44 ( X46 @ id @ ( X70 @ id @ X78 ) @ id ) ) ) => 59.46/9.44 ( X46 @ id @ ( lam @ ( X70 @ sh @ one ) ) @ id ) ) ) ) => 59.46/9.44 ( ![X80:term]: ( X46 @ id @ X80 @ id ) ) ) ) ) ) ) ) ) ) ) )), 59.46/9.44 inference('cnf.neg', [status(esa)], [zf_stmt_0])). 59.46/9.44 thf(zip_derived_cl0, plain, 59.46/9.44 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((??) @ (^[Y1 : term > $o]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y1 @ Y2) <=> (Y0 @ id @ Y2 @ 59.46/9.44 id)))))))))))) => 59.46/9.44 (((((!!) @ (^[Y0 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ Y1) => 59.46/9.44 (((Y0 @ Y2) => (Y0 @ 59.46/9.44 (ap @ Y1 @ Y2)))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ Y2) => (Y0 @ 59.46/9.44 (sub @ Y1 @ 59.46/9.44 (push @ Y2 @ id)))))))) => 59.46/9.44 (Y0 @ (lam @ Y1))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 59.46/9.44 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((!!) @ (^[Y1 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y2 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y3 : subst]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y4 : term]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y5 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 Y3 @ Y4) @ 59.46/9.44 Y5) = 59.46/9.44 (Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y3 @ Y5) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y4 @ Y5))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 Y3 @ 59.46/9.44 id) => 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 id @ Y3) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ 59.46/9.44 (Y2 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y1 @ Y2) <=> (Y0 @ 59.46/9.44 id @ Y2 @ id)))))) => 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (Y1 @ 59.46/9.44 Y3) => 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 push @ 59.46/9.44 Y3 @ id)))))))) => 59.46/9.44 (Y1 @ (lam @ Y2))))))))))))))))) => 59.46/9.44 (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)) => 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3) => 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((var @ (sub @ Y1 @ id)) => 59.46/9.44 (Y0 @ id @ Y1 @ id)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ Y1 @ 59.46/9.44 id) => 59.46/9.44 (((Y0 @ id @ 59.46/9.44 Y2 @ id) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (ap @ 59.46/9.44 (sub @ Y1 @ 59.46/9.44 id) @ 59.46/9.44 Y2) @ 59.46/9.44 id))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y2 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ Y3) @ 59.46/9.44 Y4) = 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y3 @ Y4))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ 59.46/9.44 id @ Y2 @ 59.46/9.44 id) => 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 (Y1 @ 59.46/9.44 id @ Y2) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y1 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: 59.46/9.44 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))))), 59.46/9.44 inference('cnf', [status(esa)], [zf_stmt_1])). 59.46/9.44 thf(zip_derived_cl2, plain, 59.46/9.44 (~ (((((!!) @ (^[Y0 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ Y1) => 59.46/9.44 (((Y0 @ Y2) => (Y0 @ 59.46/9.44 (ap @ Y1 @ Y2)))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ Y2) => (Y0 @ 59.46/9.44 (sub @ Y1 @ 59.46/9.44 (push @ Y2 @ id)))))))) => 59.46/9.44 (Y0 @ (lam @ Y1))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: (Y0 @ Y1))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 59.46/9.44 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((!!) @ (^[Y1 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y2 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : term]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y5 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 Y3 @ Y4) @ 59.46/9.44 Y5) = 59.46/9.44 (Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y3 @ Y5) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y4 @ Y5))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 Y3 @ 59.46/9.44 id) => 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 id @ Y3) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y2 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y1 @ Y2) <=> (Y0 @ 59.46/9.44 id @ Y2 @ id)))))) => 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (Y1 @ 59.46/9.44 Y3) => 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 push @ 59.46/9.44 Y3 @ id)))))))) => 59.46/9.44 (Y1 @ (lam @ Y2))))))))))))))))) => 59.46/9.44 (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)) => 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3) => 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((var @ (sub @ Y1 @ id)) => 59.46/9.44 (Y0 @ id @ Y1 @ id)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ Y1 @ 59.46/9.44 id) => 59.46/9.44 (((Y0 @ id @ Y2 @ 59.46/9.44 id) => (Y0 @ 59.46/9.44 id @ 59.46/9.44 (ap @ 59.46/9.44 (sub @ Y1 @ id) @ 59.46/9.44 Y2) @ 59.46/9.44 id))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y2 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y3 : term]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ Y3) @ 59.46/9.44 Y4) = 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y3 @ Y4))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ 59.46/9.44 Y2 @ id) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (Y1 @ id @ 59.46/9.44 Y2) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y1 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: 59.46/9.44 (Y0 @ id @ Y1 @ id)))))))))))))))))))))))), 59.46/9.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 59.46/9.44 thf(zip_derived_cl5, plain, 59.46/9.44 (~ (((((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0)))))) => 59.46/9.44 (((((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((!!) @ (^[Y1 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y2 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : term]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y5 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 Y3 @ Y4) @ 59.46/9.44 Y5) = 59.46/9.44 (Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y3 @ Y5) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y4 @ Y5))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (((Y0 @ 59.46/9.44 id @ Y3 @ 59.46/9.44 id) => 59.46/9.44 (Y0 @ 59.46/9.44 id @ 59.46/9.44 (Y2 @ 59.46/9.44 id @ Y3) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y2 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y1 @ Y2) <=> (Y0 @ 59.46/9.44 id @ Y2 @ id)))))) => 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (((Y1 @ 59.46/9.44 Y3) => 59.46/9.44 (Y1 @ 59.46/9.44 (sub @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 push @ 59.46/9.44 Y3 @ id)))))))) => 59.46/9.44 (Y1 @ (lam @ Y2))))))))))))))))) => 59.46/9.44 (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (((Y0 @ 59.46/9.44 Y1 @ Y2 @ 59.46/9.44 (comp @ 59.46/9.44 Y4 @ Y3)) => 59.46/9.44 (Y0 @ 59.46/9.44 (comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 (sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3) => 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((var @ (sub @ Y1 @ id)) => (Y0 @ 59.46/9.44 id @ Y1 @ id)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ Y1 @ 59.46/9.44 id) => 59.46/9.44 (((Y0 @ id @ Y2 @ 59.46/9.44 id) => (Y0 @ id @ 59.46/9.44 (ap @ 59.46/9.44 (sub @ Y1 @ id) @ 59.46/9.44 Y2) @ 59.46/9.44 id))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y2 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y3 : term]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ Y3) @ 59.46/9.44 Y4) = 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y3 @ Y4))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ 59.46/9.44 Y2 @ id) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (Y1 @ id @ Y2) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y1 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))))), 59.46/9.