0.07/0.09 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.10 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.4MJHse5DDA 0.09/0.30 % Computer : n021.cluster.edu 0.09/0.30 % Model : x86_64 x86_64 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.09/0.30 % Memory : 8042.1875MB 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64 0.09/0.30 % CPULimit : 1200 0.09/0.30 % DateTime : Tue Jul 13 12:46:40 EDT 2021 0.09/0.30 % CPUTime : 0.09/0.30 % Running portfolio for 120 s 0.09/0.30 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.09/0.30 % Number of cores: 8 0.09/0.31 % Python version: Python 3.6.8 0.09/0.31 % Running in HO mode 0.44/0.56 % Estimated wc time : 1286 0.44/0.56 % Estimated cpu time (7 cpus) : 183.71428571428572 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.45/0.66 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.45/10.48 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.15/15.48 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.23/15.69 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 122.91/18.30 % Solved by lams/old_sp2.sh. 122.91/18.30 % done 1053 iterations in 7.773s 122.91/18.30 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 122.91/18.30 % SZS output start Refutation 122.91/18.30 tff(cTHM260_pme, conjecture, 122.91/18.30 (![R:((a * a) > $o)]: 122.91/18.30 (((![Xx:a]: R(Xx,Xx)) & 122.91/18.30 (![Xx:a,Xy:a,Xz:a]: ((R(Xx,Xy) & R(Xy,Xz)) => R(Xx,Xz))) & 122.91/18.30 (![Xx:a,Xy:a]: (R(Xx,Xy) => R(Xy,Xx)))) => 122.91/18.30 ((![Xx:a]: 122.91/18.30 (?[Xp:((a > $o))]: 122.91/18.30 ((![Xx0:a]: (Xp(Xx0) => (![Xy:a]: (Xp(Xy) <=> R(Xx0,Xy))))) & 122.91/18.30 (![Xq:((a > $o))]: 122.91/18.30 (((?[Xz:a]: Xq(Xz)) & Xq(Xx) & 122.91/18.30 (![Xx0:a]: (Xq(Xx0) => (![Xy:a]: (R(Xx0,Xy) <=> Xq(Xy)))))) => 122.91/18.30 (Xq = Xp))) & 122.91/18.30 Xp(Xx) & (?[Xz:a]: Xp(Xz))))) & 122.91/18.30 (![Xp:((a > $o))]: 122.91/18.30 (((![Xx:a]: (Xp(Xx) => (![Xy:a]: (R(Xx,Xy) <=> Xp(Xy))))) & 122.91/18.30 (?[Xz:a]: Xp(Xz))) => 122.91/18.30 (?[Xz:a]: Xp(Xz)))))))). 122.91/18.30 tff(zf_stmt_0, negated_conjecture, 122.91/18.30 (~ 122.91/18.30 (![R:((a * a) > $o)]: 122.91/18.30 (((![Xx:a]: R(Xx,Xx)) & 122.91/18.30 (![Xx:a,Xy:a,Xz:a]: ((R(Xx,Xy) & R(Xy,Xz)) => R(Xx,Xz))) & 122.91/18.30 (![Xx:a,Xy:a]: (R(Xx,Xy) => R(Xy,Xx)))) => 122.91/18.30 ((![Xx:a]: 122.91/18.30 (?[Xp:((a > $o))]: 122.91/18.30 ((![Xx0:a]: (Xp(Xx0) => (![Xy:a]: (Xp(Xy) <=> R(Xx0,Xy))))) & 122.91/18.30 (![Xq:((a > $o))]: 122.91/18.30 (((?[Xz:a]: Xq(Xz)) & Xq(Xx) & 122.91/18.30 (![Xx0:a]: 122.91/18.30 (Xq(Xx0) => (![Xy:a]: (R(Xx0,Xy) <=> Xq(Xy)))))) => 122.91/18.30 (Xq = Xp))) & 122.91/18.30 Xp(Xx) & (?[Xz:a]: Xp(Xz))))) & 122.91/18.30 (![Xp:((a > $o))]: 122.91/18.30 (((![Xx:a]: (Xp(Xx) => (![Xy:a]: (R(Xx,Xy) <=> Xp(Xy))))) & 122.91/18.30 (?[Xz:a]: Xp(Xz))) => 122.91/18.30 (?[Xz:a]: Xp(Xz))))))))). 122.91/18.30 tff('0', plain, 122.91/18.30 ~ (!!((^[Y0 : (a * a) > $o]: 122.91/18.30 (((!!((^[Y1 : a]: Y0(Y1, Y1))))& 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (!!((^[Y2 : a]: 122.91/18.30 (!!((^[Y3 : a]: 122.91/18.30 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))& 122.91/18.30 (!!((^[Y1 : a]: (!!((^[Y2 : a]: (Y0(Y1, Y2) => Y0(Y2, Y1))))))))) => 122.91/18.30 ((!!((^[Y1 : a]: 122.91/18.30 (??((^[Y2 : a > $o]: 122.91/18.30 ((!!((^[Y3 : a]: 122.91/18.30 (Y2(Y3) => 122.91/18.30 (!!((^[Y4 : a]: (Y2(Y4) <=> Y0(Y3, Y4)))))))))& 122.91/18.30 (!!((^[Y3 : a > $o]: 122.91/18.30 (((??((^[Y4 : a]: Y3(Y4))))&Y3(Y1)& 122.91/18.30 (!!((^[Y4 : a]: 122.91/18.30 (Y3(Y4) => 122.91/18.30 (!!((^[Y5 : a]: 122.91/18.30 (Y0(Y4, Y5) <=> Y3(Y5)))))))))) => 122.91/18.30 (Y3 = Y2)))))& 122.91/18.30 Y2(Y1)&(??((^[Y3 : a]: Y2(Y3))))))))))) & 122.91/18.30 (!!((^[Y1 : a > $o]: 122.91/18.30 (((!!((^[Y2 : a]: 122.91/18.30 (Y1(Y2) => 122.91/18.30 (!!((^[Y3 : a]: (Y0(Y2, Y3) <=> Y1(Y3))))))))) & 122.91/18.30 (??((^[Y2 : a]: Y1(Y2))))) => 122.91/18.30 (??((^[Y2 : a]: Y1(Y2))))))))))))), 122.91/18.30 inference('cnf', [status(esa)], [zf_stmt_0])). 122.91/18.30 tff('1', plain, 122.91/18.30 ~ (!!((^[Y0 : (a * a) > $o]: 122.91/18.30 (((!!((^[Y1 : a]: Y0(Y1, Y1))))& 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (!!