0.12/0.13 % 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.SP1uBnbCa3 0.13/0.35 % Computer : n026.cluster.edu 0.13/0.35 % Model : x86_64 x86_64 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.35 % Memory : 8042.1875MB 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.35 % CPULimit : 960 0.13/0.35 % DateTime : Thu Jul 2 09:04:39 EDT 2020 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.13/0.36 % Number of cores: 8 0.13/0.36 % Python version: Python 3.6.8 0.13/0.36 % Running in HO mode 0.59/0.65 % Estimated wc time : 1286 0.59/0.65 % Estimated cpu time (7 cpus) : 183.71428571428572 0.59/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.59/0.74 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.59/0.76 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.59/0.77 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 71.12/10.80 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 103.78/15.56 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.64/15.84 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 146.14/21.72 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 146.14/21.75 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 180.63/26.76 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 188.53/27.83 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 206.05/30.46 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 258.83/38.85 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 276.37/41.79 % /export/starexec/sandbox/solver/bin/lams/c.preprocess2.sh running for 21s 304.94/46.71 % /export/starexec/sandbox/solver/bin/lams/sh.or.sh running for 26s 334.63/52.78 % /export/starexec/sandbox/solver/bin/lams/new.cs3.comb.sh running for 18s 342.79/54.41 % /export/starexec/sandbox/solver/bin/lams/old_b2.sh running for 31s 347.06/55.18 % /export/starexec/sandbox/solver/bin/lams/sp5.sh running for 36s 399.79/63.09 % /export/starexec/sandbox/solver/bin/lams/b2.sh running for 15s 413.13/65.08 % Solved by lams/b2.sh. 413.13/65.08 % done 477 iterations in 1.850s 413.13/65.08 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 413.13/65.08 % SZS output start Refutation 413.13/65.08 tff(cCS_DUC_RELNS_pme, conjecture, 413.13/65.08 (![S:(((c * b) > $o > $o))]: 413.13/65.08 ((![Xx:((c * b) > $o)]: 413.13/65.08 (S(Xx) => 413.13/65.08 (![Xc:c]: 413.13/65.08 ((![Xx0:b,Xy:b,Xz:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xb = Xc0) & (Xa = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & (Xb = cP(Xy1,Xy2)) & 413.13/65.08 R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & 413.13/65.08 (Xc0 = cP(Xz1,Xz2)))) | 413.13/65.08 ((Xb = c0) & (Xa = Xc0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx0,Xy,Xz))) & 413.13/65.08 Xx(Xc,Xy) & Xx(Xc,Xx0)) => 413.13/65.08 Xx(Xc,Xz))) & 413.13/65.08 (![Xx0:b,Xy:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xb = Xc0) & (Xa = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & R(Xx1,Xy1,Xz1) & 413.13/65.08 R(Xx2,Xy2,Xz2) & (Xc0 = cP(Xz1,Xz2)) & 413.13/65.08 (Xb = cP(Xy1,Xy2)))) | 413.13/65.08 ((Xa = Xc0) & (Xb = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx0,Xy,Xy))) & 413.13/65.08 Xx(Xc,Xy)) => 413.13/65.08 Xx(Xc,Xx0))) & 413.13/65.08 Xx(Xc,c0))))) => 413.13/65.08 (![Xc:c]: 413.13/65.08 ((![Xx:b,Xy:b,Xz:b]: 413.13/65.08 (((![R:((c * b) > $o)]: (S(R) => R(Xc,Xy))) & 413.13/65.08 (![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xa = Xc0) & (Xb = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xb = cP(Xy1,Xy2)) & (Xc0 = cP(Xz1,Xz2)) & 413.13/65.08 R(Xx1,Xy1,Xz1) & R(Xx2,Xy2,Xz2) & 413.13/65.08 (Xa = cP(Xx1,Xx2)))) | 413.13/65.08 ((Xb = Xc0) & (Xa = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx,Xy,Xz))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xx)))) => 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xz))))) & 413.13/65.08 (![Xx:b,Xy:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xa = c0) & (Xb = Xc0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & (Xb = cP(Xy1,Xy2)) & 413.13/65.08 R(Xx1,Xy1,Xz1) & R(Xx2,Xy2,Xz2) & 413.13/65.08 (Xc0 = cP(Xz1,Xz2)))) | 413.13/65.08 ((Xa = Xc0) & (Xb = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx,Xy,Xy))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xy)))) => 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xx))))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,c0)))))))). 413.13/65.08 tff(zf_stmt_0, negated_conjecture, 413.13/65.08 (~ 413.13/65.08 (![S:(((c * b) > $o > $o))]: 413.13/65.08 ((![Xx:((c * b) > $o)]: 413.13/65.08 (S(Xx) => 413.13/65.08 (![Xc:c]: 413.13/65.08 ((![Xx0:b,Xy:b,Xz:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xb = Xc0) & (Xa = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & (Xb = cP(Xy1,Xy2)) & 413.13/65.08 R(Xx2,Xy2,Xz2) & R(Xx1,Xy1,Xz1) & 413.13/65.08 (Xc0 = cP(Xz1,Xz2)))) | 413.13/65.08 ((Xb = c0) & (Xa = Xc0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx0,Xy,Xz))) & 413.13/65.08 Xx(Xc,Xy) & Xx(Xc,Xx0)) => 413.13/65.08 Xx(Xc,Xz))) & 413.13/65.08 (![Xx0:b,Xy:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xb = Xc0) & (Xa = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & R(Xx1,Xy1,Xz1) & 413.13/65.08 R(Xx2,Xy2,Xz2) & (Xc0 = cP(Xz1,Xz2)) & 413.13/65.08 (Xb = cP(Xy1,Xy2)))) | 413.13/65.08 ((Xa = Xc0) & (Xb = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx0,Xy,Xy))) & 413.13/65.08 Xx(Xc,Xy)) => 413.13/65.08 Xx(Xc,Xx0))) & 413.13/65.08 Xx(Xc,c0))))) => 413.13/65.08 (![Xc:c]: 413.13/65.08 ((![Xx:b,Xy:b,Xz:b]: 413.13/65.08 (((![R:((c * b) > $o)]: (S(R) => R(Xc,Xy))) & 413.13/65.08 (![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xa = Xc0) & (Xb = c0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xb = cP(Xy1,Xy2)) & (Xc0 = cP(Xz1,Xz2)) & 413.13/65.08 R(Xx1,Xy1,Xz1) & R(Xx2,Xy2,Xz2) & 413.13/65.08 (Xa = cP(Xx1,Xx2)))) | 413.13/65.08 ((Xb = Xc0) & (Xa = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx,Xy,Xz))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xx)))) => 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xz))))) & 413.13/65.08 (![Xx:b,Xy:b]: 413.13/65.08 (((![R:((b * b * b) > $o)]: 413.13/65.08 ((![Xa:b,Xb:b,Xc0:b]: 413.13/65.08 ((((Xa = c0) & (Xb = Xc0)) | 413.13/65.08 (?[Xx1:b,Xx2:b,Xy1:b,Xy2:b,Xz1:b,Xz2:b]: 413.13/65.08 ((Xa = cP(Xx1,Xx2)) & (Xb = cP(Xy1,Xy2)) & 413.13/65.08 R(Xx1,Xy1,Xz1) & R(Xx2,Xy2,Xz2) & 413.13/65.08 (Xc0 = cP(Xz1,Xz2)))) | 413.13/65.08 ((Xa = Xc0) & (Xb = c0))) => 413.13/65.08 R(Xa,Xb,Xc0))) => 413.13/65.08 R(Xx,Xy,Xy))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xy)))) => 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,Xx))))) & 413.13/65.08 (![R:((c * b) > $o)]: (S(R) => R(Xc,c0))))))))). 413.13/65.08 tff('0', plain, 413.13/65.08 ~ (!!((^[Y0 : ((c * b) > $o) > $o]: 413.13/65.08 ((!!((^[Y1 : (c * b) > $o]: 413.13/65.08 (Y0(Y1) => 413.13/65.08 (!!((^[Y2 : c]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 (((!!((^[Y6 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 !!(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (!!