0.06/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.06/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.7gU5H8IDKi 0.11/0.33 % Computer : n012.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 1200 0.11/0.33 % DateTime : Tue Jul 13 10:20:18 EDT 2021 0.11/0.34 % CPUTime : 0.11/0.34 % Running portfolio for 120 s 0.11/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.34 % Number of cores: 8 0.11/0.34 % Python version: Python 3.6.8 0.11/0.34 % Running in HO mode 0.45/0.62 % Estimated wc time : 1286 0.45/0.62 % Estimated cpu time (7 cpus) : 183.71428571428572 0.48/0.71 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.49/0.72 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 70.96/10.75 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 78.84/11.98 % Solved by lams/old_sp2.sh. 78.84/11.98 % done 249 iterations in 1.179s 78.84/11.98 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 78.84/11.98 % SZS output start Refutation 78.84/11.98 tff(cTHM2C_pme, conjecture, 78.84/11.98 (![K:((($i > $o) * $i) > $o)]: 78.84/11.98 (((![Xx:(($i > $o))]: 78.84/11.98 ((![Xx0]: 78.84/11.98 (Xx(Xx0) => 78.84/11.98 (?[S:(($i > $o))]: ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))))) => 78.84/11.98 (![Xx0]: 78.84/11.98 (K(Xx,Xx0) => 78.84/11.98 K(^[Xx1]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 (S(Xx1) & (![Xx2]: (S(Xx2) => K(S,Xx2))))), 78.84/11.98 Xx0))))) & 78.84/11.98 ((![Xx]: 78.84/11.98 ((?[S:(($i > $o))]: ((![Xx0]: (S(Xx0) => K(S,Xx0))) & S(Xx))) => 78.84/11.98 K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: (S(Xx0) & (![Xx1]: (S(Xx1) => K(S,Xx1))))), 78.84/11.98 Xx))) => 78.84/11.98 (![Xx]: 78.84/11.98 (K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))), 78.84/11.98 Xx) => 78.84/11.98 K(K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0)))), 78.84/11.98 Xx))))) => 78.84/11.98 (![Xx]: 78.84/11.98 ((?[S:(($i > $o))]: ((![Xx0]: (S(Xx0) => K(S,Xx0))) & S(Xx))) <=> 78.84/11.98 K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))), 78.84/11.98 Xx)))))). 78.84/11.98 tff(zf_stmt_0, negated_conjecture, 78.84/11.98 (~ 78.84/11.98 (![K:((($i > $o) * $i) > $o)]: 78.84/11.98 (((![Xx:(($i > $o))]: 78.84/11.98 ((![Xx0]: 78.84/11.98 (Xx(Xx0) => 78.84/11.98 (?[S:(($i > $o))]: ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))))) => 78.84/11.98 (![Xx0]: 78.84/11.98 (K(Xx,Xx0) => 78.84/11.98 K(^[Xx1]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 (S(Xx1) & (![Xx2]: (S(Xx2) => K(S,Xx2))))), 78.84/11.98 Xx0))))) & 78.84/11.98 ((![Xx]: 78.84/11.98 ((?[S:(($i > $o))]: ((![Xx0]: (S(Xx0) => K(S,Xx0))) & S(Xx))) => 78.84/11.98 K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 (S(Xx0) & (![Xx1]: (S(Xx1) => K(S,Xx1))))), 78.84/11.98 Xx))) => 78.84/11.98 (![Xx]: 78.84/11.98 (K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))), 78.84/11.98 Xx) => 78.84/11.98 K(K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: 78.84/11.98 ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0)))), 78.84/11.98 Xx))))) => 78.84/11.98 (![Xx]: 78.84/11.98 ((?[S:(($i > $o))]: ((![Xx0]: (S(Xx0) => K(S,Xx0))) & S(Xx))) <=> 78.84/11.98 K(^[Xx0]: 78.84/11.98 (?[S:(($i > $o))]: ((![Xx1]: (S(Xx1) => K(S,Xx1))) & S(Xx0))), 78.84/11.98 Xx))))))). 78.84/11.98 tff('0', plain, 78.84/11.98 ~ (!!((^[Y0 : ($i > $o * $i) > $o]: 78.84/11.98 (((!!((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: 78.84/11.98 (Y1(Y2) => 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 ((!!((^[Y4 : $i]: 78.84/11.98 (Y3(Y4) => Y0(Y3, Y4))))) & 78.84/11.98 Y3(Y2))))))))) => 78.84/11.98 (!!((^[Y2 : $i]: 78.84/11.98 (Y0(Y1, Y2) => 78.84/11.98 Y0( 78.84/11.98 (^[Y3 : $i]: 78.84/11.98 (??((^[Y4 : $i > $o]: 78.84/11.98 (Y4(Y3) & 78.84/11.98 (!!((^[Y5 : $i]: 78.84/11.98 (Y4(Y5) => Y0(Y4, Y5)))))))))), 78.84/11.98 Y2))))))))) & 78.84/11.98 ((!!((^[Y1 : $i]: 78.84/11.98 ((??