((^[Y2 : a]: 122.91/18.30 (!!((^[Y3 : a]: 122.91/18.30 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))& 122.91/18.30 (!!((^[Y1 : a]: (!!((^[Y2 : a]: (Y0(Y1, Y2) => Y0(Y2, Y1))))))))) => 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (??((^[Y2 : a > $o]: 122.91/18.30 ((!!((^[Y3 : a]: 122.91/18.30 (Y2(Y3) => 122.91/18.30 (!!((^[Y4 : a]: (Y2(Y4) <=> Y0(Y3, Y4)))))))))& 122.91/18.30 (!!((^[Y3 : a > $o]: 122.91/18.30 (((??((^[Y4 : a]: Y3(Y4))))&Y3(Y1)& 122.91/18.30 (!!((^[Y4 : a]: 122.91/18.30 (Y3(Y4) => 122.91/18.30 (!!((^[Y5 : a]: 122.91/18.30 (Y0(Y4, Y5) <=> Y3(Y5)))))))))) => 122.91/18.30 (Y3 = Y2)))))& 122.91/18.30 Y2(Y1)&(??((^[Y3 : a]: Y2(Y3))))))))))))))), 122.91/18.30 inference('simplify boolean subterms', [status(thm)], ['0'])). 122.91/18.30 tff('2', plain, 122.91/18.30 ~ (!!((^[Y0 : (a * a) > $o]: 122.91/18.30 (((!!((^[Y1 : a]: Y0(Y1, Y1))))& 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (!!((^[Y2 : a]: 122.91/18.30 (!!((^[Y3 : a]: 122.91/18.30 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))& 122.91/18.30 (!!((^[Y1 : a]: (!!((^[Y2 : a]: (Y0(Y1, Y2) => Y0(Y2, Y1))))))))) => 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (??((^[Y2 : a > $o]: 122.91/18.30 ((!!((^[Y3 : a]: 122.91/18.30 (Y2(Y3) => 122.91/18.30 (!!((^[Y4 : a]: (Y2(Y4) <=> Y0(Y3, Y4)))))))))& 122.91/18.30 (!!((^[Y3 : a > $o]: 122.91/18.30 (((??(Y3))&Y3(Y1)& 122.91/18.30 (!!((^[Y4 : a]: 122.91/18.30 (Y3(Y4) => 122.91/18.30 (!!((^[Y5 : a]: 122.91/18.30 (Y0(Y4, Y5) <=> Y3(Y5)))))))))) => 122.91/18.30 (Y3 = Y2)))))& 122.91/18.30 Y2(Y1)&(??(Y2))))))))))))), 122.91/18.30 inference('ho_norm', [status(thm)], ['1'])). 122.91/18.30 tff('3', plain, 122.91/18.30 ~ (((!!((^[Y0 : a]: '#sk1'(Y0, Y0))))& 122.91/18.30 (!!((^[Y0 : a]: 122.91/18.30 (!!((^[Y1 : a]: 122.91/18.30 (!!((^[Y2 : a]: 122.91/18.30 (('#sk1'(Y0, Y1) & '#sk1'(Y1, Y2)) => 122.91/18.30 '#sk1'(Y0, Y2)))))))))))& 122.91/18.30 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))) => 122.91/18.30 (!!((^[Y0 : a]: 122.91/18.30 (??((^[Y1 : a > $o]: 122.91/18.30 ((!!((^[Y2 : a]: 122.91/18.30 (Y1(Y2) => 122.91/18.30 (!!((^[Y3 : a]: (Y1(Y3) <=> '#sk1'(Y2, Y3)))))))))& 122.91/18.30 (!!((^[Y2 : a > $o]: 122.91/18.30 (((??(Y2))&Y2(Y0)& 122.91/18.30 (!!((^[Y3 : a]: 122.91/18.30 (Y2(Y3) => 122.91/18.30 (!!((^[Y4 : a]: 122.91/18.30 ('#sk1'(Y3, Y4) <=> Y2(Y4)))))))))) => 122.91/18.30 (Y2 = Y1)))))& 122.91/18.30 Y1(Y0)&(??(Y1)))))))))), 122.91/18.30 inference('lazy_cnf_exists', [status(thm)], ['2'])). 122.91/18.30 tff('4', plain, 122.91/18.30 ~ (!!((^[Y0 : a]: 122.91/18.30 (??((^[Y1 : a > $o]: 122.91/18.30 ((!!((^[Y2 : a]: 122.91/18.30 (Y1(Y2) => 122.91/18.30 (!!((^[Y3 : a]: (Y1(Y3) <=> '#sk1'(Y2, Y3)))))))))& 122.91/18.30 (!!((^[Y2 : a > $o]: 122.91/18.30 (((??(Y2))&Y2(Y0)& 122.91/18.30 (!!((^[Y3 : a]: 122.91/18.30 (Y2(Y3) => 122.91/18.30 (!!((^[Y4 : a]: 122.91/18.30 ('#sk1'(Y3, Y4) <=> Y2(Y4)))))))))) => 123.33/18.30 (Y2 = Y1)))))& 123.33/18.30 Y1(Y0)&(??(Y1))))))))), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['3'])). 123.33/18.30 tff('5', plain, 123.33/18.30 ~ (??((^[Y0 : a > $o]: 123.33/18.30 ((!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: (Y0(Y2) <=> '#sk1'(Y1, Y2)))))))))& 123.33/18.30 (!!((^[Y1 : a > $o]: 123.33/18.30 (((??(Y1))&Y1('#sk2')& 123.33/18.30 (!!((^[Y2 : a]: 123.33/18.30 (Y1(Y2) => 123.33/18.30 (!!((^[Y3 : a]: ('#sk1'(Y2, Y3) <=> Y1(Y3)))))))))) => 123.33/18.30 (Y1 = Y0)))))& 123.33/18.30 Y0('#sk2')&(??(Y0)))))), 123.33/18.30 inference('lazy_cnf_exists', [status(thm)], ['4'])). 123.33/18.30 tff('6', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ~ ((!!((^[Y0 : a]: 123.33/18.30 (X1(Y0) => (!!((^[Y1 : a]: (X1(Y1) <=> '#sk1'(Y0, Y1)))))))))& 123.33/18.30 (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1)))))& 123.33/18.30 X1('#sk2')&(??(X1))), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['5'])). 123.33/18.30 tff('7', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ (!!((^[Y0 : a]: 123.33/18.30 (X1(Y0) => (!!((^[Y1 : a]: (X1(Y1) <=> '#sk1'(Y0, Y1))))))))) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1))))) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (??