0.12/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.CnmmpA956n 0.13/0.34 % Computer : n002.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1200 0.13/0.34 % DateTime : Tue Jul 13 11:35:03 EDT 2021 0.13/0.35 % CPUTime : 0.13/0.35 % Running portfolio for 120 s 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.53/0.64 % Estimated wc time : 1286 0.53/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.54/0.70 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 71.16/10.77 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.01/15.57 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.49/15.79 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 144.54/21.45 % Solved by lams/b.sh. 144.54/21.45 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.CnmmpA956n/e_input092bbf --cpu-limit=12 --auto -s -p. 144.54/21.45 % done 107 iterations in 5.816s 144.54/21.45 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 144.54/21.45 % SZS output start Refutation 144.54/21.45 tff(cTHM250G_pme, conjecture, 144.54/21.45 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 144.54/21.45 ((~ 144.54/21.45 (((![Xx0:a,Xy0:a]: 144.54/21.45 (((![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 144.54/21.45 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 144.54/21.45 Xp1(Xx0,Xy0))) | 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 144.54/21.45 Xp1(Xx0,Xy0)))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 144.54/21.45 Xp1(Xx0,Xy0))))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 (((![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 144.54/21.45 (![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 144.54/21.45 Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 144.54/21.45 Xp1(Xy0,Xz)))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 144.54/21.45 Xp1(Xx0,Xz)))))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 144.54/21.45 Xp1(Xx,Xy))))) | 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 144.54/21.45 Xp1(Xx,Xy)))))). 144.54/21.45 tff(zf_stmt_0, negated_conjecture, 144.54/21.45 (~ 144.54/21.45 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 144.54/21.45 ((~ 144.54/21.45 (((![Xx0:a,Xy0:a]: 144.54/21.45 (((![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 144.54/21.45 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 144.54/21.45 Xp1(Xx0,Xy0))) | 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 144.54/21.45 Xp1(Xx0,Xy0)))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 144.54/21.45 Xp1(Xx0,Xy0))))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 (((![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 144.54/21.45 (![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 144.54/21.45 Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 144.54/21.45 Xp1(Xy0,Xz)))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx1:a,Xy1:a]: 144.54/21.45 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 144.54/21.45 (![Xx1:a,Xy1:a,Xz0:a]: 144.54/21.45 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 144.54/21.45 Xp1(Xx0,Xz)))))) => 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 144.54/21.45 Xp1(Xx,Xy))))) | 144.54/21.45 (![Xp1:((a * a) > $o)]: 144.54/21.45 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 144.54/21.45 (![Xx0:a,Xy0:a,Xz:a]: 144.54/21.45 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 144.54/21.45 Xp1(Xx,Xy))))))). 144.54/21.45 tff('0', plain, 144.54/21.45 ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.45 (!!((^[Y1 : (a * a) > $o]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 ((~((((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (((!!((^[Y6 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9))))))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (Y1(Y7, 144.54/21.45 Y8) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8))))))))) => 144.54/21.45 Y6(Y4, Y5))))) | 144.54/21.45 (!!((^[Y6 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (Y0(Y7, 144.54/21.45 Y8) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8)))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9)))))))))))) => 144.54/21.45 Y6(Y4, Y5)))))) => 144.54/21.45 (!!((^[Y6 : (a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y0(Y7, 144.54/21.45 Y8) | 144.54/21.45 Y1(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8)))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9)))))))))))) => 144.54/21.45 Y6(Y4, Y5)))))))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (((!!((^[Y7 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (( 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y10 : a]: 144.54/21.45 (( 144.54/21.45 Y7(Y8, 144.54/21.45 Y9) & 144.54/21.45 Y7(Y9, 144.54/21.45 Y10)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y10))))))))))) & 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y1(Y8, 144.54/21.45 Y9) | 144.54/21.45 Y0(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y9))))))))) => 144.54/21.45 Y7(Y4, 144.54/21.45 Y5))))) & 144.54/21.45 (!!((^[Y7 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (( 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y1(Y8, 144.54/21.45 Y9) | 144.54/21.45 Y0(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y9)))))))) & 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y10 : a]: 144.54/21.45 (( 144.54/21.45 Y7(Y8, 144.54/21.45 Y9) & 144.54/21.45 Y7(Y9, 144.54/21.45 Y10)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y10)))))))))))) => 144.54/21.45 Y7(Y5, 144.54/21.45 Y6)))))) => 144.54/21.45 (!!((^[Y7 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (( 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y1(Y8, 144.54/21.45 Y9) | 144.54/21.45 Y0(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y9)))))))) & 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y10 : a]: 144.54/21.45 (( 144.54/21.45 Y7(Y8, 144.54/21.45 Y9) & 144.54/21.45 Y7(Y9, 144.54/21.45 Y10)) => 144.54/21.45 Y7(Y8, 144.54/21.45 Y10)))))))))))) => 144.54/21.45 Y7(Y4, 144.54/21.45 Y6)))))))))))))))) => 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y1(Y5, Y6) | 144.54/21.45 Y0(Y5, Y6)) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!((^[Y7 : a]: 144.54/21.45 (( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7)))))))))))) => 144.54/21.45 Y4(Y2, Y3)))))))) | 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y1(Y5, Y6) | 144.54/21.45 Y0(Y5, Y6)) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!((^[Y7 : a]: 144.54/21.45 ((Y4(Y5, Y6) & 144.54/21.45 Y4(Y6, Y7)) => 144.54/21.45 Y4(Y5, Y7)))))))))))) => 144.54/21.45 Y4(Y2, Y3)))))))))))))))))), 144.54/21.45 inference('cnf', [status(esa)], [zf_stmt_0])). 144.54/21.45 tff('1', plain, 144.54/21.45 ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 ((~((((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (((!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8))))))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 Y0(Y6, 144.54/21.45 Y7) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7))))))))) => 144.54/21.45 Y5(Y3, Y4))))) | 144.54/21.45 (!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 '#sk1'( 144.54/21.45 Y6, Y7) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7)))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8)))))))))))) => 144.54/21.45 Y5(Y3, Y4)))))) => 144.54/21.45 (!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (( 144.54/21.45 '#sk1'( 144.54/21.45 Y6, Y7) | 144.54/21.45 Y0(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7)))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8)))))))))))) => 144.54/21.45 Y5(Y3, Y4)))))))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (((!!((^[Y6 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9))))))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y0(Y7, 144.54/21.45 Y8) | 144.54/21.45 '#sk1'( 144.54/21.45 Y7, Y8)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8))))))))) => 144.54/21.45 Y6(Y3, Y4))))) & 144.54/21.45 (!!((^[Y6 : ( 144.54/21.45 a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y0(Y7, 144.54/21.45 Y8) | 144.54/21.45 '#sk1'( 144.54/21.45 Y7, Y8)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8)))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9)))))))))))) => 144.54/21.45 Y6(Y4, Y5)))))) => 144.54/21.45 (!!