0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.rZeZBzmfN2 0.14/0.35 % Computer : n010.cluster.edu 0.14/0.35 % Model : x86_64 x86_64 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.35 % Memory : 8042.1875MB 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.35 % CPULimit : 1200 0.14/0.35 % DateTime : Tue Jul 13 11:33:06 EDT 2021 0.14/0.35 % CPUTime : 0.14/0.35 % Running portfolio for 120 s 0.14/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.35 % Number of cores: 8 0.14/0.35 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.50/0.64 % Estimated wc time : 1286 0.50/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.55/0.70 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.55/0.70 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.55/0.75 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.55/0.76 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 70.82/10.77 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 104.96/15.77 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 104.96/15.78 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 144.17/21.48 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 144.90/21.56 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 181.51/26.79 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 187.10/27.65 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 188.05/27.81 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 262.28/38.55 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 284.09/41.72 % /export/starexec/sandbox/solver/bin/lams/c.preprocess2.sh running for 21s 319.46/46.83 % /export/starexec/sandbox/solver/bin/lams/sh.or.sh running for 26s 359.67/52.60 % /export/starexec/sandbox/solver/bin/lams/new.cs3.comb.sh running for 18s 364.44/53.37 % /export/starexec/sandbox/solver/bin/lams/old_b2.sh running for 31s 366.78/53.77 % /export/starexec/sandbox/solver/bin/lams/sp5.sh running for 36s 405.78/59.42 % Solved by lams/old_b2.sh. 405.78/59.42 % Running : timeout 15 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.rZeZBzmfN2/e_input395913 --cpu-limit=13 --auto -s -p. 405.78/59.42 % done 27 iterations in 6.033s 405.78/59.42 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 405.78/59.42 % SZS output start Refutation 405.78/59.42 tff(cTHM112B, conjecture, 405.78/59.42 (![P:(($i > $o))]: 405.78/59.42 (?[Xm_9:((($i > $i) * $i) > $o),Xm_10:((($i > $i) * $i) > $o)]: 405.78/59.42 ((![G:(($i > $i)),H:(($i > $i))]: 405.78/59.42 (((![Xw_1]: (Xm_9(H,Xw_1) | Xm_10(H,Xw_1))) & 405.78/59.42 (![Xw_1]: (Xm_10(G,Xw_1) | Xm_9(G,Xw_1)))) => 405.78/59.42 ((![Xw_1]: 405.78/59.42 (Xm_10(^[Xx]: G(H(Xx)),Xw_1) | Xm_9(^[Xx]: G(H(Xx)),Xw_1))) & 405.78/59.42 (![Y]: (P(Y) => P(G(Y))))))) & 405.78/59.42 (![Xw_1]: (Xm_10(^[Xx]: Xx,Xw_1) | Xm_9(^[Xx]: Xx,Xw_1))))))). 405.78/59.42 tff(zf_stmt_0, negated_conjecture, 405.78/59.42 (~ 405.78/59.42 (![P:(($i > $o))]: 405.78/59.42 (?[Xm_9:((($i > $i) * $i) > $o),Xm_10:((($i > $i) * $i) > $o)]: 405.78/59.42 ((![G:(($i > $i)),H:(($i > $i))]: 405.78/59.42 (((![Xw_1]: (Xm_9(H,Xw_1) | Xm_10(H,Xw_1))) & 405.78/59.42 (![Xw_1]: (Xm_10(G,Xw_1) | Xm_9(G,Xw_1)))) => 405.78/59.42 ((![Xw_1]: 405.78/59.42 (Xm_10(^[Xx]: G(H(Xx)),Xw_1) | Xm_9(^[Xx]: G(H(Xx)),Xw_1))) & 405.78/59.42 (![Y]: (P(Y) => P(G(Y))))))) & 405.78/59.42 (![Xw_1]: (Xm_10(^[Xx]: Xx,Xw_1) | Xm_9(^[Xx]: Xx,Xw_1)))))))). 405.78/59.42 tff('0', plain, 405.78/59.42 ~ (!!