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => Y0(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))) => 78.84/11.98 Y0( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 (Y3(Y2) & 78.84/11.98 (!!((^[Y4 : $i]: (Y3(Y4) => Y0(Y3, Y4)))))))))), 78.84/11.98 Y1))))) => 78.84/11.98 (!!((^[Y1 : $i]: 78.84/11.98 (Y0( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 ((!!((^[Y4 : $i]: (Y3(Y4) => Y0(Y3, Y4))))) & 78.84/11.98 Y3(Y2)))))), Y1) => 78.84/11.98 Y0( 78.84/11.98 Y0( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 ((!!((^[Y4 : $i]: 78.84/11.98 (Y3(Y4) => Y0(Y3, Y4))))) & 78.84/11.98 Y3(Y2))))))), Y1))))))) => 78.84/11.98 (!!((^[Y1 : $i]: 78.84/11.98 ((??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => Y0(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))) <=> 78.84/11.98 Y0( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 ((!!((^[Y4 : $i]: (Y3(Y4) => Y0(Y3, Y4))))) & 78.84/11.98 Y3(Y2)))))), Y1))))))))), 78.84/11.98 inference('cnf', [status(esa)], [zf_stmt_0])). 78.84/11.98 tff('1', plain, 78.84/11.98 ~ (((!!((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: 78.84/11.98 (Y0(Y1) => 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))))) => 78.84/11.98 (!!((^[Y1 : $i]: 78.84/11.98 ('#sk1'(Y0, Y1) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 (Y3(Y2) & 78.84/11.98 (!!((^[Y4 : $i]: 78.84/11.98 (Y3(Y4) => '#sk1'(Y3, Y4)))))))))), 78.84/11.98 Y1))))))))) & 78.84/11.98 ((!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) => 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0))))))) => 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) <=> 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0)))))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['0'])). 78.84/11.98 tff('2', plain, 78.84/11.98 ~ (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0))))) <=> 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['1'])). 78.84/11.98 tff('3', plain, 78.84/11.98 ~ ((??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2'))))) <=> 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['2'])). 78.84/11.98 tff('4', plain, 78.84/11.98 (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2'))))) 78.84/11.98 != '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2'), 78.84/11.98 inference('simplify nested equalities', [status(thm)], ['3'])). 78.84/11.98 tff('5', plain, 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2'))))) 78.84/11.98 | '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')), 78.84/11.98 inference('eq_elim', [status(thm)], ['4'])). 78.84/11.98 tff('6', plain, 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')) | 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))), 78.84/11.98 inference('split', [status(esa)], ['5'])). 78.84/11.98 tff('7', plain, 78.84/11.98 ((!!((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: 78.84/11.98 (Y0(Y1) => 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))))) => 78.84/11.98 (!!((^[Y1 : $i]: 78.84/11.98 ('#sk1'(Y0, Y1) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 (Y3(Y2) & 78.84/11.98 (!!((^[Y4 : $i]: 78.84/11.98 (Y3(Y4) => '#sk1'(Y3, Y4)))))))))), 78.84/11.98 Y1))))))))) & 78.84/11.98 ((!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) => 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['1'])). 78.84/11.98 tff('8', plain, 78.84/11.98 ((!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) => 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0)))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['7'])). 78.84/11.98 tff('9', plain, 78.84/11.98 (~ (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0)))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['8'])). 78.84/11.98 tff('10', plain, 78.84/11.98 (~ (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('split', [status(esa)], ['9'])). 78.84/11.98 tff('11', plain, 78.84/11.98 (~ ((??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk8'))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2)))))))))), 78.84/11.98 '#sk8'))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['10'])). 