0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.AZc9qXVzVu 0.13/0.34 % Computer : n008.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 10:58:59 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 120 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.52/0.63 % Estimated wc time : 1286 0.52/0.63 % Estimated cpu time (7 cpus) : 183.71428571428572 0.58/0.73 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.58/0.74 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.59/0.74 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.59/0.76 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.59/0.79 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 66.28/10.64 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 101.62/15.67 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 110.71/17.26 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 133.79/20.61 % Solved by lams/b.sh. 133.79/20.61 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.AZc9qXVzVu/e_input2f2897 --cpu-limit=12 --auto -s -p. 133.79/20.61 % done 74 iterations in 4.823s 133.79/20.61 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 133.79/20.61 % SZS output start Refutation 133.79/20.61 tff(cTHM250D_pme, conjecture, 133.79/20.61 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 133.79/20.61 ((((![Xx0:a,Xy0:a]: 133.79/20.61 (((![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xy1,Xz) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz)))) => 133.79/20.61 Xp1(Xx0,Xy0))) | 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 133.79/20.61 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 133.79/20.61 (![Xx1:a,Xy1:a]: ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0))))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 (((![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: 133.79/20.61 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 133.79/20.61 Xp1(Xy0,Xz))) & 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 133.79/20.61 (![Xx1:a,Xy1:a]: 133.79/20.61 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 133.79/20.61 Xp1(Xx0,Xz)))))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 133.79/20.61 Xp1(Xx,Xy)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 133.79/20.61 Xp1(Xx,Xy)))))). 133.79/20.61 tff(zf_stmt_0, negated_conjecture, 133.79/20.61 (~ 133.79/20.61 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 133.79/20.61 ((((![Xx0:a,Xy0:a]: 133.79/20.61 (((![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xy1,Xz) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz)))) => 133.79/20.61 Xp1(Xx0,Xy0))) | 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 133.79/20.61 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 133.79/20.61 (![Xx1:a,Xy1:a]: 133.79/20.61 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0))))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 (((![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: 133.79/20.61 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 133.79/20.61 Xp1(Xy0,Xz))) & 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 133.79/20.61 (![Xx1:a,Xy1:a]: 133.79/20.61 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 133.79/20.61 Xp1(Xx0,Xy0)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx1:a,Xy1:a]: 133.79/20.61 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 133.79/20.61 (![Xx1:a,Xy1:a,Xz0:a]: 133.79/20.61 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 133.79/20.61 Xp1(Xx0,Xz)))))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 133.79/20.61 Xp1(Xx,Xy)))) => 133.79/20.61 (![Xp1:((a * a) > $o)]: 133.79/20.61 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 133.79/20.61 (![Xx0:a,Xy0:a,Xz:a]: 133.79/20.61 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 133.79/20.61 Xp1(Xx,Xy))))))). 133.79/20.61 tff('0', plain, 133.79/20.61 ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (((!!((^[Y6 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (Y0(Y7, 133.79/20.61 Y8) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y8)))))))) & 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y6(Y8, 133.79/20.61 Y9) & 133.79/20.61 Y6(Y7, 133.79/20.61 Y8)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y9)))))))))))) => 133.79/20.61 Y6(Y4, Y5))))) | 133.79/20.61 (!!((^[Y6 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y6(Y7, 133.79/20.61 Y8) & 133.79/20.61 Y6(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y9))))))))))) & 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (Y1(Y7, 133.79/20.61 Y8) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y8))))))))) => 133.79/20.61 Y6(Y4, Y5)))))) => 133.79/20.61 (!!((^[Y6 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y7 : a]: 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y6(Y7, 133.79/20.61 Y8) & 133.79/20.61 Y6(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y9))))))))))) & 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y1(Y7, 133.79/20.61 Y8) | 133.79/20.61 Y0(Y7, 133.79/20.61 Y8)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y8))))))))) => 133.79/20.61 Y6(Y4, Y5)))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (((!!((^[Y7 : ( 133.79/20.61 a * a) > $o]: 133.79/20.61 (( 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y1(Y8, 133.79/20.61 Y9) | 133.79/20.61 Y0(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y9)))))))) & 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y10 : a]: 133.79/20.61 (( 133.79/20.61 Y7(Y8, 133.79/20.61 Y9) & 133.79/20.61 Y7(Y9, 133.79/20.61 Y10)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y10)))))))))))) => 133.79/20.61 Y7(Y5, 133.79/20.61 Y6))))) & 133.79/20.61 (!!((^[Y7 : ( 133.79/20.61 a * a) > $o]: 133.79/20.61 (( 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y10 : a]: 133.79/20.61 (( 133.79/20.61 Y7(Y8, 133.79/20.61 Y9) & 133.79/20.61 Y7(Y9, 133.79/20.61 Y10)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y10))))))))))) & 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y1(Y8, 133.79/20.61 Y9) | 133.79/20.61 Y0(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y9))))))))) => 133.79/20.61 Y7(Y4, 133.79/20.61 Y5)))))) => 133.79/20.61 (!!((^[Y7 : ( 133.79/20.61 a * a) > $o]: 133.79/20.61 ((( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y0(Y8, 133.79/20.61 Y9) | 133.79/20.61 Y1(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y9)))))))) & 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y10 : a]: 133.79/20.61 (( 133.79/20.61 Y7(Y8, 133.79/20.61 Y9) & 133.79/20.61 Y7(Y9, 133.79/20.61 Y10)) => 133.79/20.61 Y7(Y8, 133.79/20.61 Y10)))))))))))) => 133.79/20.61 Y7(Y4, Y6)))))))))))))))) => 133.79/20.61 (!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y0(Y5, Y6) | 133.79/20.61 Y1(Y5, Y6)) => 133.79/20.61 Y4(Y5, Y6)))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ((Y4(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y4(Y5, 133.79/20.61 Y6)) => 133.79/20.61 Y4(Y5, Y7)))))))))))) => 133.79/20.61 Y4(Y2, Y3)))))) => 133.79/20.61 (!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y0(Y5, Y6) | 133.79/20.61 Y1(Y5, Y6)) => 133.79/20.61 Y4(Y5, Y6)))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ((Y4(Y5, Y6) & 133.79/20.61 Y4(Y6, Y7)) => 133.79/20.61 Y4(Y5, Y7)))))))))))) => 133.79/20.61 Y4(Y2, Y3)))))))))))))))))), 133.79/20.61 inference('cnf', [status(esa)], [zf_stmt_0])). 