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 59.46/9.44 thf(zip_derived_cl12, plain, 59.46/9.44 (~ (((((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((!!) @ (^[Y1 : term > $o]: 59.46/9.44 (((((!!) @ (^[Y2 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : term]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y5 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y2 @ 59.46/9.44 Y3 @ Y4) @ 59.46/9.44 Y5) = 59.46/9.44 (Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y3 @ Y5) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y4 @ Y5))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (((Y0 @ id @ 59.46/9.44 Y3 @ id) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (Y2 @ id @ 59.46/9.44 Y3) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y2 @ sh @ one)) @ 59.46/9.44 id)))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y1 @ Y2) <=> (Y0 @ id @ 59.46/9.44 Y2 @ id)))))) => 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((((!!) @ (^[Y3 : term]: 59.46/9.44 (((Y1 @ Y3) => 59.46/9.44 (Y1 @ 59.46/9.44 (sub @ Y2 @ 59.46/9.44 (push @ 59.46/9.44 Y3 @ id)))))))) => 59.46/9.44 (Y1 @ (lam @ Y2))))))))))))))))) => 59.46/9.44 (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (((Y0 @ Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 (comp @ 59.46/9.44 Y4 @ Y3)) => 59.46/9.44 (Y0 @ 59.46/9.44 (comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 (sub @ Y2 @ 59.46/9.44 Y4) @ 59.46/9.44 Y3))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (((Y0 @ 59.46/9.44 (comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 (sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3) => 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ Y2 @ 59.46/9.44 (comp @ 59.46/9.44 Y4 @ Y3)))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((var @ (sub @ Y1 @ id)) => (Y0 @ 59.46/9.44 id @ Y1 @ id)))))) => 59.46/9.44 (((((!!) @ (^[Y1 : term]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ Y1 @ id) => 59.46/9.44 (((Y0 @ id @ Y2 @ 59.46/9.44 id) => (Y0 @ id @ 59.46/9.44 (ap @ 59.46/9.44 (sub @ Y1 @ id) @ 59.46/9.44 Y2) @ 59.46/9.44 id))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.44 (((((!!) @ (^[Y2 : subst]: 59.46/9.44 (((!!) @ (^[Y3 : term]: 59.46/9.44 (( 59.46/9.44 (!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (sub @ 59.46/9.44 ( 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ Y3) @ 59.46/9.44 Y4) = 59.46/9.44 (Y1 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y3 @ Y4))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y2 : term]: 59.46/9.44 (((Y0 @ id @ Y2 @ 59.46/9.44 id) => (Y0 @ 59.46/9.44 id @ 59.46/9.44 (Y1 @ id @ Y2) @ 59.46/9.44 id)))))) => 59.46/9.44 (Y0 @ id @ 59.46/9.44 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 59.46/9.44 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))))), 59.46/9.44 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 59.46/9.44 thf(zip_derived_cl17, plain, 59.46/9.44 (~ (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ (^[Y4 : subst]: 59.46/9.44 (( 59.46/9.44 (Y0 @ 59.46/9.44 Y1 @ 59.46/9.44 Y2 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y4 @ Y3)) => 59.46/9.44 (Y0 @ 59.46/9.44 ( 59.46/9.44 comp @ 59.46/9.44 Y1 @ Y4) @ 59.46/9.44 ( 59.46/9.44 sub @ 59.46/9.44 Y2 @ Y4) @ 59.46/9.44 Y3))))))))))))))) => 59.46/9.44 (((((!!) @ (^[Y1 : subst]: 59.46/9.44 (((!!) @ (^[Y2 : term]: 59.46/9.44 (((!!) @ (^[Y3 : subst]: 59.46/9.44 (((!!) @ ( 59.46/9.44 ^[Y4 : subst]: 59.46/9.45 (((Y0 @ 59.46/9.45 (comp @ 59.46/9.45 Y1 @ Y4) @ 59.46/9.45 (sub @ Y2 @ 59.46/9.45 Y4) @ 59.46/9.45 Y3) => 59.46/9.45 (Y0 @ Y1 @ 59.46/9.45 Y2 @ 59.46/9.45 (comp @ 59.46/9.45 Y4 @ Y3)))))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((var @ (sub @ Y1 @ id)) => (Y0 @ id @ 59.46/9.45 Y1 @ id)))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ id @ Y1 @ id) => 59.46/9.45 (((Y0 @ id @ Y2 @ id) => 59.46/9.45 (Y0 @ id @ 59.46/9.45 (ap @ 59.46/9.45 (sub @ Y1 @ id) @ Y2) @ 59.46/9.45 id))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : term]: 59.46/9.45 (( 59.46/9.45 (!!) @ ( 59.46/9.45 ^[Y4 : subst]: 59.46/9.45 (( 59.46/9.45 (sub @ 59.46/9.45 ( 59.46/9.45 Y1 @ 59.46/9.45 Y2 @ Y3) @ 59.46/9.45 Y4) = 59.46/9.45 (Y1 @ 59.46/9.45 ( 59.46/9.45 comp @ 59.46/9.45 Y2 @ Y4) @ 59.46/9.45 ( 59.46/9.45 sub @ 59.46/9.45 Y3 @ Y4))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ id @ Y2 @ 59.46/9.45 id) => (Y0 @ id @ 59.46/9.45 (Y1 @ id @ Y2) @ 59.46/9.45 id)))))) => 59.46/9.45 (Y0 @ id @ 59.46/9.45 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((!!) @ (^[Y1 : term]: (Y0 @ id @ Y1 @ id)))))))))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 59.46/9.45 thf(zip_derived_cl24, plain, 59.46/9.45 (~ (((((!!) @ (^[Y0 : subst]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 ((('#sk31' @ Y0 @ 59.46/9.45 Y1 @ 59.46/9.45 (comp @ Y3 @ Y2)) => 59.46/9.45 ('#sk31' @ 59.46/9.45 (comp @ Y0 @ Y3) @ 59.46/9.45 (sub @ Y1 @ Y3) @ 59.46/9.45 Y2))))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : subst]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 ((('#sk31' @ 59.46/9.45 (comp @ Y0 @ Y3) @ 59.46/9.45 (sub @ Y1 @ Y3) @ 59.46/9.45 Y2) => 59.46/9.45 ('#sk31' @ Y0 @ 59.46/9.45 Y1 @ 59.46/9.45 (comp @ Y3 @ Y2)))))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((var @ (sub @ Y0 @ id)) => ('#sk31' @ id @ Y0 @ 59.46/9.45 id)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y0 @ id) => 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (( 59.46/9.45 (sub @ 59.46/9.45 ( 59.46/9.45 Y0 @ 59.46/9.45 Y1 @ Y2) @ 59.46/9.45 Y3) = 59.46/9.45 (Y0 @ 59.46/9.45 ( 59.46/9.45 comp @ 59.46/9.45 Y1 @ Y3) @ 59.46/9.45 ( 59.46/9.45 sub @ 59.46/9.45 Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ 59.46/9.45 id)))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))))))))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 59.46/9.45 thf(zip_derived_cl32, plain, 59.46/9.45 (~ (((((!!) @ (^[Y0 : subst]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 ((('#sk31' @ 59.46/9.45 (comp @ Y0 @ Y3) @ 59.46/9.45 (sub @ Y1 @ Y3) @ 59.46/9.45 Y2) => ('#sk31' @ 59.46/9.45 Y0 @ Y1 @ 59.46/9.45 (comp @ Y3 @ Y2)))))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((var @ (sub @ Y0 @ id)) => ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y0 @ id) => 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ 59.46/9.45 Y1 @ Y2) @ 59.46/9.45 Y3) = 59.46/9.45 (Y0 @ 59.46/9.45 (comp @ 59.46/9.45 Y1 @ Y3) @ 59.46/9.45 (sub @ 59.46/9.45 Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl24])). 59.46/9.45 thf(zip_derived_cl38, plain, 59.46/9.45 (~ (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((var @ (sub @ Y0 @ id)) => ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y0 @ id) => 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ 59.46/9.45 Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ 59.46/9.45 Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ 59.46/9.45 Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ 59.46/9.45 id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl32])). 59.46/9.45 thf(zip_derived_cl45, plain, 59.46/9.45 (~ (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y0 @ id) => 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => ('#sk31' @ 59.46/9.45 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ 59.46/9.45 Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 59.46/9.45 thf(zip_derived_cl54, plain, 59.46/9.45 (~ (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 59.46/9.45 thf(zip_derived_cl68, plain, 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 59.46/9.45 thf(zip_derived_cl83, plain, (~ ('#sk31' @ id @ '#sk251' @ id)), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl68])). 