78.84/11.98 tff('12', plain, 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk8')))))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['11'])). 78.84/11.98 tff('13', plain, 78.84/11.98 ( ((!!((^[Y0 : $i]: ('#sk17'(Y0) => '#sk1'('#sk17', Y0))))) & 78.84/11.98 '#sk17'('#sk8'))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['12'])). 78.84/11.98 tff('14', plain, 78.84/11.98 ( (!!((^[Y0 : $i]: ('#sk17'(Y0) => '#sk1'('#sk17', Y0)))))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['13'])). 78.84/11.98 tff('15', plain, 78.84/11.98 (![X1]: ('#sk17'(X1) => '#sk1'('#sk17', X1))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['14'])). 78.84/11.98 tff('16', plain, 78.84/11.98 (![X1]: (~ '#sk17'(X1) | '#sk1'('#sk17', X1))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['15'])). 78.84/11.98 tff('17', plain, 78.84/11.98 (!!((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: 78.84/11.98 (Y0(Y1) => 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))))) => 78.84/11.98 (!!((^[Y1 : $i]: 78.84/11.98 ('#sk1'(Y0, Y1) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y2 : $i]: 78.84/11.98 (??((^[Y3 : $i > $o]: 78.84/11.98 (Y3(Y2) & 78.84/11.98 (!!((^[Y4 : $i]: (Y3(Y4) => '#sk1'(Y3, Y4)))))))))), 78.84/11.98 Y1))))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['7'])). 78.84/11.98 tff('18', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 ((!!((^[Y0 : $i]: 78.84/11.98 (X1(Y0) => 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))))))) => 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['17'])). 78.84/11.98 tff('19', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ (!!((^[Y0 : $i]: 78.84/11.98 (X1(Y0) => 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))))))) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['18'])). 78.84/11.98 tff('20', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ (X1('#sk7'(X1)) => 78.84/11.98 (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk7'(X1))))))) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['19'])). 78.84/11.98 tff('21', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 ( X1('#sk7'(X1)) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['20'])). 78.84/11.98 tff('22', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ '#form14'(X1) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 define([status(thm)])). 78.84/11.98 tff('23', plain, 78.84/11.98 ![X1 : $i > $o, X2]: 78.84/11.98 ( ('#sk1'(X1, X2) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2)))))))))), 78.84/11.98 X2)) 78.84/11.98 | ~ '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['22'])). 78.84/11.98 tff('24', plain, 78.84/11.98 ![X1 : $i > $o, X2]: 78.84/11.98 (~ '#sk1'(X1, X2) 78.84/11.98 | '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & 78.84/11.98 (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2)))))))))), 78.84/11.98 X2) 78.84/11.98 | ~ '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['23'])). 78.84/11.98 tff('25', plain, 78.84/11.98 (~ '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2)))))))))), 78.84/11.98 '#sk8')) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['11'])). 78.84/11.98 tff('26', plain, 78.84/11.98 (![X0 : $i > $o]: (~ '#form14'(X0) | ~ '#sk1'(X0, '#sk8'))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('sup-', [status(thm)], ['24', '25'])). 78.84/11.98 tff('27', plain, 78.84/11.98 ((~ '#sk17'('#sk8') | ~ '#form14'('#sk17'))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('sup-', [status(thm)], ['16', '26'])). 78.84/11.98 tff('28', plain, 78.84/11.98 ( '#sk17'('#sk8')) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['13'])). 78.84/11.98 tff('29', plain, 78.84/11.98 (~ '#form14'('#sk17')) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('demod', [status(thm)], ['27', '28'])). 78.84/11.98 tff('30', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 ( X1('#sk7'(X1)) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['20'])). 