((^[Y6 : (a * a) > $o]: 144.54/21.45 (((!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y0(Y7, 144.54/21.45 Y8) | 144.54/21.45 '#sk1'( 144.54/21.45 Y7, Y8)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y8)))))))) & 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y9 : a]: 144.54/21.45 (( 144.54/21.45 Y6(Y7, 144.54/21.45 Y8) & 144.54/21.45 Y6(Y8, 144.54/21.45 Y9)) => 144.54/21.45 Y6(Y7, 144.54/21.45 Y9)))))))))))) => 144.54/21.45 Y6(Y3, Y5)))))))))))))))) => 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y0(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2)))))))) | 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y0(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2))))))))))))))), 144.54/21.45 inference('lazy_cnf_exists', [status(thm)], ['0'])). 144.54/21.45 tff('2', plain, 144.54/21.45 ~ (!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 ((~((((!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (((!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7))))))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ('#sk2'(Y5, 144.54/21.45 Y6) => 144.54/21.45 Y4(Y5, Y6))))))))) => 144.54/21.45 Y4(Y2, Y3))))) | 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ('#sk1'(Y5, 144.54/21.45 Y6) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7)))))))))))) => 144.54/21.45 Y4(Y2, Y3)))))) => 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (('#sk1'(Y5, 144.54/21.45 Y6) | 144.54/21.45 '#sk2'(Y5, 144.54/21.45 Y6)) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7)))))))))))) => 144.54/21.45 Y4(Y2, Y3)))))))))))) & 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (((!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8))))))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 '#sk2'( 144.54/21.45 Y6, Y7) | 144.54/21.45 '#sk1'( 144.54/21.45 Y6, Y7)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7))))))))) => 144.54/21.45 Y5(Y2, Y3))))) & 144.54/21.45 (!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 '#sk2'( 144.54/21.45 Y6, Y7) | 144.54/21.45 '#sk1'( 144.54/21.45 Y6, Y7)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7)))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 !!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8)))))))))))) => 144.54/21.45 Y5(Y3, Y4)))))) => 144.54/21.45 (!!((^[Y5 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (( 144.54/21.45 '#sk2'( 144.54/21.45 Y6, Y7) | 144.54/21.45 '#sk1'( 144.54/21.45 Y6, Y7)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y7)))))))) & 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y8 : a]: 144.54/21.45 (( 144.54/21.45 Y5(Y6, 144.54/21.45 Y7) & 144.54/21.45 Y5(Y7, 144.54/21.45 Y8)) => 144.54/21.45 Y5(Y6, 144.54/21.45 Y8)))))))))))) => 144.54/21.45 Y5(Y2, Y4)))))))))))))))) => 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (('#sk2'(Y3, Y4) | 144.54/21.45 '#sk1'(Y3, Y4)) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))))) | 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (('#sk2'(Y3, Y4) | '#sk1'(Y3, Y4)) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))))))))), 144.54/21.45 inference('lazy_cnf_exists', [status(thm)], ['1'])). 144.54/21.45 tff('3', plain, 144.54/21.45 ~ (!!((^[Y0 : a]: 144.54/21.45 ((~((((!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6))))))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ('#sk2'(Y4, Y5) => 144.54/21.45 Y3(Y4, Y5))))))))) => 144.54/21.45 Y3(Y1, Y2))))) | 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ('#sk1'(Y4, Y5) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2)))))) => 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk1'(Y4, Y5) | 144.54/21.45 '#sk2'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2)))))))))))) & 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (((!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7))))))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (('#sk2'( 144.54/21.45 Y5, Y6) | 144.54/21.45 '#sk1'( 144.54/21.45 Y5, Y6)) => 144.54/21.45 Y4(Y5, Y6))))))))) => 144.54/21.45 Y4(Y1, Y2))))) & 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (('#sk2'( 144.54/21.45 Y5, Y6) | 144.54/21.45 '#sk1'( 144.54/21.45 Y5, Y6)) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 ( 144.54/21.45 ( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7)))))))))))) => 144.54/21.45 Y4(Y2, Y3)))))) => 144.54/21.45 (!!((^[Y4 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (('#sk2'(Y5, 144.54/21.45 Y6) | 144.54/21.45 '#sk1'(Y5, 144.54/21.45 Y6)) => 144.54/21.45 Y4(Y5, Y6)))))))) & 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 (!!(( 144.54/21.45 ^[Y7 : a]: 144.54/21.45 (( 144.54/21.45 Y4(Y5, 144.54/21.45 Y6) & 144.54/21.45 Y4(Y6, 144.54/21.45 Y7)) => 144.54/21.45 Y4(Y5, 144.54/21.45 Y7)))))))))))) => 144.54/21.45 Y4(Y1, Y3)))))))))))))))) => 144.54/21.45 (!!((^[Y1 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.45 Y1(Y2, Y3)))))))) & 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.45 Y1(Y2, Y4)))))))))))) => 144.54/21.45 Y1('#sk3', Y0)))))))) | 144.54/21.45 (!!((^[Y1 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.45 Y1(Y2, Y3)))))))) & 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.45 Y1(Y2, Y4)))))))))))) => 144.54/21.45 Y1('#sk3', Y0))))))))), 144.54/21.45 inference('lazy_cnf_exists', [status(thm)], ['2'])). 144.54/21.45 tff('4', plain, 144.54/21.45 ~ ((~((((!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5))))))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk2'(Y3, Y4) => 144.54/21.45 Y2(Y3, Y4))))))))) => 144.54/21.45 Y2(Y0, Y1))))) | 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk1'(Y3, Y4) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))) => 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (('#sk1'(Y3, Y4) | 144.54/21.45 '#sk2'(Y3, Y4)) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))))))))) & 144.54/21.45 (!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6))))))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5))))))))) => 144.54/21.45 Y3(Y0, Y1))))) & 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2)))))) => 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y0, Y2)))))))))))))))) => 144.54/21.45 (!!((^[Y0 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.45 Y0(Y1, Y2)))))))) & 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.45 Y0(Y1, Y3)))))))))))) => 144.54/21.45 Y0('#sk3', '#sk4')))))))) | 144.54/21.45 (!!((^[Y0 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.45 Y0(Y1, Y2)))))))) & 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.45 Y0('#sk3', '#sk4')))))), 144.54/21.45 inference('lazy_cnf_exists', [status(thm)], ['3'])). 144.54/21.45 tff('5', plain, 144.54/21.45 (((!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5))))))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 144.54/21.45 Y2(Y0, Y1))))) | 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))) => 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (('#sk1'(Y3, Y4) | 144.54/21.45 '#sk2'(Y3, Y4)) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))))))))) & 144.54/21.45 (!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6))))))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5))))))))) => 144.54/21.45 Y3(Y0, Y1))))) & 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y1, Y2)))))) => 144.54/21.45 (!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (('#sk2'(Y4, Y5) | 144.54/21.45 '#sk1'(Y4, Y5)) => 144.54/21.45 Y3(Y4, Y5)))))))) & 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 (!!((^[Y6 : a]: 144.54/21.45 ((Y3(Y4, Y5) & 144.54/21.45 Y3(Y5, Y6)) => 144.54/21.45 Y3(Y4, Y6)))))))))))) => 144.54/21.45 Y3(Y0, Y2)))))))))))))))) => 144.54/21.45 (!!((^[Y0 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.45 Y0('#sk3', '#sk4')))))), 144.54/21.45 inference('lazy_cnf_or', [status(thm)], ['4'])). 144.54/21.45 tff('6', plain, 144.54/21.45 (~ ((!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5))))))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 144.54/21.45 Y2(Y0, Y1))))) | 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))) => 144.54/21.45 (!!