0.03/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.0vm6iGSE67 0.13/0.33 % Computer : n014.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1200 0.13/0.33 % DateTime : Tue Jul 13 12:41:49 EDT 2021 0.13/0.33 % CPUTime : 0.13/0.34 % Running portfolio for 120 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % Running in HO mode 0.51/0.62 % Estimated wc time : 1286 0.51/0.62 % Estimated cpu time (7 cpus) : 183.71428571428572 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 0.52/0.74 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 70.11/10.70 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 70.72/10.77 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 104.55/15.75 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 104.99/15.92 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 132.19/19.79 % Solved by lams/b.sh. 132.19/19.79 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.0vm6iGSE67/e_inputf79e7a --cpu-limit=12 --auto -s -p. 132.19/19.79 % done 169 iterations in 8.984s 132.19/19.79 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 132.19/19.79 % SZS output start Refutation 132.19/19.79 tff(thm, conjecture, (induction2_gthm)). 132.19/19.79 tff(zf_stmt_0, negated_conjecture, (~induction2_gthm)). 132.19/19.79 tff('0', plain, ~ induction2_gthm, 132.19/19.79 inference('cnf', [status(esa)], [zf_stmt_0])). 132.19/19.79 tff(induction2_gthm, axiom, ~ induction2_gthm => 132.19/19.79 ((axapp => 132.19/19.79 (axvarcons => 132.19/19.79 (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 (axvarshift => 132.19/19.79 (axscons => 132.19/19.79 (ulamvar1 => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))))))))) 132.19/19.79 != $true)). 132.19/19.79 tff('1', plain, 132.19/19.79 (~induction2_gthm) <=> 132.19/19.79 (~ 132.19/19.79 (axapp => 132.19/19.79 (axvarcons => 132.19/19.79 (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 (axvarshift => 132.19/19.79 (axscons => 132.19/19.79 (ulamvar1 => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2)))))))))))))))))))))))))), 132.19/19.79 inference('rw.lit', [status(esa)], [induction2_gthm])). 132.19/19.79 tff('2', plain, 132.19/19.79 ~ (axapp => 132.19/19.79 (axvarcons => 132.19/19.79 (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 (axvarshift => 132.19/19.79 (axscons => 132.19/19.79 (ulamvar1 => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))))))))), 132.19/19.79 inference('rw_clause', [status(thm)], ['0', '1'])). 132.19/19.79 tff(axvarshift, axiom, axvarshift() = (push(one, sh) = id)). 132.19/19.79 tff('3', plain, axvarshift = (push(one,sh) = id), define([status(thm)])). 132.19/19.79 tff(ulamvar1, axiom, ulamvar1() = var(one)). 132.19/19.79 tff('4', plain, ulamvar1 = var(one), define([status(thm)])). 132.19/19.79 tff('5', plain, 132.19/19.79 ~ (axapp => 132.19/19.79 (axvarcons => 132.19/19.79 (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))))))))), 132.19/19.79 inference('rw', [status(thm)], ['2', '3', '4'])). 132.19/19.79 tff('6', plain, 132.19/19.79 ~ (axvarcons => 132.19/19.79 (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2)))))))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['5'])). 132.19/19.79 tff('7', plain, 132.19/19.79 ~ (axvarid => 132.19/19.79 (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['6'])). 132.19/19.79 tff('8', plain, 132.19/19.79 ~ (axabs => 132.19/19.79 (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2)))))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['7'])). 132.19/19.79 tff('9', plain, 132.19/19.79 ~ (axclos => 132.19/19.79 (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['8'])). 132.19/19.79 tff('10', plain, 132.19/19.79 ~ (axidl => 132.19/19.79 (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2)))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['9'])). 132.19/19.79 tff('11', plain, 132.19/19.79 ~ (axshiftcons => 132.19/19.79 (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2))))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['10'])). 132.19/19.79 tff('12', plain, 132.19/19.79 ~ (axassoc => 132.19/19.79 (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => 132.19/19.79 (pushprop => (induction2lem => induction2)))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['11'])). 