(X1))), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['6'])). 123.33/18.30 tff('8', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ (X1('#sk11'(X1)) => 123.33/18.30 (!!((^[Y0 : a]: (X1(Y0) <=> '#sk1'('#sk11'(X1), Y0)))))) 123.33/18.30 | ~ (??(X1)) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1)))))), 123.33/18.30 inference('lazy_cnf_exists', [status(thm)], ['7'])). 123.33/18.30 tff('9', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( X1('#sk11'(X1)) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1))))) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (??(X1))), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['8'])). 123.33/18.30 tff('10', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( X1('#sk11'(X1)) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1))))) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (??(X1))), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['8'])). 123.33/18.30 tff('11', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( '#form20'(X1) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1)))))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('12', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form20'(X1) | ~ (??(X1)) | ~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('renaming', [status(thm)], ['9', '11'])). 123.33/18.30 tff('13', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form20'(X1) | ~ (??(X1)) | ~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('renaming', [status(thm)], ['9', '11'])). 123.33/18.30 tff('14', plain, ![X1 : a > $o]: ( '#form28'(X1) | ~ (??(X1))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('15', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form28'(X1) | X1('#sk11'(X1)) | ~ X1('#sk2') | ~ '#form20'(X1)), 123.33/18.30 inference('renaming', [status(thm)], ['12', '14'])). 123.33/18.30 tff('16', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form28'(X1) | X1('#sk11'(X1)) | ~ X1('#sk2') | ~ '#form20'(X1)), 123.33/18.30 inference('renaming', [status(thm)], ['12', '14'])). 123.33/18.30 tff('17', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( '#form20'(X1) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1)))))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('18', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ (((??('#sk31'(X1)))&'#sk31'(X1, '#sk2')& 123.33/18.30 (!!((^[Y0 : a]: 123.33/18.30 ('#sk31'(X1, Y0) => 123.33/18.30 (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) <=> '#sk31'(X1, Y1)))))))))) => 123.33/18.30 ('#sk31'(X1) = X1)) 123.33/18.30 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_exists', [status(thm)], ['17'])). 123.33/18.30 tff('19', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( ((??('#sk31'(X1)))&'#sk31'(X1, '#sk2')& 123.33/18.30 (!!((^[Y0 : a]: 123.33/18.30 ('#sk31'(X1, Y0) => 123.33/18.30 (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) <=> '#sk31'(X1, Y1)))))))))) 123.33/18.30 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['18'])). 123.33/18.30 tff('20', plain, ![X1 : a > $o]: ( '#sk31'(X1, '#sk2') | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['19'])). 123.33/18.30 tff('21', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( (!!((^[Y0 : a]: 123.33/18.30 ('#sk31'(X1, Y0) => 123.33/18.30 (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) <=> '#sk31'(X1, Y1))))))))) 123.33/18.30 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['19'])). 123.33/18.30 tff('22', plain, 123.33/18.30 ![X1 : a > $o, X2 : a]: 123.33/18.30 ( ('#sk31'(X1, X2) => 123.33/18.30 (!!((^[Y0 : a]: ('#sk1'(X2, Y0) <=> '#sk31'(X1, Y0)))))) 123.33/18.30 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['21'])). 123.33/18.30 tff('23', plain, 123.33/18.30 ![X1 : a > $o, X2 : a]: 123.33/18.30 (~ '#sk31'(X1, X2) 123.33/18.30 | (!!((^[Y0 : a]: ('#sk1'(X2, Y0) <=> '#sk31'(X1, Y0))))) 123.33/18.30 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['22'])). 123.33/18.30 tff('24', plain, 123.33/18.30 ![X1 : a > $o, X2 : a, X3 : a]: 123.33/18.30 ( ('#sk1'(X2, X3) <=> '#sk31'(X1, X3)) 123.33/18.30 | '#form20'(X1) 123.33/18.30 | ~ '#sk31'(X1, X2)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['23'])). 