((^[Y0 : $i > $o]: 405.78/59.42 (??((^[Y1 : ($i > $i * $i) > $o]: 405.78/59.42 (??((^[Y2 : ($i > $i * $i) > $o]: 405.78/59.42 ((!!((^[Y3 : $i > $i]: 405.78/59.42 (!!((^[Y4 : $i > $i]: 405.78/59.42 (((!!((^[Y5 : $i]: 405.78/59.42 (Y1(Y4, Y5) | Y2(Y4, Y5))))) & 405.78/59.42 (!!((^[Y5 : $i]: 405.78/59.42 (Y2(Y3, Y5) | Y1(Y3, Y5)))))) => 405.78/59.42 ((!!((^[Y5 : $i]: 405.78/59.42 (Y2( 405.78/59.42 (^[Y6 : $i]: Y3(Y4(Y6))), 405.78/59.42 Y5) | 405.78/59.42 Y1( 405.78/59.42 (^[Y6 : $i]: Y3(Y4(Y6))), 405.78/59.42 Y5))))) & 405.78/59.42 (!!((^[Y5 : $i]: 405.78/59.42 (Y0(Y5) => Y0(Y3(Y5)))))))))))))) & 405.78/59.42 (!!((^[Y3 : $i]: 405.78/59.42 (Y2((^[Y4 : $i]: Y4), Y3) | 405.78/59.42 Y1((^[Y4 : $i]: Y4), Y3))))))))))))))), 405.78/59.42 inference('cnf', [status(esa)], [zf_stmt_0])). 405.78/59.42 tff('1', plain, 405.78/59.42 ~ (??((^[Y0 : ($i > $i * $i) > $o]: 405.78/59.42 (??((^[Y1 : ($i > $i * $i) > $o]: 405.78/59.42 ((!!((^[Y2 : $i > $i]: 405.78/59.42 (!!((^[Y3 : $i > $i]: 405.78/59.42 (((!!((^[Y4 : $i]: 405.78/59.42 (Y0(Y3, Y4) | Y1(Y3, Y4))))) & 405.78/59.42 (!!((^[Y4 : $i]: 405.78/59.42 (Y1(Y2, Y4) | Y0(Y2, Y4)))))) => 405.78/59.42 ((!!((^[Y4 : $i]: 405.78/59.42 (Y1((^[Y5 : $i]: Y2(Y3(Y5))), Y4) | 405.78/59.42 Y0((^[Y5 : $i]: Y2(Y3(Y5))), Y4))))) & 405.78/59.42 (!!((^[Y4 : $i]: 405.78/59.42 ('#sk1'(Y4) => '#sk1'(Y2(Y4)))))))))))))) & 405.78/59.42 (!!((^[Y2 : $i]: 405.78/59.42 (Y1((^[Y3 : $i]: Y3), Y2) | 405.78/59.42 Y0((^[Y3 : $i]: Y3), Y2)))))))))))), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['0'])). 405.78/59.42 tff('2', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o]: 405.78/59.42 ~ (??((^[Y0 : ($i > $i * $i) > $o]: 405.78/59.42 ((!!((^[Y1 : $i > $i]: 405.78/59.42 (!!((^[Y2 : $i > $i]: 405.78/59.42 (((!!((^[Y3 : $i]: (X1(Y2, Y3) | Y0(Y2, Y3))))) & 405.78/59.42 (!!((^[Y3 : $i]: (Y0(Y1, Y3) | X1(Y1, Y3)))))) => 405.78/59.42 ((!!((^[Y3 : $i]: 405.78/59.42 (Y0((^[Y4 : $i]: Y1(Y2(Y4))), Y3) | 405.78/59.42 X1((^[Y4 : $i]: Y1(Y2(Y4))), Y3))))) & 405.78/59.42 (!!((^[Y3 : $i]: 405.78/59.42 ('#sk1'(Y3) => '#sk1'(Y1(Y3)))))))))))))) & 405.78/59.42 (!!((^[Y1 : $i]: 405.78/59.42 (Y0((^[Y2 : $i]: Y2), Y1) | X1((^[Y2 : $i]: Y2), Y1))))))))), 405.78/59.42 inference('lazy_cnf_forall', [status(thm)], ['1'])). 405.78/59.42 tff('3', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ~ ((!!((^[Y0 : $i > $i]: 405.78/59.42 (!!((^[Y1 : $i > $i]: 405.78/59.42 (((!!((^[Y2 : $i]: (X1(Y1, Y2) | X2(Y1, Y2))))) & 405.78/59.42 (!!((^[Y2 : $i]: (X2(Y0, Y2) | X1(Y0, Y2)))))) => 405.78/59.42 ((!!((^[Y2 : $i]: 405.78/59.42 (X2((^[Y3 : $i]: Y0(Y1(Y3))), Y2) | 405.78/59.42 X1((^[Y3 : $i]: Y0(Y1(Y3))), Y2))))) & 405.78/59.42 (!!((^[Y2 : $i]: ('#sk1'(Y2) => '#sk1'(Y0(Y2)))))))))))))) & 405.78/59.42 (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_forall', [status(thm)], ['2'])). 405.78/59.42 tff('4', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (!!((^[Y0 : $i > $i]: 405.78/59.42 (!!((^[Y1 : $i > $i]: 405.78/59.42 (((!!((^[Y2 : $i]: (X1(Y1, Y2) | X2(Y1, Y2))))) & 405.78/59.42 (!!((^[Y2 : $i]: (X2(Y0, Y2) | X1(Y0, Y2)))))) => 405.78/59.42 ((!!((^[Y2 : $i]: 405.78/59.42 (X2((^[Y3 : $i]: Y0(Y1(Y3))), Y2) | 405.78/59.42 X1((^[Y3 : $i]: Y0(Y1(Y3))), Y2))))) & 405.78/59.42 (!!((^[Y2 : $i]: ('#sk1'(Y2) => '#sk1'(Y0(Y2)))))))))))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_and', [status(thm)], ['3'])). 405.78/59.42 tff('5', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (!!