133.79/20.61 tff('1', plain, 133.79/20.61 ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (((!!((^[Y5 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ('#sk1'( 133.79/20.61 Y6, Y7) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y7)))))))) & 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y5(Y7, 133.79/20.61 Y8) & 133.79/20.61 Y5(Y6, 133.79/20.61 Y7)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y8)))))))))))) => 133.79/20.61 Y5(Y3, Y4))))) | 133.79/20.61 (!!((^[Y5 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y5(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y5(Y7, 133.79/20.61 Y8)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y8))))))))))) & 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (Y0(Y6, 133.79/20.61 Y7) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y7))))))))) => 133.79/20.61 Y5(Y3, Y4)))))) => 133.79/20.61 (!!((^[Y5 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ( 133.79/20.61 !!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y5(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y5(Y7, 133.79/20.61 Y8)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y8))))))))))) & 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ( 133.79/20.61 ( 133.79/20.61 Y0(Y6, 133.79/20.61 Y7) | 133.79/20.61 '#sk1'( 133.79/20.61 Y6, Y7)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y7))))))))) => 133.79/20.61 Y5(Y3, Y4)))))))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (((!!((^[Y6 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y0(Y7, 133.79/20.61 Y8) | 133.79/20.61 '#sk1'( 133.79/20.61 Y7, Y8)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y8)))))))) & 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y6(Y7, 133.79/20.61 Y8) & 133.79/20.61 Y6(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y9)))))))))))) => 133.79/20.61 Y6(Y4, Y5))))) & 133.79/20.61 (!!((^[Y6 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y9 : a]: 133.79/20.61 (( 133.79/20.61 Y6(Y7, 133.79/20.61 Y8) & 133.79/20.61 Y6(Y8, 133.79/20.61 Y9)) => 133.79/20.61 Y6(Y7, 133.79/20.61 Y9))))))))))) & 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y0(Y7, 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133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y5, Y6) & 133.79/20.61 Y3(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 Y0(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))))))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['0'])). 133.79/20.61 tff('2', plain, 133.79/20.61 ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 ((((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (((!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ('#sk1'(Y5, Y6) => 133.79/20.61 Y4(Y5, Y6)))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (( 133.79/20.61 Y4(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y4(Y5, 133.79/20.61 Y6)) => 133.79/20.61 Y4(Y5, 133.79/20.61 Y7)))))))))))) => 133.79/20.61 Y4(Y2, Y3))))) | 133.79/20.61 (!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (( 133.79/20.61 Y4(Y5, 133.79/20.61 Y6) & 133.79/20.61 Y4(Y6, 133.79/20.61 Y7)) => 133.79/20.61 Y4(Y5, 133.79/20.61 Y7))))))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ('#sk2'(Y5, Y6) => 133.79/20.61 Y4(Y5, Y6))))))))) => 133.79/20.61 Y4(Y2, Y3)))))) => 133.79/20.61 (!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 ( 133.79/20.61 ( 133.79/20.61 Y4(Y5, 133.79/20.61 Y6) & 133.79/20.61 Y4(Y6, 133.79/20.61 Y7)) => 133.79/20.61 Y4(Y5, 133.79/20.61 Y7))))))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (('#sk2'(Y5, Y6) | 133.79/20.61 '#sk1'(Y5, Y6)) => 133.79/20.61 Y4(Y5, Y6))))))))) => 133.79/20.61 Y4(Y2, Y3)))))))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (((!!((^[Y5 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (( 133.79/20.61 '#sk2'( 133.79/20.61 Y6, Y7) | 133.79/20.61 '#sk1'( 133.79/20.61 Y6, Y7)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y7)))))))) & 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y5(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y5(Y7, 133.79/20.61 Y8)) => 133.79/20.61 Y5(Y6, 133.79/20.61 Y8)))))))))))) => 133.79/20.61 Y5(Y3, Y4))))) & 133.79/20.61 (!!((^[Y5 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (!!(( 133.79/20.61 ^[Y8 : a]: 133.79/20.61 (( 133.79/20.61 Y5(Y6, 133.79/20.61 Y7) & 133.79/20.61 Y5(Y7, 133.79/20.61 Y8)) => 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Y2)))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (((!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (('#sk2'(Y5, 133.79/20.61 Y6) | 133.79/20.61 '#sk1'(Y5, 133.79/20.61 Y6)) => 133.79/20.61 Y4(Y5, Y6)))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (( 133.79/20.61 Y4(Y5, 133.79/20.61 Y6) & 133.79/20.61 Y4(Y6, 133.79/20.61 Y7)) => 133.79/20.61 Y4(Y5, 133.79/20.61 Y7)))))))))))) => 133.79/20.61 Y4(Y2, Y3))))) & 133.79/20.61 (!!((^[Y4 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (!!((^[Y7 : a]: 133.79/20.61 (( 133.79/20.61 Y4(Y5, 133.79/20.61 Y6) & 133.79/20.61 Y4(Y6, 133.79/20.61 Y7)) => 133.79/20.61 Y4(Y5, 133.79/20.61 Y7))))))))))) & 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 (('#sk2'(Y5, 133.79/20.61 Y6) | 133.79/20.61 '#sk1'(Y5, 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133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2)))))))))))))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['3'])). 133.79/20.61 tff('5', plain, 133.79/20.61 (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (((!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y4, Y5) & 133.79/20.61 Y2(Y3, Y4)) => 133.79/20.61 Y2(Y3, Y5)))))))))))) => 133.79/20.61 Y2(Y0, Y1))))) | 133.79/20.61 (!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & 133.79/20.61 Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5))))))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 133.79/20.61 Y2(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5))))))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (('#sk2'(Y3, Y4) | 133.79/20.61 '#sk1'(Y3, Y4)) => 133.79/20.61 Y2(Y3, 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133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2)))))))))))))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['4'])). 133.79/20.61 tff('6', plain, 133.79/20.61 (~ ((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (((!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : 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Y2(Y3, Y4))))))))) => 133.79/20.61 Y2(Y0, Y1)))))))))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) 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133.79/20.61 ('#sk1'(Y2, Y3) => Y1(Y2, Y3)))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y3, Y4) & Y1(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y4)))))))))))) => 133.79/20.61 Y1('#sk6', Y0))))) | 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4))))))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 133.79/20.61 Y1('#sk6', Y0)))))) => 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4))))))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3))))))))) => 133.79/20.61 Y1('#sk6', Y0))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4'))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2)))))))))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['7'])). 