123.33/18.30 tff('25', plain, 123.33/18.30 ![X1 : a > $o, X2 : a, X3 : a]: 123.33/18.30 ('#sk1'(X2, X3) = '#sk31'(X1, X3) | '#form20'(X1) | ~ '#sk31'(X1, X2)), 123.33/18.30 inference('simplify nested equalities', [status(thm)], ['24'])). 123.33/18.30 tff('26', plain, 123.33/18.30 ![X0 : a > $o, X1 : a]: 123.33/18.30 ( '#form20'(X0) | '#form20'(X0) | '#sk1'('#sk2', X1) = '#sk31'(X0, X1)), 123.33/18.30 inference('sup-', [status(thm)], ['20', '25'])). 123.33/18.30 tff('27', plain, 123.33/18.30 ![X0 : a > $o, X1 : a]: 123.33/18.30 ('#sk1'('#sk2', X1) = '#sk31'(X0, X1) | '#form20'(X0)), 123.33/18.30 inference('simplify', [status(thm)], ['26'])). 123.33/18.30 tff('28', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 ( '#sk31'(X0, '#sk11'((^[Y0 : a]: '#sk1'('#sk2', Y0)))) 123.33/18.30 | ~ '#form20'( 123.33/18.30 (^[Y0 : a]: '#sk1'((^[Y1 : a]: '#sk2')(Y0), (^[Y1 : a]: Y1)(Y0)))) 123.33/18.30 | ~ (^[Y0 : a]: '#sk1'((^[Y1 : a]: '#sk2')(Y0), (^[Y1 : a]: Y1)(Y0)))( 123.33/18.30 '#sk2') 123.33/18.30 | ~ '#form28'( 123.33/18.30 (^[Y0 : a]: '#sk1'((^[Y1 : a]: '#sk2')(Y0), (^[Y1 : a]: Y1)(Y0)))) 123.33/18.30 | '#form20'(X0)), 123.33/18.30 inference('sup+', [status(thm)], ['16', '27'])). 123.33/18.30 tff('29', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 ( '#sk31'(X0, '#sk11'('#sk1'('#sk2'))) 123.33/18.30 | ~ '#form20'('#sk1'('#sk2')) 123.33/18.30 | ~ '#sk1'('#sk2', '#sk2') 123.33/18.30 | ~ '#form28'('#sk1'('#sk2')) 123.33/18.30 | '#form20'(X0)), 123.33/18.30 inference('ho_norm', [status(thm)], ['28'])). 123.33/18.30 tff('30', plain, ![X1 : a > $o]: ( '#sk31'(X1, '#sk2') | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['19'])). 123.33/18.30 tff('31', plain, 123.33/18.30 ![X1 : a > $o, X2 : a, X3 : a]: 123.33/18.30 ('#sk1'(X2, X3) = '#sk31'(X1, X3) | '#form20'(X1) | ~ '#sk31'(X1, X2)), 123.33/18.30 inference('simplify nested equalities', [status(thm)], ['24'])). 123.33/18.30 tff('32', plain, 123.33/18.30 ![X1 : a > $o, X2 : a]: 123.33/18.30 ('#sk1'(X2) = '#sk31'(X1) | ~ '#sk31'(X1, X2) | '#form20'(X1)), 123.33/18.30 inference('ho_ext_pos_general', [status(thm)], ['31'])). 123.33/18.30 tff('33', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 ( '#form20'(X0) | '#form20'(X0) | '#sk1'('#sk2') = '#sk31'(X0)), 123.33/18.30 inference('sup-', [status(thm)], ['30', '32'])). 123.33/18.30 tff('34', plain, 123.33/18.30 ![X0 : a > $o]: ('#sk1'('#sk2') = '#sk31'(X0) | '#form20'(X0)), 123.33/18.30 inference('simplify', [status(thm)], ['33'])). 123.33/18.30 tff('35', plain, ![X1 : a > $o]: ('#sk31'(X1) != X1 | '#form20'(X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['18'])). 123.33/18.30 tff('36', plain, 123.33/18.30 ![X0 : a > $o]: ('#sk1'('#sk2') != X0 | '#form20'(X0) | '#form20'(X0)), 123.33/18.30 inference('sup-', [status(thm)], ['34', '35'])). 123.33/18.30 tff('37', plain, ![X0 : a > $o]: ( '#form20'(X0) | '#sk1'('#sk2') != X0), 123.33/18.30 inference('simplify', [status(thm)], ['36'])). 123.33/18.30 tff('38', plain, '#form20'('#sk1'('#sk2')), 123.33/18.30 inference('eq_res', [status(thm)], ['37'])). 123.33/18.30 tff('39', plain, 123.33/18.30 ((!!((^[Y0 : a]: '#sk1'(Y0, Y0))))& 123.33/18.30 (!!((^[Y0 : a]: 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (!!((^[Y2 : a]: 123.33/18.30 (('#sk1'(Y0, Y1) & '#sk1'(Y1, Y2)) => 123.33/18.30 '#sk1'(Y0, Y2)))))))))))& 123.33/18.30 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0))))))))), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['3'])). 123.33/18.30 tff('40', plain, (!!((^[Y0 : a]: '#sk1'(Y0, Y0)))), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['39'])). 123.33/18.30 tff('41', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('42', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('43', plain, 123.33/18.30 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => '#sk1'(Y1, Y0)))))))), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['39'])). 123.33/18.30 tff('44', plain, 123.33/18.30 ![X1 : a]: (!!((^[Y0 : a]: ('#sk1'(X1, Y0) => '#sk1'(Y0, X1))))), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['43'])). 123.33/18.30 tff('45', plain, ![X1 : a, X2 : a]: ('#sk1'(X1, X2) => '#sk1'(X2, X1)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['44'])). 