((^[Y0 : $i > $i]: 405.78/59.42 (((!!((^[Y1 : $i]: (X1(Y0, Y1) | X2(Y0, Y1))))) & 405.78/59.42 (!!((^[Y1 : $i]: 405.78/59.42 (X2('#sk42'(X1, X2), Y1) | X1('#sk42'(X1, X2), Y1)))))) => 405.78/59.42 ((!!((^[Y1 : $i]: 405.78/59.42 (X2((^[Y2 : $i]: '#sk42'(X1, X2, Y0(Y2))), Y1) | 405.78/59.42 X1((^[Y2 : $i]: '#sk42'(X1, X2, Y0(Y2))), Y1))))) & 405.78/59.42 (!!((^[Y1 : $i]: 405.78/59.42 ('#sk1'(Y1) => '#sk1'('#sk42'(X1, X2, Y1))))))))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['4'])). 405.78/59.42 tff('6', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (((!!((^[Y0 : $i]: 405.78/59.42 (X1('#sk75'(X1, X2), Y0) | X2('#sk75'(X1, X2), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: 405.78/59.42 (X2('#sk42'(X1, X2), Y0) | X1('#sk42'(X1, X2), Y0)))))) => 405.78/59.42 ((!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0) | 405.78/59.42 X1((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['5'])). 405.78/59.42 tff('7', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ ((!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0) | 405.78/59.42 X1((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0))))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_imply', [status(thm)], ['6'])). 405.78/59.42 tff('8', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( ((!!((^[Y0 : $i]: (X1('#sk75'(X1, X2), Y0) | X2('#sk75'(X1, X2), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: (X2('#sk42'(X1, X2), Y0) | X1('#sk42'(X1, X2), Y0)))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_imply', [status(thm)], ['6'])). 405.78/59.42 tff('9', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form142'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('10', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, X2) 405.78/59.42 | ~ ((!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), 405.78/59.42 Y0) | 405.78/59.42 X1((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), 405.78/59.42 Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))))), 405.78/59.42 inference('renaming', [status(thm)], ['7', '9'])). 405.78/59.42 tff('11', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0) | 405.78/59.42 X1((^[Y1 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y1))), Y0))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_and', [status(thm)], ['10'])). 405.78/59.42 tff('12', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (X2((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2)) | 405.78/59.42 X1((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2))) 405.78/59.42 | ~ '#form142'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0))))))), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['11'])). 405.78/59.42 tff('13', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X2((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2)) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['12'])). 405.78/59.42 tff('14', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form407'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0))))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('15', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ ('#sk1'('#sk456'(X1, X2)) => 405.78/59.42 '#sk1'('#sk42'(X1, X2, '#sk456'(X1, X2)))) 405.78/59.42 | '#form407'(X1, X2)), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['14'])). 