133.79/20.61 tff('9', plain, 133.79/20.61 (~ (((!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) | 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['8'])). 133.79/20.61 tff('10', plain, 133.79/20.61 ( ((!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) | 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4'))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2)))))))))))))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['9'])). 133.79/20.61 tff('11', plain, 133.79/20.61 ( (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 inference('lazy_cnf_or', [status(thm)], ['10'])). 133.79/20.61 tff('12', plain, 133.79/20.61 (~ '#form9' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('13', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) => 133.79/20.61 X1('#sk3', '#sk4')) 133.79/20.61 | ~ '#form9'), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['12'])). 133.79/20.61 tff('14', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['13'])). 133.79/20.61 tff('15', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['14'])). 133.79/20.61 tff('16', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (('#sk1'('#sk37'(X1), Y0) | '#sk2'('#sk37'(X1), Y0)) => 133.79/20.61 X1('#sk37'(X1), Y0))))) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['15'])). 133.79/20.61 tff('17', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (('#sk1'('#sk37'(X1), '#sk52'(X1)) | 133.79/20.61 '#sk2'('#sk37'(X1), '#sk52'(X1))) => 133.79/20.61 X1('#sk37'(X1), '#sk52'(X1))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['16'])). 133.79/20.61 tff('18', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['17'])). 133.79/20.61 tff('19', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 ((X1(Y0, Y1) & X1('#sk106'(X1), Y0)) => 133.79/20.61 X1('#sk106'(X1), Y1)))))))) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['18'])). 133.79/20.61 tff('20', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 ((X1('#sk149'(X1), Y0) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.61 X1('#sk106'(X1), Y0))))) 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9'), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['19'])). 133.79/20.61 tff('21', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.61 X1('#sk106'(X1), '#sk228'(X1))) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['20'])). 133.79/20.61 tff('22', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ X1('#sk106'(X1), '#sk228'(X1)) 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['21'])). 133.79/20.61 tff('23', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['21'])). 133.79/20.61 tff('24', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( X1('#sk106'(X1), '#sk149'(X1)) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['23'])). 133.79/20.61 tff('25', plain, 133.79/20.61 ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4'))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['4'])). 133.79/20.61 tff('26', plain, 133.79/20.61 ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 133.79/20.61 '#sk5'(Y0, Y2)))))))))))) => 133.79/20.61 '#sk5'('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['25'])). 133.79/20.61 tff('27', plain, 133.79/20.61 ((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 133.79/20.61 '#sk5'(Y0, Y2)))))))))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['26'])). 133.79/20.61 tff('28', plain, 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['27'])). 133.79/20.61 tff('29', plain, 133.79/20.61 ![X1 : a]: 133.79/20.61 (!!((^[Y0 : a]: (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk5'(X1, Y0))))), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['28'])). 133.79/20.61 tff('30', plain, 133.79/20.61 ![X1 : a, X2 : a]: (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk5'(X1, X2)), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['29'])). 133.79/20.61 tff('31', plain, 133.79/20.61 ![X1 : a, X2 : a]: 133.79/20.61 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk5'(X1, X2)), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['30'])). 133.79/20.61 tff('32', plain, ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X1, X2)), 133.79/20.61 inference('lazy_cnf_or', [status(thm)], ['31'])). 133.79/20.61 tff('33', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( ('#sk1'('#sk37'(X1), '#sk52'(X1)) | '#sk2'('#sk37'(X1), '#sk52'(X1))) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['17'])). 133.79/20.61 tff('34', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_or', [status(thm)], ['33'])). 133.79/20.61 tff('35', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 ((X1(Y0, Y1) & X1('#sk106'(X1), Y0)) => 133.79/20.61 X1('#sk106'(X1), Y1)))))))) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['34'])). 133.79/20.61 tff('36', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 ((X1('#sk149'(X1), Y0) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.61 X1('#sk106'(X1), Y0))))) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['35'])). 133.79/20.61 tff('37', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.61 X1('#sk106'(X1), '#sk228'(X1))) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['36'])). 133.79/20.61 tff('38', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ X1('#sk106'(X1), '#sk228'(X1)) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['37'])). 133.79/20.61 tff('39', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X1, X2)), 133.79/20.61 inference('lazy_cnf_or', [status(thm)], ['31'])). 133.79/20.61 tff('40', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['37'])). 133.79/20.61 tff('41', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( X1('#sk106'(X1), '#sk149'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['40'])). 133.79/20.61 tff('42', plain, ~ '#sk5'('#sk3', '#sk4'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['26'])). 133.79/20.61 tff('43', plain, 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 133.79/20.61 '#sk5'(Y0, Y2))))))))))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['27'])). 133.79/20.61 tff('44', plain, 133.79/20.61 ![X1 : a]: 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk5'(X1, Y0) & '#sk5'(Y0, Y1)) => '#sk5'(X1, Y1)))))))), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['43'])). 133.79/20.61 tff('45', plain, 133.79/20.61 ![X1 : a, X2 : a]: 133.79/20.61 (!!((^[Y0 : a]: (('#sk5'(X1, X2) & '#sk5'(X2, Y0)) => '#sk5'(X1, Y0))))), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['44'])). 133.79/20.61 tff('46', plain, 133.79/20.61 ![X1 : a, X2 : a, X3 : a]: 133.79/20.61 (('#sk5'(X1, X2) & '#sk5'(X2, X3)) => '#sk5'(X1, X3)), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['45'])). 133.79/20.61 tff('47', plain, 133.79/20.61 ![X1 : a, X2 : a, X3 : a]: 133.79/20.61 (~ ('#sk5'(X1, X2) & '#sk5'(X2, X3)) | '#sk5'(X1, X3)), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['46'])). 133.79/20.61 tff('48', plain, 133.79/20.61 ![X1 : a, X2 : a, X3 : a]: 133.79/20.61 (~ '#sk5'(X1, X2) | ~ '#sk5'(X2, X3) | '#sk5'(X1, X3)), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['47'])). 133.79/20.61 tff('49', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( X1('#sk149'(X1), '#sk228'(X1)) 133.79/20.61 | ~ '#form9' 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ X1('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['23'])). 