123.33/18.30 tff('46', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk1'(X2, X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['45'])). 123.33/18.30 tff('47', plain, ![X1 : a > $o]: ( '#form28'(X1) | ~ (??(X1))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('48', plain, ![X1 : a > $o, X2 : a]: (~ X1(X2) | '#form28'(X1)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['47'])). 123.33/18.30 tff('49', plain, 123.33/18.30 ![X0 : a > a, X1 : a]: 123.33/18.30 (~ '#sk1'(X1, X0(X1)) 123.33/18.30 | '#form28'( 123.33/18.30 (^[Y0 : a]: '#sk1'((^[Y1 : a]: X0(Y1))(Y0), (^[Y1 : a]: Y1)(Y0))))), 123.33/18.30 inference('sup-', [status(thm)], ['46', '48'])). 123.33/18.30 tff('50', plain, 123.33/18.30 ![X0 : a > a, X1 : a]: 123.33/18.30 (~ '#sk1'(X1, X0(X1)) | '#form28'((^[Y0 : a]: '#sk1'(X0(Y0), Y0)))), 123.33/18.30 inference('ho_norm', [status(thm)], ['49'])). 123.33/18.30 tff('51', plain, 123.33/18.30 ![X0 : a]: 123.33/18.30 '#form28'( 123.33/18.30 (^[Y0 : a]: '#sk1'((^[Y1 : a]: (^[Y2 : a]: X0)(Y1))(Y0), Y0))), 123.33/18.30 inference('sup-', [status(thm)], ['42', '50'])). 123.33/18.30 tff('52', plain, ![X0 : a]: '#form28'('#sk1'(X0)), 123.33/18.30 inference('ho_norm', [status(thm)], ['51'])). 123.33/18.30 tff('53', plain, 123.33/18.30 ![X0 : a > $o]: ( '#sk31'(X0, '#sk11'('#sk1'('#sk2'))) | '#form20'(X0)), 123.33/18.30 inference('demod', [status(thm)], ['29', '38', '41', '52'])). 123.33/18.30 tff('54', plain, 123.33/18.30 ![X1 : a > $o, X2 : a, X3 : a]: 123.33/18.30 ('#sk1'(X2, X3) = '#sk31'(X1, X3) | '#form20'(X1) | ~ '#sk31'(X1, X2)), 123.33/18.30 inference('simplify nested equalities', [status(thm)], ['24'])). 123.33/18.30 tff('55', plain, 123.33/18.30 ![X0 : a > $o, X1 : a]: 123.33/18.30 ( '#form20'(X0) 123.33/18.30 | '#form20'(X0) 123.33/18.30 | '#sk1'('#sk11'('#sk1'('#sk2')), X1) = '#sk31'(X0, X1)), 123.33/18.30 inference('sup-', [status(thm)], ['53', '54'])). 123.33/18.30 tff('56', plain, 123.33/18.30 ![X0 : a > $o, X1 : a]: 123.33/18.30 ('#sk1'('#sk11'('#sk1'('#sk2')), X1) = '#sk31'(X0, X1) | '#form20'(X0)), 123.33/18.30 inference('simplify', [status(thm)], ['55'])). 123.33/18.30 tff('57', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ (!!((^[Y0 : a]: (X1(Y0) <=> '#sk1'('#sk11'(X1), Y0))))) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1))))) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (??(X1))), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['8'])). 123.33/18.30 tff('58', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 ( '#form20'(X1) 123.33/18.30 | ~ (!!((^[Y0 : a > $o]: 123.33/18.30 (((??(Y0))&Y0('#sk2')& 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (Y0(Y1) => 123.33/18.30 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) <=> Y0(Y2)))))))))) => 123.33/18.30 (Y0 = X1)))))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('59', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form20'(X1) 123.33/18.30 | ~ (??(X1)) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ (!!((^[Y0 : a]: (X1(Y0) <=> '#sk1'('#sk11'(X1), Y0)))))), 123.33/18.30 inference('renaming', [status(thm)], ['57', '58'])). 123.33/18.30 tff('60', plain, ![X1 : a > $o]: ( '#form28'(X1) | ~ (??(X1))), 123.33/18.30 define([status(thm)])). 123.33/18.30 tff('61', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ '#form28'(X1) 123.33/18.30 | ~ (!!((^[Y0 : a]: (X1(Y0) <=> '#sk1'('#sk11'(X1), Y0))))) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ '#form20'(X1)), 123.33/18.30 inference('renaming', [status(thm)], ['59', '60'])). 123.33/18.30 tff('62', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ (X1('#sk52'(X1)) <=> '#sk1'('#sk11'(X1), '#sk52'(X1))) 123.33/18.30 | ~ '#form20'(X1) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ '#form28'(X1)), 123.33/18.30 inference('lazy_cnf_exists', [status(thm)], ['61'])). 123.33/18.30 tff('63', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (X1('#sk52'(X1)) != '#sk1'('#sk11'(X1), '#sk52'(X1)) 123.33/18.30 | ~ '#form20'(X1) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ '#form28'(X1)), 123.33/18.30 inference('simplify nested equalities', [status(thm)], ['62'])). 