(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y8 = Y9) & 413.13/65.08 ( 413.13/65.08 Y7 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y14 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y15 : b]: 413.13/65.08 (( 413.13/65.08 Y7 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11))& 413.13/65.08 (Y8 = 413.13/65.08 cP(Y12, 413.13/65.08 Y13))& 413.13/65.08 Y6(Y11, 413.13/65.08 Y13, Y15)& 413.13/65.08 Y6(Y10, 413.13/65.08 Y12, Y14)& 413.13/65.08 (Y9 = 413.13/65.08 cP(Y14, 413.13/65.08 Y15)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y8 = c0) & 413.13/65.08 ( 413.13/65.08 Y7 = Y9))) => 413.13/65.08 Y6(Y7, 413.13/65.08 Y8, Y9))))))))))) => 413.13/65.08 Y6(Y3, Y4, Y5)))))& 413.13/65.08 Y1(Y2, Y4)&Y1(Y2, Y3)) => 413.13/65.08 Y1(Y2, Y5)))))))))))& 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (((!!((^[Y5 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 !!(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y7 = Y8) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y14 : b]: 413.13/65.08 (( 413.13/65.08 Y6 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 Y5(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 Y5(Y10, 413.13/65.08 Y12, Y14)& 413.13/65.08 (Y8 = 413.13/65.08 cP(Y13, 413.13/65.08 Y14))& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y6 = Y8) & 413.13/65.08 ( 413.13/65.08 Y7 = c0))) => 413.13/65.08 Y5(Y6, 413.13/65.08 Y7, Y8))))))))))) => 413.13/65.08 Y5(Y3, Y4, Y4))))) & 413.13/65.08 Y1(Y2, Y4)) => 413.13/65.08 Y1(Y2, Y3))))))))& 413.13/65.08 Y1(Y2, c0))))))))) => 413.13/65.08 (!!((^[Y1 : c]: 413.13/65.08 ((!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (((!!((^[Y5 : (c * b) > $o]: 413.13/65.08 (Y0(Y5) => Y5(Y1, Y3)))))& 413.13/65.08 (!!((^[Y5 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 (!!(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y6 = Y8) & 413.13/65.08 ( 413.13/65.08 Y7 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y14 : b]: 413.13/65.08 (( 413.13/65.08 Y7 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12))& 413.13/65.08 (Y8 = 413.13/65.08 cP(Y13, 413.13/65.08 Y14))& 413.13/65.08 Y5(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 Y5(Y10, 413.13/65.08 Y12, Y14)& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y7 = Y8) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))) => 413.13/65.08 Y5(Y6, 413.13/65.08 Y7, Y8))))))))))) => 413.13/65.08 Y5(Y2, Y3, Y4)))))& 413.13/65.08 (!!((^[Y5 : (c * b) > $o]: 413.13/65.08 (Y0(Y5) => Y5(Y1, Y2)))))) => 413.13/65.08 (!!((^[Y5 : (c * b) > $o]: 413.13/65.08 (Y0(Y5) => Y5(Y1, Y4)))))))))))))))& 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (((!!((^[Y4 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y5 = c0) & 413.13/65.08 ( 413.13/65.08 Y6 = Y7))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (( 413.13/65.08 Y5 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11))& 413.13/65.08 Y4(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 Y4(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y12, 413.13/65.08 Y13)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y5 = Y7) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))) => 413.13/65.08 Y4(Y5, 413.13/65.08 Y6, Y7))))))))))) => 413.13/65.08 Y4(Y2, Y3, Y3))))) & 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 (Y0(Y4) => Y4(Y1, Y3)))))) => 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 (Y0(Y4) => Y4(Y1, Y2))))))))))))& 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: (Y0(Y2) => Y2(Y1, c0))))))))))))), 413.13/65.08 inference('cnf', [status(esa)], [zf_stmt_0])). 413.13/65.08 tff('1', plain, 413.13/65.08 ~ ((!!((^[Y0 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y0) => 413.13/65.08 (!!((^[Y1 : c]: 413.13/65.08 ((!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (((!!((^[Y5 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 !!(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y7 = Y8) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y14 : b]: 413.13/65.08 (( 413.13/65.08 Y6 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12))& 413.13/65.08 Y5(Y10, 413.13/65.08 Y12, Y14)& 413.13/65.08 Y5(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 (Y8 = 413.13/65.08 cP(Y13, 413.13/65.08 Y14)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y7 = c0) & 413.13/65.08 ( 413.13/65.08 Y6 = Y8))) => 413.13/65.08 Y5(Y6, 413.13/65.08 Y7, Y8))))))))))) => 413.13/65.08 Y5(Y2, Y3, Y4)))))& 413.13/65.08 Y0(Y1, Y3)&Y0(Y1, Y2)) => 413.13/65.08 Y0(Y1, Y4)))))))))))& 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (((!!((^[Y4 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y6 = Y7) & 413.13/65.08 ( 413.13/65.08 Y5 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (( 413.13/65.08 Y5 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y4(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 Y4(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y12, 413.13/65.08 Y13))& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y5 = Y7) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))) => 413.13/65.08 Y4(Y5, 413.13/65.08 Y6, Y7))))))))))) => 413.13/65.08 Y4(Y2, Y3, Y3))))) & 413.13/65.08 Y0(Y1, Y3)) => 413.13/65.08 Y0(Y1, Y2))))))))& 413.13/65.08 Y0(Y1, c0))))))))) => 413.13/65.08 (!!((^[Y0 : c]: 413.13/65.08 ((!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (((!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y2)))))& 413.13/65.08 (!!((^[Y4 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 (( 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y5 = Y7) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (( 413.13/65.08 Y6 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11))& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y12, 413.13/65.08 Y13))& 413.13/65.08 Y4(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 Y4(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y6 = Y7) & 413.13/65.08 ( 413.13/65.08 Y5 = c0))) => 413.13/65.08 Y4(Y5, 413.13/65.08 Y6, Y7))))))))))) => 413.13/65.08 Y4(Y1, Y2, Y3)))))& 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y1)))))) => 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y3)))))))))))))))& 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (((!!((^[Y3 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 ((((Y4 = c0) & 413.13/65.08 (Y5 = Y6))| 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (( 413.13/65.08 Y4 = 413.13/65.08 cP(Y7, 413.13/65.08 Y8))& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 Y3(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 Y3(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12)))))))))))))))))))))| 413.13/65.08 ((Y4 = Y6) & 413.13/65.08 (Y5 = c0))) => 413.13/65.08 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.08 Y3(Y1, Y2, Y2))))) & 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3(Y0, Y2)))))) => 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3(Y0, Y1))))))))))))& 413.13/65.08 (!!((^[Y1 : (c * b) > $o]: ('#sk1'(Y1) => Y1(Y0, c0)))))))))), 413.13/65.08 inference('lazy_cnf_exists', [status(thm)], ['0'])). 413.13/65.08 tff('2', plain, 413.13/65.08 ~ (!!((^[Y0 : c]: 413.13/65.08 ((!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (((!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y2)))))& 413.13/65.08 (!!((^[Y4 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 (!!