((^[Y2 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (('#sk1'(Y3, Y4) | 144.54/21.45 '#sk2'(Y3, Y4)) => 144.54/21.45 Y2(Y3, Y4)))))))) & 144.54/21.45 (!!((^[Y3 : a]: 144.54/21.45 (!!((^[Y4 : a]: 144.54/21.45 (!!((^[Y5 : a]: 144.54/21.45 ((Y2(Y3, Y4) & 144.54/21.45 Y2(Y4, Y5)) => 144.54/21.45 Y2(Y3, Y5)))))))))))) => 144.54/21.45 Y2(Y0, Y1)))))))))))) & 144.54/21.45 (!!((^[Y0 : a]: 144.54/21.45 (!!((^[Y1 : a]: 144.54/21.45 (!!((^[Y2 : a]: 144.54/21.45 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.45 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2)))))))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['5'])). 144.54/21.46 tff('7', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5))))))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 144.54/21.46 Y2(Y0, Y1))))) | 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2(Y0, Y1)))))) => 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk1'(Y3, Y4) | 144.54/21.46 '#sk2'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2(Y0, Y1)))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2))))))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['6'])). 144.54/21.46 tff('8', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (((!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4))))))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 144.54/21.46 Y1('#sk6', Y0))))) | 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ('#sk1'(Y2, Y3) => Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk6', Y0)))))) => 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk6', Y0))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4'))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2)))))))))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['7'])). 144.54/21.46 tff('9', plain, 144.54/21.46 (~ (((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) | 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))) => 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2))))))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['8'])). 144.54/21.46 tff('10', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4'))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2)))))))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['9'])). 144.54/21.46 tff('11', plain, 144.54/21.46 (~ '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('12', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 144.54/21.46 X1('#sk3', '#sk4')) 144.54/21.46 | ~ '#form8'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['11'])). 144.54/21.46 tff('13', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['12'])). 144.54/21.46 tff('14', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['13'])). 144.54/21.46 tff('15', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (('#sk2'('#sk36'(X1), Y0) | '#sk1'('#sk36'(X1), Y0)) => 144.54/21.46 X1('#sk36'(X1), Y0))))) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['14'])). 144.54/21.46 tff('16', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (('#sk2'('#sk36'(X1), '#sk51'(X1)) | 144.54/21.46 '#sk1'('#sk36'(X1), '#sk51'(X1))) => 144.54/21.46 X1('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['15'])). 144.54/21.46 tff('17', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['16'])). 144.54/21.46 tff('18', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk98'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk98'(X1), Y1)))))))) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['17'])). 144.54/21.46 tff('19', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk98'(X1), '#sk150'(X1)) & X1('#sk150'(X1), Y0)) => 144.54/21.46 X1('#sk98'(X1), Y0))))) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['18'])). 144.54/21.46 tff('20', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk98'(X1), '#sk150'(X1)) & X1('#sk150'(X1), '#sk214'(X1))) => 144.54/21.46 X1('#sk98'(X1), '#sk214'(X1))) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['19'])). 144.54/21.46 tff('21', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk98'(X1), '#sk214'(X1)) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['20'])). 144.54/21.46 tff('22', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk98'(X1), '#sk150'(X1)) & X1('#sk150'(X1), '#sk214'(X1))) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['20'])). 144.54/21.46 tff('23', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk98'(X1), '#sk150'(X1)) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['22'])). 144.54/21.46 tff('24', plain, 144.54/21.46 ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4'))))), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['4'])). 144.54/21.46 tff('25', plain, 144.54/21.46 ~ (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 144.54/21.46 '#sk5'(Y0, Y2)))))))))))) => 144.54/21.46 '#sk5'('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['24'])). 144.54/21.46 tff('26', plain, 144.54/21.46 ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 144.54/21.46 '#sk5'(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['25'])). 144.54/21.46 tff('27', plain, 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['26'])). 144.54/21.46 tff('28', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 (!!((^[Y0 : a]: (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk5'(X1, Y0))))), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['27'])). 144.54/21.46 tff('29', plain, 144.54/21.46 ![X1 : a, X2 : a]: (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk5'(X1, X2)), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['28'])). 144.54/21.46 tff('30', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk5'(X1, X2)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['29'])). 144.54/21.46 tff('31', plain, ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['30'])). 144.54/21.46 tff('32', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['30'])). 144.54/21.46 tff('33', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk150'(X1), '#sk214'(X1)) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['22'])). 144.54/21.46 tff('34', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( ('#sk2'('#sk36'(X1), '#sk51'(X1)) | '#sk1'('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['16'])). 144.54/21.46 tff('35', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['34'])). 144.54/21.46 tff('36', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk137'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk137'(X1), Y1)))))))) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['35'])). 144.54/21.46 tff('37', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk137'(X1), '#sk199'(X1)) & X1('#sk199'(X1), Y0)) => 144.54/21.46 X1('#sk137'(X1), Y0))))) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['36'])). 144.54/21.46 tff('38', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk137'(X1), '#sk199'(X1)) & X1('#sk199'(X1), '#sk283'(X1))) => 144.54/21.46 X1('#sk137'(X1), '#sk283'(X1))) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['37'])). 144.54/21.46 tff('39', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk137'(X1), '#sk283'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['38'])). 144.54/21.46 tff('40', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk137'(X1), '#sk199'(X1)) & X1('#sk199'(X1), '#sk283'(X1))) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | ~ '#form8' 144.54/21.46 | X1('#sk3', '#sk4')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['38'])). 144.54/21.46 tff('41', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk137'(X1), '#sk199'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['40'])). 144.54/21.46 tff('42', plain, ~ '#sk5'('#sk3', '#sk4'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['25'])). 144.54/21.46 tff('43', plain, 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 144.54/21.46 '#sk5'(Y0, Y2))))))))))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['26'])). 144.54/21.46 tff('44', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk5'(X1, Y0) & '#sk5'(Y0, Y1)) => '#sk5'(X1, Y1)))))))), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['43'])). 144.54/21.46 tff('45', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (!!