132.19/19.79 tff('13', plain, 132.19/19.79 ~ (axmap => 132.19/19.79 (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['12'])). 132.19/19.79 tff('14', plain, 132.19/19.79 ~ (axidr => 132.19/19.79 ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['13'])). 132.19/19.79 tff('15', plain, 132.19/19.79 ~ ((push(one, sh) = id) => 132.19/19.79 (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['14'])). 132.19/19.79 tff('16', plain, 132.19/19.79 ~ (axscons => 132.19/19.79 (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['15'])). 132.19/19.79 tff('17', plain, 132.19/19.79 ~ (var(one) => 132.19/19.79 (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['16'])). 132.19/19.79 tff('18', plain, 132.19/19.79 ~ (ulamvarsh => 132.19/19.79 (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['17'])). 132.19/19.79 tff('19', plain, 132.19/19.79 ~ (ulamvarind => 132.19/19.79 (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['18'])). 132.19/19.79 tff('20', plain, 132.19/19.79 ~ (apinj1 => 132.19/19.79 (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['19'])). 132.19/19.79 tff('21', plain, 132.19/19.79 ~ (apinj2 => 132.19/19.79 (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['20'])). 132.19/19.79 tff('22', plain, 132.19/19.79 ~ (laminj => 132.19/19.79 (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['21'])). 132.19/19.79 tff('23', plain, 132.19/19.79 ~ (shinj => 132.19/19.79 (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['22'])). 132.19/19.79 tff('24', plain, 132.19/19.79 ~ (lamnotap => 132.19/19.79 (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['23'])). 132.19/19.79 tff('25', plain, 132.19/19.79 ~ (apnotvar => 132.19/19.79 (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['24'])). 132.19/19.79 tff('26', plain, 132.19/19.79 ~ (lamnotvar => 132.19/19.79 (induction => (pushprop => (induction2lem => induction2)))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['25'])). 132.19/19.79 tff('27', plain, 132.19/19.79 ~ (induction => (pushprop => (induction2lem => induction2))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['26'])). 132.19/19.79 tff('28', plain, ~ (pushprop => (induction2lem => induction2)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['27'])). 132.19/19.79 tff('29', plain, ~ (induction2lem => induction2), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['28'])). 132.19/19.79 tff('30', plain, ~ induction2, 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['29'])). 132.19/19.79 tff(induction2, axiom, ~ induction2 => 132.19/19.79 ((!!((^[Y0 : term > $o]: 132.19/19.79 ((!!((^[Y1 : term]: (var(Y1) => Y0(Y1))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : term]: (Y0(Y1) => (Y0(Y2) => Y0(ap(Y1, Y2)))))))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ((!!((^[Y2 : term]: (Y0(Y2) => Y0(sub(Y1, push(Y2, id))))))) => 132.19/19.79 Y0(lam(Y1)))))) => 132.19/19.79 (!!((^[Y1 : term]: Y0(Y1)))))))))) 132.19/19.79 != $true)). 132.19/19.79 tff('31', plain, 132.19/19.79 (~induction2) <=> 132.19/19.79 (~ 132.19/19.79 (![X5:((term > $o))]: 132.19/19.79 ((![X7:term]: (var(X7) => X5(X7))) => 132.19/19.79 ((![X9:term,X11:term]: (X5(X9) => (X5(X11) => X5(ap(X9,X11))))) => 132.19/19.79 ((![X13:term]: 132.19/19.79 ((![X15:term]: (X5(X15) => X5(sub(X13,push(X15,id))))) => 132.19/19.79 X5(lam(X13)))) => 132.19/19.79 (![X17:term]: X5(X17))))))), 132.19/19.79 inference('rw.lit', [status(esa)], [induction2])). 132.19/19.79 tff('32', plain, 132.19/19.79 ~ (!!((^[Y0 : term > $o]: 132.19/19.79 ((!!((^[Y1 : term]: (var(Y1) => Y0(Y1))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : term]: 132.19/19.79 (Y0(Y1) => (Y0(Y2) => Y0(ap(Y1, Y2)))))))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ((!!((^[Y2 : term]: 132.19/19.79 (Y0(Y2) => Y0(sub(Y1, push(Y2, id))))))) => 132.19/19.79 Y0(lam(Y1)))))) => 132.19/19.79 (!!((^[Y1 : term]: Y0(Y1)))))))))), 132.19/19.79 inference('rw_clause', [status(thm)], ['30', '31'])). 132.19/19.79 tff('33', plain, 132.19/19.79 ~ (!!((^[Y0 : term > $o]: 132.19/19.79 ((!!