78.84/11.98 tff('31', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ '#form14'(X1) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 define([status(thm)])). 78.84/11.98 tff('32', plain, ![X1 : $i > $o]: ( '#form14'(X1) | X1('#sk7'(X1))), 78.84/11.98 inference('renaming', [status(thm)], ['30', '31'])). 78.84/11.98 tff('33', plain, 78.84/11.98 (![X1]: (~ '#sk17'(X1) | '#sk1'('#sk17', X1))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['15'])). 78.84/11.98 tff('34', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk7'(X1)))))) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['20'])). 78.84/11.98 tff('35', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 (~ '#form14'(X1) 78.84/11.98 | (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'(X1, Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 define([status(thm)])). 78.84/11.98 tff('36', plain, 78.84/11.98 ![X1 : $i > $o]: 78.84/11.98 ( '#form14'(X1) 78.84/11.98 | ~ (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk7'(X1))))))), 78.84/11.98 inference('renaming', [status(thm)], ['34', '35'])). 78.84/11.98 tff('37', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 (~ ((!!((^[Y0 : $i]: (X2(Y0) => '#sk1'(X2, Y0))))) & X2('#sk7'(X1))) 78.84/11.98 | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['36'])). 78.84/11.98 tff('38', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 (~ (!!((^[Y0 : $i]: (X2(Y0) => '#sk1'(X2, Y0))))) 78.84/11.98 | ~ X2('#sk7'(X1)) 78.84/11.98 | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['37'])). 78.84/11.98 tff('39', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 (~ (X2('#sk36'(X2)) => '#sk1'(X2, '#sk36'(X2))) 78.84/11.98 | '#form14'(X1) 78.84/11.98 | ~ X2('#sk7'(X1))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['38'])). 78.84/11.98 tff('40', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 (~ '#sk1'(X2, '#sk36'(X2)) | ~ X2('#sk7'(X1)) | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['39'])). 78.84/11.98 tff('41', plain, 78.84/11.98 (![X0 : $i > $o]: 78.84/11.98 (~ '#sk17'('#sk36'('#sk17')) | '#form14'(X0) | ~ '#sk17'('#sk7'(X0)))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('sup-', [status(thm)], ['33', '40'])). 78.84/11.98 tff('42', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 ( X2('#sk36'(X2)) | ~ X2('#sk7'(X1)) | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['39'])). 78.84/11.98 tff('43', plain, 78.84/11.98 (![X0 : $i > $o]: (~ '#sk17'('#sk7'(X0)) | '#form14'(X0))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('clc', [status(thm)], ['41', '42'])). 78.84/11.98 tff('44', plain, 78.84/11.98 (( '#form14'((^[Y0 : $i]: '#sk17'((^[Y1 : $i]: Y1)(Y0)))) 78.84/11.98 | '#form14'((^[Y0 : $i]: '#sk17'(Y0))))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('sup-', [status(thm)], ['32', '43'])). 78.84/11.98 tff('45', plain, 78.84/11.98 (( '#form14'('#sk17') | '#form14'('#sk17'))) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('ho_norm', [status(thm)], ['44'])). 78.84/11.98 tff('46', plain, 78.84/11.98 ( '#form14'('#sk17')) 78.84/11.98 <= (~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))))), 78.84/11.98 inference('simplify', [status(thm)], ['45'])). 78.84/11.98 tff('47', plain, 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('demod', [status(thm)], ['29', '46'])). 78.84/11.98 tff('48', plain, 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0)))))) | 78.84/11.98 ~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0)))))), 78.84/11.98 inference('split', [status(esa)], ['9'])). 78.84/11.98 tff('49', plain, 78.84/11.98 (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2'))))) 78.84/11.98 != '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2'), 78.84/11.98 inference('simplify nested equalities', [status(thm)], ['3'])). 