59.46/9.45 thf(zip_derived_cl4, plain, 59.46/9.45 ( (((!!) @ (^[Y0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: (((var @ Y1) => (Y0 @ Y1)))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ Y1) => 59.46/9.45 (((Y0 @ Y2) => (Y0 @ 59.46/9.45 (ap @ Y1 @ Y2)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ Y2) => (Y0 @ 59.46/9.45 (sub @ Y1 @ 59.46/9.45 (push @ Y2 @ id)))))))) => 59.46/9.45 (Y0 @ (lam @ Y1))))))) => 59.46/9.45 (((!!) @ (^[Y1 : term]: (Y0 @ Y1)))))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])). 59.46/9.45 thf(zip_derived_cl9, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0))))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 59.46/9.45 thf(zip_derived_cl14, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl9])). 59.46/9.45 thf(zip_derived_cl19, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((var @ ('#sk30' @ X2)) => (X2 @ ('#sk30' @ X2)))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 59.46/9.45 thf(zip_derived_cl26, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (X2 @ ('#sk30' @ X2)) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 59.46/9.45 thf(zip_derived_cl34, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))) 59.46/9.45 | ~ (X2 @ ('#sk30' @ X2)))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl26])). 59.46/9.45 thf(zip_derived_cl40, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ ('#sk103' @ X2)) => 59.46/9.45 (((X2 @ Y0) => (X2 @ (ap @ ('#sk103' @ X2) @ Y0))))))))) 59.46/9.45 | ~ (X2 @ ('#sk30' @ X2)) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl34])). 59.46/9.45 thf(zip_derived_cl47, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((X2 @ ('#sk103' @ X2)) => 59.46/9.45 (((X2 @ ('#sk135' @ X2)) => (X2 @ 59.46/9.45 (ap @ ('#sk103' @ X2) @ ('#sk135' @ X2))))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))) 59.46/9.45 | ~ (X2 @ ('#sk30' @ X2)))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl40])). 59.46/9.45 thf(zip_derived_cl57, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ ('#form178' @ X2) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 59.46/9.45 define([status(thm)])). 59.46/9.45 thf(zip_derived_cl58, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 59.46/9.45 | ~ ('#form178' @ X2))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 59.46/9.45 thf(zip_derived_cl73, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ Y0) => (X2 @ 59.46/9.45 (sub @ ('#sk225' @ X2) @ (push @ Y0 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ ('#sk225' @ X2))))) 59.46/9.45 | ~ ('#form178' @ X2) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl58])). 59.46/9.45 thf(zip_derived_cl91, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (X2 @ (lam @ ('#sk225' @ X2))) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 59.46/9.45 | ~ ('#form178' @ X2))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 59.46/9.45 thf(zip_derived_cl101, plain, 59.46/9.45 (![X2 : term > $o, X4 : term]: 59.46/9.45 ( (X2 @ X4) | ~ ('#form178' @ X2) | ~ (X2 @ (lam @ ('#sk225' @ X2))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl91])). 59.46/9.45 thf(zip_derived_cl90, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 ( (((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ Y0) => (X2 @ 59.46/9.45 (sub @ ('#sk225' @ X2) @ (push @ Y0 @ id)))))))) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 59.46/9.45 | ~ ('#form178' @ X2))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl73])). 59.46/9.45 thf(zip_derived_cl100, plain, 59.46/9.45 (![X2 : term > $o, X4 : term]: 59.46/9.45 ( (((X2 @ X4) => (X2 @ (sub @ ('#sk225' @ X2) @ (push @ X4 @ id))))) 59.46/9.45 | ~ ('#form178' @ X2) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl90])). 59.46/9.45 thf(zip_derived_cl108, plain, 59.46/9.45 (![X2 : term > $o, X4 : term]: 59.46/9.45 (~ (X2 @ X4) 59.46/9.45 | (X2 @ (sub @ ('#sk225' @ X2) @ (push @ X4 @ id))) 59.46/9.45 | (((!!) @ (^[Y0 : term]: (X2 @ Y0)))) 59.46/9.45 | ~ ('#form178' @ X2))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl100])). 59.46/9.45 thf(zip_derived_cl112, plain, 59.46/9.45 (![X2 : term > $o, X4 : term, X6 : term]: 59.46/9.45 ( (X2 @ X6) 59.46/9.45 | ~ ('#form178' @ X2) 59.46/9.45 | (X2 @ (sub @ ('#sk225' @ X2) @ (push @ X4 @ id))) 59.46/9.45 | ~ (X2 @ X4))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl108])). 59.46/9.45 thf(zip_derived_cl115, plain, 59.46/9.45 (![X0 : term > $o, X1 : term]: 59.46/9.45 (~ (X0 @ X1) 59.46/9.45 | ~ ('#form178' @ X0) 59.46/9.45 | (X0 @ (sub @ ('#sk225' @ X0) @ (push @ X1 @ id))))), 59.46/9.45 inference('condensation', [status(thm)], [zip_derived_cl112])). 59.46/9.45 thf(zip_derived_cl9, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => (X2 @ Y0)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y0) => 59.46/9.45 (((X2 @ Y1) => (X2 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: (X2 @ Y0))))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl4])). 59.46/9.45 thf(zip_derived_cl10, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk5' @ X0 @ Y0)))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.45 (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0))))))))))), 59.46/9.45 inference('triggered_bool_instantiation', [status(thm)], 59.46/9.45 [zip_derived_cl9])). 59.46/9.45 thf(zip_derived_cl129, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: (((var @ Y0) => ('#sk5' @ X0 @ Y0)))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl10])). 59.46/9.45 thf(zip_derived_cl130, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ (((var @ ('#sk30' @ ('#sk5' @ X0))) => ('#sk5' @ X0 @ 59.46/9.45 ('#sk30' @ ('#sk5' @ X0))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl129])). 59.46/9.45 thf(zip_derived_cl1, plain, 59.46/9.45 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.45 (((??) @ (^[Y1 : term > $o]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y1 @ Y2) <=> (Y0 @ id @ Y2 @ id))))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl0])). 59.46/9.45 thf(zip_derived_cl3, plain, 59.46/9.45 (![X2 : subst > term > subst > $o]: 59.46/9.45 (((??) @ (^[Y0 : term > $o]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((Y0 @ Y1) <=> (X2 @ id @ Y1 @ id)))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1])). 59.46/9.45 thf(zip_derived_cl6, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((??) @ (^[Y0 : term > $o]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((Y0 @ Y1) <=> 59.46/9.45 ((^[Y2 : subst,Y3 : term,Y4 : subst]: 59.46/9.45 (X2 @ Y3)) @ 59.46/9.45 id @ Y1 @ id)))))))))), 59.46/9.45 inference('prune_arg_fun', [status(thm)], [zip_derived_cl3])). 59.46/9.45 thf(zip_derived_cl7, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((??) @ (^[Y0 : term > $o]: 59.46/9.45 (((!!) @ (^[Y1 : term]: (((Y0 @ Y1) <=> (X2 @ Y1)))))))))), 59.46/9.45 inference('ho_norm', [status(thm)], [zip_derived_cl6])). 59.46/9.45 thf(zip_derived_cl8, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((!!) @ (^[Y0 : term]: ((('#sk5' @ X2 @ Y0) <=> (X2 @ Y0))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 59.46/9.45 thf(zip_derived_cl13, plain, 59.46/9.45 (![X2 : term > $o, X4 : term]: ((('#sk5' @ X2 @ X4) <=> (X2 @ X4)))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl8])). 59.46/9.45 thf(zip_derived_cl18, plain, 59.46/9.45 (![X2 : term > $o, X4 : term]: (('#sk5' @ X2 @ X4) = (X2 @ X4))), 59.46/9.45 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 59.46/9.45 thf(zip_derived_cl131, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ ((('#sk5' @ var @ ('#sk30' @ ('#sk5' @ X0))) => ('#sk5' @ X0 @ 59.46/9.45 ('#sk30' @ ('#sk5' @ X0))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 inference('demod', [status(thm)], [zip_derived_cl130, zip_derived_cl18])). 