((^[Y7 : b]: 413.13/65.08 ((( 413.13/65.08 ( 413.13/65.08 Y5 = Y7) & 413.13/65.08 ( 413.13/65.08 Y6 = c0))| 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y13 : b]: 413.13/65.08 (( 413.13/65.08 Y6 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11))& 413.13/65.08 (Y7 = 413.13/65.08 cP(Y12, 413.13/65.08 Y13))& 413.13/65.08 Y4(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 Y4(Y9, 413.13/65.08 Y11, Y13)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9)))))))))))))))))))))| 413.13/65.08 ( 413.13/65.08 ( 413.13/65.08 Y6 = Y7) & 413.13/65.08 ( 413.13/65.08 Y5 = c0))) => 413.13/65.08 Y4(Y5, 413.13/65.08 Y6, Y7))))))))))) => 413.13/65.08 Y4(Y1, Y2, Y3)))))& 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y1)))))) => 413.13/65.08 (!!((^[Y4 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y4) => Y4(Y0, Y3)))))))))))))))& 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (((!!((^[Y3 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 ((((Y4 = c0) & 413.13/65.08 (Y5 = Y6))| 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (( 413.13/65.08 Y4 = 413.13/65.08 cP(Y7, 413.13/65.08 Y8))& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 Y3(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 Y3(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12)))))))))))))))))))))| 413.13/65.08 ((Y4 = Y6) & 413.13/65.08 (Y5 = c0))) => 413.13/65.08 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.08 Y3(Y1, Y2, Y2))))) & 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3(Y0, Y2)))))) => 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3(Y0, Y1))))))))))))& 413.13/65.08 (!!((^[Y1 : (c * b) > $o]: ('#sk1'(Y1) => Y1(Y0, c0))))))))), 413.13/65.08 inference('lazy_cnf_imply', [status(thm)], ['1'])). 413.13/65.08 tff('3', plain, 413.13/65.08 ~ ((!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (((!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y1)))))& 413.13/65.08 (!!((^[Y3 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 ((((Y4 = Y6) & 413.13/65.08 (Y5 = c0))| 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (( 413.13/65.08 Y5 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12))& 413.13/65.08 Y3(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 Y3(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y7, 413.13/65.08 Y8)))))))))))))))))))))| 413.13/65.08 ((Y5 = Y6) & 413.13/65.08 (Y4 = c0))) => 413.13/65.08 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.08 Y3(Y0, Y1, Y2)))))& 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y0)))))) => 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y2)))))))))))))))& 413.13/65.08 (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = c0) & (Y4 = Y5))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (( 413.13/65.08 Y3 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7))& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y2(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 Y2(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11)))))))))))))))))))))| 413.13/65.08 ((Y3 = Y5) & (Y4 = c0))) => 413.13/65.08 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.08 Y2(Y0, Y1, Y1))))) & 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))& 413.13/65.08 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0)))))), 413.13/65.08 inference('lazy_cnf_exists', [status(thm)], ['2'])). 413.13/65.08 tff('4', plain, 413.13/65.08 (~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (((!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y1)))))& 413.13/65.08 (!!((^[Y3 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 (!!((^[Y6 : b]: 413.13/65.08 ((((Y4 = Y6) & 413.13/65.08 (Y5 = c0))| 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y12 : b]: 413.13/65.08 (( 413.13/65.08 Y5 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 (Y6 = 413.13/65.08 cP(Y11, 413.13/65.08 Y12))& 413.13/65.08 Y3(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 Y3(Y8, 413.13/65.08 Y10, Y12)& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y7, 413.13/65.08 Y8)))))))))))))))))))))| 413.13/65.08 ((Y5 = Y6) & 413.13/65.08 (Y4 = c0))) => 413.13/65.08 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.08 Y3(Y0, Y1, Y2)))))& 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y0)))))) => 413.13/65.08 (!!((^[Y3 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y3) => Y3('#sk28', Y2))))))))))))))) 413.13/65.08 | ~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = c0) & 413.13/65.08 (Y4 = Y5))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (( 413.13/65.08 Y3 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7))& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y2(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 Y2(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11)))))))))))))))))))))| 413.13/65.08 ((Y3 = Y5) & 413.13/65.08 (Y4 = c0))) => 413.13/65.08 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.08 Y2(Y0, Y1, Y1))))) & 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y0)))))))))))) 413.13/65.08 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0)))))), 413.13/65.08 inference('lazy_cnf_and', [status(thm)], ['3'])). 413.13/65.08 tff('5', plain, 413.13/65.08 (~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y0)))))& 413.13/65.08 (!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = Y5) & (Y4 = c0))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (( 413.13/65.08 Y4 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11))& 413.13/65.08 Y2(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 Y2(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 (Y3 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7)))))))))))))))))))))| 413.13/65.08 ((Y4 = Y5) & (Y3 = c0))) => 413.13/65.08 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.08 Y2('#sk29', Y0, Y1)))))& 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', '#sk29')))))) => 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y1)))))))))))) 413.13/65.08 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0))))) 413.13/65.08 | ~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = c0) & 413.13/65.08 (Y4 = Y5))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (( 413.13/65.08 Y3 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7))& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y2(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 Y2(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11)))))))))))))))))))))| 413.13/65.08 ((Y3 = Y5) & 413.13/65.08 (Y4 = c0))) => 413.13/65.08 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.08 Y2(Y0, Y1, Y1))))) & 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))), 413.13/65.08 inference('lazy_cnf_exists', [status(thm)], ['4'])). 413.13/65.08 tff('6', plain, 413.13/65.08 (~ (!!((^[Y0 : b]: 413.13/65.08 (((!!((^[Y1 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y1) => Y1('#sk28', '#sk197')))))& 413.13/65.08 (!!((^[Y1 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 ((((Y2 = Y4) & (Y3 = c0))| 413.13/65.08 (??