123.33/18.30 tff('64', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 ('#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk31'(X0, '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | '#form20'(X0) 123.33/18.30 | ~ '#form28'('#sk1'('#sk2')) 123.33/18.30 | ~ '#sk1'('#sk2', '#sk2') 123.33/18.30 | ~ '#form20'('#sk1'('#sk2'))), 123.33/18.30 inference('sup-', [status(thm)], ['56', '63'])). 123.33/18.30 tff('65', plain, ![X0 : a]: '#form28'('#sk1'(X0)), 123.33/18.30 inference('ho_norm', [status(thm)], ['51'])). 123.33/18.30 tff('66', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('67', plain, '#form20'('#sk1'('#sk2')), 123.33/18.30 inference('eq_res', [status(thm)], ['37'])). 123.33/18.30 tff('68', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 ('#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk31'(X0, '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | '#form20'(X0)), 123.33/18.30 inference('demod', [status(thm)], ['64', '65', '66', '67'])). 123.33/18.30 tff('69', plain, 123.33/18.30 ![X0 : a > $o, X1 : a]: 123.33/18.30 ('#sk1'('#sk2', X1) = '#sk31'(X0, X1) | '#form20'(X0)), 123.33/18.30 inference('simplify', [status(thm)], ['26'])). 123.33/18.30 tff('70', plain, ![X0 : a > $o]: '#form20'(X0), 123.33/18.30 inference('clc', [status(thm)], ['68', '69'])). 123.33/18.30 tff('71', plain, 123.33/18.30 ![X1 : a > $o]: (~ '#form28'(X1) | X1('#sk11'(X1)) | ~ X1('#sk2')), 123.33/18.30 inference('demod', [status(thm)], ['15', '70'])). 123.33/18.30 tff('72', plain, ![X1 : a > $o, X2 : a]: (~ X1(X2) | '#form28'(X1)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['47'])). 123.33/18.30 tff('73', plain, ![X1 : a > $o]: (~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('clc', [status(thm)], ['71', '72'])). 123.33/18.30 tff('74', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('75', plain, ![X1 : a > $o]: (~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('clc', [status(thm)], ['71', '72'])). 123.33/18.30 tff('76', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (X1('#sk52'(X1)) != '#sk1'('#sk11'(X1), '#sk52'(X1)) 123.33/18.30 | ~ '#form20'(X1) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ '#form28'(X1)), 123.33/18.30 inference('simplify nested equalities', [status(thm)], ['62'])). 123.33/18.30 tff('77', plain, ![X0 : a > $o]: '#form20'(X0), 123.33/18.30 inference('clc', [status(thm)], ['68', '69'])). 123.33/18.30 tff('78', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (X1('#sk52'(X1)) != '#sk1'('#sk11'(X1), '#sk52'(X1)) 123.33/18.30 | ~ X1('#sk2') 123.33/18.30 | ~ '#form28'(X1)), 123.33/18.30 inference('demod', [status(thm)], ['76', '77'])). 123.33/18.30 tff('79', plain, ![X1 : a > $o, X2 : a]: (~ X1(X2) | '#form28'(X1)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['47'])). 123.33/18.30 tff('80', plain, 123.33/18.30 ![X1 : a > $o]: 123.33/18.30 (~ X1('#sk2') | X1('#sk52'(X1)) != '#sk1'('#sk11'(X1), '#sk52'(X1))), 123.33/18.30 inference('clc', [status(thm)], ['78', '79'])). 123.33/18.30 tff('81', plain, 123.33/18.30 ![X0 : a > $o, X1 : a > $o]: 123.33/18.30 (X1('#sk2') != X0('#sk11'(X0)) 123.33/18.30 | ~ X0('#sk2') 123.33/18.30 | X1('#sk52'(X1)) != '#sk1'('#sk11'(X1), '#sk52'(X1))), 123.33/18.30 inference('sup-', [status(thm)], ['75', '80'])). 123.33/18.30 tff('82', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 (~ X0('#sk11'(X0)) 123.33/18.30 | (^[Y0 : a]: 123.33/18.30 '#sk1'((^[Y1 : a]: (^[Y2 : a]: '#sk2')(Y1))(Y0), 123.33/18.30 (^[Y1 : a]: Y1)(Y0)))( 123.33/18.30 '#sk52'( 123.33/18.30 (^[Y0 : a]: 123.33/18.30 '#sk1'((^[Y1 : a]: (^[Y2 : a]: '#sk2')(Y1))(Y0), 123.33/18.30 (^[Y1 : a]: Y1)(Y0))))) 123.33/18.30 != '#sk1'( 123.33/18.30 '#sk11'( 123.33/18.30 (^[Y0 : a]: 123.33/18.30 '#sk1'((^[Y1 : a]: (^[Y2 : a]: '#sk2')(Y1))(Y0), 123.33/18.30 (^[Y1 : a]: Y1)(Y0)))), 123.33/18.30 '#sk52'( 123.33/18.30 (^[Y0 : a]: 123.33/18.30 '#sk1'((^[Y1 : a]: (^[Y2 : a]: '#sk2')(Y1))(Y0), 123.33/18.30 (^[Y1 : a]: Y1)(Y0))))) 123.33/18.30 | ~ X0('#sk2')), 123.33/18.30 inference('sup-', [status(thm)], ['74', '81'])). 