59.46/9.45 thf(zip_derived_cl133, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ ('#sk5' @ X0 @ ('#sk30' @ ('#sk5' @ X0))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])). 59.46/9.45 thf(zip_derived_cl132, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 ( ('#sk5' @ var @ ('#sk30' @ ('#sk5' @ X0))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])). 59.46/9.45 thf(zip_derived_cl134, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ ('#form632' @ X0) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.45 define([status(thm)])). 59.46/9.45 thf(zip_derived_cl137, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 ( ('#form632' @ X0) | ~ ('#sk5' @ X0 @ ('#sk30' @ ('#sk5' @ X0))))), 59.46/9.45 inference('renaming', [status(thm)], 59.46/9.45 [zip_derived_cl133, zip_derived_cl134])). 59.46/9.45 thf(zip_derived_cl16, plain, 59.46/9.45 ( (((!!) @ (^[Y0 : subst > term > subst > $o]: 59.46/9.45 (((!!) @ (^[Y1 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y2 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y3 : subst]: 59.46/9.45 (((!!) @ (^[Y4 : term]: 59.46/9.45 (( 59.46/9.45 (!!) @ ( 59.46/9.45 ^[Y5 : subst]: 59.46/9.45 (( 59.46/9.45 (sub @ 59.46/9.45 ( 59.46/9.45 Y2 @ 59.46/9.45 Y3 @ Y4) @ 59.46/9.45 Y5) = 59.46/9.45 (Y2 @ 59.46/9.45 ( 59.46/9.45 comp @ 59.46/9.45 Y3 @ Y5) @ 59.46/9.45 ( 59.46/9.45 sub @ 59.46/9.45 Y4 @ Y5))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y3 : term]: 59.46/9.45 (((Y0 @ id @ 59.46/9.45 Y3 @ id) => 59.46/9.45 (Y0 @ id @ 59.46/9.45 (Y2 @ id @ Y3) @ 59.46/9.45 id)))))) => 59.46/9.45 (Y0 @ id @ 59.46/9.45 (lam @ (Y2 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y1 @ Y2) <=> (Y0 @ id @ 59.46/9.45 Y2 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((((!!) @ (^[Y3 : term]: 59.46/9.45 (((Y1 @ Y3) => 59.46/9.45 (Y1 @ 59.46/9.45 (sub @ Y2 @ 59.46/9.45 (push @ Y3 @ 59.46/9.45 id)))))))) => 59.46/9.45 (Y1 @ (lam @ Y2)))))))))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 59.46/9.45 thf(zip_derived_cl21, plain, 59.46/9.45 (![X2 : subst > term > subst > $o]: 59.46/9.45 (((!!) @ (^[Y0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : term]: 59.46/9.45 (((!!) @ ( 59.46/9.45 ^[Y4 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y1 @ Y2 @ 59.46/9.45 Y3) @ 59.46/9.45 Y4) = 59.46/9.45 (Y1 @ 59.46/9.45 (comp @ 59.46/9.45 Y2 @ Y4) @ 59.46/9.45 (sub @ 59.46/9.45 Y3 @ Y4))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((X2 @ id @ Y2 @ id) => 59.46/9.45 (X2 @ id @ 59.46/9.45 (Y1 @ id @ Y2) @ id)))))) => 59.46/9.45 (X2 @ id @ (lam @ (Y1 @ sh @ one)) @ 59.46/9.45 id)))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((Y0 @ Y1) <=> (X2 @ id @ Y1 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ Y2) => (Y0 @ 59.46/9.45 (sub @ Y1 @ 59.46/9.45 (push @ Y2 @ id)))))))) => 59.46/9.45 (Y0 @ (lam @ Y1))))))))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 59.46/9.45 thf(zip_derived_cl22, plain, 59.46/9.45 ( (((!!) @ (^[Y0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : term]: 59.46/9.45 (((!!) @ (^[Y4 : subst]: 59.46/9.45 (( 59.46/9.45 (sub @ 59.46/9.45 ( 59.46/9.45 Y1 @ 59.46/9.45 Y2 @ Y3) @ 59.46/9.45 Y4) = 59.46/9.45 (Y1 @ 59.46/9.45 ( 59.46/9.45 comp @ 59.46/9.45 Y2 @ Y4) @ 59.46/9.45 ( 59.46/9.45 sub @ 59.46/9.45 Y3 @ Y4))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 ((('#sk31' @ id @ Y2 @ id) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (Y1 @ id @ Y2) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 (lam @ (Y1 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((Y0 @ Y1) <=> ('#sk31' @ id @ Y1 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y1 : term]: 59.46/9.45 (((((!!) @ (^[Y2 : term]: 59.46/9.45 (((Y0 @ Y2) => (Y0 @ 59.46/9.45 (sub @ Y1 @ 59.46/9.45 (push @ Y2 @ id)))))))) => 59.46/9.45 (Y0 @ (lam @ Y1))))))))))))))), 59.46/9.45 inference('triggered_bool_instantiation', [status(thm)], 59.46/9.45 [zip_derived_cl21])). 59.46/9.45 thf(zip_derived_cl184, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0)))))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 59.46/9.45 thf(zip_derived_cl186, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0)))))))))))), 59.46/9.45 inference('triggered_bool_instantiation', [status(thm)], 59.46/9.45 [zip_derived_cl184])). 59.46/9.45 thf(zip_derived_cl214, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])). 59.46/9.45 thf(zip_derived_cl214, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl186])). 59.46/9.45 thf(zip_derived_cl215, plain, 59.46/9.45 (( ('#form922') 59.46/9.45 | ~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))))), 59.46/9.45 define([status(thm)])). 59.46/9.45 thf(zip_derived_cl217, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ ('#form922') 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.45 X0 @ (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))))))), 59.46/9.45 inference('renaming', [status(thm)], 59.46/9.45 [zip_derived_cl214, zip_derived_cl215])). 59.46/9.45 thf(zip_derived_cl218, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) 59.46/9.45 | (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))) 59.46/9.45 | ~ ('#form922'))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl217])). 59.46/9.45 thf(zip_derived_cl221, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 (~ ((('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) <=> 59.46/9.45 ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id))) 59.46/9.45 | ~ ('#form922') 59.46/9.45 | (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl218])). 59.46/9.45 thf(zip_derived_cl225, plain, 59.46/9.45 (![X0 : term > $o]: 59.46/9.45 ((('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) 59.46/9.45 != ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id)) 59.46/9.45 | ~ ('#form922') 59.46/9.45 | (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ Y0))))))))), 59.46/9.45 inference('simplify nested equalities', [status(thm)], 59.46/9.45 [zip_derived_cl221])). 59.46/9.45 thf(zip_derived_cl226, plain, 59.46/9.45 (![X0 : term > $o, X2 : term]: 59.46/9.45 ( (((((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ X2 @ (push @ Y0 @ id)))))))) => 59.46/9.45 ('#sk5' @ X0 @ (lam @ X2)))) 59.46/9.45 | ~ ('#form922') 59.46/9.45 | (('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) 59.46/9.45 != ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id)))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl225])). 59.46/9.45 thf(zip_derived_cl229, plain, 59.46/9.45 (![X0 : term > $o, X2 : term]: 59.46/9.45 (~ (((!!) @ (^[Y0 : term]: 59.46/9.45 ((('#sk5' @ X0 @ Y0) => ('#sk5' @ X0 @ 59.46/9.45 (sub @ X2 @ (push @ Y0 @ id)))))))) 59.46/9.45 | ('#sk5' @ X0 @ (lam @ X2)) 59.46/9.45 | (('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) 59.46/9.45 != ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id)) 59.46/9.45 | ~ ('#form922'))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl226])). 59.46/9.45 thf(zip_derived_cl232, plain, 59.46/9.45 (![X0 : term > $o, X2 : term]: 59.46/9.45 (~ ((('#sk5' @ X0 @ ('#sk417' @ ('#sk5' @ X0) @ X2)) => ('#sk5' @ 59.46/9.45 X0 @ (sub @ X2 @ (push @ ('#sk417' @ ('#sk5' @ X0) @ X2) @ id))))) 59.46/9.45 | ~ ('#form922') 59.46/9.45 | (('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) 59.46/9.45 != ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id)) 59.46/9.45 | ('#sk5' @ X0 @ (lam @ X2)))), 59.46/9.45 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl229])). 