((^[Y5 : b]: 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (( 413.13/65.08 Y3 = 413.13/65.08 cP(Y7, 413.13/65.08 Y8))& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y9, 413.13/65.08 Y10))& 413.13/65.08 Y1(Y5, 413.13/65.08 Y7, Y9)& 413.13/65.08 Y1(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 (Y2 = 413.13/65.08 cP(Y5, 413.13/65.08 Y6)))))))))))))))))))))| 413.13/65.08 ((Y3 = Y4) & (Y2 = c0))) => 413.13/65.08 Y1(Y2, Y3, Y4))))))))))) => 413.13/65.08 Y1('#sk29', '#sk197', Y0)))))& 413.13/65.08 (!!((^[Y1 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y1) => Y1('#sk28', '#sk29')))))) => 413.13/65.08 (!!((^[Y1 : (c * b) > $o]: ('#sk1'(Y1) => Y1('#sk28', Y0))))))))) 413.13/65.08 | ~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = c0) & 413.13/65.08 (Y4 = Y5))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y11 : b]: 413.13/65.08 (( 413.13/65.08 Y3 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7))& 413.13/65.08 (Y4 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y2(Y6, 413.13/65.08 Y8, Y10)& 413.13/65.08 Y2(Y7, 413.13/65.08 Y9, Y11)& 413.13/65.08 (Y5 = 413.13/65.08 cP(Y10, 413.13/65.08 Y11)))))))))))))))))))))| 413.13/65.08 ((Y3 = Y5) & 413.13/65.08 (Y4 = c0))) => 413.13/65.08 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.08 Y2(Y0, Y1, Y1))))) & 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.08 (!!((^[Y2 : (c * b) > $o]: 413.13/65.08 ('#sk1'(Y2) => Y2('#sk28', Y0)))))))))))) 413.13/65.08 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0)))))), 413.13/65.08 inference('lazy_cnf_exists', [status(thm)], ['5'])). 413.13/65.08 tff('7', plain, 413.13/65.08 (~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.08 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y1 : b]: 413.13/65.08 (!!((^[Y2 : b]: 413.13/65.08 (!!((^[Y3 : b]: 413.13/65.08 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.08 (??((^[Y4 : b]: 413.13/65.08 (??((^[Y5 : b]: 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 ( 413.13/65.08 ??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (( 413.13/65.08 Y2 = 413.13/65.08 cP(Y6, 413.13/65.08 Y7))& 413.13/65.08 (Y3 = 413.13/65.08 cP(Y8, 413.13/65.08 Y9))& 413.13/65.08 Y0(Y4, 413.13/65.08 Y6, Y8)& 413.13/65.08 Y0(Y5, 413.13/65.08 Y7, Y9)& 413.13/65.08 (Y1 = 413.13/65.08 cP(Y4, 413.13/65.08 Y5)))))))))))))))))))))| 413.13/65.08 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.08 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.08 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.08 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.08 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198')))))) 413.13/65.08 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0))))) 413.13/65.08 | ~ (!!((^[Y0 : b]: 413.13/65.08 (!!((^[Y1 : b]: 413.13/65.08 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.08 ((!!((^[Y3 : b]: 413.13/65.08 (!!((^[Y4 : b]: 413.13/65.08 (!!((^[Y5 : b]: 413.13/65.08 ((((Y3 = c0) & 413.13/65.08 (Y4 = Y5))| 413.13/65.08 (??((^[Y6 : b]: 413.13/65.08 (??((^[Y7 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y8 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y9 : b]: 413.13/65.08 (??(( 413.13/65.08 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))), 413.13/65.09 inference('lazy_cnf_exists', [status(thm)], ['6'])). 413.13/65.09 tff('8', plain, 413.13/65.09 (~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.09 (??((^[Y4 : b]: 413.13/65.09 (??((^[Y5 : b]: 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (( 413.13/65.09 Y2 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y3 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y0(Y4, 413.13/65.09 Y6, Y8)& 413.13/65.09 Y0(Y5, 413.13/65.09 Y7, Y9)& 413.13/65.09 (Y1 = 413.13/65.09 cP(Y4, 413.13/65.09 Y5)))))))))))))))))))))| 413.13/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198')))))) 413.13/65.09 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0))))) 413.13/65.09 | ~ (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y3 = c0) & 413.13/65.09 (Y4 = Y5))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))), 413.13/65.09 inference('lazy_cnf_exists', [status(thm)], ['6'])). 413.13/65.09 tff('9', plain, 413.13/65.09 ( '#form199' 413.13/65.09 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0)))))), 413.13/65.09 define([status(thm)])). 413.13/65.09 tff('10', plain, 413.13/65.09 (~ '#form199' 413.13/65.09 | ~ (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y3 = c0) & 413.13/65.09 (Y4 = Y5))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0)))))))))))) 413.13/65.09 | ~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.09 (??((^[Y4 : b]: 413.13/65.09 (??((^[Y5 : b]: 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (( 413.13/65.09 Y2 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y3 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y0(Y4, 413.13/65.09 Y6, Y8)& 413.13/65.09 Y0(Y5, 413.13/65.09 Y7, Y9)& 413.13/65.09 (Y1 = 413.13/65.09 cP(Y4, 413.13/65.09 Y5)))))))))))))))))))))| 413.13/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198'))))))), 413.13/65.09 inference('renaming', [status(thm)], ['7', '9'])). 413.13/65.09 tff('11', plain, 413.13/65.09 (~ '#form199' 413.13/65.09 | ~ (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y3 = c0) & 413.13/65.09 (Y4 = Y5))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0)))))))))))) 413.13/65.09 | ~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.09 (??((^[Y4 : b]: 413.13/65.09 (??((^[Y5 : b]: 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (( 413.13/65.09 Y2 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y3 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y0(Y4, 413.13/65.09 Y6, Y8)& 413.13/65.09 Y0(Y5, 413.13/65.09 Y7, Y9)& 413.13/65.09 (Y1 = 413.13/65.09 cP(Y4, 413.13/65.09 Y5)))))))))))))))))))))| 413.13/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198'))))))), 413.13/65.09 inference('renaming', [status(thm)], ['7', '9'])). 413.13/65.09 tff('12', plain, 413.13/65.09 ( '#form200' 413.13/65.09 | ~ (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y3 = c0) & 413.13/65.09 (Y4 = Y5))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.13/65.09 (!!((^[Y2 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))), 413.13/65.09 define([status(thm)])). 413.13/65.09 tff('13', plain, 413.13/65.09 (~ '#form200' 413.13/65.09 | ~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.09 (??((^[Y4 : b]: 413.13/65.09 (??((^[Y5 : b]: 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (( 413.13/65.09 Y2 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y3 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y0(Y4, 413.13/65.09 Y6, Y8)& 413.13/65.09 Y0(Y5, 413.13/65.09 Y7, Y9)& 413.13/65.09 (Y1 = 413.13/65.09 cP(Y4, 413.13/65.09 Y5)))))))))))))))))))))| 413.13/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198')))))) 413.13/65.09 | ~ '#form199'), 413.13/65.09 inference('renaming', [status(thm)], ['10', '12'])). 413.13/65.09 tff('14', plain, 413.13/65.09 ( '#form199' 413.13/65.09 | ~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', c0)))))), 413.13/65.09 define([status(thm)])). 413.13/65.09 tff('15', plain, 413.13/65.09 (~ ('#sk1'('#sk201') => '#sk201'('#sk28', c0)) | '#form199'), 413.13/65.09 inference('lazy_cnf_exists', [status(thm)], ['14'])). 413.13/65.09 tff('16', plain, ( '#sk1'('#sk201') | '#form199'), 413.13/65.09 inference('lazy_cnf_imply', [status(thm)], ['15'])). 