78.84/11.98 tff('50', plain, 78.84/11.98 (~ (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2'))))) 78.84/11.98 | ~ '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')), 78.84/11.98 inference('eq_elim', [status(thm)], ['49'])). 78.84/11.98 tff('51', plain, 78.84/11.98 (~ (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('split', [status(esa)], ['50'])). 78.84/11.98 tff('52', plain, 78.84/11.98 (![X1 : $i > $o]: 78.84/11.98 ~ ((!!((^[Y0 : $i]: (X1(Y0) => '#sk1'(X1, Y0))))) & X1('#sk2'))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['51'])). 78.84/11.98 tff('53', plain, 78.84/11.98 (~ ((!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & 78.84/11.98 (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) & 78.84/11.98 (??((^[Y0 : $i > $o]: 78.84/11.98 (Y0('#sk2') & (!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('triggered_bool_instantiation', [status(thm)], ['52'])). 78.84/11.98 tff('54', plain, 78.84/11.98 ((~ (!!((^[Y0 : $i]: 78.84/11.98 ((??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & 78.84/11.98 (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))))))) => 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 (Y2(Y1) & 78.84/11.98 (!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3)))))))))), 78.84/11.98 Y0))))) 78.84/11.98 | ~ (??((^[Y0 : $i > $o]: 78.84/11.98 (Y0('#sk2') & (!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['53'])). 78.84/11.98 tff('55', plain, 78.84/11.98 (~ (??((^[Y0 : $i > $o]: 78.84/11.98 (Y0('#sk2') & (!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1)))))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('split', [status(esa)], ['54'])). 78.84/11.98 tff('56', plain, 78.84/11.98 (![X1 : $i > $o]: 78.84/11.98 ~ (X1('#sk2') & (!!((^[Y0 : $i]: (X1(Y0) => '#sk1'(X1, Y0))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['55'])). 78.84/11.98 tff('57', plain, 78.84/11.98 (~ ('#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2') & 78.84/11.98 (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('triggered_bool_instantiation', [status(thm)], ['56'])). 78.84/11.98 tff('58', plain, 78.84/11.98 ((~ '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2') 78.84/11.98 | ~ (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0))))))) 78.84/11.98 <= (~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['57'])). 78.84/11.98 tff('59', plain, 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))) | 78.84/11.98 ~ 78.84/11.98 ( (!!((^[Y0 : $i]: 78.84/11.98 ('#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1)))))), Y0) => 78.84/11.98 '#sk1'( 78.84/11.98 '#sk1'( 78.84/11.98 (^[Y1 : $i]: 78.84/11.98 (??((^[Y2 : $i > $o]: 78.84/11.98 ((!!((^[Y3 : $i]: (Y2(Y3) => '#sk1'(Y2, Y3))))) & 78.84/11.98 Y2(Y1))))))), Y0)))))) | 78.84/11.98 ~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')), 78.84/11.98 inference('split', [status(esa)], ['58'])). 78.84/11.98 tff('60', plain, 78.84/11.98 ~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')) | 78.84/11.98 ~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))), 78.84/11.98 inference('split', [status(esa)], ['50'])). 78.84/11.98 tff('61', plain, ![X1 : $i > $o]: ( '#form14'(X1) | X1('#sk7'(X1))), 78.84/11.98 inference('renaming', [status(thm)], ['30', '31'])). 78.84/11.98 tff('62', plain, 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('split', [status(esa)], ['5'])). 78.84/11.98 tff('63', plain, 78.84/11.98 ( ((!!((^[Y0 : $i]: ('#sk668'(Y0) => '#sk1'('#sk668', Y0))))) & 78.84/11.98 '#sk668'('#sk2'))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_exists', [status(thm)], ['62'])). 78.84/11.98 tff('64', plain, 78.84/11.98 ( (!!((^[Y0 : $i]: ('#sk668'(Y0) => '#sk1'('#sk668', Y0)))))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['63'])). 78.84/11.98 tff('65', plain, 78.84/11.98 (![X1]: ('#sk668'(X1) => '#sk1'('#sk668', X1))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_forall', [status(thm)], ['64'])). 78.84/11.98 tff('66', plain, 78.84/11.98 (![X1]: (~ '#sk668'(X1) | '#sk1'('#sk668', X1))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['65'])). 