((^[Y1 : term]: (var(Y1) => Y0(Y1))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : term]: 132.19/19.79 (Y0(Y1) => (Y0(Y2) => Y0(ap(Y1, Y2)))))))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ((!!((^[Y2 : term]: 132.19/19.79 (Y0(Y2) => Y0(sub(Y1, push(Y2, id))))))) => 132.19/19.79 Y0(lam(Y1)))))) => 132.19/19.79 (!!(Y0)))))))), 132.19/19.79 inference('ho_norm', [status(thm)], ['32'])). 132.19/19.79 tff('34', plain, 132.19/19.79 ~ ((!!((^[Y0 : term]: (var(Y0) => '#sk53'(Y0))))) => 132.19/19.79 ((!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y0) => ('#sk53'(Y1) => '#sk53'(ap(Y0, Y1)))))))))) => 132.19/19.79 ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y1) => '#sk53'(sub(Y0, push(Y1, id))))))) => 132.19/19.79 '#sk53'(lam(Y0)))))) => 132.19/19.79 (!!('#sk53'))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['33'])). 132.19/19.79 tff('35', plain, 132.19/19.79 ~ ((!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y0) => ('#sk53'(Y1) => '#sk53'(ap(Y0, Y1)))))))))) => 132.19/19.79 ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y1) => '#sk53'(sub(Y0, push(Y1, id))))))) => 132.19/19.79 '#sk53'(lam(Y0)))))) => 132.19/19.79 (!!('#sk53')))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['34'])). 132.19/19.79 tff('36', plain, 132.19/19.79 ~ ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y1) => '#sk53'(sub(Y0, push(Y1, id))))))) => 132.19/19.79 '#sk53'(lam(Y0)))))) => 132.19/19.79 (!!('#sk53'))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['35'])). 132.19/19.79 tff('37', plain, ~ (!!('#sk53')), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['36'])). 132.19/19.79 tff('38', plain, ~ '#sk53'('#sk173'), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['37'])). 132.19/19.79 tff('39', plain, induction2lem, 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['29'])). 132.19/19.79 tff(induction2lem, axiom, induction2lem => 132.19/19.79 ((!!((^[Y0 : term > $o]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : term]: (Y0(Y1) => (Y0(Y2) => Y0(ap(Y1, Y2)))))))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ((!!((^[Y2 : term]: (Y0(Y2) => Y0(sub(Y1, push(Y2, id))))))) => 132.19/19.79 Y0(lam(Y1)))))) => 132.19/19.79 (!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : subst]: 132.19/19.79 ((!!((^[Y3 : term]: (var(Y3) => Y0(sub(Y3, Y2)))))) => 132.19/19.79 Y0(sub(Y1, Y2)))))))))))))) 132.19/19.79 = $true)). 132.19/19.79 tff('40', plain, 132.19/19.79 induction2lem <=> 132.19/19.79 (![X5:((term > $o))]: 132.19/19.79 ((![X7:term,X9:term]: (X5(X7) => (X5(X9) => X5(ap(X7,X9))))) => 132.19/19.79 ((![X11:term]: 132.19/19.79 ((![X13:term]: (X5(X13) => X5(sub(X11,push(X13,id))))) => 132.19/19.79 X5(lam(X11)))) => 132.19/19.79 (![X15:term,X17:subst]: 132.19/19.79 ((![X19:term]: (var(X19) => X5(sub(X19,X17)))) => 132.19/19.79 X5(sub(X15,X17))))))), 132.19/19.79 inference('rw.lit', [status(esa)], [induction2lem])). 132.19/19.79 tff('41', plain, 132.19/19.79 (!!((^[Y0 : term > $o]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : term]: (Y0(Y1) => (Y0(Y2) => Y0(ap(Y1, Y2)))))))))) => 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ((!!((^[Y2 : term]: 132.19/19.79 (Y0(Y2) => Y0(sub(Y1, push(Y2, id))))))) => 132.19/19.79 Y0(lam(Y1)))))) => 132.19/19.79 (!!((^[Y1 : term]: 132.19/19.79 (!!((^[Y2 : subst]: 132.19/19.79 ((!!((^[Y3 : term]: (var(Y3) => Y0(sub(Y3, Y2)))))) => 132.19/19.79 Y0(sub(Y1, Y2)))))))))))))), 132.19/19.79 inference('rw_clause', [status(thm)], ['39', '40'])). 132.19/19.79 tff('42', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ((!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : term]: (X1(Y0) => (X1(Y1) => X1(ap(Y0, Y1)))))))))) => 132.19/19.79 ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['41'])). 132.19/19.79 tff('43', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : term]: (X1(Y0) => (X1(Y1) => X1(ap(Y0, Y1)))))))))) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['42'])). 132.19/19.79 tff('44', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (!!((^[Y0 : term]: 132.19/19.79 (X1('#sk109'(X1)) => (X1(Y0) => X1(ap('#sk109'(X1), Y0))))))) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['43'])). 