413.13/65.09 tff('17', plain, 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: 413.13/65.09 ('#sk1'(Y0) => 413.13/65.09 (!!((^[Y1 : c]: 413.13/65.09 ((!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (((!!((^[Y5 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y6 : b]: 413.13/65.09 (!!((^[Y7 : b]: 413.13/65.09 (!!(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (( 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y7 = Y8) & 413.13/65.09 ( 413.13/65.09 Y6 = c0))| 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y13 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y14 : b]: 413.13/65.09 (( 413.13/65.09 Y6 = 413.13/65.09 cP(Y9, 413.13/65.09 Y10))& 413.13/65.09 (Y7 = 413.13/65.09 cP(Y11, 413.13/65.09 Y12))& 413.13/65.09 Y5(Y10, 413.13/65.09 Y12, Y14)& 413.13/65.09 Y5(Y9, 413.13/65.09 Y11, Y13)& 413.13/65.09 (Y8 = 413.13/65.09 cP(Y13, 413.13/65.09 Y14)))))))))))))))))))))| 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y7 = c0) & 413.13/65.09 ( 413.13/65.09 Y6 = Y8))) => 413.13/65.09 Y5(Y6, 413.13/65.09 Y7, Y8))))))))))) => 413.13/65.09 Y5(Y2, Y3, Y4)))))& 413.13/65.09 Y0(Y1, Y3)&Y0(Y1, Y2)) => 413.13/65.09 Y0(Y1, Y4)))))))))))& 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 (((!!((^[Y4 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 (!!((^[Y7 : b]: 413.13/65.09 ((( 413.13/65.09 ( 413.13/65.09 Y6 = Y7) & 413.13/65.09 ( 413.13/65.09 Y5 = c0))| 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y13 : b]: 413.13/65.09 (( 413.13/65.09 Y5 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y4(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 Y4(Y9, 413.13/65.09 Y11, Y13)& 413.13/65.09 (Y7 = 413.13/65.09 cP(Y12, 413.13/65.09 Y13))& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11)))))))))))))))))))))| 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y5 = Y7) & 413.13/65.09 ( 413.13/65.09 Y6 = c0))) => 413.13/65.09 Y4(Y5, 413.13/65.09 Y6, Y7))))))))))) => 413.13/65.09 Y4(Y2, Y3, Y3))))) & 413.13/65.09 Y0(Y1, Y3)) => 413.13/65.09 Y0(Y1, Y2))))))))& 413.13/65.09 Y0(Y1, c0))))))))), 413.13/65.09 inference('lazy_cnf_imply', [status(thm)], ['1'])). 413.13/65.09 tff('18', plain, 413.13/65.09 ![X1 : (c * b) > $o]: 413.13/65.09 ('#sk1'(X1) => 413.13/65.09 (!!((^[Y0 : c]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 (((!!((^[Y4 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 (!!((^[Y7 : b]: 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y6 = Y7) & 413.13/65.09 ( 413.13/65.09 Y5 = c0))| 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y13 : b]: 413.13/65.09 (( 413.13/65.09 Y5 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11))& 413.13/65.09 Y4(Y9, 413.13/65.09 Y11, Y13)& 413.13/65.09 Y4(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 (Y7 = 413.13/65.09 cP(Y12, 413.13/65.09 Y13)))))))))))))))))))))| 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y6 = c0) & 413.13/65.09 ( 413.13/65.09 Y5 = Y7))) => 413.13/65.09 Y4(Y5, 413.13/65.09 Y6, Y7))))))))))) => 413.13/65.09 Y4(Y1, Y2, Y3)))))& 413.13/65.09 X1(Y0, Y2)&X1(Y0, Y1)) => 413.13/65.09 X1(Y0, Y3)))))))))))& 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (((!!((^[Y3 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 ((((Y5 = Y6) & 413.13/65.09 (Y4 = c0))| 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (( 413.13/65.09 Y4 = 413.13/65.09 cP(Y7, 413.13/65.09 Y8))& 413.13/65.09 Y3(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 Y3(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y11, 413.13/65.09 Y12))& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y9, 413.13/65.09 Y10)))))))))))))))))))))| 413.13/65.09 ((Y4 = Y6) & 413.13/65.09 (Y5 = c0))) => 413.13/65.09 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.09 Y3(Y1, Y2, Y2))))) & 413.13/65.09 X1(Y0, Y2)) => 413.13/65.09 X1(Y0, Y1))))))))& 413.13/65.09 X1(Y0, c0)))))), 413.13/65.09 inference('lazy_cnf_forall', [status(thm)], ['17'])). 413.13/65.09 tff('19', plain, 413.13/65.09 ![X1 : (c * b) > $o]: 413.13/65.09 (~ '#sk1'(X1) 413.13/65.09 | (!!((^[Y0 : c]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 (((!!((^[Y4 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 (!!((^[Y7 : b]: 413.13/65.09 (( 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y6 = Y7) & 413.13/65.09 ( 413.13/65.09 Y5 = c0))| 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y13 : b]: 413.13/65.09 (( 413.13/65.09 Y5 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11))& 413.13/65.09 Y4(Y9, 413.13/65.09 Y11, Y13)& 413.13/65.09 Y4(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 (Y7 = 413.13/65.09 cP(Y12, 413.13/65.09 Y13)))))))))))))))))))))| 413.13/65.09 ( 413.13/65.09 ( 413.13/65.09 Y6 = c0) & 413.13/65.09 ( 413.13/65.09 Y5 = Y7))) => 413.13/65.09 Y4(Y5, 413.13/65.09 Y6, Y7))))))))))) => 413.13/65.09 Y4(Y1, Y2, Y3)))))& 413.13/65.09 X1(Y0, Y2)&X1(Y0, Y1)) => 413.13/65.09 X1(Y0, Y3)))))))))))& 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (((!!((^[Y3 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 ((((Y5 = Y6) & 413.13/65.09 (Y4 = c0))| 413.13/65.09 (??(( 413.13/65.09 ^[Y7 : b]: 413.13/65.09 ( 413.13/65.09 ??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (( 413.13/65.09 Y4 = 413.13/65.09 cP(Y7, 413.13/65.09 Y8))& 413.13/65.09 Y3(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 Y3(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y11, 413.13/65.09 Y12))& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y9, 413.13/65.09 Y10)))))))))))))))))))))| 413.13/65.09 ((Y4 = Y6) & 413.13/65.09 (Y5 = c0))) => 413.13/65.09 Y3(Y4, Y5, 413.13/65.09 Y6))))))))))) => 413.13/65.09 Y3(Y1, Y2, Y2))))) & 413.13/65.09 X1(Y0, Y2)) => 413.13/65.09 X1(Y0, Y1))))))))& 413.13/65.09 X1(Y0, c0)))))), 413.13/65.09 inference('lazy_cnf_imply', [status(thm)], ['18'])). 413.13/65.09 tff('20', plain, 413.13/65.09 ![X1 : (c * b) > $o, X2 : c]: 413.13/65.09 ( ((!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (((!!((^[Y3 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 (!!((^[Y6 : b]: 413.13/65.09 ((((Y5 = Y6) & 413.13/65.09 (Y4 = c0))| 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y12 : b]: 413.13/65.09 (( 413.13/65.09 Y4 = 413.13/65.09 cP(Y7, 413.13/65.09 Y8))& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y9, 413.13/65.09 Y10))& 413.13/65.09 Y3(Y8, 413.13/65.09 Y10, Y12)& 413.13/65.09 Y3(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y6 = 413.13/65.09 cP(Y11, 413.13/65.09 Y12)))))))))))))))))))))| 413.13/65.09 ((Y5 = c0) & 413.13/65.09 (Y4 = Y6))) => 413.13/65.09 Y3(Y4, Y5, Y6))))))))))) => 413.13/65.09 Y3(Y0, Y1, Y2)))))& 413.13/65.09 X1(X2, Y1)&X1(X2, Y0)) => 413.13/65.09 X1(X2, Y2)))))))))))& 413.13/65.09 (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y4 = Y5) & 413.13/65.09 (Y3 = c0))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y10 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y11 : b]: 413.13/65.09 (( 413.13/65.09 Y3 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 Y2(Y6, 413.13/65.09 Y8, Y10)& 413.13/65.09 Y2(Y7, 413.13/65.09 Y9, Y11)& 413.13/65.09 (Y5 = 413.13/65.09 cP(Y10, 413.13/65.09 Y11))& 413.13/65.09 (Y4 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9)))))))))))))))))))))| 413.13/65.09 ((Y3 = Y5) & 413.13/65.09 (Y4 = c0))) => 413.13/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.13/65.09 Y2(Y0, Y1, Y1))))) & 413.13/65.09 X1(X2, Y1)) => 413.13/65.09 X1(X2, Y0))))))))& 413.13/65.09 X1(X2, c0)) 413.13/65.09 | ~ '#sk1'(X1)), 413.13/65.09 inference('lazy_cnf_forall', [status(thm)], ['19'])). 