59.46/9.45 thf(zip_derived_cl234, plain, 59.46/9.45 (![X0 : term > $o, X2 : term]: 59.46/9.45 ( ('#sk5' @ X0 @ ('#sk417' @ ('#sk5' @ X0) @ X2)) 59.46/9.45 | ('#sk5' @ X0 @ (lam @ X2)) 59.46/9.45 | (('#sk5' @ X0 @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0))) 59.46/9.45 != ('#sk31' @ id @ 59.46/9.45 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.45 ('#sk5' @ X0)) @ 59.46/9.45 id)) 59.46/9.45 | ~ ('#form922'))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl232])). 59.46/9.45 thf(zip_derived_cl184, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) => 59.46/9.45 (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0)))))))))))), 59.46/9.45 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl22])). 59.46/9.45 thf(zip_derived_cl187, plain, 59.46/9.45 (![X2 : term > $o]: 59.46/9.45 (~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y1 : subst]: 59.46/9.45 (((!!) @ (^[Y2 : term]: 59.46/9.45 (((!!) @ (^[Y3 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y0 @ Y1 @ Y2) @ 59.46/9.45 Y3) = (Y0 @ 59.46/9.45 (comp @ Y1 @ Y3) @ 59.46/9.45 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.45 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.45 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))) 59.46/9.45 | (((((!!) @ (^[Y0 : term]: 59.46/9.45 (((X2 @ Y0) <=> ('#sk31' @ id @ Y0 @ id)))))) => 59.46/9.45 (((!!) @ (^[Y0 : term]: 59.46/9.45 (((((!!) @ (^[Y1 : term]: 59.46/9.45 (((X2 @ Y1) => (X2 @ 59.46/9.45 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.45 (X2 @ (lam @ Y0))))))))))), 59.46/9.45 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl184])). 59.46/9.45 thf(zip_derived_cl21, plain, 59.46/9.45 (![X2 : subst > term > subst > $o]: 59.46/9.45 (((!!) @ (^[Y0 : term > $o]: 59.46/9.45 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.45 (((((!!) @ (^[Y2 : subst]: 59.46/9.45 (((!!) @ (^[Y3 : term]: 59.46/9.45 (((!!) @ ( 59.46/9.45 ^[Y4 : subst]: 59.46/9.45 (((sub @ 59.46/9.45 (Y1 @ Y2 @ 59.46/9.45 Y3) @ 59.46/9.45 Y4) = 59.46/9.46 (Y1 @ 59.46/9.46 (comp @ 59.46/9.46 Y2 @ Y4) @ 59.46/9.46 (sub @ 59.46/9.46 Y3 @ Y4))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 (((X2 @ id @ Y2 @ id) => 59.46/9.46 (X2 @ id @ 59.46/9.46 (Y1 @ id @ Y2) @ id)))))) => 59.46/9.46 (X2 @ id @ (lam @ (Y1 @ sh @ one)) @ 59.46/9.46 id)))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((Y0 @ Y1) <=> (X2 @ id @ Y1 @ id)))))) => 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 (((Y0 @ Y2) => (Y0 @ 59.46/9.46 (sub @ Y1 @ 59.46/9.46 (push @ Y2 @ id)))))))) => 59.46/9.46 (Y0 @ (lam @ Y1))))))))))))))), 59.46/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 59.46/9.46 thf(zip_derived_cl27, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 (((!!) @ (^[Y0 : term > $o]: 59.46/9.46 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y2 : subst]: 59.46/9.46 (((!!) @ (^[Y3 : term]: 59.46/9.46 (((!!) @ ( 59.46/9.46 ^[Y4 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y1 @ Y2 @ 59.46/9.46 Y3) @ 59.46/9.46 Y4) = 59.46/9.46 (Y1 @ 59.46/9.46 (comp @ 59.46/9.46 Y2 @ Y4) @ 59.46/9.46 (sub @ 59.46/9.46 Y3 @ Y4))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 ((((^[Y3 : subst,Y4 : term, 59.46/9.46 Y5 : subst]: 59.46/9.46 (X2 @ Y4)) @ 59.46/9.46 id @ Y2 @ id) => 59.46/9.46 ((^[Y3 : subst,Y4 : term, 59.46/9.46 Y5 : subst]: 59.46/9.46 (X2 @ Y4)) @ 59.46/9.46 id @ (Y1 @ id @ Y2) @ id)))))) => 59.46/9.46 ((^[Y2 : subst,Y3 : term,Y4 : subst]: 59.46/9.46 (X2 @ Y3)) @ 59.46/9.46 id @ (lam @ (Y1 @ sh @ one)) @ id)))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((Y0 @ Y1) <=> 59.46/9.46 ((^[Y2 : subst,Y3 : term,Y4 : subst]: 59.46/9.46 (X2 @ Y3)) @ 59.46/9.46 id @ Y1 @ id)))))) => 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 (((Y0 @ Y2) => (Y0 @ 59.46/9.46 (sub @ Y1 @ 59.46/9.46 (push @ Y2 @ id)))))))) => 59.46/9.46 (Y0 @ (lam @ Y1))))))))))))))), 59.46/9.46 inference('prune_arg_fun', [status(thm)], [zip_derived_cl21])). 59.46/9.46 thf(zip_derived_cl28, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 (((!!) @ (^[Y0 : term > $o]: 59.46/9.46 (((((!!) @ (^[Y1 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y2 : subst]: 59.46/9.46 (((!!) @ (^[Y3 : term]: 59.46/9.46 (((!!) @ ( 59.46/9.46 ^[Y4 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y1 @ Y2 @ 59.46/9.46 Y3) @ 59.46/9.46 Y4) = 59.46/9.46 (Y1 @ 59.46/9.46 (comp @ 59.46/9.46 Y2 @ Y4) @ 59.46/9.46 (sub @ 59.46/9.46 Y3 @ Y4))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 (((X2 @ Y2) => (X2 @ 59.46/9.46 (Y1 @ id @ Y2))))))) => 59.46/9.46 (X2 @ (lam @ (Y1 @ sh @ one)))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: (((Y0 @ Y1) <=> (X2 @ Y1)))))) => 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((((!!) @ (^[Y2 : term]: 59.46/9.46 (((Y0 @ Y2) => (Y0 @ 59.46/9.46 (sub @ Y1 @ 59.46/9.46 (push @ Y2 @ id)))))))) => 59.46/9.46 (Y0 @ (lam @ Y1))))))))))))))), 59.46/9.46 inference('ho_norm', [status(thm)], [zip_derived_cl27])). 59.46/9.46 thf(zip_derived_cl29, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o]: 59.46/9.46 (((((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ Y3) @ 59.46/9.46 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X2 @ Y1) => (X2 @ (Y0 @ id @ Y1))))))) => 59.46/9.46 (X2 @ (lam @ (Y0 @ sh @ one)))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0)))))))))))), 59.46/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl28])). 59.46/9.46 thf(zip_derived_cl35, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o]: 59.46/9.46 (~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ Y3) @ 59.46/9.46 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X2 @ Y1) => (X2 @ (Y0 @ id @ Y1))))))) => 59.46/9.46 (X2 @ (lam @ (Y0 @ sh @ one)))))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0))))))))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl29])). 59.46/9.46 thf(zip_derived_cl41, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o]: 59.46/9.46 (~ (((((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 ('#sk124' @ X2 @ Y0 @ Y1) @ 59.46/9.46 Y2) = ('#sk124' @ X2 @ 59.46/9.46 (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 (((X2 @ Y0) => (X2 @ ('#sk124' @ X2 @ id @ Y0))))))) => 59.46/9.46 (X2 @ (lam @ ('#sk124' @ X2 @ sh @ one))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0))))))))))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl35])). 59.46/9.46 thf(zip_derived_cl48, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o]: 59.46/9.46 ( (((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 ('#sk124' @ X2 @ Y0 @ Y1) @ 59.46/9.46 Y2) = ('#sk124' @ X2 @ 59.46/9.46 (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0))))))))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 59.46/9.46 thf(zip_derived_cl60, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o, X6 : subst]: 59.46/9.46 ( (((!!) @ (^[Y0 : term]: 59.46/9.46 (((!!) @ (^[Y1 : subst]: 59.46/9.46 (((sub @ ('#sk124' @ X2 @ X6 @ Y0) @ Y1) = 59.46/9.46 ('#sk124' @ X2 @ (comp @ X6 @ Y1) @ 59.46/9.46 (sub @ Y0 @ Y1)))))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0))))))))))), 59.46/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl48])). 59.46/9.46 thf(zip_derived_cl74, plain, 59.46/9.46 (![X2 : term > $o, X4 : term > $o]: 59.46/9.46 (~ ('#form234' @ X2 @ X4) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: (((X4 @ Y0) <=> (X2 @ Y0)))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 (((X4 @ Y1) => (X4 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 (X4 @ (lam @ Y0))))))))))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl188, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 ( ('#form234' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.46 (^[Y0 : term]: (X2 @ Y0))) 59.46/9.46 | ~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ 59.46/9.46 Y3) @ 59.46/9.46 (sub @ Y2 @ 59.46/9.46 Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.46 ('#sk31' @ id @ (Y0 @ id @ Y1) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))))), 59.46/9.46 inference('renaming', [status(thm)], 59.46/9.46 [zip_derived_cl187, zip_derived_cl74])). 