133.79/20.61 tff('50', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( X1('#sk149'(X1), '#sk228'(X1)) 133.79/20.61 | X1('#sk3', '#sk4') 133.79/20.61 | ~ '#form9' 133.79/20.61 | '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | '#sk1'('#sk37'(X1), '#sk52'(X1))), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['40'])). 133.79/20.61 tff('51', plain, 133.79/20.61 (~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4'))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2)))))))))))))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['9'])). 133.79/20.61 tff('52', plain, 133.79/20.61 (~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7')) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 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Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 inference('renaming', [status(thm)], ['52', '53'])). 133.79/20.61 tff('55', plain, 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (((!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (('#sk2'(Y3, Y4) | 133.79/20.61 '#sk1'(Y3, Y4)) => 133.79/20.61 Y2(Y3, Y4)))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & 133.79/20.61 Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5)))))))))))) => 133.79/20.61 Y2(Y0, Y1))))) & 133.79/20.61 (!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & 133.79/20.61 Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5))))))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (('#sk2'(Y3, Y4) | 133.79/20.61 '#sk1'(Y3, Y4)) => 133.79/20.61 Y2(Y3, Y4))))))))) => 133.79/20.61 Y2('#sk10', Y0)))))) => 133.79/20.61 (!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (('#sk1'(Y3, Y4) | 133.79/20.61 '#sk2'(Y3, Y4)) => 133.79/20.61 Y2(Y3, Y4)))))))) & 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5)))))))))))) => 133.79/20.61 Y2('#sk10', Y1)))))))))))) 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 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(('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3))))))))) => 133.79/20.61 Y1('#sk10', '#sk11')))))) => 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3)))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4)))))))))))) => 133.79/20.61 Y1('#sk10', Y0))))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['55'])). 133.79/20.61 tff('57', plain, 133.79/20.61 (~ (((!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk11', '#sk20'))))) & 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk10', '#sk11')))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk10', '#sk20')))))) 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7')) 133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['56'])). 133.79/20.61 tff('58', plain, 133.79/20.61 (~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk10', '#sk20'))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['57'])). 133.79/20.61 tff('59', plain, 133.79/20.61 (~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk10', '#sk20'))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['57'])). 133.79/20.61 tff('60', plain, 133.79/20.61 ( '#form53' 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('61', plain, 133.79/20.61 (~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk10', '#sk20')))))), 133.79/20.61 inference('renaming', [status(thm)], ['58', '60'])). 133.79/20.61 tff('62', plain, 133.79/20.61 (~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.61 '#sk73'(Y0, Y2)))))))))))) => 133.79/20.61 '#sk73'('#sk10', '#sk20')) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53'), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['61'])). 133.79/20.61 tff('63', plain, (~ '#sk73'('#sk10', '#sk20') | ~ '#form53' | '#form9'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['62'])). 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133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['64'])). 133.79/20.61 tff('66', plain, 133.79/20.61 ( '#form53' 133.79/20.61 | ~ (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.61 '#sk8'(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.61 '#sk8'('#sk6', '#sk7'))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('67', plain, 133.79/20.61 (~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk10', '#sk11')))))), 133.79/20.61 inference('renaming', [status(thm)], ['65', '66'])). 133.79/20.61 tff('68', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) => 133.79/20.61 X1('#sk10', '#sk11')) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53'), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['67'])). 133.79/20.61 tff('69', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) 133.79/20.61 | X1('#sk10', '#sk11') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['68'])). 133.79/20.61 tff('70', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk10', '#sk11')), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['69'])). 133.79/20.61 tff('71', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 ((X1('#sk106'(X1), Y0) & X1(Y0, Y1)) => 133.79/20.61 X1('#sk106'(X1), Y1)))))))) 133.79/20.61 | X1('#sk10', '#sk11') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['70'])). 133.79/20.61 tff('72', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 ((X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), Y0)) => 133.79/20.61 X1('#sk106'(X1), Y0))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk10', '#sk11')), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['71'])). 133.79/20.61 tff('73', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1))) => 133.79/20.61 X1('#sk106'(X1), '#sk228'(X1))) 133.79/20.61 | X1('#sk10', '#sk11') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['72'])). 133.79/20.61 tff('74', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ X1('#sk106'(X1), '#sk228'(X1)) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk10', '#sk11')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['73'])). 133.79/20.61 tff('75', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk10', '#sk11')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['73'])). 133.79/20.61 tff('76', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( '#form775'(X1) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('77', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ '#form775'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.61 | X1('#sk10', '#sk11') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ X1('#sk106'(X1), '#sk228'(X1))), 133.79/20.61 inference('renaming', [status(thm)], ['74', '76'])). 133.79/20.61 tff('78', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ '#form775'(X1) 133.79/20.61 | X1('#sk10', '#sk11') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ X1('#sk106'(X1), '#sk228'(X1))), 133.79/20.61 inference('ho_norm', [status(thm)], ['77'])). 133.79/20.61 tff('79', plain, 133.79/20.61 ( (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, 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133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 inference('lazy_cnf_or', [status(thm)], ['10'])). 133.79/20.61 tff('87', plain, 133.79/20.61 (~ '#form9' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk3', '#sk4')))))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('88', plain, 133.79/20.61 ( '#form9' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (((!