413.13/65.09 tff('21', plain, ![X1 : (c * b) > $o, X2 : c]: ( X1(X2, c0) | ~ '#sk1'(X1)), 413.13/65.09 inference('lazy_cnf_and', [status(thm)], ['20'])). 413.13/65.09 tff('22', plain, ![X0 : c]: ( '#form199' | '#sk201'(X0, c0)), 413.13/65.09 inference('sup-', [status(thm)], ['16', '21'])). 413.13/65.09 tff('23', plain, 413.13/65.09 (~ ('#sk1'('#sk201') => '#sk201'('#sk28', c0)) | '#form199'), 413.13/65.09 inference('lazy_cnf_exists', [status(thm)], ['14'])). 413.13/65.09 tff('24', plain, (~ ('#sk1'('#sk201') => $true) | '#form199' | '#form199'), 413.13/65.09 inference('sup-', [status(thm)], ['22', '23'])). 413.13/65.09 tff('25', plain, ( '#form199' | ~ ('#sk1'('#sk201') => $true)), 413.13/65.09 inference('simplify', [status(thm)], ['24'])). 413.13/65.09 tff('26', plain, '#form199', 413.13/65.09 inference('simplify boolean subterms', [status(thm)], ['25'])). 413.13/65.09 tff('27', plain, 413.13/65.09 (~ '#form200' 413.13/65.09 | ~ (((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.13/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y1 : b]: 413.13/65.09 (!!((^[Y2 : b]: 413.13/65.09 (!!((^[Y3 : b]: 413.13/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.13/65.09 (??((^[Y4 : b]: 413.13/65.09 (??((^[Y5 : b]: 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y9 : b]: 413.13/65.09 (( 413.13/65.09 Y2 = 413.13/65.09 cP(Y6, 413.13/65.09 Y7))& 413.13/65.09 (Y3 = 413.13/65.09 cP(Y8, 413.13/65.09 Y9))& 413.13/65.09 Y0(Y4, 413.13/65.09 Y6, Y8)& 413.13/65.09 Y0(Y5, 413.13/65.09 Y7, Y9)& 413.13/65.09 (Y1 = 413.13/65.09 cP(Y4, 413.13/65.09 Y5)))))))))))))))))))))| 413.13/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.13/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.13/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) => 413.13/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198'))))))), 413.13/65.09 inference('demod', [status(thm)], ['13', '26'])). 413.13/65.09 tff('28', plain, 413.13/65.09 (~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk198'))))) 413.13/65.09 | ~ '#form200'), 413.13/65.09 inference('lazy_cnf_imply', [status(thm)], ['27'])). 413.13/65.09 tff('29', plain, 413.13/65.09 (~ ('#sk1'('#sk244') => '#sk244'('#sk28', '#sk198')) | ~ '#form200'), 413.13/65.09 inference('lazy_cnf_exists', [status(thm)], ['28'])). 413.13/65.09 tff('30', plain, ( '#sk1'('#sk244') | ~ '#form200'), 413.13/65.09 inference('lazy_cnf_imply', [status(thm)], ['29'])). 413.13/65.09 tff('31', plain, 413.13/65.09 ( '#form200' 413.13/65.09 | ~ (!!((^[Y0 : b]: 413.13/65.09 (!!((^[Y1 : b]: 413.13/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.13/65.09 ((!!((^[Y3 : b]: 413.13/65.09 (!!((^[Y4 : b]: 413.13/65.09 (!!((^[Y5 : b]: 413.13/65.09 ((((Y3 = c0) & 413.13/65.09 (Y4 = Y5))| 413.13/65.09 (??((^[Y6 : b]: 413.13/65.09 (??((^[Y7 : b]: 413.13/65.09 (??(( 413.13/65.09 ^[Y8 : b]: 413.13/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y11 : b]: 413.84/65.09 (( 413.84/65.09 Y3 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 Y2(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 Y2(Y7, 413.84/65.09 Y9, Y11)& 413.84/65.09 (Y5 = 413.84/65.09 cP(Y10, 413.84/65.09 Y11)))))))))))))))))))))| 413.84/65.09 ((Y3 = Y5) & 413.84/65.09 (Y4 = c0))) => 413.84/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.84/65.09 Y2(Y0, Y1, Y1))))) & 413.84/65.09 (!!((^[Y2 : (c * b) > $o]: 413.84/65.09 ('#sk1'(Y2) => Y2('#sk28', Y1)))))) => 413.84/65.09 (!!((^[Y2 : (c * b) > $o]: 413.84/65.09 ('#sk1'(Y2) => Y2('#sk28', Y0))))))))))))), 413.84/65.09 define([status(thm)])). 413.84/65.09 tff('32', plain, 413.84/65.09 (~ (!!((^[Y0 : b]: 413.84/65.09 (((!!((^[Y1 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 ((((Y2 = c0) & (Y3 = Y4))| 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 ( 413.84/65.09 ??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y5, 413.84/65.09 Y6))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y7, 413.84/65.09 Y8))& 413.84/65.09 Y1(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 Y1(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y9, 413.84/65.09 Y10)))))))))))))))))))))| 413.84/65.09 ((Y2 = Y4) & (Y3 = c0))) => 413.84/65.09 Y1(Y2, Y3, Y4))))))))))) => 413.84/65.09 Y1('#sk202', Y0, Y0))))) & 413.84/65.09 (!!((^[Y1 : (c * b) > $o]: ('#sk1'(Y1) => Y1('#sk28', Y0)))))) => 413.84/65.09 (!!((^[Y1 : (c * b) > $o]: 413.84/65.09 ('#sk1'(Y1) => Y1('#sk28', '#sk202'))))))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_exists', [status(thm)], ['31'])). 413.84/65.09 tff('33', plain, 413.84/65.09 (~ (((!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = c0) & (Y2 = Y3))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 ( 413.84/65.09 ??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y1 = Y3) & (Y2 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk202', '#sk245', '#sk245'))))) & 413.84/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk245')))))) => 413.84/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk202')))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_exists', [status(thm)], ['32'])). 413.84/65.09 tff('34', plain, 413.84/65.09 (~ (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk202'))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['33'])). 413.84/65.09 tff('35', plain, 413.84/65.09 (~ ('#sk1'('#sk246') => '#sk246'('#sk28', '#sk202')) | '#form200'), 413.84/65.09 inference('lazy_cnf_exists', [status(thm)], ['34'])). 413.84/65.09 tff('36', plain, ( '#sk1'('#sk246') | '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['35'])). 413.84/65.09 tff('37', plain, 413.84/65.09 ( ((!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = c0) & (Y2 = Y3))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y1 = Y3) & (Y2 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk202', '#sk245', '#sk245'))))) & 413.84/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk245')))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['33'])). 413.84/65.09 tff('38', plain, 413.84/65.09 ( (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk245'))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['37'])). 413.84/65.09 tff('39', plain, 413.84/65.09 ![X1 : (c * b) > $o]: 413.84/65.09 ( ('#sk1'(X1) => X1('#sk28', '#sk245')) | '#form200'), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['38'])). 413.84/65.09 tff('40', plain, 413.84/65.09 ( ($true => '#sk246'('#sk28', '#sk245')) | '#form200' | '#form200'), 413.84/65.09 inference('sup+', [status(thm)], ['36', '39'])). 413.84/65.09 tff('41', plain, ( '#form200' | ($true => '#sk246'('#sk28', '#sk245'))), 413.84/65.09 inference('simplify', [status(thm)], ['40'])). 413.84/65.09 tff('42', plain, ( '#form200' | '#sk246'('#sk28', '#sk245')), 413.84/65.09 inference('simplify boolean subterms', [status(thm)], ['41'])). 413.84/65.09 tff('43', plain, 413.84/65.09 ( (!