78.84/11.98 tff('67', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 (~ '#sk1'(X2, '#sk36'(X2)) | ~ X2('#sk7'(X1)) | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['39'])). 78.84/11.98 tff('68', plain, 78.84/11.98 (![X0 : $i > $o]: 78.84/11.98 (~ '#sk668'('#sk36'('#sk668')) 78.84/11.98 | '#form14'(X0) 78.84/11.98 | ~ '#sk668'('#sk7'(X0)))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('sup-', [status(thm)], ['66', '67'])). 78.84/11.98 tff('69', plain, 78.84/11.98 ![X1 : $i > $o, X2 : $i > $o]: 78.84/11.98 ( X2('#sk36'(X2)) | ~ X2('#sk7'(X1)) | '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['39'])). 78.84/11.98 tff('70', plain, 78.84/11.98 (![X0 : $i > $o]: (~ '#sk668'('#sk7'(X0)) | '#form14'(X0))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('clc', [status(thm)], ['68', '69'])). 78.84/11.98 tff('71', plain, 78.84/11.98 (( '#form14'((^[Y0 : $i]: '#sk668'((^[Y1 : $i]: Y1)(Y0)))) 78.84/11.98 | '#form14'((^[Y0 : $i]: '#sk668'(Y0))))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('sup-', [status(thm)], ['61', '70'])). 78.84/11.98 tff('72', plain, 78.84/11.98 (( '#form14'('#sk668') | '#form14'('#sk668'))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('ho_norm', [status(thm)], ['71'])). 78.84/11.98 tff('73', plain, 78.84/11.98 ( '#form14'('#sk668')) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('simplify', [status(thm)], ['72'])). 78.84/11.98 tff('74', plain, 78.84/11.98 (![X1]: (~ '#sk668'(X1) | '#sk1'('#sk668', X1))) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['65'])). 78.84/11.98 tff('75', plain, 78.84/11.98 ![X1 : $i > $o, X2]: 78.84/11.98 (~ '#sk1'(X1, X2) 78.84/11.98 | '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 (Y1(Y0) & 78.84/11.98 (!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2)))))))))), 78.84/11.98 X2) 78.84/11.98 | ~ '#form14'(X1)), 78.84/11.98 inference('lazy_cnf_imply', [status(thm)], ['23'])). 78.84/11.98 tff('76', plain, 78.84/11.98 (~ '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')) 78.84/11.98 <= (~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0)))))), '#sk2'))), 78.84/11.98 inference('split', [status(esa)], ['50'])). 78.84/11.98 tff('77', plain, 78.84/11.98 (![X0 : $i > $o]: (~ '#form14'(X0) | ~ '#sk1'(X0, '#sk2'))) 78.84/11.98 <= (~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0)))))), '#sk2'))), 78.84/11.98 inference('sup-', [status(thm)], ['75', '76'])). 78.84/11.98 tff('78', plain, 78.84/11.98 ((~ '#sk668'('#sk2') | ~ '#form14'('#sk668'))) 78.84/11.98 <= (~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0)))))), '#sk2')) & 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('sup-', [status(thm)], ['74', '77'])). 78.84/11.98 tff('79', plain, 78.84/11.98 ( '#sk668'('#sk2')) 78.84/11.98 <= (( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('lazy_cnf_and', [status(thm)], ['63'])). 78.84/11.98 tff('80', plain, 78.84/11.98 (~ '#form14'('#sk668')) 78.84/11.98 <= (~ 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & 78.84/11.98 Y1(Y0)))))), '#sk2')) & 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & 78.84/11.98 Y0('#sk2'))))))), 78.84/11.98 inference('demod', [status(thm)], ['78', '79'])). 78.84/11.98 tff('81', plain, 78.84/11.98 ( '#sk1'( 78.84/11.98 (^[Y0 : $i]: 78.84/11.98 (??((^[Y1 : $i > $o]: 78.84/11.98 ((!!((^[Y2 : $i]: (Y1(Y2) => '#sk1'(Y1, Y2))))) & Y1(Y0)))))), 78.84/11.98 '#sk2')) | 78.84/11.98 ~ 78.84/11.98 ( (??((^[Y0 : $i > $o]: 78.84/11.98 ((!!((^[Y1 : $i]: (Y0(Y1) => '#sk1'(Y0, Y1))))) & Y0('#sk2')))))), 78.84/11.98 inference('sup-', [status(thm)], ['73', '80'])). 78.84/11.98 tff('82', plain, $false, 78.84/11.98 inference('sat_resolution*', [status(thm)], 78.84/11.98 ['6', '47', '48', '59', '60', '81'])). 78.84/11.98 78.84/11.98 % SZS output end Refutation 78.84/11.98 78.84/11.98 78.84/11.98 % Terminating... 79.35/12.05 % Runner terminated. 79.35/12.06 % Zipperpin 1.5 exiting 79.35/12.07 EOF