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y1, Y2))))) & 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6))))))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk2'(Y4, Y5) | 133.79/20.61 '#sk1'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5))))))))) => 133.79/20.61 Y3(Y0, Y1)))))) => 133.79/20.61 (!!((^[Y3 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (('#sk1'(Y4, Y5) | 133.79/20.61 '#sk2'(Y4, Y5)) => 133.79/20.61 Y3(Y4, Y5)))))))) & 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 (!!((^[Y5 : a]: 133.79/20.61 (!!((^[Y6 : a]: 133.79/20.61 ((Y3(Y4, Y5) & 133.79/20.61 Y3(Y5, Y6)) => 133.79/20.61 Y3(Y4, Y6)))))))))))) => 133.79/20.61 Y3(Y0, Y2))))))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))), 133.79/20.61 inference('renaming', [status(thm)], ['86', '87'])). 133.79/20.61 tff('89', plain, 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (((!!((^[Y2 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 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(!!((^[Y5 : a]: 133.79/20.61 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 133.79/20.61 Y2(Y3, Y5)))))))))))) => 133.79/20.61 Y2('#sk10', Y1)))))))))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['88'])). 133.79/20.61 tff('90', plain, 133.79/20.61 (~ (!!((^[Y0 : a]: 133.79/20.61 (((!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3)))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4)))))))))))) => 133.79/20.61 Y1('#sk11', Y0))))) & 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4))))))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3))))))))) => 133.79/20.61 Y1('#sk10', '#sk11')))))) => 133.79/20.61 (!!((^[Y1 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 133.79/20.61 Y1(Y2, Y3)))))))) & 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 (!!((^[Y4 : a]: 133.79/20.61 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 133.79/20.61 Y1(Y2, Y4)))))))))))) => 133.79/20.61 Y1('#sk10', Y0))))))))) 133.79/20.61 | '#form9' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['89'])). 133.79/20.61 tff('91', plain, 133.79/20.61 (~ (((!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk11', '#sk20'))))) & 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk10', '#sk11')))))) => 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk10', '#sk20')))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['90'])). 133.79/20.61 tff('92', plain, 133.79/20.61 ( ((!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk11', '#sk20'))))) & 133.79/20.61 (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk10', '#sk11')))))) 133.79/20.61 | '#form9' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['91'])). 133.79/20.61 tff('93', plain, 133.79/20.61 ( (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk11', '#sk20'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.61 Y0(Y1, Y3))))))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.61 Y0('#sk6', '#sk7'))))) 133.79/20.61 | '#form9'), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['92'])). 133.79/20.61 tff('94', plain, 133.79/20.61 (~ '#form54' 133.79/20.61 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.61 (((!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 (!!((^[Y3 : a]: 133.79/20.61 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.61 Y0(Y1, Y3)))))))))))) => 133.79/20.61 Y0('#sk6', '#sk7')))))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('95', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) => 133.79/20.61 X1('#sk6', '#sk7')) 133.79/20.61 | ~ '#form54'), 133.79/20.61 inference('lazy_cnf_forall', [status(thm)], ['94'])). 133.79/20.61 tff('96', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ ((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 133.79/20.61 (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) 133.79/20.61 | X1('#sk6', '#sk7') 133.79/20.61 | ~ '#form54'), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['95'])). 133.79/20.61 tff('97', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 133.79/20.61 | ~ '#form54' 133.79/20.61 | X1('#sk6', '#sk7')), 133.79/20.61 inference('lazy_cnf_and', [status(thm)], ['96'])). 133.79/20.61 tff('98', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (!!((^[Y0 : a]: ('#sk1'('#sk261'(X1), Y0) => X1('#sk261'(X1), Y0))))) 133.79/20.61 | X1('#sk6', '#sk7') 133.79/20.61 | ~ '#form54' 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['97'])). 133.79/20.61 tff('99', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( '#form349'(X1) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (!!((^[Y2 : a]: 133.79/20.61 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.61 define([status(thm)])). 133.79/20.61 tff('100', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ '#form349'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk11', '#sk20') 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.61 X1('#sk37'(X1), Y0)))))), 133.79/20.61 inference('renaming', [status(thm)], ['85', '99'])). 133.79/20.61 tff('101', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ '#form349'(X1) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk11', '#sk20') 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.61 X1('#sk37'(X1), Y0)))))), 133.79/20.61 inference('ho_norm', [status(thm)], ['100'])). 133.79/20.61 tff('102', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ (('#sk2'('#sk37'(X1), '#sk52'(X1)) | 133.79/20.61 '#sk1'('#sk37'(X1), '#sk52'(X1))) => 133.79/20.61 X1('#sk37'(X1), '#sk52'(X1))) 133.79/20.61 | X1('#sk11', '#sk20') 133.79/20.61 | ~ '#form53' 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form349'(X1)), 133.79/20.61 inference('lazy_cnf_exists', [status(thm)], ['101'])). 133.79/20.61 tff('103', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 (~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.61 | ~ '#form349'(X1) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk11', '#sk20')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['102'])). 133.79/20.61 tff('104', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( (X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1))) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.61 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.61 | '#form9' 133.79/20.61 | ~ '#form53' 133.79/20.61 | X1('#sk10', '#sk11')), 133.79/20.61 inference('lazy_cnf_imply', [status(thm)], ['73'])). 133.79/20.61 tff('105', plain, 133.79/20.61 ![X1 : (a * a) > $o]: 133.79/20.61 ( '#form775'(X1) 133.79/20.61 | ~ (!!((^[Y0 : a]: 133.79/20.61 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('106', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form775'(X1) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9' 133.79/20.62 | (X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1)))), 133.79/20.62 inference('renaming', [status(thm)], ['104', '105'])). 133.79/20.62 tff('107', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( X1('#sk106'(X1), '#sk149'(X1)) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53' 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['106'])). 