59.46/9.46 thf(zip_derived_cl189, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 ( ('#form234' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2) 59.46/9.46 | ~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ 59.46/9.46 Y3) @ 59.46/9.46 (sub @ Y2 @ 59.46/9.46 Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.46 ('#sk31' @ id @ (Y0 @ id @ Y1) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))))), 59.46/9.46 inference('ho_norm', [status(thm)], [zip_derived_cl188])). 59.46/9.46 thf(zip_derived_cl190, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 (~ (((((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 Y0 @ Y1) @ 59.46/9.46 Y2) = ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ id @ 59.46/9.46 Y0) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ 59.46/9.46 one)) @ 59.46/9.46 id))))) 59.46/9.46 | ('#form234' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl189])). 59.46/9.46 thf(zip_derived_cl192, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 (~ (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ id @ Y0) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ one)) @ 59.46/9.46 id))) 59.46/9.46 | ('#form234' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl190])). 59.46/9.46 thf(zip_derived_cl195, plain, 59.46/9.46 (![X2 : term > $o]: 59.46/9.46 (~ ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ one)) @ 59.46/9.46 id) 59.46/9.46 | ('#form234' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl192])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl4002, plain, 59.46/9.46 (![X0 : term > $o, X2 : term]: 59.46/9.46 ( ('#sk5' @ X0 @ ('#sk417' @ ('#sk5' @ X0) @ X2)) 59.46/9.46 | ('#sk5' @ X0 @ (lam @ X2)) 59.46/9.46 | (('#sk5' @ X0 @ ('#sk294' @ '#l_lift5217' @ ('#sk5' @ X0))) 59.46/9.46 != ('#sk31' @ id @ ('#sk294' @ '#l_lift5217' @ ('#sk5' @ X0)) @ 59.46/9.46 id)) 59.46/9.46 | ~ ('#form922'))), 59.46/9.46 inference('lambda_lifting', [status(thm)], 59.46/9.46 [zip_derived_cl234, zip_derived_cl3996, zip_derived_cl3996])). 59.46/9.46 thf(zip_derived_cl235, plain, 59.46/9.46 (![X0 : term > $o, X2 : term]: 59.46/9.46 (~ ('#sk5' @ X0 @ 59.46/9.46 (sub @ X2 @ (push @ ('#sk417' @ ('#sk5' @ X0) @ X2) @ id))) 59.46/9.46 | ('#sk5' @ X0 @ (lam @ X2)) 59.46/9.46 | (('#sk5' @ X0 @ 59.46/9.46 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.46 ('#sk5' @ X0))) 59.46/9.46 != ('#sk31' @ id @ 59.46/9.46 ('#sk294' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.46 ('#sk5' @ X0)) @ 59.46/9.46 id)) 59.46/9.46 | ~ ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl232])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl4003, plain, 59.46/9.46 (![X0 : term > $o, X2 : term]: 59.46/9.46 (~ ('#sk5' @ X0 @ 59.46/9.46 (sub @ X2 @ (push @ ('#sk417' @ ('#sk5' @ X0) @ X2) @ id))) 59.46/9.46 | ('#sk5' @ X0 @ (lam @ X2)) 59.46/9.46 | (('#sk5' @ X0 @ ('#sk294' @ '#l_lift5217' @ ('#sk5' @ X0))) 59.46/9.46 != ('#sk31' @ id @ ('#sk294' @ '#l_lift5217' @ ('#sk5' @ X0)) @ 59.46/9.46 id)) 59.46/9.46 | ~ ('#form922'))), 59.46/9.46 inference('lambda_lifting', [status(thm)], 59.46/9.46 [zip_derived_cl235, zip_derived_cl3996, zip_derived_cl3996])). 59.46/9.46 thf(zip_derived_cl132, plain, 59.46/9.46 (![X0 : term > $o]: 59.46/9.46 ( ('#sk5' @ var @ ('#sk30' @ ('#sk5' @ X0))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk5' @ X0 @ Y0) => 59.46/9.46 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.46 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.46 X0 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl131])). 59.46/9.46 thf(zip_derived_cl134, plain, 59.46/9.46 (![X0 : term > $o]: 59.46/9.46 (~ ('#form632' @ X0) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk5' @ X0 @ Y0) => 59.46/9.46 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.46 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.46 X0 @ 59.46/9.46 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.46 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.46 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl136, plain, 59.46/9.46 (![X0 : term > $o]: 59.46/9.46 ( ('#form632' @ X0) | ('#sk5' @ var @ ('#sk30' @ ('#sk5' @ X0))))), 59.46/9.46 inference('renaming', [status(thm)], 59.46/9.46 [zip_derived_cl132, zip_derived_cl134])). 59.46/9.46 thf(zip_derived_cl67, plain, 59.46/9.46 ( (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ Y3) @ 59.46/9.46 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk31' @ id @ Y1 @ id) => ('#sk31' @ 59.46/9.46 id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id))))))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl54])). 59.46/9.46 thf(zip_derived_cl82, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ (X2 @ Y0 @ Y1) @ Y2) = 59.46/9.46 (X2 @ (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id)))))), 59.46/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl67])). 59.46/9.46 thf(zip_derived_cl99, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ (((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ (X2 @ Y0 @ Y1) @ Y2) = 59.46/9.46 (X2 @ (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl82])). 59.46/9.46 thf(zip_derived_cl107, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ (((!!) @ (^[Y0 : term]: 59.46/9.46 (((!!) @ (^[Y1 : subst]: 59.46/9.46 (((sub @ (X2 @ ('#sk372' @ X2) @ Y0) @ 59.46/9.46 Y1) = (X2 @ 59.46/9.46 (comp @ ('#sk372' @ X2) @ Y1) @ 59.46/9.46 (sub @ Y0 @ Y1)))))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl99])). 59.46/9.46 thf(zip_derived_cl111, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ (((!!) @ (^[Y0 : subst]: 59.46/9.46 (((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ 59.46/9.46 Y0) = (X2 @ (comp @ ('#sk372' @ X2) @ Y0) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ Y0))))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl107])). 59.46/9.46 thf(zip_derived_cl114, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ (((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ 59.46/9.46 ('#sk428' @ X2)) = (X2 @ 59.46/9.46 (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2))))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl111])). 59.46/9.46 thf(zip_derived_cl118, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ ('#sk428' @ X2)) 59.46/9.46 != (X2 @ (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2)))) 59.46/9.46 | (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))))), 59.46/9.46 inference('simplify nested equalities', [status(thm)], 59.46/9.46 [zip_derived_cl114])). 59.46/9.46 thf(zip_derived_cl119, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ (((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ Y0) @ id)))))) 59.46/9.46 | ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id) 59.46/9.46 | ((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ ('#sk428' @ X2)) 59.46/9.46 != (X2 @ (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2)))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl118])). 