405.78/59.42 tff('16', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#sk1'('#sk456'(X1, X2)) | '#form407'(X1, X2)), 405.78/59.42 inference('lazy_cnf_imply', [status(thm)], ['15'])). 405.78/59.42 tff('17', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#sk1'('#sk42'(X1, X2, '#sk456'(X1, X2))) | '#form407'(X1, X2)), 405.78/59.42 inference('lazy_cnf_imply', [status(thm)], ['15'])). 405.78/59.42 tff('18', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X2((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2)) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['12'])). 405.78/59.42 tff('19', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form407'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0))))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('20', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form407'(X1, X2) 405.78/59.42 | ~ '#form142'(X1, X2) 405.78/59.42 | ~ X2((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2))), 405.78/59.42 inference('renaming', [status(thm)], ['18', '19'])). 405.78/59.42 tff('21', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 '#l_lift79556'(X1, X2, X3) = '#sk42'(X1, X2, '#sk75'(X1, X2, X3)), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('22', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X1((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2)) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0)))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['12'])). 405.78/59.42 tff('23', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form407'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: ('#sk1'(Y0) => '#sk1'('#sk42'(X1, X2, Y0))))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('24', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form407'(X1, X2) 405.78/59.42 | ~ '#form142'(X1, X2) 405.78/59.42 | ~ X1((^[Y0 : $i]: '#sk42'(X1, X2, '#sk75'(X1, X2, Y0))), 405.78/59.42 '#sk290'(X1, X2))), 405.78/59.42 inference('renaming', [status(thm)], ['22', '23'])). 405.78/59.42 tff('25', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 '#l_lift79556'(X1, X2, X3) = '#sk42'(X1, X2, '#sk75'(X1, X2, X3)), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('26', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form407'(X1, X2) 405.78/59.42 | ~ '#form142'(X1, X2) 405.78/59.42 | ~ X1('#l_lift79556'(X1, X2), '#sk290'(X1, X2))), 405.78/59.42 inference('lambda_lifting', [status(thm)], ['24', '25'])). 405.78/59.42 tff('27', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( ((!!((^[Y0 : $i]: (X1('#sk75'(X1, X2), Y0) | X2('#sk75'(X1, X2), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: (X2('#sk42'(X1, X2), Y0) | X1('#sk42'(X1, X2), Y0)))))) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 inference('lazy_cnf_imply', [status(thm)], ['6'])). 405.78/59.42 tff('28', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form142'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('29', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, X2) 405.78/59.42 | ((!!((^[Y0 : $i]: 405.78/59.42 (X1('#sk75'(X1, X2), Y0) | X2('#sk75'(X1, X2), Y0))))) & 405.78/59.42 (!!((^[Y0 : $i]: 405.78/59.42 (X2('#sk42'(X1, X2), Y0) | X1('#sk42'(X1, X2), Y0))))))), 405.78/59.42 inference('renaming', [status(thm)], ['27', '28'])). 405.78/59.42 tff('30', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( (!!((^[Y0 : $i]: (X1('#sk75'(X1, X2), Y0) | X2('#sk75'(X1, X2), Y0))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_and', [status(thm)], ['29'])). 