123.33/18.30 tff('83', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 (~ X0('#sk11'(X0)) 123.33/18.30 | '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | ~ X0('#sk2')), 123.33/18.30 inference('ho_norm', [status(thm)], ['82'])). 123.33/18.30 tff('84', plain, ![X1 : a > $o]: (~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('clc', [status(thm)], ['71', '72'])). 123.33/18.30 tff('85', plain, 123.33/18.30 ![X0 : a > $o]: 123.33/18.30 (~ X0('#sk2') 123.33/18.30 | '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('clc', [status(thm)], ['83', '84'])). 123.33/18.30 tff('86', plain, 123.33/18.30 ![X0 : $o]: 123.33/18.30 (~ (^[Y0 : a]: X0)('#sk2') 123.33/18.30 | '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('prune_arg_fun', [status(thm)], ['85'])). 123.33/18.30 tff('87', plain, 123.33/18.30 ![X0 : $o]: 123.33/18.30 (~ X0 123.33/18.30 | '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('ho_norm', [status(thm)], ['86'])). 123.33/18.30 tff('88', plain, 123.33/18.30 '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))), 123.33/18.30 inference('ho_elim_pred', [status(thm)], ['87'])). 123.33/18.30 tff('89', plain, 123.33/18.30 ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('eq_elim', [status(thm)], ['88'])). 123.33/18.30 tff('90', plain, 123.33/18.30 ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) 123.33/18.30 <= (( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('split', [status(esa)], ['89'])). 123.33/18.30 tff('91', plain, 123.33/18.30 '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 != '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))), 123.33/18.30 inference('ho_elim_pred', [status(thm)], ['87'])). 123.33/18.30 tff('92', plain, 123.33/18.30 (~ '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | ~ '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('eq_elim', [status(thm)], ['91'])). 123.33/18.30 tff('93', plain, 123.33/18.30 ~ ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))) | 123.33/18.30 ~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('split', [status(esa)], ['92'])). 123.33/18.30 tff('94', plain, ![X1 : a > $o]: (~ X1('#sk2') | X1('#sk11'(X1))), 123.33/18.30 inference('clc', [status(thm)], ['71', '72'])). 123.33/18.30 tff('95', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk1'(X2, X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['45'])). 123.33/18.30 tff('96', plain, 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))) 123.33/18.30 <= (( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('split', [status(esa)], ['89'])). 123.33/18.30 tff('97', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk1'(X2, X1)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['45'])). 123.33/18.30 tff('98', plain, 123.33/18.30 (!!((^[Y0 : a]: 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (!!((^[Y2 : a]: 123.33/18.30 (('#sk1'(Y0, Y1) & '#sk1'(Y1, Y2)) => 123.33/18.30 '#sk1'(Y0, Y2))))))))))), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['39'])). 123.33/18.30 tff('99', plain, 123.33/18.30 ![X1 : a]: 123.33/18.30 (!!((^[Y0 : a]: 123.33/18.30 (!!((^[Y1 : a]: 123.33/18.30 (('#sk1'(X1, Y0) & '#sk1'(Y0, Y1)) => '#sk1'(X1, Y1)))))))), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['98'])). 123.33/18.30 tff('100', plain, 123.33/18.30 ![X1 : a, X2 : a]: 123.33/18.30 (!!((^[Y0 : a]: (('#sk1'(X1, X2) & '#sk1'(X2, Y0)) => '#sk1'(X1, Y0))))), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['99'])). 123.33/18.30 tff('101', plain, 123.33/18.30 ![X1 : a, X2 : a, X3 : a]: 123.33/18.30 (('#sk1'(X1, X2) & '#sk1'(X2, X3)) => '#sk1'(X1, X3)), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['100'])). 123.33/18.30 tff('102', plain, 123.33/18.30 ![X1 : a, X2 : a, X3 : a]: 123.33/18.30 (~ ('#sk1'(X1, X2) & '#sk1'(X2, X3)) | '#sk1'(X1, X3)), 123.33/18.30 inference('lazy_cnf_imply', [status(thm)], ['101'])). 123.33/18.30 tff('103', plain, 123.33/18.30 ![X1 : a, X2 : a, X3 : a]: 123.33/18.30 (~ '#sk1'(X1, X2) | ~ '#sk1'(X2, X3) | '#sk1'(X1, X3)), 123.33/18.30 inference('lazy_cnf_and', [status(thm)], ['102'])). 123.33/18.30 tff('104', plain, 123.33/18.30 ![X0 : a, X1 : a, X2 : a]: 123.33/18.30 (~ '#sk1'(X0, X1) | '#sk1'(X1, X2) | ~ '#sk1'(X0, X2)), 123.33/18.30 inference('sup-', [status(thm)], ['97', '103'])). 