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = c0) & (Y2 = Y3))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 ( 413.84/65.09 ??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y1 = Y3) & (Y2 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk202', '#sk245', '#sk245'))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['37'])). 413.84/65.09 tff('44', plain, ( '#sk1'('#sk246') | '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['35'])). 413.84/65.09 tff('45', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c]: 413.84/65.09 ( (!!((^[Y0 : b]: 413.84/65.09 (!!((^[Y1 : b]: 413.84/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 (!!((^[Y5 : b]: 413.84/65.09 ((((Y4 = Y5) & (Y3 = c0))| 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y11 : b]: 413.84/65.09 (( 413.84/65.09 Y3 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y2(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 Y2(Y7, 413.84/65.09 Y9, Y11)& 413.84/65.09 (Y5 = 413.84/65.09 cP(Y10, 413.84/65.09 Y11))& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y3 = Y5) & (Y4 = c0))) => 413.84/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.84/65.09 Y2(Y0, Y1, Y1))))) & 413.84/65.09 X1(X2, Y1)) => 413.84/65.09 X1(X2, Y0)))))))) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['20'])). 413.84/65.09 tff('46', plain, 413.84/65.09 ![X0 : c]: 413.84/65.09 ( '#form200' 413.84/65.09 | (!!((^[Y0 : b]: 413.84/65.09 (!!((^[Y1 : b]: 413.84/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 (!!((^[Y5 : b]: 413.84/65.09 ((((Y4 = Y5) & 413.84/65.09 (Y3 = c0))| 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y11 : b]: 413.84/65.09 (( 413.84/65.09 Y3 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y2(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 Y2(Y7, 413.84/65.09 Y9, Y11)& 413.84/65.09 (Y5 = 413.84/65.09 cP(Y10, 413.84/65.09 Y11))& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y3 = Y5) & 413.84/65.09 (Y4 = c0))) => 413.84/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.84/65.09 Y2(Y0, Y1, Y1))))) & 413.84/65.09 '#sk246'(X0, Y1)) => 413.84/65.09 '#sk246'(X0, Y0))))))))), 413.84/65.09 inference('sup-', [status(thm)], ['44', '45'])). 413.84/65.09 tff('47', plain, 413.84/65.09 ![X0 : c, X1 : b]: 413.84/65.09 ( (!!((^[Y0 : b]: 413.84/65.09 (((!!((^[Y1 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 ((((Y3 = Y4) & (Y2 = c0))| 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y5, 413.84/65.09 Y6))& 413.84/65.09 Y1(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 Y1(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y9, 413.84/65.09 Y10))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y7, 413.84/65.09 Y8)))))))))))))))))))))| 413.84/65.09 ((Y2 = Y4) & (Y3 = c0))) => 413.84/65.09 Y1(Y2, Y3, Y4))))))))))) => 413.84/65.09 Y1(X1, Y0, Y0))))) & 413.84/65.09 '#sk246'(X0, Y0)) => 413.84/65.09 '#sk246'(X0, X1))))) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['46'])). 413.84/65.09 tff('48', plain, 413.84/65.09 ![X0 : c, X1 : b, X2 : b]: 413.84/65.09 ( (((!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y2 = Y3) & (Y1 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7)))))))))))))))))))))| 413.84/65.09 ((Y1 = Y3) & (Y2 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0(X1, X2, X2))))) & 413.84/65.09 '#sk246'(X0, X2)) => 413.84/65.09 '#sk246'(X0, X1)) 413.84/65.09 | '#form200'), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['47'])). 413.84/65.09 tff('49', plain, 413.84/65.09 ![X0 : c]: 413.84/65.09 ( (($true & '#sk246'(X0, '#sk245')) => '#sk246'(X0, '#sk202')) 413.84/65.09 | '#form200' 413.84/65.09 | '#form200'), 413.84/65.09 inference('sup+', [status(thm)], ['43', '48'])). 413.84/65.09 tff('50', plain, 413.84/65.09 ![X0 : c]: 413.84/65.09 ( '#form200' 413.84/65.09 | (($true & '#sk246'(X0, '#sk245')) => '#sk246'(X0, '#sk202'))), 413.84/65.09 inference('simplify', [status(thm)], ['49'])). 413.84/65.09 tff('51', plain, 413.84/65.09 ![X0 : c]: 413.84/65.09 ( '#form200' | ('#sk246'(X0, '#sk245') => '#sk246'(X0, '#sk202'))), 413.84/65.09 inference('simplify boolean subterms', [status(thm)], ['50'])). 413.84/65.09 tff('52', plain, 413.84/65.09 ( ($true => '#sk246'('#sk28', '#sk202')) | '#form200' | '#form200'), 413.84/65.09 inference('sup+', [status(thm)], ['42', '51'])). 413.84/65.09 tff('53', plain, ( '#form200' | ($true => '#sk246'('#sk28', '#sk202'))), 413.84/65.09 inference('simplify', [status(thm)], ['52'])). 413.84/65.09 tff('54', plain, ( '#form200' | '#sk246'('#sk28', '#sk202')), 413.84/65.09 inference('simplify boolean subterms', [status(thm)], ['53'])). 413.84/65.09 tff('55', plain, (~ '#sk246'('#sk28', '#sk202') | '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['35'])). 413.84/65.09 tff('56', plain, '#form200', inference('clc', [status(thm)], ['54', '55'])). 413.84/65.09 tff('57', plain, '#sk1'('#sk244'), 413.84/65.09 inference('demod', [status(thm)], ['30', '56'])). 413.84/65.09 tff('58', plain, 413.84/65.09 ( ((!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197')))))& 413.84/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5)))))))))))))))))))))| 413.84/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk29', '#sk197', '#sk198')))))& 413.84/65.09 (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29')))))) 413.84/65.09 | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['27'])). 413.84/65.09 tff('59', plain, 413.84/65.09 ( (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk29'))))) 413.84/65.09 | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['58'])). 413.84/65.09 tff('60', plain, 413.84/65.09 ![X1 : (c * b) > $o]: 413.84/65.09 ( ('#sk1'(X1) => X1('#sk28', '#sk29')) | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['59'])). 413.84/65.09 tff('61', plain, 413.84/65.09 ![X1 : (c * b) > $o]: 413.84/65.09 (~ '#sk1'(X1) | X1('#sk28', '#sk29') | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['60'])). 413.84/65.09 tff('62', plain, '#form200', inference('clc', [status(thm)], ['54', '55'])). 413.84/65.09 tff('63', plain, 413.84/65.09 ![X1 : (c * b) > $o]: (~ '#sk1'(X1) | X1('#sk28', '#sk29')), 413.84/65.09 inference('demod', [status(thm)], ['61', '62'])). 413.84/65.09 tff('64', plain, '#sk244'('#sk28', '#sk29'), 413.84/65.09 inference('sup-', [status(thm)], ['57', '63'])). 413.84/65.09 tff('65', plain, '#sk1'('#sk244'), 413.84/65.09 inference('demod', [status(thm)], ['30', '56'])). 413.84/65.09 tff('66', plain, 413.84/65.09 ( (!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 ( 413.84/65.09 ??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5)))))))))))))))))))))| 413.84/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk29', '#sk197', '#sk198'))))) 413.84/65.09 | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['58'])). 413.84/65.09 tff('67', plain, '#form200', inference('clc', [status(thm)], ['54', '55'])). 413.84/65.09 tff('68', plain, 413.84/65.09 (!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y1 = Y3) & (Y2 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5)))))))))))))))))))))| 413.84/65.09 ((Y2 = Y3) & (Y1 = c0))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0('#sk29', '#sk197', '#sk198'))))), 413.84/65.09 inference('demod', [status(thm)], ['66', '67'])). 