133.79/20.62 tff('108', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form775'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('109', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.62 X1('#sk37'(X1), Y0))))) 133.79/20.62 | '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['108'])). 133.79/20.62 tff('110', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (('#sk2'('#sk37'(X1), '#sk52'(X1)) | 133.79/20.62 '#sk1'('#sk37'(X1), '#sk52'(X1))) => 133.79/20.62 X1('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['109'])). 133.79/20.62 tff('111', plain, 133.79/20.62 ![X1 : (a * a) > $o]: (~ X1('#sk37'(X1), '#sk52'(X1)) | '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['110'])). 133.79/20.62 tff('112', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( X1('#sk149'(X1), '#sk228'(X1)) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53' 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['106'])). 133.79/20.62 tff('113', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( ('#sk2'('#sk37'(X1), '#sk52'(X1)) | '#sk1'('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53' 133.79/20.62 | X1('#sk11', '#sk20')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['102'])). 133.79/20.62 tff('114', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['113'])). 133.79/20.62 tff('115', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( ('#sk2'('#sk37'(X1), '#sk52'(X1)) | '#sk1'('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['110'])). 133.79/20.62 tff('116', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#form775'(X1)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['115'])). 133.79/20.62 tff('117', plain, 133.79/20.62 ( ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.62 '#sk73'(Y0, Y2)))))))))))) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['62'])). 133.79/20.62 tff('118', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['117'])). 133.79/20.62 tff('119', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk73'(X1, Y0))))) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['118'])). 133.79/20.62 tff('120', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk73'(X1, X2)) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['119'])). 133.79/20.62 tff('121', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) 133.79/20.62 | '#sk73'(X1, X2) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['120'])). 133.79/20.62 tff('122', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ '#sk2'(X1, X2) | '#form9' | ~ '#form53' | '#sk73'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['121'])). 133.79/20.62 tff('123', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ '#sk1'(X1, X2) | '#form9' | ~ '#form53' | '#sk73'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['121'])). 133.79/20.62 tff('124', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.62 '#sk73'(Y0, Y2))))))))))) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['117'])). 133.79/20.62 tff('125', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk73'(X1, Y0) & '#sk73'(Y0, Y1)) => '#sk73'(X1, Y1)))))))) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['124'])). 133.79/20.62 tff('126', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (('#sk73'(X1, X2) & '#sk73'(X2, Y0)) => '#sk73'(X1, Y0))))) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['125'])). 133.79/20.62 tff('127', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 ( (('#sk73'(X1, X2) & '#sk73'(X2, X3)) => '#sk73'(X1, X3)) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['126'])). 133.79/20.62 tff('128', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ ('#sk73'(X1, X2) & '#sk73'(X2, X3)) 133.79/20.62 | '#sk73'(X1, X3) 133.79/20.62 | '#form9' 133.79/20.62 | ~ '#form53'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['127'])). 133.79/20.62 tff('129', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ '#sk73'(X1, X2) 133.79/20.62 | ~ '#sk73'(X2, X3) 133.79/20.62 | ~ '#form53' 133.79/20.62 | '#form9' 133.79/20.62 | '#sk73'(X1, X3)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['128'])). 133.79/20.62 tff('130', plain, 133.79/20.62 (~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk10', '#sk20'))))) 133.79/20.62 | '#form9' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['91'])). 133.79/20.62 tff('131', plain, 133.79/20.62 (~ '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('132', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( (((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) => 133.79/20.62 X1('#sk6', '#sk7')) 133.79/20.62 | ~ '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['131'])). 133.79/20.62 tff('133', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['132'])). 133.79/20.62 tff('134', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['133'])). 133.79/20.62 tff('135', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 ((X1('#sk106'(X1), Y0) & X1(Y0, Y1)) => 133.79/20.62 X1('#sk106'(X1), Y1)))))))) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38' 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['134'])). 133.79/20.62 tff('136', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 ((X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), Y0)) => 133.79/20.62 X1('#sk106'(X1), Y0))))) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['135'])). 133.79/20.62 tff('137', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ((X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1))) => 133.79/20.62 X1('#sk106'(X1), '#sk228'(X1))) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38' 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['136'])). 133.79/20.62 tff('138', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk106'(X1), '#sk228'(X1)) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['137'])). 133.79/20.62 tff('139', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk106'(X1), '#sk228'(X1)) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['137'])). 133.79/20.62 tff('140', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form621'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('141', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form621'(X1) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38' 133.79/20.62 | ~ X1('#sk106'(X1), '#sk228'(X1))), 133.79/20.62 inference('renaming', [status(thm)], ['138', '140'])). 133.79/20.62 tff('142', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( (X1('#sk106'(X1), '#sk149'(X1)) & X1('#sk149'(X1), '#sk228'(X1))) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['137'])). 133.79/20.62 tff('143', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( X1('#sk106'(X1), '#sk149'(X1)) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38' 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['142'])). 133.79/20.62 tff('144', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form621'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('145', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form621'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | X1('#sk106'(X1), '#sk149'(X1))), 133.79/20.62 inference('renaming', [status(thm)], ['143', '144'])). 133.79/20.62 tff('146', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form621'(X1) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | X1('#sk106'(X1), '#sk149'(X1))), 133.79/20.62 inference('ho_norm', [status(thm)], ['145'])). 