132.19/19.79 tff('45', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (X1('#sk109'(X1)) => 132.19/19.79 (X1('#sk141'(X1)) => X1(ap('#sk109'(X1), '#sk141'(X1))))) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['44'])). 132.19/19.79 tff('46', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( X1('#sk109'(X1)) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['45'])). 132.19/19.79 tff('47', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | X1('#sk109'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['46'])). 132.19/19.79 tff('48', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ ((!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) => 132.19/19.79 X1(lam('#sk250'(X1)))) 132.19/19.79 | X1('#sk109'(X1)) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['47'])). 132.19/19.79 tff('49', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( (!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | X1('#sk109'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['48'])). 132.19/19.79 tff('50', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ '#form358'(X1) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 define([status(thm)])). 132.19/19.79 tff('51', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 ( (!!((^[Y0 : subst]: 132.19/19.79 ((!!((^[Y1 : term]: (var(Y1) => X1(sub(Y1, Y0)))))) => 132.19/19.79 X1(sub(X2, Y0)))))) 132.19/19.79 | ~ '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['50'])). 132.19/19.79 tff('52', plain, 132.19/19.79 ![X1 : term > $o, X2 : term, X3 : subst]: 132.19/19.79 ( ((!!((^[Y0 : term]: (var(Y0) => X1(sub(Y0, X3)))))) => 132.19/19.79 X1(sub(X2, X3))) 132.19/19.79 | ~ '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['51'])). 132.19/19.79 tff('53', plain, 132.19/19.79 ![X1 : term > $o, X2 : term, X3 : subst]: 132.19/19.79 (~ (!!((^[Y0 : term]: (var(Y0) => X1(sub(Y0, X3)))))) 132.19/19.79 | X1(sub(X2, X3)) 132.19/19.79 | ~ '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['52'])). 132.19/19.79 tff('54', plain, 132.19/19.79 ![X1 : term > $o, X2 : term, X3 : subst]: 132.19/19.79 (~ (var('#sk128'(X1, X3)) => X1(sub('#sk128'(X1, X3), X3))) 132.19/19.79 | ~ '#form358'(X1) 132.19/19.79 | X1(sub(X2, X3))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['53'])). 132.19/19.79 tff('55', plain, 132.19/19.79 ![X1 : term > $o, X2 : term, X3 : subst]: 132.19/19.79 ( var('#sk128'(X1, X3)) | X1(sub(X2, X3)) | ~ '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['54'])). 132.19/19.79 tff('56', plain, (!!((^[Y0 : term]: (var(Y0) => '#sk53'(Y0))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['34'])). 132.19/19.79 tff('57', plain, ![X1 : term]: (var(X1) => '#sk53'(X1)), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['56'])). 132.19/19.79 tff('58', plain, ![X1 : term]: (~ var(X1) | '#sk53'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['57'])). 132.19/19.79 tff('59', plain, axvarid, inference('lazy_cnf_imply', [status(thm)], ['7'])). 132.19/19.79 tff(axvarid, axiom, axvarid => 132.19/19.79 ((!!((^[Y0 : term]: (sub(Y0, id) = Y0)))) = $true)). 132.19/19.79 tff('60', plain, axvarid <=> (![X5:term]: (sub(X5,id) = X5)), 132.19/19.79 inference('rw.lit', [status(esa)], [axvarid])). 132.19/19.79 tff('61', plain, (!!((^[Y0 : term]: (sub(Y0, id) = Y0)))), 132.19/19.79 inference('rw_clause', [status(thm)], ['59', '60'])). 132.19/19.79 tff('62', plain, ![X1 : term]: sub(X1, id) = X1, 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['61'])). 132.19/19.79 tff('63', plain, 132.19/19.79 ![X1 : term > $o, X2 : term, X3 : subst]: 132.19/19.79 (~ X1(sub('#sk128'(X1, X3), X3)) | X1(sub(X2, X3)) | ~ '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['54'])). 132.19/19.79 tff('64', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (X1('#sk141'(X1)) => X1(ap('#sk109'(X1), '#sk141'(X1)))) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['45'])). 132.19/19.79 tff('65', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['64'])). 132.19/19.79 tff('66', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1)))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['65'])). 132.19/19.79 tff('67', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ ((!