59.46/9.46 thf(zip_derived_cl120, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 (~ ((('#sk31' @ id @ ('#sk500' @ X2) @ id) => ('#sk31' @ id @ 59.46/9.46 (X2 @ id @ ('#sk500' @ X2)) @ id))) 59.46/9.46 | ((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ ('#sk428' @ X2)) 59.46/9.46 != (X2 @ (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2)))) 59.46/9.46 | ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 59.46/9.46 thf(zip_derived_cl121, plain, 59.46/9.46 (![X2 : subst > term > term]: 59.46/9.46 ( ('#sk31' @ id @ ('#sk500' @ X2) @ id) 59.46/9.46 | ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id) 59.46/9.46 | ((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ ('#sk428' @ X2)) 59.46/9.46 != (X2 @ (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.46 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2)))))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 59.46/9.46 thf(zip_derived_cl215, plain, 59.46/9.46 (( ('#form922') 59.46/9.46 | ~ (((!!) @ (^[Y0 : subst > term > term]: 59.46/9.46 (((((!!) @ (^[Y1 : subst]: 59.46/9.46 (((!!) @ (^[Y2 : term]: 59.46/9.46 (((!!) @ (^[Y3 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 (Y0 @ Y1 @ Y2) @ 59.46/9.46 Y3) = (Y0 @ 59.46/9.46 (comp @ Y1 @ Y3) @ 59.46/9.46 (sub @ Y2 @ Y3))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y1 : term]: 59.46/9.46 ((('#sk31' @ id @ Y1 @ id) => 59.46/9.46 ('#sk31' @ id @ (Y0 @ id @ Y1) @ id)))))) => 59.46/9.46 ('#sk31' @ id @ (lam @ (Y0 @ sh @ one)) @ id)))))))))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl216, plain, 59.46/9.46 ((~ (((((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 Y0 @ Y1) @ 59.46/9.46 Y2) = ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) => 59.46/9.46 (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ id @ Y0) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ one)) @ 59.46/9.46 id))))) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl215])). 59.46/9.46 thf(zip_derived_cl220, plain, 59.46/9.46 ((~ (((((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ id @ Y0) @ 59.46/9.46 id)))))) => 59.46/9.46 ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ one)) @ 59.46/9.46 id))) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 59.46/9.46 thf(zip_derived_cl223, plain, 59.46/9.46 (( (((!!) @ (^[Y0 : term]: 59.46/9.46 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ 59.46/9.46 id @ Y0) @ 59.46/9.46 id)))))) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl220])). 59.46/9.46 thf(zip_derived_cl228, plain, 59.46/9.46 (![X2 : term]: 59.46/9.46 ( ((('#sk31' @ id @ X2 @ id) => ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ id @ X2) @ 59.46/9.46 id))) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl223])). 59.46/9.46 thf(zip_derived_cl231, plain, 59.46/9.46 (![X2 : term]: 59.46/9.46 (~ ('#sk31' @ id @ X2 @ id) 59.46/9.46 | ('#sk31' @ id @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ id @ X2) @ 59.46/9.46 id) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl228])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl4000, plain, 59.46/9.46 (![X2 : term]: 59.46/9.46 (~ ('#sk31' @ id @ X2 @ id) 59.46/9.46 | ('#sk31' @ id @ ('#sk124' @ '#l_lift5217' @ id @ X2) @ id) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lambda_lifting', [status(thm)], 59.46/9.46 [zip_derived_cl231, zip_derived_cl3996])). 59.46/9.46 thf(zip_derived_cl224, plain, 59.46/9.46 ((~ ('#sk31' @ id @ 59.46/9.46 (lam @ 59.46/9.46 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ sh @ one)) @ 59.46/9.46 id) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl220])). 59.46/9.46 thf(zip_derived_cl3996, plain, 59.46/9.46 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.46 define([status(thm)])). 59.46/9.46 thf(zip_derived_cl3999, plain, 59.46/9.46 ((~ ('#sk31' @ id @ (lam @ ('#sk124' @ '#l_lift5217' @ sh @ one)) @ id) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lambda_lifting', [status(thm)], 59.46/9.46 [zip_derived_cl224, zip_derived_cl3996])). 59.46/9.46 thf(zip_derived_cl219, plain, 59.46/9.46 (( (((!!) @ (^[Y0 : subst]: 59.46/9.46 (((!!) @ (^[Y1 : term]: 59.46/9.46 (((!!) @ (^[Y2 : subst]: 59.46/9.46 (((sub @ 59.46/9.46 ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 Y0 @ Y1) @ 59.46/9.46 Y2) = ('#sk124' @ 59.46/9.46 (^[Y3 : term]: 59.46/9.46 ('#sk31' @ id @ Y3 @ id)) @ 59.46/9.46 (comp @ Y0 @ Y2) @ 59.46/9.46 (sub @ Y1 @ Y2))))))))))))) 59.46/9.46 | ('#form922'))), 59.46/9.46 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 59.46/9.46 thf(zip_derived_cl222, plain, 59.46/9.46 (![X2 : subst]: 59.46/9.46 ( (((!!) @ (^[Y0 : term]: 59.46/9.46 (((!!) @ (^[Y1 : subst]: 59.46/9.46 (((sub @ 59.46/9.47 ('#sk124' @ 59.46/9.47 (^[Y2 : term]: ('#sk31' @ id @ Y2 @ id)) @ 59.46/9.47 X2 @ Y0) @ 59.46/9.47 Y1) = ('#sk124' @ 59.46/9.47 (^[Y2 : term]: ('#sk31' @ id @ Y2 @ id)) @ 59.46/9.47 (comp @ X2 @ Y1) @ (sub @ Y0 @ Y1)))))))))) 59.46/9.47 | ('#form922'))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl219])). 59.46/9.47 thf(zip_derived_cl227, plain, 59.46/9.47 (![X2 : subst, X4 : term]: 59.46/9.47 ( (((!!) @ (^[Y0 : subst]: 59.46/9.47 (((sub @ 59.46/9.47 ('#sk124' @ 59.46/9.47 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ X2 @ X4) @ 59.46/9.47 Y0) = ('#sk124' @ 59.46/9.47 (^[Y1 : term]: ('#sk31' @ id @ Y1 @ id)) @ 59.46/9.47 (comp @ X2 @ Y0) @ (sub @ X4 @ Y0))))))) 59.46/9.47 | ('#form922'))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl222])). 59.46/9.47 thf(zip_derived_cl230, plain, 59.46/9.47 (![X2 : subst, X4 : term, X6 : subst]: 59.46/9.47 ( (((sub @ 59.46/9.47 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2 @ X4) @ 59.46/9.47 X6) = ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.47 (comp @ X2 @ X6) @ (sub @ X4 @ X6)))) 59.46/9.47 | ('#form922'))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl227])). 59.46/9.47 thf(zip_derived_cl233, plain, 59.46/9.47 (![X2 : subst, X4 : term, X6 : subst]: 59.46/9.47 (((sub @ 59.46/9.47 ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ X2 @ X4) @ 59.46/9.47 X6) 59.46/9.47 = ('#sk124' @ (^[Y0 : term]: ('#sk31' @ id @ Y0 @ id)) @ 59.46/9.47 (comp @ X2 @ X6) @ (sub @ X4 @ X6))) 59.46/9.47 | ('#form922'))), 59.46/9.47 inference('simplify nested equalities', [status(thm)], 59.46/9.47 [zip_derived_cl230])). 59.46/9.47 thf(zip_derived_cl3996, plain, 59.46/9.47 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.47 define([status(thm)])). 59.46/9.47 thf(zip_derived_cl3996, plain, 59.46/9.47 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.47 define([status(thm)])). 59.46/9.47 thf(zip_derived_cl4001, plain, 59.46/9.47 (![X2 : subst, X4 : term, X6 : subst]: 59.46/9.47 (((sub @ ('#sk124' @ '#l_lift5217' @ X2 @ X4) @ X6) 59.46/9.47 = ('#sk124' @ '#l_lift5217' @ (comp @ X2 @ X6) @ (sub @ X4 @ X6))) 59.46/9.47 | ('#form922'))), 59.46/9.47 inference('lambda_lifting', [status(thm)], 59.46/9.47 [zip_derived_cl233, zip_derived_cl3996, zip_derived_cl3996])). 59.46/9.47 thf(zip_derived_cl44, plain, 59.46/9.47 ( (((!!) @ (^[Y0 : term]: 59.46/9.47 (((var @ (sub @ Y0 @ id)) => ('#sk31' @ id @ Y0 @ id))))))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl38])). 59.46/9.47 thf(zip_derived_cl52, plain, 59.46/9.47 (![X2 : term]: (((var @ (sub @ X2 @ id)) => ('#sk31' @ id @ X2 @ id)))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl44])). 59.46/9.47 thf(zip_derived_cl65, plain, 59.46/9.47 (![X2 : term]: (~ (var @ (sub @ X2 @ id)) | ('#sk31' @ id @ X2 @ id))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl52])). 59.46/9.47 thf(zip_derived_cl11, plain, 59.46/9.47 ( (((!!) @ (^[Y0 : term]: (((sub @ Y0 @ id) = (Y0))))))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl5])). 59.46/9.47 thf(zip_derived_cl15, plain, (![X2 : term]: (((sub @ X2 @ id) = (X2)))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl11])). 59.46/9.47 thf(zip_derived_cl20, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 59.46/9.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl15])). 59.46/9.47 thf(zip_derived_cl18, plain, 59.46/9.47 (![X2 : term > $o, X4 : term]: (('#sk5' @ X2 @ X4) = (X2 @ X4))), 59.46/9.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 59.46/9.47 thf(zip_derived_cl126, plain, 59.46/9.47 (![X2 : term]: (~ ('#sk5' @ var @ X2) | ('#sk31' @ id @ X2 @ id))), 59.46/9.47 inference('demod', [status(thm)], 59.46/9.47 [zip_derived_cl65, zip_derived_cl20, zip_derived_cl18])). 