133.79/20.62 tff('147', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form621'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('148', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: ('#sk2'('#sk748'(X1), Y0) => X1('#sk748'(X1), Y0))))) 133.79/20.62 | '#form621'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['147'])). 133.79/20.62 tff('149', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ('#sk2'('#sk748'(X1), '#sk859'(X1)) => 133.79/20.62 X1('#sk748'(X1), '#sk859'(X1))) 133.79/20.62 | '#form621'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['148'])). 133.79/20.62 tff('150', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk748'(X1), '#sk859'(X1)) | '#form621'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['149'])). 133.79/20.62 tff('151', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( X1('#sk149'(X1), '#sk228'(X1)) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form38' 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['142'])). 133.79/20.62 tff('152', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form621'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('153', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form621'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | X1('#sk149'(X1), '#sk228'(X1))), 133.79/20.62 inference('renaming', [status(thm)], ['151', '152'])). 133.79/20.62 tff('154', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form621'(X1) 133.79/20.62 | ~ '#form38' 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | X1('#sk149'(X1), '#sk228'(X1))), 133.79/20.62 inference('ho_norm', [status(thm)], ['153'])). 133.79/20.62 tff('155', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk2'('#sk748'(X1), '#sk859'(X1)) | '#form621'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['149'])). 133.79/20.62 tff('156', plain, 133.79/20.62 ( '#form53' 133.79/20.62 | ~ (((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.62 '#sk8'(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) => 133.79/20.62 '#sk8'('#sk6', '#sk7'))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('157', plain, 133.79/20.62 ( ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.62 '#sk8'(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1))))))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['156'])). 133.79/20.62 tff('158', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk8'(Y0, Y1)))))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['157'])). 133.79/20.62 tff('159', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk8'(X1, Y0))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['158'])). 133.79/20.62 tff('160', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk8'(X1, X2)) | '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['159'])). 133.79/20.62 tff('161', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk8'(X1, X2) | '#form53'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['160'])). 133.79/20.62 tff('162', plain, 133.79/20.62 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form53' | '#sk8'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['161'])). 133.79/20.62 tff('163', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: ('#sk1'('#sk261'(X1), Y0) => X1('#sk261'(X1), Y0))))) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form54' 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['97'])). 133.79/20.62 tff('164', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form349'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('165', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form349'(X1) 133.79/20.62 | ~ '#form54' 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk261'(X1), Y0) => X1('#sk261'(X1), Y0)))))), 133.79/20.62 inference('renaming', [status(thm)], ['163', '164'])). 133.79/20.62 tff('166', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ('#sk1'('#sk261'(X1), '#sk453'(X1)) => 133.79/20.62 X1('#sk261'(X1), '#sk453'(X1))) 133.79/20.62 | X1('#sk6', '#sk7') 133.79/20.62 | ~ '#form54' 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['165'])). 133.79/20.62 tff('167', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk261'(X1), '#sk453'(X1)) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | ~ '#form54' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['166'])). 133.79/20.62 tff('168', plain, 133.79/20.62 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form53' | '#sk8'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['161'])). 133.79/20.62 tff('169', plain, (~ '#sk8'('#sk6', '#sk7') | '#form53'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['156'])). 133.79/20.62 tff('170', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk1'('#sk261'(X1), '#sk453'(X1)) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | ~ '#form54' 133.79/20.62 | X1('#sk6', '#sk7')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['166'])). 133.79/20.62 tff('171', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk8'(Y0, Y1) & '#sk8'(Y1, Y2)) => 133.79/20.62 '#sk8'(Y0, Y2))))))))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['157'])). 133.79/20.62 tff('172', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk8'(X1, Y0) & '#sk8'(Y0, Y1)) => '#sk8'(X1, Y1)))))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['171'])). 133.79/20.62 tff('173', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: (('#sk8'(X1, X2) & '#sk8'(X2, Y0)) => '#sk8'(X1, Y0))))) 133.79/20.62 | '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['172'])). 133.79/20.62 tff('174', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 ( (('#sk8'(X1, X2) & '#sk8'(X2, X3)) => '#sk8'(X1, X3)) | '#form53'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['173'])). 133.79/20.62 tff('175', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ ('#sk8'(X1, X2) & '#sk8'(X2, X3)) | '#sk8'(X1, X3) | '#form53'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['174'])). 133.79/20.62 tff('176', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ '#sk8'(X1, X2) | ~ '#sk8'(X2, X3) | '#form53' | '#sk8'(X1, X3)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['175'])). 133.79/20.62 tff('177', plain, 133.79/20.62 (~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk10', '#sk20'))))) 133.79/20.62 | '#form9' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['91'])). 133.79/20.62 tff('178', plain, 133.79/20.62 (~ '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('179', plain, 133.79/20.62 ( '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | '#form9' 133.79/20.62 | ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk10', '#sk20')))))), 133.79/20.62 inference('renaming', [status(thm)], ['177', '178'])). 133.79/20.62 tff('180', plain, 133.79/20.62 (~ '#form54' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('181', plain, 133.79/20.62 ( '#form54' 133.79/20.62 | ~ (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk10', '#sk20'))))) 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('renaming', [status(thm)], ['179', '180'])). 133.79/20.62 tff('182', plain, 133.79/20.62 (~ (((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.62 '#sk73'(Y0, Y2)))))))))))) => 133.79/20.62 '#sk73'('#sk10', '#sk20')) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['181'])). 