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) => 132.19/19.79 X1(lam('#sk250'(X1)))) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['66'])). 132.19/19.79 tff('68', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ '#form358'(X1) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 define([status(thm)])). 132.19/19.79 tff('69', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( '#form358'(X1) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | ~ ((!!((^[Y0 : term]: 132.19/19.79 (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) => 132.19/19.79 X1(lam('#sk250'(X1))))), 132.19/19.79 inference('renaming', [status(thm)], ['67', '68'])). 132.19/19.79 tff('70', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( (!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['69'])). 132.19/19.79 tff('71', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 ( (X1(X2) => X1(sub('#sk250'(X1), push(X2, id)))) 132.19/19.79 | '#form358'(X1) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1)))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['70'])). 132.19/19.79 tff('72', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 (~ X1(X2) 132.19/19.79 | X1(sub('#sk250'(X1), push(X2, id))) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['71'])). 132.19/19.79 tff('73', plain, 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y1) => '#sk53'(sub(Y0, push(Y1, id))))))) => 132.19/19.79 '#sk53'(lam(Y0)))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['36'])). 132.19/19.79 tff('74', plain, 132.19/19.79 ![X1 : term]: 132.19/19.79 ((!!((^[Y0 : term]: ('#sk53'(Y0) => '#sk53'(sub(X1, push(Y0, id))))))) => 132.19/19.79 '#sk53'(lam(X1))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['73'])). 132.19/19.79 tff('75', plain, 132.19/19.79 ![X1 : term]: 132.19/19.79 (~ (!!((^[Y0 : term]: ('#sk53'(Y0) => '#sk53'(sub(X1, push(Y0, id))))))) 132.19/19.79 | '#sk53'(lam(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['74'])). 132.19/19.79 tff('76', plain, 132.19/19.79 ![X1 : term]: 132.19/19.79 (~ ('#sk53'('#sk270'(X1)) => '#sk53'(sub(X1, push('#sk270'(X1), id)))) 132.19/19.79 | '#sk53'(lam(X1))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['75'])). 132.19/19.79 tff('77', plain, 132.19/19.79 ![X1 : term]: 132.19/19.79 (~ '#sk53'(sub(X1, push('#sk270'(X1), id))) | '#sk53'(lam(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['76'])). 132.19/19.79 tff('78', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( (!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | X1('#sk109'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['48'])). 132.19/19.79 tff('79', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ '#form358'(X1) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 define([status(thm)])). 132.19/19.79 tff('80', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( '#form358'(X1) 132.19/19.79 | X1('#sk109'(X1)) 132.19/19.79 | (!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id)))))))), 132.19/19.79 inference('renaming', [status(thm)], ['78', '79'])). 132.19/19.79 tff('81', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 ( (X1(X2) => X1(sub('#sk250'(X1), push(X2, id)))) 132.19/19.79 | X1('#sk109'(X1)) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['80'])). 132.19/19.79 tff('82', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 (~ X1(X2) 132.19/19.79 | X1(sub('#sk250'(X1), push(X2, id))) 132.19/19.79 | '#form358'(X1) 132.19/19.79 | X1('#sk109'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['81'])). 132.19/19.79 tff('83', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ X1(lam('#sk250'(X1))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | X1('#sk109'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['48'])). 132.19/19.79 tff('84', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ '#form358'(X1) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 define([status(thm)])). 132.19/19.79 tff('85', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( '#form358'(X1) | X1('#sk109'(X1)) | ~ X1(lam('#sk250'(X1)))), 132.19/19.79 inference('renaming', [status(thm)], ['83', '84'])). 132.19/19.79 tff('86', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( X1('#sk141'(X1)) 132.19/19.79 | ((!