405.78/59.42 tff('31', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 ( (X1('#sk75'(X1, X2), X3) | X2('#sk75'(X1, X2), X3)) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_forall', [status(thm)], ['30'])). 405.78/59.42 tff('32', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 ( X1('#sk75'(X1, X2), X3) 405.78/59.42 | X2('#sk75'(X1, X2), X3) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['31'])). 405.78/59.42 tff('33', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 ( X1('#sk75'(X1, X2), X3) 405.78/59.42 | X2('#sk75'(X1, X2), X3) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['31'])). 405.78/59.42 tff('34', plain, 405.78/59.42 ![X0 : $o, X1]: 405.78/59.42 (~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)) 405.78/59.42 | (^[Y0 : $i > $i,Y1 : $i]: X0)( 405.78/59.42 '#sk75'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)), X1)), 405.78/59.42 inference('eq_fact', [status(thm)], ['33'])). 405.78/59.42 tff('35', plain, 405.78/59.42 ![X0 : $o]: 405.78/59.42 (~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)) 405.78/59.42 | X0), 405.78/59.42 inference('ho_norm', [status(thm)], ['34'])). 405.78/59.42 tff('36', plain, 405.78/59.42 ~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: $false), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: $false)), 405.78/59.42 inference('elim_bool_vars', [status(thm)], ['35'])). 405.78/59.42 tff('37', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'( 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)(Y0, 405.78/59.42 Y1), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)(Y0, 405.78/59.42 Y1)))) 405.78/59.42 | X1( 405.78/59.42 '#sk75'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'( 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)( 405.78/59.42 Y0, Y1), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)( 405.78/59.42 Y0, Y1)))), X0)), 405.78/59.42 inference('sup-', [status(thm)], ['32', '36'])). 405.78/59.42 tff('38', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'((^[Y2 : $i > $i,Y3 : $i]: $false), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i]: $false)))) 405.78/59.42 | X1( 405.78/59.42 '#sk75'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'((^[Y2 : $i > $i,Y3 : $i]: $false), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i]: $false)))), X0)), 405.78/59.42 inference('ho_norm', [status(thm)], ['37'])). 405.78/59.42 tff('39', plain, 405.78/59.42 ![X0 : $o]: 405.78/59.42 (~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)) 405.78/59.42 | X0), 405.78/59.42 inference('ho_norm', [status(thm)], ['34'])). 405.78/59.42 tff('40', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('41', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('42', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('43', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('44', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('45', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('46', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 '#l_lift79558'( 405.78/59.42 '#form142'('#l_lift79558'($false), '#l_lift79558'($false)))) 405.78/59.42 | X1( 405.78/59.42 '#sk75'(X1, 405.78/59.42 '#l_lift79558'( 405.78/59.42 '#form142'('#l_lift79558'($false), '#l_lift79558'($false)))), 405.78/59.42 X0)), 405.78/59.42 inference('lambda_lifting', [status(thm)], 405.78/59.42 ['38', '40', '41', '42', '43', '44', '45'])). 