((^[Y0 : a]: (('#sk5'(X1, X2) & '#sk5'(X2, Y0)) => '#sk5'(X1, Y0))))), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['44'])). 144.54/21.46 tff('46', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (('#sk5'(X1, X2) & '#sk5'(X2, X3)) => '#sk5'(X1, X3)), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['45'])). 144.54/21.46 tff('47', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ ('#sk5'(X1, X2) & '#sk5'(X2, X3)) | '#sk5'(X1, X3)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['46'])). 144.54/21.46 tff('48', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ '#sk5'(X1, X2) | ~ '#sk5'(X2, X3) | '#sk5'(X1, X3)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['47'])). 144.54/21.46 tff('49', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk199'(X1), '#sk283'(X1)) 144.54/21.46 | X1('#sk3', '#sk4') 144.54/21.46 | ~ '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['40'])). 144.54/21.46 tff('50', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4'))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2)))))))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['9'])). 144.54/21.46 tff('51', plain, 144.54/21.46 (~ '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('52', plain, 144.54/21.46 ( '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2))))))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('renaming', [status(thm)], ['50', '51'])). 144.54/21.46 tff('53', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5))))))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4))))))))) => 144.54/21.46 Y2('#sk9', Y0))))) & 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2(Y0, Y1)))))) => 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2('#sk9', Y1)))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['52'])). 144.54/21.46 tff('54', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (((!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4))))))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3))))))))) => 144.54/21.46 Y1('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk10', Y0)))))) => 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk9', Y0))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['53'])). 144.54/21.46 tff('55', plain, 144.54/21.46 (~ (((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))) => 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19')))))) 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['54'])). 144.54/21.46 tff('56', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['55'])). 144.54/21.46 tff('57', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['55'])). 144.54/21.46 tff('58', plain, 144.54/21.46 ( '#form37' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('59', plain, 144.54/21.46 (~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19')))))), 144.54/21.46 inference('renaming', [status(thm)], ['56', '58'])). 144.54/21.46 tff('60', plain, 144.54/21.46 (~ (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2)))))))))))) => 144.54/21.46 '#sk53'('#sk9', '#sk19')) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['59'])). 144.54/21.46 tff('61', plain, (~ '#sk53'('#sk9', '#sk19') | ~ '#form37' | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['60'])). 144.54/21.46 tff('62', plain, 144.54/21.46 ( ((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['55'])). 144.54/21.46 tff('63', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['62'])). 144.54/21.46 tff('64', plain, 144.54/21.46 ( '#form37' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('65', plain, 144.54/21.46 (~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10')))))), 144.54/21.46 inference('renaming', [status(thm)], ['63', '64'])). 144.54/21.46 tff('66', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) => 144.54/21.46 X1('#sk9', '#sk10')) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['65'])). 144.54/21.46 tff('67', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['66'])). 144.54/21.46 tff('68', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['67'])). 144.54/21.46 tff('69', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk256'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk256'(X1), Y1)))))))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['68'])). 144.54/21.46 tff('70', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk256'(X1), '#sk349'(X1)) & X1('#sk349'(X1), Y0)) => 144.54/21.46 X1('#sk256'(X1), Y0))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['69'])). 144.54/21.46 tff('71', plain, 144.54/21.46 ( ((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) | 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4'))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2)))))))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['9'])). 144.54/21.46 tff('72', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2))))))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['71'])). 144.54/21.46 tff('73', plain, 144.54/21.46 (~ '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk3', '#sk4')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('74', plain, 144.54/21.46 ( '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (((!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6))))))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5))))))))) => 144.54/21.46 Y3(Y0, Y1))))) & 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y1, Y2)))))) => 144.54/21.46 (!!((^[Y3 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (('#sk2'(Y4, Y5) | 144.54/21.46 '#sk1'(Y4, Y5)) => 144.54/21.46 Y3(Y4, Y5)))))))) & 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 (!!((^[Y6 : a]: 144.54/21.46 ((Y3(Y4, Y5) & 144.54/21.46 Y3(Y5, Y6)) => 144.54/21.46 Y3(Y4, Y6)))))))))))) => 144.54/21.46 Y3(Y0, Y2))))))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('renaming', [status(thm)], ['72', '73'])). 144.54/21.46 tff('75', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (((!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5))))))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4))))))))) => 144.54/21.46 Y2('#sk9', Y0))))) & 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & 144.54/21.46 Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2(Y0, Y1)))))) => 144.54/21.46 (!!((^[Y2 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (('#sk2'(Y3, Y4) | 144.54/21.46 '#sk1'(Y3, Y4)) => 144.54/21.46 Y2(Y3, Y4)))))))) & 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 (!!((^[Y5 : a]: 144.54/21.46 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 144.54/21.46 Y2(Y3, Y5)))))))))))) => 144.54/21.46 Y2('#sk9', Y1)))))))))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['74'])). 144.54/21.46 tff('76', plain, 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (((!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4))))))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3))))))))) => 144.54/21.46 Y1('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk10', Y0)))))) => 144.54/21.46 (!!((^[Y1 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 144.54/21.46 Y1(Y2, Y3)))))))) & 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 (!!((^[Y4 : a]: 144.54/21.46 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 144.54/21.46 Y1(Y2, Y4)))))))))))) => 144.54/21.46 Y1('#sk9', Y0))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['75'])). 144.54/21.46 tff('77', plain, 144.54/21.46 (~ (((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))) => 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19')))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['76'])). 144.54/21.46 tff('78', plain, 144.54/21.46 ( ((!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) & 144.54/21.46 (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))) 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['77'])). 144.54/21.46 tff('79', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['78'])). 144.54/21.46 tff('80', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['78'])). 144.54/21.46 tff('81', plain, 144.54/21.46 (~ '#form73' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('82', plain, 144.54/21.46 ( '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))), 144.54/21.46 inference('renaming', [status(thm)], ['79', '81'])). 