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) => 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['64'])). 132.19/19.79 tff('87', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ (!!((^[Y0 : term]: 132.19/19.79 ((!!((^[Y1 : term]: (X1(Y1) => X1(sub(Y0, push(Y1, id))))))) => 132.19/19.79 X1(lam(Y0)))))) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1))))))))) 132.19/19.79 | X1('#sk141'(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['86'])). 132.19/19.79 tff('88', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ ((!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) => 132.19/19.79 X1(lam('#sk250'(X1)))) 132.19/19.79 | X1('#sk141'(X1)) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 inference('lazy_cnf_exists', [status(thm)], ['87'])). 132.19/19.79 tff('89', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ '#form358'(X1) 132.19/19.79 | (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : subst]: 132.19/19.79 ((!!((^[Y2 : term]: (var(Y2) => X1(sub(Y2, Y1)))))) => 132.19/19.79 X1(sub(Y0, Y1)))))))))), 132.19/19.79 define([status(thm)])). 132.19/19.79 tff('90', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( '#form358'(X1) 132.19/19.79 | X1('#sk141'(X1)) 132.19/19.79 | ~ ((!!((^[Y0 : term]: 132.19/19.79 (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) => 132.19/19.79 X1(lam('#sk250'(X1))))), 132.19/19.79 inference('renaming', [status(thm)], ['88', '89'])). 132.19/19.79 tff('91', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ X1(lam('#sk250'(X1))) | X1('#sk141'(X1)) | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['90'])). 132.19/19.79 tff('92', plain, 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 (!!((^[Y1 : term]: 132.19/19.79 ('#sk53'(Y0) => ('#sk53'(Y1) => '#sk53'(ap(Y0, Y1)))))))))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['35'])). 132.19/19.79 tff('93', plain, 132.19/19.79 ![X1 : term]: 132.19/19.79 (!!((^[Y0 : term]: 132.19/19.79 ('#sk53'(X1) => ('#sk53'(Y0) => '#sk53'(ap(X1, Y0))))))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['92'])). 132.19/19.79 tff('94', plain, 132.19/19.79 ![X1 : term, X2 : term]: 132.19/19.79 ('#sk53'(X1) => ('#sk53'(X2) => '#sk53'(ap(X1, X2)))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['93'])). 132.19/19.79 tff('95', plain, 132.19/19.79 ![X1 : term, X2 : term]: 132.19/19.79 (~ '#sk53'(X1) | ('#sk53'(X2) => '#sk53'(ap(X1, X2)))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['94'])). 132.19/19.79 tff('96', plain, 132.19/19.79 ![X1 : term, X2 : term]: 132.19/19.79 (~ '#sk53'(X2) | '#sk53'(ap(X1, X2)) | ~ '#sk53'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['95'])). 132.19/19.79 tff('97', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 (~ X1(lam('#sk250'(X1))) 132.19/19.79 | ~ X1(ap('#sk109'(X1), '#sk141'(X1))) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['69'])). 132.19/19.79 tff('98', plain, ![X1 : term]: ( '#sk53'('#sk270'(X1)) | '#sk53'(lam(X1))), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['76'])). 132.19/19.79 tff('99', plain, 132.19/19.79 ![X1 : term > $o]: 132.19/19.79 ( (!!((^[Y0 : term]: (X1(Y0) => X1(sub('#sk250'(X1), push(Y0, id))))))) 132.19/19.79 | X1('#sk141'(X1)) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['90'])). 132.19/19.79 tff('100', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 ( (X1(X2) => X1(sub('#sk250'(X1), push(X2, id)))) 132.19/19.79 | '#form358'(X1) 132.19/19.79 | X1('#sk141'(X1))), 132.19/19.79 inference('lazy_cnf_forall', [status(thm)], ['99'])). 132.19/19.79 tff('101', plain, 132.19/19.79 ![X1 : term > $o, X2 : term]: 132.19/19.79 (~ X1(X2) 132.19/19.79 | X1(sub('#sk250'(X1), push(X2, id))) 132.19/19.79 | X1('#sk141'(X1)) 132.19/19.79 | '#form358'(X1)), 132.19/19.79 inference('lazy_cnf_imply', [status(thm)], ['100'])). 132.19/19.79 tff('102', plain, $false, 132.19/19.79 inference('eprover', [status(thm)], 132.19/19.79 ['38', '55', '58', '62', '63', '72', '77', '82', '85', '91', 132.19/19.79 '96', '97', '98', '101'])). 132.19/19.79 132.19/19.79 % SZS output end Refutation 132.19/19.79 132.19/19.79 132.19/19.79 % Terminating... 132.75/19.88 % Runner terminated. 132.75/19.89 % Zipperpin 1.5 exiting 132.75/19.89 EOF