405.78/59.42 tff('47', plain, 405.78/59.42 ![X0 : $o]: 405.78/59.42 (~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)) 405.78/59.42 | X0), 405.78/59.42 inference('ho_norm', [status(thm)], ['34'])). 405.78/59.42 tff('48', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('49', plain, 405.78/59.42 ![X0 : $o]: 405.78/59.42 (~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: X0), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: X0)) 405.78/59.42 | X0), 405.78/59.42 inference('ho_norm', [status(thm)], ['34'])). 405.78/59.42 tff('50', plain, 405.78/59.42 ~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: $false), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: $false)), 405.78/59.42 inference('elim_bool_vars', [status(thm)], ['35'])). 405.78/59.42 tff('51', plain, ![X1 : $i > $i, X2]: ~ '#l_lift79557'(X1, X2), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('52', plain, '#l_lift79558'($false) = '#l_lift79557', 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('53', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('54', plain, 405.78/59.42 ![X0 : $o]: (~ '#form142'('#l_lift79558'(X0), '#l_lift79558'(X0)) | X0), 405.78/59.42 inference('lambda_lifting', [status(thm)], ['47', '48', '52', '53'])). 405.78/59.42 tff('55', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( '#form142'(X1, X2) 405.78/59.42 | ~ (!!((^[Y0 : $i]: 405.78/59.42 (X2((^[Y1 : $i]: Y1), Y0) | X1((^[Y1 : $i]: Y1), Y0)))))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('56', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ (X2((^[Y0 : $i]: Y0), '#sk197'(X1, X2)) | 405.78/59.42 X1((^[Y0 : $i]: Y0), '#sk197'(X1, X2))) 405.78/59.42 | '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_exists', [status(thm)], ['55'])). 405.78/59.42 tff('57', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X2((^[Y0 : $i]: Y0), '#sk197'(X1, X2)) | '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['56'])). 405.78/59.42 tff('58', plain, ![X3]: '#l_lift79555'(X3) = X3, define([status(thm)])). 405.78/59.42 tff('59', plain, 405.78/59.42 ~ (!!((^[Y0 : $i > $o]: 405.78/59.42 (??((^[Y1 : ($i > $i * $i) > $o]: 405.78/59.42 (??((^[Y2 : ($i > $i * $i) > $o]: 405.78/59.42 ((!!((^[Y3 : $i > $i]: 405.78/59.42 (!!((^[Y4 : $i > $i]: 405.78/59.42 (((!!((^[Y5 : $i]: 405.78/59.42 (Y1(Y4, Y5) | Y2(Y4, Y5))))) & 405.78/59.42 (!!((^[Y5 : $i]: 405.78/59.42 (Y2(Y3, Y5) | Y1(Y3, Y5)))))) => 405.78/59.42 ((!!((^[Y5 : $i]: 405.78/59.42 (Y2( 405.78/59.42 (^[Y6 : $i]: Y3(Y4(Y6))), 405.78/59.42 Y5) | 405.78/59.42 Y1( 405.78/59.42 (^[Y6 : $i]: Y3(Y4(Y6))), 405.78/59.42 Y5))))) & 405.78/59.42 (!!((^[Y5 : $i]: 405.78/59.42 (Y0(Y5) => Y0(Y3(Y5)))))))))))))) & 405.78/59.42 (!!((^[Y3 : $i]: 405.78/59.42 (Y2((^[Y4 : $i]: Y4), Y3) | 405.78/59.42 Y1((^[Y4 : $i]: Y4), Y3))))))))))))))), 405.78/59.42 inference('cnf', [status(esa)], [zf_stmt_0])). 405.78/59.42 tff('60', plain, 405.78/59.42 ![X20 : $i > $o, X21 : $i > $i, X22]: 405.78/59.42 '#l_lift79566'(X20, X21, X22) = (X20(X22) => X20(X21(X22))), 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('61', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X1((^[Y0 : $i]: Y0), '#sk197'(X1, X2)) | '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['56'])). 405.78/59.42 tff('62', plain, ![X3]: '#l_lift79555'(X3) = X3, define([status(thm)])). 