59.46/9.47 thf(zip_derived_cl134, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ ('#form632' @ X0) 59.46/9.47 | (((((!!) @ (^[Y0 : term]: 59.46/9.47 (((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk5' @ X0 @ Y0) => 59.46/9.47 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.47 X0 @ (ap @ Y0 @ Y1)))))))))))) => 59.46/9.47 (((((!!) @ (^[Y0 : term]: 59.46/9.47 (((((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.47 X0 @ 59.46/9.47 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.47 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.47 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))))))), 59.46/9.47 define([status(thm)])). 59.46/9.47 thf(zip_derived_cl135, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ (((!!) @ (^[Y0 : term]: 59.46/9.47 (((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk5' @ X0 @ Y0) => 59.46/9.47 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.47 (ap @ Y0 @ Y1)))))))))))) 59.46/9.47 | (((((!!) @ (^[Y0 : term]: 59.46/9.47 (((((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ 59.46/9.47 X0 @ (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.47 ('#sk5' @ X0 @ (lam @ Y0))))))) => 59.46/9.47 (((!!) @ (^[Y0 : term]: ('#sk5' @ X0 @ Y0)))))) 59.46/9.47 | ~ ('#form632' @ X0))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl134])). 59.46/9.47 thf(zip_derived_cl57, plain, 59.46/9.47 (![X2 : term > $o]: 59.46/9.47 (~ ('#form178' @ X2) 59.46/9.47 | (((((!!) @ (^[Y0 : term]: 59.46/9.47 (((((!!) @ (^[Y1 : term]: 59.46/9.47 (((X2 @ Y1) => (X2 @ 59.46/9.47 (sub @ Y0 @ (push @ Y1 @ id)))))))) => 59.46/9.47 (X2 @ (lam @ Y0))))))) => 59.46/9.47 (((!!) @ (^[Y0 : term]: (X2 @ Y0)))))))), 59.46/9.47 define([status(thm)])). 59.46/9.47 thf(zip_derived_cl138, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 ( ('#form178' @ ('#sk5' @ X0)) 59.46/9.47 | ~ ('#form632' @ X0) 59.46/9.47 | ~ (((!!) @ (^[Y0 : term]: 59.46/9.47 (((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk5' @ X0 @ Y0) => 59.46/9.47 ((('#sk5' @ X0 @ Y1) => ('#sk5' @ X0 @ 59.46/9.47 (ap @ Y0 @ Y1)))))))))))))), 59.46/9.47 inference('renaming', [status(thm)], 59.46/9.47 [zip_derived_cl135, zip_derived_cl57])). 59.46/9.47 thf(zip_derived_cl139, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ (((!!) @ (^[Y0 : term]: 59.46/9.47 ((('#sk5' @ X0 @ ('#sk103' @ ('#sk5' @ X0))) => 59.46/9.47 ((('#sk5' @ X0 @ Y0) => ('#sk5' @ X0 @ 59.46/9.47 (ap @ ('#sk103' @ ('#sk5' @ X0)) @ Y0))))))))) 59.46/9.47 | ~ ('#form632' @ X0) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)))), 59.46/9.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 59.46/9.47 thf(zip_derived_cl140, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ ((('#sk5' @ X0 @ ('#sk103' @ ('#sk5' @ X0))) => 59.46/9.47 ((('#sk5' @ X0 @ ('#sk135' @ ('#sk5' @ X0))) => ('#sk5' @ X0 @ 59.46/9.47 (ap @ ('#sk103' @ ('#sk5' @ X0)) @ ('#sk135' @ ('#sk5' @ X0)))))))) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)) 59.46/9.47 | ~ ('#form632' @ X0))), 59.46/9.47 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl139])). 59.46/9.47 thf(zip_derived_cl141, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 ( ('#sk5' @ X0 @ ('#sk103' @ ('#sk5' @ X0))) 59.46/9.47 | ~ ('#form632' @ X0) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 59.46/9.47 thf(zip_derived_cl122, plain, 59.46/9.47 (![X2 : subst > term > term]: 59.46/9.47 (~ ('#sk31' @ id @ (X2 @ id @ ('#sk500' @ X2)) @ id) 59.46/9.47 | ('#sk31' @ id @ (lam @ (X2 @ sh @ one)) @ id) 59.46/9.47 | ((sub @ (X2 @ ('#sk372' @ X2) @ ('#sk405' @ X2)) @ ('#sk428' @ X2)) 59.46/9.47 != (X2 @ (comp @ ('#sk372' @ X2) @ ('#sk428' @ X2)) @ 59.46/9.47 (sub @ ('#sk405' @ X2) @ ('#sk428' @ X2)))))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl120])). 59.46/9.47 thf(zip_derived_cl142, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ ((('#sk5' @ X0 @ ('#sk135' @ ('#sk5' @ X0))) => ('#sk5' @ X0 @ 59.46/9.47 (ap @ ('#sk103' @ ('#sk5' @ X0)) @ ('#sk135' @ ('#sk5' @ X0)))))) 59.46/9.47 | ~ ('#form632' @ X0) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl140])). 59.46/9.47 thf(zip_derived_cl143, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 ( ('#sk5' @ X0 @ ('#sk135' @ ('#sk5' @ X0))) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)) 59.46/9.47 | ~ ('#form632' @ X0))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 59.46/9.47 thf(zip_derived_cl3996, plain, 59.46/9.47 (![X3 : term]: (('#l_lift5217' @ X3) = ('#sk31' @ id @ X3 @ id))), 59.46/9.47 define([status(thm)])). 59.46/9.47 thf(zip_derived_cl18, plain, 59.46/9.47 (![X2 : term > $o, X4 : term]: (('#sk5' @ X2 @ X4) = (X2 @ X4))), 59.46/9.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl13])). 59.46/9.47 thf(zip_derived_cl53, plain, 59.46/9.47 ( (((!!) @ (^[Y0 : term]: 59.46/9.47 (((!!) @ (^[Y1 : term]: 59.46/9.47 ((('#sk31' @ id @ Y0 @ id) => 59.46/9.47 ((('#sk31' @ id @ Y1 @ id) => ('#sk31' @ 59.46/9.47 id @ (ap @ (sub @ Y0 @ id) @ Y1) @ id)))))))))))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])). 59.46/9.47 thf(zip_derived_cl66, plain, 59.46/9.47 (![X2 : term]: 59.46/9.47 (((!!) @ (^[Y0 : term]: 59.46/9.47 ((('#sk31' @ id @ X2 @ id) => 59.46/9.47 ((('#sk31' @ id @ Y0 @ id) => ('#sk31' @ id @ 59.46/9.47 (ap @ (sub @ X2 @ id) @ Y0) @ id))))))))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl53])). 59.46/9.47 thf(zip_derived_cl81, plain, 59.46/9.47 (![X2 : term, X4 : term]: 59.46/9.47 ((('#sk31' @ id @ X2 @ id) => 59.46/9.47 ((('#sk31' @ id @ X4 @ id) => ('#sk31' @ id @ 59.46/9.47 (ap @ (sub @ X2 @ id) @ X4) @ id)))))), 59.46/9.47 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl66])). 59.46/9.47 thf(zip_derived_cl98, plain, 59.46/9.47 (![X2 : term, X4 : term]: 59.46/9.47 (~ ('#sk31' @ id @ X2 @ id) 59.46/9.47 | ((('#sk31' @ id @ X4 @ id) => ('#sk31' @ id @ 59.46/9.47 (ap @ (sub @ X2 @ id) @ X4) @ id))))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl81])). 59.46/9.47 thf(zip_derived_cl106, plain, 59.46/9.47 (![X2 : term, X4 : term]: 59.46/9.47 (~ ('#sk31' @ id @ X4 @ id) 59.46/9.47 | ('#sk31' @ id @ (ap @ (sub @ X2 @ id) @ X4) @ id) 59.46/9.47 | ~ ('#sk31' @ id @ X2 @ id))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl98])). 59.46/9.47 thf(zip_derived_cl20, plain, (![X2 : term]: ((sub @ X2 @ id) = (X2))), 59.46/9.47 inference('simplify nested equalities', [status(thm)], [zip_derived_cl15])). 59.46/9.47 thf(zip_derived_cl145, plain, 59.46/9.47 (![X2 : term, X4 : term]: 59.46/9.47 (~ ('#sk31' @ id @ X4 @ id) 59.46/9.47 | ('#sk31' @ id @ (ap @ X2 @ X4) @ id) 59.46/9.47 | ~ ('#sk31' @ id @ X2 @ id))), 59.46/9.47 inference('demod', [status(thm)], [zip_derived_cl106, zip_derived_cl20])). 59.46/9.47 thf(zip_derived_cl144, plain, 59.46/9.47 (![X0 : term > $o]: 59.46/9.47 (~ ('#sk5' @ X0 @ 59.46/9.47 (ap @ ('#sk103' @ ('#sk5' @ X0)) @ ('#sk135' @ ('#sk5' @ X0)))) 59.46/9.47 | ('#form178' @ ('#sk5' @ X0)) 59.46/9.47 | ~ ('#form632' @ X0))), 59.46/9.47 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl142])). 59.46/9.47 thf(zip_derived_cl4015, plain, ($false), 59.46/9.47 inference('eprover', [status(thm)], 59.46/9.47 [zip_derived_cl83, zip_derived_cl101, zip_derived_cl115, 59.46/9.47 zip_derived_cl137, zip_derived_cl4002, zip_derived_cl4003, 59.46/9.47 zip_derived_cl136, zip_derived_cl121, zip_derived_cl4000, 59.46/9.47 zip_derived_cl3999, zip_derived_cl4001, zip_derived_cl126, 59.46/9.47 zip_derived_cl141, zip_derived_cl122, zip_derived_cl143, 59.46/9.47 zip_derived_cl3996, zip_derived_cl18, zip_derived_cl145, 59.46/9.47 zip_derived_cl144])). 59.46/9.47 59.46/9.47 % SZS output end Refutation 59.46/9.47 59.46/9.47 59.46/9.47 % Terminating... 59.46/9.47 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s 10.78/9.57 % Runner terminated. 10.84/9.62 % Zipperpin 1.5 exiting 10.84/9.66 EOF