413.84/65.09 tff('69', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c]: 413.84/65.09 ( (!!((^[Y0 : b]: 413.84/65.09 (!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (((!!((^[Y3 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y4 : b]: 413.84/65.09 (!!((^[Y5 : b]: 413.84/65.09 (!!((^[Y6 : b]: 413.84/65.09 ((((Y5 = Y6) & 413.84/65.09 (Y4 = c0))| 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y11 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y12 : b]: 413.84/65.09 (( 413.84/65.09 Y4 = 413.84/65.09 cP(Y7, 413.84/65.09 Y8))& 413.84/65.09 (Y5 = 413.84/65.09 cP(Y9, 413.84/65.09 Y10))& 413.84/65.09 Y3(Y8, 413.84/65.09 Y10, Y12)& 413.84/65.09 Y3(Y7, 413.84/65.09 Y9, Y11)& 413.84/65.09 (Y6 = 413.84/65.09 cP(Y11, 413.84/65.09 Y12)))))))))))))))))))))| 413.84/65.09 ((Y5 = c0) & 413.84/65.09 (Y4 = Y6))) => 413.84/65.09 Y3(Y4, Y5, Y6))))))))))) => 413.84/65.09 Y3(Y0, Y1, Y2)))))& 413.84/65.09 X1(X2, Y1)&X1(X2, Y0)) => 413.84/65.09 X1(X2, Y2))))))))))) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['20'])). 413.84/65.09 tff('70', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c, X3 : b]: 413.84/65.09 ( (!!((^[Y0 : b]: 413.84/65.09 (!!((^[Y1 : b]: 413.84/65.09 (((!!((^[Y2 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 (!!((^[Y5 : b]: 413.84/65.09 ((((Y4 = Y5) & (Y3 = c0))| 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y11 : b]: 413.84/65.09 (( 413.84/65.09 Y3 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9))& 413.84/65.09 Y2(Y7, 413.84/65.09 Y9, Y11)& 413.84/65.09 Y2(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 (Y5 = 413.84/65.09 cP(Y10, 413.84/65.09 Y11)))))))))))))))))))))| 413.84/65.09 ((Y4 = c0) & (Y3 = Y5))) => 413.84/65.09 Y2(Y3, Y4, Y5))))))))))) => 413.84/65.09 Y2(X3, Y0, Y1)))))& 413.84/65.09 X1(X2, Y0)&X1(X2, X3)) => 413.84/65.09 X1(X2, Y1)))))))) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['69'])). 413.84/65.09 tff('71', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c, X3 : b, X4 : b]: 413.84/65.09 ( (!!((^[Y0 : b]: 413.84/65.09 (((!!((^[Y1 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 (!!((^[Y4 : b]: 413.84/65.09 ((((Y3 = Y4) & (Y2 = c0))| 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y10 : b]: 413.84/65.09 (( 413.84/65.09 Y2 = 413.84/65.09 cP(Y5, 413.84/65.09 Y6))& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y7, 413.84/65.09 Y8))& 413.84/65.09 Y1(Y6, 413.84/65.09 Y8, Y10)& 413.84/65.09 Y1(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 (Y4 = 413.84/65.09 cP(Y9, 413.84/65.09 Y10)))))))))))))))))))))| 413.84/65.09 ((Y3 = c0) & (Y2 = Y4))) => 413.84/65.09 Y1(Y2, Y3, Y4))))))))))) => 413.84/65.09 Y1(X3, X4, Y0)))))& 413.84/65.09 X1(X2, X4)&X1(X2, X3)) => 413.84/65.09 X1(X2, Y0))))) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['70'])). 413.84/65.09 tff('72', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c, X3 : b, X4 : b, X5 : b]: 413.84/65.09 ( (((!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y2 = Y3) & (Y1 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y2 = c0) & (Y1 = Y3))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0(X3, X4, X5)))))& 413.84/65.09 X1(X2, X4)&X1(X2, X3)) => 413.84/65.09 X1(X2, X5)) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['71'])). 413.84/65.09 tff('73', plain, 413.84/65.09 ![X1 : (c * b) > $o, X2 : c, X3 : b, X4 : b, X5 : b]: 413.84/65.09 (~ ((!!((^[Y0 : (b * b * b) > $o]: 413.84/65.09 ((!!((^[Y1 : b]: 413.84/65.09 (!!((^[Y2 : b]: 413.84/65.09 (!!((^[Y3 : b]: 413.84/65.09 ((((Y2 = Y3) & (Y1 = c0))| 413.84/65.09 (??((^[Y4 : b]: 413.84/65.09 (??((^[Y5 : b]: 413.84/65.09 (??((^[Y6 : b]: 413.84/65.09 (??((^[Y7 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y8 : b]: 413.84/65.09 (??(( 413.84/65.09 ^[Y9 : b]: 413.84/65.09 (( 413.84/65.09 Y1 = 413.84/65.09 cP(Y4, 413.84/65.09 Y5))& 413.84/65.09 (Y2 = 413.84/65.09 cP(Y6, 413.84/65.09 Y7))& 413.84/65.09 Y0(Y5, 413.84/65.09 Y7, Y9)& 413.84/65.09 Y0(Y4, 413.84/65.09 Y6, Y8)& 413.84/65.09 (Y3 = 413.84/65.09 cP(Y8, 413.84/65.09 Y9)))))))))))))))))))))| 413.84/65.09 ((Y2 = c0) & (Y1 = Y3))) => 413.84/65.09 Y0(Y1, Y2, Y3))))))))))) => 413.84/65.09 Y0(X3, X4, X5)))))& 413.84/65.09 X1(X2, X4)&X1(X2, X3)) 413.84/65.09 | X1(X2, X5) 413.84/65.09 | ~ '#sk1'(X1)), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['72'])). 413.84/65.09 tff('74', plain, 413.84/65.09 ![X0 : (c * b) > $o, X1 : c]: 413.84/65.09 (~ ($true&X0(X1, '#sk197')&X0(X1, '#sk29')) 413.84/65.09 | ~ '#sk1'(X0) 413.84/65.09 | X0(X1, '#sk198')), 413.84/65.09 inference('sup-', [status(thm)], ['68', '73'])). 413.84/65.09 tff('75', plain, 413.84/65.09 ![X0 : (c * b) > $o, X1 : c]: 413.84/65.09 (~ (X0(X1, '#sk29') & X0(X1, '#sk197')) 413.84/65.09 | ~ '#sk1'(X0) 413.84/65.09 | X0(X1, '#sk198')), 413.84/65.09 inference('simplify boolean subterms', [status(thm)], ['74'])). 413.84/65.09 tff('76', plain, 413.84/65.09 ![X0 : c]: 413.84/65.09 ( '#sk244'(X0, '#sk198') 413.84/65.09 | ~ ('#sk244'(X0, '#sk29') & '#sk244'(X0, '#sk197'))), 413.84/65.09 inference('sup-', [status(thm)], ['65', '75'])). 413.84/65.09 tff('77', plain, 413.84/65.09 (~ ($true & '#sk244'('#sk28', '#sk197')) | '#sk244'('#sk28', '#sk198')), 413.84/65.09 inference('sup-', [status(thm)], ['64', '76'])). 413.84/65.09 tff('78', plain, '#sk1'('#sk244'), 413.84/65.09 inference('demod', [status(thm)], ['30', '56'])). 413.84/65.09 tff('79', plain, 413.84/65.09 ( (!!((^[Y0 : (c * b) > $o]: ('#sk1'(Y0) => Y0('#sk28', '#sk197'))))) 413.84/65.09 | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_and', [status(thm)], ['58'])). 413.84/65.09 tff('80', plain, 413.84/65.09 ![X1 : (c * b) > $o]: 413.84/65.09 ( ('#sk1'(X1) => X1('#sk28', '#sk197')) | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_forall', [status(thm)], ['79'])). 413.84/65.09 tff('81', plain, 413.84/65.09 ![X1 : (c * b) > $o]: 413.84/65.09 (~ '#sk1'(X1) | X1('#sk28', '#sk197') | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['80'])). 413.84/65.09 tff('82', plain, '#form200', inference('clc', [status(thm)], ['54', '55'])). 413.84/65.09 tff('83', plain, 413.84/65.09 ![X1 : (c * b) > $o]: (~ '#sk1'(X1) | X1('#sk28', '#sk197')), 413.84/65.09 inference('demod', [status(thm)], ['81', '82'])). 413.84/65.09 tff('84', plain, '#sk244'('#sk28', '#sk197'), 413.84/65.09 inference('sup-', [status(thm)], ['78', '83'])). 413.84/65.09 tff('85', plain, (~ '#sk244'('#sk28', '#sk198') | ~ '#form200'), 413.84/65.09 inference('lazy_cnf_imply', [status(thm)], ['29'])). 413.84/65.09 tff('86', plain, '#form200', inference('clc', [status(thm)], ['54', '55'])). 413.84/65.09 tff('87', plain, ~ '#sk244'('#sk28', '#sk198'), 413.84/65.09 inference('demod', [status(thm)], ['85', '86'])). 413.84/65.09 tff('88', plain, ~ ($true & $true), 413.84/65.09 inference('demod', [status(thm)], ['77', '84', '87'])). 413.84/65.09 tff('89', plain, $false, 413.84/65.09 inference('simplify boolean subterms', [status(thm)], ['88'])). 413.84/65.09 413.84/65.09 % SZS output end Refutation 413.84/65.09 413.84/65.09 413.84/65.09 % Terminating... 413.84/65.09 % /export/starexec/sandbox/solver/bin/lams/b.lcnf.od.sh running for 26s 413.99/65.17 % Runner terminated. 413.99/65.18 % Zipperpin 1.5 exiting 413.99/65.18 EOF