144.54/21.46 tff('83', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['77'])). 144.54/21.46 tff('84', plain, 144.54/21.46 (~ '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('85', plain, 144.54/21.46 ( '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('renaming', [status(thm)], ['82', '84'])). 144.54/21.46 tff('86', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 144.54/21.46 X1('#sk10', '#sk19')) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['85'])). 144.54/21.46 tff('87', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['86'])). 144.54/21.46 tff('88', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['87'])). 144.54/21.46 tff('89', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form431'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('90', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form431'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk256'(X1), '#sk349'(X1)) & X1('#sk349'(X1), Y0)) => 144.54/21.46 X1('#sk256'(X1), Y0)))))), 144.54/21.46 inference('renaming', [status(thm)], ['70', '89'])). 144.54/21.46 tff('91', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form431'(X1) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk256'(X1), '#sk349'(X1)) & X1('#sk349'(X1), Y0)) => 144.54/21.46 X1('#sk256'(X1), Y0)))))), 144.54/21.46 inference('ho_norm', [status(thm)], ['90'])). 144.54/21.46 tff('92', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk256'(X1), '#sk349'(X1)) & X1('#sk349'(X1), '#sk608'(X1))) => 144.54/21.46 X1('#sk256'(X1), '#sk608'(X1))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['91'])). 144.54/21.46 tff('93', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk256'(X1), '#sk608'(X1)) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['92'])). 144.54/21.46 tff('94', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk256'(X1), '#sk349'(X1)) & X1('#sk349'(X1), '#sk608'(X1))) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['92'])). 144.54/21.46 tff('95', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk256'(X1), '#sk349'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['94'])). 144.54/21.46 tff('96', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19'))))) 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['62'])). 144.54/21.46 tff('97', plain, 144.54/21.46 ( '#form37' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('98', plain, 144.54/21.46 (~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk10', '#sk19')))))), 144.54/21.46 inference('renaming', [status(thm)], ['96', '97'])). 144.54/21.46 tff('99', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 144.54/21.46 X1('#sk10', '#sk19')) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['98'])). 144.54/21.46 tff('100', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['99'])). 144.54/21.46 tff('101', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['100'])). 144.54/21.46 tff('102', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (('#sk2'('#sk36'(X1), Y0) | '#sk1'('#sk36'(X1), Y0)) => 144.54/21.46 X1('#sk36'(X1), Y0))))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['101'])). 144.54/21.46 tff('103', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (('#sk2'('#sk36'(X1), '#sk51'(X1)) | 144.54/21.46 '#sk1'('#sk36'(X1), '#sk51'(X1))) => 144.54/21.46 X1('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['102'])). 144.54/21.46 tff('104', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['103'])). 144.54/21.46 tff('105', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk633'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk633'(X1), Y1)))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['104'])). 144.54/21.46 tff('106', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk633'(X1), '#sk780'(X1)) & X1('#sk780'(X1), Y0)) => 144.54/21.46 X1('#sk633'(X1), Y0))))) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['105'])). 144.54/21.46 tff('107', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk633'(X1), '#sk780'(X1)) & X1('#sk780'(X1), '#sk901'(X1))) => 144.54/21.46 X1('#sk633'(X1), '#sk901'(X1))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['106'])). 144.54/21.46 tff('108', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk633'(X1), '#sk901'(X1)) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['107'])). 144.54/21.46 tff('109', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk633'(X1), '#sk780'(X1)) & X1('#sk780'(X1), '#sk901'(X1))) 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['107'])). 144.54/21.46 tff('110', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk633'(X1), '#sk780'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['109'])). 144.54/21.46 tff('111', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk349'(X1), '#sk608'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['94'])). 144.54/21.46 tff('112', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk780'(X1), '#sk901'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ X1('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['109'])). 144.54/21.46 tff('113', plain, 144.54/21.46 ( ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2)))))))))))) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['60'])). 144.54/21.46 tff('114', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['113'])). 144.54/21.46 tff('115', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk53'(X1, Y0))))) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['114'])). 144.54/21.46 tff('116', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk53'(X1, X2)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['115'])). 144.54/21.46 tff('117', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) 144.54/21.46 | '#sk53'(X1, X2) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['116'])). 144.54/21.46 tff('118', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ '#sk2'(X1, X2) | '#form8' | ~ '#form37' | '#sk53'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['117'])). 144.54/21.46 tff('119', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ '#sk1'(X1, X2) | '#form8' | ~ '#form37' | '#sk53'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['117'])). 144.54/21.46 tff('120', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( ('#sk2'('#sk36'(X1), '#sk51'(X1)) | '#sk1'('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['103'])). 144.54/21.46 tff('121', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['120'])). 144.54/21.46 tff('122', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk767'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk767'(X1), Y1)))))))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['121'])). 144.54/21.46 tff('123', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk767'(X1), '#sk886'(X1)) & X1('#sk886'(X1), Y0)) => 144.54/21.46 X1('#sk767'(X1), Y0))))) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['122'])). 144.54/21.46 tff('124', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk767'(X1), '#sk886'(X1)) & X1('#sk886'(X1), '#sk1011'(X1))) => 144.54/21.46 X1('#sk767'(X1), '#sk1011'(X1))) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['123'])). 144.54/21.46 tff('125', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk767'(X1), '#sk1011'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['124'])). 144.54/21.46 tff('126', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk767'(X1), '#sk886'(X1)) & X1('#sk886'(X1), '#sk1011'(X1))) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['124'])). 144.54/21.46 tff('127', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk767'(X1), '#sk886'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['126'])). 144.54/21.46 tff('128', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk886'(X1), '#sk1011'(X1)) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk2'('#sk36'(X1), '#sk51'(X1))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['126'])). 144.54/21.46 tff('129', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2))))))))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['113'])). 