123.33/18.30 tff('105', plain, 123.33/18.30 (~ '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('split', [status(esa)], ['92'])). 123.33/18.30 tff('106', plain, 123.33/18.30 (![X0 : a]: 123.33/18.30 (~ '#sk1'(X0, '#sk52'('#sk1'('#sk2'))) | ~ '#sk1'(X0, '#sk2'))) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('sup-', [status(thm)], ['104', '105'])). 123.33/18.30 tff('107', plain, 123.33/18.30 (~ '#sk1'('#sk11'('#sk1'('#sk2')), '#sk2')) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) & 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('sup-', [status(thm)], ['96', '106'])). 123.33/18.30 tff('108', plain, 123.33/18.30 (~ '#sk1'('#sk2', '#sk11'('#sk1'('#sk2')))) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) & 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('sup-', [status(thm)], ['95', '107'])). 123.33/18.30 tff('109', plain, 123.33/18.30 (~ (^[Y0 : a]: '#sk1'((^[Y1 : a]: '#sk2')(Y0), (^[Y1 : a]: Y1)(Y0)))( 123.33/18.30 '#sk2')) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) & 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('sup-', [status(thm)], ['94', '108'])). 123.33/18.30 tff('110', plain, 123.33/18.30 (~ '#sk1'('#sk2', '#sk2')) 123.33/18.30 <= (~ ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) & 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('ho_norm', [status(thm)], ['109'])). 123.33/18.30 tff('111', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('112', plain, 123.33/18.30 ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) | 123.33/18.30 ~ ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('demod', [status(thm)], ['110', '111'])). 123.33/18.30 tff('113', plain, 123.33/18.30 ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))) | 123.33/18.30 ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('split', [status(esa)], ['89'])). 123.33/18.30 tff('114', plain, ( '#sk1'('#sk2', '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('sat_resolution*', [status(thm)], ['93', '112', '113'])). 123.33/18.30 tff('115', plain, '#sk1'('#sk2', '#sk52'('#sk1'('#sk2'))), 123.33/18.30 inference('simpl_trail', [status(thm)], ['90', '114'])). 123.33/18.30 tff('116', plain, 123.33/18.30 ![X0 : a, X1 : a, X2 : a]: 123.33/18.30 (~ '#sk1'(X0, X1) | '#sk1'(X1, X2) | ~ '#sk1'(X0, X2)), 123.33/18.30 inference('sup-', [status(thm)], ['97', '103'])). 123.33/18.30 tff('117', plain, 123.33/18.30 (~ '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))) 123.33/18.30 <= (~ ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('split', [status(esa)], ['92'])). 123.33/18.30 tff('118', plain, 123.33/18.30 (![X0 : a]: 123.33/18.30 (~ '#sk1'(X0, '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | ~ '#sk1'(X0, '#sk11'('#sk1'('#sk2'))))) 123.33/18.30 <= (~ ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2'))))), 123.33/18.30 inference('sup-', [status(thm)], ['116', '117'])). 123.33/18.30 tff('119', plain, 123.33/18.30 ~ ( '#sk1'('#sk11'('#sk1'('#sk2')), '#sk52'('#sk1'('#sk2')))), 123.33/18.30 inference('sat_resolution*', [status(thm)], ['93', '112'])). 123.33/18.30 tff('120', plain, 123.33/18.30 ![X0 : a]: 123.33/18.30 (~ '#sk1'(X0, '#sk52'('#sk1'('#sk2'))) 123.33/18.30 | ~ '#sk1'(X0, '#sk11'('#sk1'('#sk2')))), 123.33/18.30 inference('simpl_trail', [status(thm)], ['118', '119'])). 123.33/18.30 tff('121', plain, ~ '#sk1'('#sk2', '#sk11'('#sk1'('#sk2'))), 123.33/18.30 inference('sup-', [status(thm)], ['115', '120'])). 123.33/18.30 tff('122', plain, 123.33/18.30 ~ (^[Y0 : a]: '#sk1'((^[Y1 : a]: '#sk2')(Y0), (^[Y1 : a]: Y1)(Y0)))( 123.33/18.30 '#sk2'), 123.33/18.30 inference('sup-', [status(thm)], ['73', '121'])). 123.33/18.30 tff('123', plain, ~ '#sk1'('#sk2', '#sk2'), 123.33/18.30 inference('ho_norm', [status(thm)], ['122'])). 123.33/18.30 tff('124', plain, ![X1 : a]: '#sk1'(X1, X1), 123.33/18.30 inference('lazy_cnf_forall', [status(thm)], ['40'])). 123.33/18.30 tff('125', plain, $false, inference('demod', [status(thm)], ['123', '124'])). 123.33/18.30 123.33/18.30 % SZS output end Refutation 123.33/18.30 123.33/18.30 123.33/18.30 % Terminating... 123.72/18.41 % Runner terminated. 123.72/18.42 % Zipperpin 1.5 exiting 123.72/18.42 EOF