405.78/59.42 tff('63', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 (~ X1('#l_lift79555', '#sk197'(X1, X2)) | '#form142'(X1, X2)), 405.78/59.42 inference('lambda_lifting', [status(thm)], ['61', '62'])). 405.78/59.42 tff('64', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o]: 405.78/59.42 ( (!!((^[Y0 : $i]: (X2('#sk42'(X1, X2), Y0) | X1('#sk42'(X1, X2), Y0))))) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_and', [status(thm)], ['29'])). 405.78/59.42 tff('65', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 ( (X2('#sk42'(X1, X2), X3) | X1('#sk42'(X1, X2), X3)) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_forall', [status(thm)], ['64'])). 405.78/59.42 tff('66', plain, 405.78/59.42 ![X1 : ($i > $i * $i) > $o, X2 : ($i > $i * $i) > $o, X3]: 405.78/59.42 ( X2('#sk42'(X1, X2), X3) 405.78/59.42 | X1('#sk42'(X1, X2), X3) 405.78/59.42 | ~ '#form142'(X1, X2)), 405.78/59.42 inference('lazy_cnf_or', [status(thm)], ['65'])). 405.78/59.42 tff('67', plain, 405.78/59.42 ~ '#form142'((^[Y0 : $i > $i,Y1 : $i]: $false), 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: $false)), 405.78/59.42 inference('elim_bool_vars', [status(thm)], ['35'])). 405.78/59.42 tff('68', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'( 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)(Y0, 405.78/59.42 Y1), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)(Y0, 405.78/59.42 Y1)))) 405.78/59.42 | X1( 405.78/59.42 '#sk42'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'( 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)( 405.78/59.42 Y0, Y1), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i,Y4 : $i > $i,Y5 : $i]: $false)( 405.78/59.42 Y0, Y1)))), X0)), 405.78/59.42 inference('sup-', [status(thm)], ['66', '67'])). 405.78/59.42 tff('69', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'((^[Y2 : $i > $i,Y3 : $i]: $false), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i]: $false)))) 405.78/59.42 | X1( 405.78/59.42 '#sk42'(X1, 405.78/59.42 (^[Y0 : $i > $i,Y1 : $i]: 405.78/59.42 '#form142'((^[Y2 : $i > $i,Y3 : $i]: $false), 405.78/59.42 (^[Y2 : $i > $i,Y3 : $i]: $false)))), X0)), 405.78/59.42 inference('ho_norm', [status(thm)], ['68'])). 405.78/59.42 tff('70', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('71', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('72', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('73', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('74', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('75', plain, 405.78/59.42 ![X0 : $o, X1 : $i > $i, X2]: '#l_lift79558'(X0, X1, X2) = X0, 405.78/59.42 define([status(thm)])). 405.78/59.42 tff('76', plain, 405.78/59.42 ![X0, X1 : ($i > $i * $i) > $o]: 405.78/59.42 (~ '#form142'(X1, 405.78/59.42 '#l_lift79558'( 405.78/59.42 '#form142'('#l_lift79558'($false), '#l_lift79558'($false)))) 405.78/59.42 | X1( 405.78/59.42 '#sk42'(X1, 405.78/59.42 '#l_lift79558'( 405.78/59.42 '#form142'('#l_lift79558'($false), '#l_lift79558'($false)))), 405.78/59.42 X0)), 405.78/59.42 inference('lambda_lifting', [status(thm)], 405.78/59.42 ['69', '70', '71', '72', '73', '74', '75'])). 405.78/59.42 tff('77', plain, $false, 405.78/59.42 inference('eprover', [status(thm)], 405.78/59.42 ['16', '17', '21', '26', '46', '54', '58', '60', '63', '76'])). 405.78/59.42 405.78/59.42 % SZS output end Refutation 405.78/59.42 405.78/59.42 405.78/59.42 % Terminating... 406.42/59.50 % Runner terminated. 406.42/59.51 % Zipperpin 1.5 exiting 406.42/59.51 EOF