144.54/21.46 tff('130', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk53'(X1, Y0) & '#sk53'(Y0, Y1)) => '#sk53'(X1, Y1)))))))) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['129'])). 144.54/21.46 tff('131', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk53'(X1, X2) & '#sk53'(X2, Y0)) => '#sk53'(X1, Y0))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['130'])). 144.54/21.46 tff('132', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 ( (('#sk53'(X1, X2) & '#sk53'(X2, X3)) => '#sk53'(X1, X3)) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['131'])). 144.54/21.46 tff('133', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ ('#sk53'(X1, X2) & '#sk53'(X2, X3)) 144.54/21.46 | '#sk53'(X1, X3) 144.54/21.46 | '#form8' 144.54/21.46 | ~ '#form37'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['132'])). 144.54/21.46 tff('134', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ '#sk53'(X1, X2) 144.54/21.46 | ~ '#sk53'(X2, X3) 144.54/21.46 | ~ '#form37' 144.54/21.46 | '#form8' 144.54/21.46 | '#sk53'(X1, X3)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['133'])). 144.54/21.46 tff('135', plain, 144.54/21.46 (~ '#form73' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('136', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) => 144.54/21.46 X1('#sk6', '#sk7')) 144.54/21.46 | ~ '#form73'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['135'])). 144.54/21.46 tff('137', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['136'])). 144.54/21.46 tff('138', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['137'])). 144.54/21.46 tff('139', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk316'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk316'(X1), Y1)))))))) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['138'])). 144.54/21.46 tff('140', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk316'(X1), '#sk422'(X1)) & X1('#sk422'(X1), Y0)) => 144.54/21.46 X1('#sk316'(X1), Y0))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['139'])). 144.54/21.46 tff('141', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk316'(X1), '#sk422'(X1)) & X1('#sk422'(X1), '#sk547'(X1))) => 144.54/21.46 X1('#sk316'(X1), '#sk547'(X1))) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['140'])). 144.54/21.46 tff('142', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk316'(X1), '#sk547'(X1)) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['141'])). 144.54/21.46 tff('143', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk316'(X1), '#sk547'(X1)) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['141'])). 144.54/21.46 tff('144', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form810'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('145', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form810'(X1) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73' 144.54/21.46 | ~ X1('#sk316'(X1), '#sk547'(X1))), 144.54/21.46 inference('renaming', [status(thm)], ['142', '144'])). 144.54/21.46 tff('146', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk316'(X1), '#sk422'(X1)) & X1('#sk422'(X1), '#sk547'(X1))) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['141'])). 144.54/21.46 tff('147', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk316'(X1), '#sk422'(X1)) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['146'])). 144.54/21.46 tff('148', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form810'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('149', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form810'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | X1('#sk316'(X1), '#sk422'(X1))), 144.54/21.46 inference('renaming', [status(thm)], ['147', '148'])). 144.54/21.46 tff('150', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form810'(X1) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | X1('#sk316'(X1), '#sk422'(X1))), 144.54/21.46 inference('ho_norm', [status(thm)], ['149'])). 144.54/21.46 tff('151', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form810'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('152', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: ('#sk2'('#sk938'(X1), Y0) => X1('#sk938'(X1), Y0))))) 144.54/21.46 | '#form810'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['151'])). 144.54/21.46 tff('153', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ('#sk2'('#sk938'(X1), '#sk1075'(X1)) => 144.54/21.46 X1('#sk938'(X1), '#sk1075'(X1))) 144.54/21.46 | '#form810'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['152'])). 144.54/21.46 tff('154', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk938'(X1), '#sk1075'(X1)) | '#form810'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['153'])). 144.54/21.46 tff('155', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk422'(X1), '#sk547'(X1)) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['146'])). 144.54/21.46 tff('156', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form810'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('157', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form810'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | X1('#sk422'(X1), '#sk547'(X1))), 144.54/21.46 inference('renaming', [status(thm)], ['155', '156'])). 144.54/21.46 tff('158', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form810'(X1) 144.54/21.46 | ~ '#form73' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | X1('#sk422'(X1), '#sk547'(X1))), 144.54/21.46 inference('ho_norm', [status(thm)], ['157'])). 144.54/21.46 tff('159', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#sk2'('#sk938'(X1), '#sk1075'(X1)) | '#form810'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['153'])). 144.54/21.46 tff('160', plain, 144.54/21.46 ( '#form37' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('161', plain, 144.54/21.46 (~ (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk54'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk54'(Y0, Y1) & '#sk54'(Y1, Y2)) => 144.54/21.46 '#sk54'(Y0, Y2)))))))))))) => 144.54/21.46 '#sk54'('#sk6', '#sk7')) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['160'])). 144.54/21.46 tff('162', plain, 144.54/21.46 ( ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk54'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk54'(Y0, Y1) & '#sk54'(Y1, Y2)) => 144.54/21.46 '#sk54'(Y0, Y2)))))))))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['161'])). 144.54/21.46 tff('163', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk54'(Y0, Y1)))))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['162'])). 144.54/21.46 tff('164', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk54'(X1, Y0))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['163'])). 144.54/21.46 tff('165', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk54'(X1, X2)) | '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['164'])). 144.54/21.46 tff('166', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk54'(X1, X2) | '#form37'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['165'])). 144.54/21.46 tff('167', plain, 144.54/21.46 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form37' | '#sk54'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['166'])). 144.54/21.46 tff('168', plain, 144.54/21.46 (~ '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('169', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 144.54/21.46 X1('#sk6', '#sk7')) 144.54/21.46 | ~ '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['168'])). 144.54/21.46 tff('170', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form52'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['169'])). 144.54/21.46 tff('171', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ '#form52' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['170'])). 144.54/21.46 tff('172', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ '#form52' 144.54/21.46 | X1('#sk6', '#sk7')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['170'])). 144.54/21.46 tff('173', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form247'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('174', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form247'(X1) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form52' 144.54/21.46 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1))))))))), 144.54/21.46 inference('renaming', [status(thm)], ['171', '173'])). 144.54/21.46 tff('175', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: ('#sk1'('#sk329'(X1), Y0) => X1('#sk329'(X1), Y0))))) 144.54/21.46 | ~ '#form52' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['174'])). 144.54/21.46 tff('176', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ('#sk1'('#sk329'(X1), '#sk439'(X1)) => 144.54/21.46 X1('#sk329'(X1), '#sk439'(X1))) 144.54/21.46 | ~ '#form247'(X1) 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form52'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['175'])). 144.54/21.46 tff('177', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk329'(X1), '#sk439'(X1)) 144.54/21.46 | ~ '#form52' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['176'])). 144.54/21.46 tff('178', plain, 144.54/21.46 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form37' | '#sk54'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['166'])). 144.54/21.46 tff('179', plain, (~ '#sk54'('#sk6', '#sk7') | '#form37'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['161'])). 144.54/21.46 tff('180', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form247'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('181', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk338'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk338'(X1), Y1)))))))) 144.54/21.46 | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['180'])). 144.54/21.46 tff('182', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk338'(X1), '#sk450'(X1)) & X1('#sk450'(X1), Y0)) => 144.54/21.46 X1('#sk338'(X1), Y0))))) 144.54/21.46 | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['181'])). 144.54/21.46 tff('183', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk338'(X1), '#sk450'(X1)) & X1('#sk450'(X1), '#sk583'(X1))) => 144.54/21.46 X1('#sk338'(X1), '#sk583'(X1))) 144.54/21.46 | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['182'])). 144.54/21.46 tff('184', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk338'(X1), '#sk583'(X1)) | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['183'])). 144.54/21.46 tff('185', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk338'(X1), '#sk450'(X1)) & X1('#sk450'(X1), '#sk583'(X1))) 144.54/21.46 | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['183'])). 144.54/21.46 tff('186', plain, 144.54/21.46 ![X1 : (a * a) > $o]: ( X1('#sk338'(X1), '#sk450'(X1)) | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['185'])). 144.54/21.46 tff('187', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#sk1'('#sk329'(X1), '#sk439'(X1)) 144.54/21.46 | ~ '#form52' 144.54/21.46 | X1('#sk6', '#sk7') 144.54/21.46 | ~ '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['176'])). 144.54/21.46 tff('188', plain, 144.54/21.46 ![X1 : (a * a) > $o]: ( X1('#sk450'(X1), '#sk583'(X1)) | '#form247'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['185'])). 144.54/21.46 tff('189', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk54'(Y0, Y1) & '#sk54'(Y1, Y2)) => 144.54/21.46 '#sk54'(Y0, Y2))))))))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['162'])). 144.54/21.46 tff('190', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk54'(X1, Y0) & '#sk54'(Y0, Y1)) => '#sk54'(X1, Y1)))))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['189'])). 144.54/21.46 tff('191', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk54'(X1, X2) & '#sk54'(X2, Y0)) => '#sk54'(X1, Y0))))) 144.54/21.46 | '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['190'])). 144.54/21.46 tff('192', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 ( (('#sk54'(X1, X2) & '#sk54'(X2, X3)) => '#sk54'(X1, X3)) | '#form37'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['191'])). 144.54/21.46 tff('193', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ ('#sk54'(X1, X2) & '#sk54'(X2, X3)) | '#sk54'(X1, X3) | '#form37'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['192'])). 144.54/21.46 tff('194', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ '#sk54'(X1, X2) | ~ '#sk54'(X2, X3) | '#form37' | '#sk54'(X1, X3)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['193'])). 144.54/21.46 tff('195', plain, 144.54/21.46 (~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['77'])). 144.54/21.46 tff('196', plain, 144.54/21.46 (~ '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('197', plain, 144.54/21.46 ( '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19')))))), 144.54/21.46 inference('renaming', [status(thm)], ['195', '196'])). 144.54/21.46 tff('198', plain, 144.54/21.46 (~ '#form73' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('199', plain, 144.54/21.46 ( '#form73' 144.54/21.46 | ~ (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk9', '#sk19'))))) 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('renaming', [status(thm)], ['197', '198'])). 144.54/21.46 tff('200', plain, 144.54/21.46 (~ (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2)))))))))))) => 144.54/21.46 '#sk53'('#sk9', '#sk19')) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['199'])). 144.54/21.46 tff('201', plain, 144.54/21.46 (~ '#sk53'('#sk9', '#sk19') | '#form73' | '#form8' | '#form52'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['200'])). 144.54/21.46 tff('202', plain, 144.54/21.46 ( (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | '#form8'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['78'])). 144.54/21.46 tff('203', plain, 144.54/21.46 (~ '#form73' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('204', plain, 144.54/21.46 ( '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7'))))) 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10')))))), 144.54/21.46 inference('renaming', [status(thm)], ['202', '203'])). 144.54/21.46 tff('205', plain, 144.54/21.46 (~ '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3)))))))))))) => 144.54/21.46 Y0('#sk6', '#sk7')))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('206', plain, 144.54/21.46 ( '#form52' 144.54/21.46 | (!!((^[Y0 : (a * a) > $o]: 144.54/21.46 (((!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (!!((^[Y3 : a]: 144.54/21.46 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 144.54/21.46 Y0(Y1, Y3))))))))))) & 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 144.54/21.46 Y0(Y1, Y2))))))))) => 144.54/21.46 Y0('#sk9', '#sk10'))))) 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('renaming', [status(thm)], ['204', '205'])). 144.54/21.46 tff('207', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) => 144.54/21.46 X1('#sk9', '#sk10')) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['206'])). 144.54/21.46 tff('208', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['207'])). 144.54/21.46 tff('209', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['208'])). 144.54/21.46 tff('210', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk411'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk411'(X1), Y1)))))))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['209'])). 144.54/21.46 tff('211', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form431'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('212', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form431'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk411'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk411'(X1), Y1))))))))), 144.54/21.46 inference('renaming', [status(thm)], ['210', '211'])). 144.54/21.46 tff('213', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form431'(X1) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk411'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk411'(X1), Y1))))))))), 144.54/21.46 inference('ho_norm', [status(thm)], ['212'])). 144.54/21.46 tff('214', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk411'(X1), '#sk678'(X1)) & X1('#sk678'(X1), Y0)) => 144.54/21.46 X1('#sk411'(X1), Y0))))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['213'])). 144.54/21.46 tff('215', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk411'(X1), '#sk678'(X1)) & X1('#sk678'(X1), '#sk793'(X1))) => 144.54/21.46 X1('#sk411'(X1), '#sk793'(X1))) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['214'])). 144.54/21.46 tff('216', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk411'(X1), '#sk793'(X1)) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['215'])). 144.54/21.46 tff('217', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['87'])). 144.54/21.46 tff('218', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form431'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('219', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ '#form431'(X1) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 144.54/21.46 inference('renaming', [status(thm)], ['217', '218'])). 144.54/21.46 tff('220', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 ((X1('#sk556'(X1), Y0) & X1(Y0, Y1)) => 144.54/21.46 X1('#sk556'(X1), Y1)))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['219'])). 144.54/21.46 tff('221', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 ((X1('#sk556'(X1), '#sk703'(X1)) & X1('#sk703'(X1), Y0)) => 144.54/21.46 X1('#sk556'(X1), Y0))))) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['220'])). 144.54/21.46 tff('222', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ ((X1('#sk556'(X1), '#sk703'(X1)) & X1('#sk703'(X1), '#sk823'(X1))) => 144.54/21.46 X1('#sk556'(X1), '#sk823'(X1))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['221'])). 144.54/21.46 tff('223', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ X1('#sk556'(X1), '#sk823'(X1)) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['222'])). 144.54/21.46 tff('224', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk411'(X1), '#sk678'(X1)) & X1('#sk678'(X1), '#sk793'(X1))) 144.54/21.46 | X1('#sk9', '#sk10') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['215'])). 144.54/21.46 tff('225', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk411'(X1), '#sk678'(X1)) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['224'])). 144.54/21.46 tff('226', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk678'(X1), '#sk793'(X1)) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk9', '#sk10')), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['224'])). 144.54/21.46 tff('227', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( (X1('#sk556'(X1), '#sk703'(X1)) & X1('#sk703'(X1), '#sk823'(X1))) 144.54/21.46 | ~ '#form431'(X1) 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['222'])). 144.54/21.46 tff('228', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk556'(X1), '#sk703'(X1)) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['227'])). 144.54/21.46 tff('229', plain, 144.54/21.46 ( ((!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) & 144.54/21.46 (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2)))))))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['200'])). 144.54/21.46 tff('230', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (!!((^[Y2 : a]: 144.54/21.46 (('#sk53'(Y0, Y1) & '#sk53'(Y1, Y2)) => 144.54/21.46 '#sk53'(Y0, Y2))))))))))) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['229'])). 144.54/21.46 tff('231', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk53'(X1, Y0) & '#sk53'(Y0, Y1)) => '#sk53'(X1, Y1)))))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['230'])). 144.54/21.46 tff('232', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk53'(X1, X2) & '#sk53'(X2, Y0)) => '#sk53'(X1, Y0))))) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['231'])). 144.54/21.46 tff('233', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 ( (('#sk53'(X1, X2) & '#sk53'(X2, X3)) => '#sk53'(X1, X3)) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['232'])). 144.54/21.46 tff('234', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ ('#sk53'(X1, X2) & '#sk53'(X2, X3)) 144.54/21.46 | '#sk53'(X1, X3) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['233'])). 144.54/21.46 tff('235', plain, 144.54/21.46 ![X1 : a, X2 : a, X3 : a]: 144.54/21.46 (~ '#sk53'(X1, X2) 144.54/21.46 | ~ '#sk53'(X2, X3) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | '#sk53'(X1, X3)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['234'])). 144.54/21.46 tff('236', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( X1('#sk703'(X1), '#sk823'(X1)) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52' 144.54/21.46 | X1('#sk10', '#sk19') 144.54/21.46 | ~ '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['227'])). 144.54/21.46 tff('237', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#form431'(X1) 144.54/21.46 | ~ (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 144.54/21.46 define([status(thm)])). 144.54/21.46 tff('238', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (!!((^[Y0 : a]: 144.54/21.46 (('#sk2'('#sk36'(X1), Y0) | '#sk1'('#sk36'(X1), Y0)) => 144.54/21.46 X1('#sk36'(X1), Y0))))) 144.54/21.46 | '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['237'])). 144.54/21.46 tff('239', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 (~ (('#sk2'('#sk36'(X1), '#sk51'(X1)) | 144.54/21.46 '#sk1'('#sk36'(X1), '#sk51'(X1))) => 144.54/21.46 X1('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_exists', [status(thm)], ['238'])). 144.54/21.46 tff('240', plain, 144.54/21.46 ![X1 : (a * a) > $o]: (~ X1('#sk36'(X1), '#sk51'(X1)) | '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['239'])). 144.54/21.46 tff('241', plain, 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (!!((^[Y1 : a]: 144.54/21.46 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk53'(Y0, Y1)))))))) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_and', [status(thm)], ['229'])). 144.54/21.46 tff('242', plain, 144.54/21.46 ![X1 : a]: 144.54/21.46 ( (!!((^[Y0 : a]: 144.54/21.46 (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk53'(X1, Y0))))) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['241'])). 144.54/21.46 tff('243', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 ( (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk53'(X1, X2)) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73'), 144.54/21.46 inference('lazy_cnf_forall', [status(thm)], ['242'])). 144.54/21.46 tff('244', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) 144.54/21.46 | '#sk53'(X1, X2) 144.54/21.46 | '#form73' 144.54/21.46 | '#form8' 144.54/21.46 | '#form52'), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['243'])). 144.54/21.46 tff('245', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ '#sk2'(X1, X2) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | '#sk53'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['244'])). 144.54/21.46 tff('246', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( ('#sk2'('#sk36'(X1), '#sk51'(X1)) | '#sk1'('#sk36'(X1), '#sk51'(X1))) 144.54/21.46 | '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_imply', [status(thm)], ['239'])). 144.54/21.46 tff('247', plain, 144.54/21.46 ![X1 : (a * a) > $o]: 144.54/21.46 ( '#sk2'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#sk1'('#sk36'(X1), '#sk51'(X1)) 144.54/21.46 | '#form431'(X1)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['246'])). 144.54/21.46 tff('248', plain, 144.54/21.46 ![X1 : a, X2 : a]: 144.54/21.46 (~ '#sk1'(X1, X2) 144.54/21.46 | '#form52' 144.54/21.46 | '#form8' 144.54/21.46 | '#form73' 144.54/21.46 | '#sk53'(X1, X2)), 144.54/21.46 inference('lazy_cnf_or', [status(thm)], ['244'])). 144.54/21.46 tff('249', plain, $false, 144.54/21.46 inference('eprover', [status(thm)], 144.54/21.46 ['21', '23', '31', '32', '33', '39', '41', '42', '48', '49', 144.54/21.46 '61', '93', '95', '108', '110', '111', '112', '118', '119', 144.54/21.46 '125', '127', '128', '134', '145', '150', '154', '158', 144.54/21.46 '159', '167', '177', '178', '179', '184', '186', '187', 144.54/21.46 '188', '194', '201', '216', '223', '225', '226', '228', 144.54/21.46 '235', '236', '240', '245', '247', '248'])). 144.54/21.46 144.54/21.46 % SZS output end Refutation 144.54/21.46 144.54/21.46 144.54/21.46 % Terminating... 144.77/21.51 % Runner terminated. 144.77/21.52 % Zipperpin 1.5 exiting 144.77/21.53 EOF