133.79/20.62 tff('183', plain, 133.79/20.62 (~ '#sk73'('#sk10', '#sk20') | '#form54' | '#form9' | '#form38'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['182'])). 133.79/20.62 tff('184', plain, 133.79/20.62 ( (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk10', '#sk11'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['92'])). 133.79/20.62 tff('185', plain, 133.79/20.62 (~ '#form54' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('186', plain, 133.79/20.62 ( '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk10', '#sk11')))))), 133.79/20.62 inference('renaming', [status(thm)], ['184', '185'])). 133.79/20.62 tff('187', plain, 133.79/20.62 (~ '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('188', plain, 133.79/20.62 ( '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk10', '#sk11'))))) 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('renaming', [status(thm)], ['186', '187'])). 133.79/20.62 tff('189', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( (((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) => 133.79/20.62 X1('#sk10', '#sk11')) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['188'])). 133.79/20.62 tff('190', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['189'])). 133.79/20.62 tff('191', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk10', '#sk11')), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['190'])). 133.79/20.62 tff('192', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form349'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('193', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form349'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.62 inference('renaming', [status(thm)], ['191', '192'])). 133.79/20.62 tff('194', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form349'(X1) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1))))))))), 133.79/20.62 inference('ho_norm', [status(thm)], ['193'])). 133.79/20.62 tff('195', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.62 X1('#sk37'(X1), Y0))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['194'])). 133.79/20.62 tff('196', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (('#sk2'('#sk37'(X1), '#sk52'(X1)) | 133.79/20.62 '#sk1'('#sk37'(X1), '#sk52'(X1))) => 133.79/20.62 X1('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['195'])). 133.79/20.62 tff('197', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['196'])). 133.79/20.62 tff('198', plain, 133.79/20.62 ( (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk11', '#sk20'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | '#form9'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['92'])). 133.79/20.62 tff('199', plain, 133.79/20.62 (~ '#form54' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('200', plain, 133.79/20.62 ( '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7'))))) 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk11', '#sk20')))))), 133.79/20.62 inference('renaming', [status(thm)], ['198', '199'])). 133.79/20.62 tff('201', plain, 133.79/20.62 (~ '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3))))))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 133.79/20.62 Y0('#sk6', '#sk7')))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('202', plain, 133.79/20.62 ( '#form38' 133.79/20.62 | (!!((^[Y0 : (a * a) > $o]: 133.79/20.62 (((!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 133.79/20.62 Y0(Y1, Y2)))))))) & 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (!!((^[Y3 : a]: 133.79/20.62 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 133.79/20.62 Y0(Y1, Y3)))))))))))) => 133.79/20.62 Y0('#sk11', '#sk20'))))) 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('renaming', [status(thm)], ['200', '201'])). 133.79/20.62 tff('203', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( (((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 133.79/20.62 X1('#sk11', '#sk20')) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['202'])). 133.79/20.62 tff('204', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['203'])). 133.79/20.62 tff('205', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk11', '#sk20')), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['204'])). 133.79/20.62 tff('206', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.62 X1('#sk37'(X1), Y0))))) 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['205'])). 133.79/20.62 tff('207', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form349'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('208', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form349'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.62 X1('#sk37'(X1), Y0)))))), 133.79/20.62 inference('renaming', [status(thm)], ['206', '207'])). 133.79/20.62 tff('209', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ '#form349'(X1) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (('#sk2'('#sk37'(X1), Y0) | '#sk1'('#sk37'(X1), Y0)) => 133.79/20.62 X1('#sk37'(X1), Y0)))))), 133.79/20.62 inference('ho_norm', [status(thm)], ['208'])). 133.79/20.62 tff('210', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (('#sk2'('#sk37'(X1), '#sk52'(X1)) | 133.79/20.62 '#sk1'('#sk37'(X1), '#sk52'(X1))) => 133.79/20.62 X1('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['209'])). 133.79/20.62 tff('211', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk11', '#sk20')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['210'])). 133.79/20.62 tff('212', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( ('#sk2'('#sk37'(X1), '#sk52'(X1)) | '#sk1'('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['196'])). 133.79/20.62 tff('213', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | X1('#sk10', '#sk11') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['212'])). 133.79/20.62 tff('214', plain, 133.79/20.62 ( ((!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) & 133.79/20.62 (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.62 '#sk73'(Y0, Y2)))))))))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['182'])). 133.79/20.62 tff('215', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk73'(Y0, Y1)))))))) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['214'])). 133.79/20.62 tff('216', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk73'(X1, Y0))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['215'])). 133.79/20.62 tff('217', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk73'(X1, X2)) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['216'])). 133.79/20.62 tff('218', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) 133.79/20.62 | '#sk73'(X1, X2) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['217'])). 133.79/20.62 tff('219', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ '#sk2'(X1, X2) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | '#sk73'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['218'])). 133.79/20.62 tff('220', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 (~ '#sk1'(X1, X2) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | '#sk73'(X1, X2)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['218'])). 133.79/20.62 tff('221', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( ('#sk2'('#sk37'(X1), '#sk52'(X1)) | '#sk1'('#sk37'(X1), '#sk52'(X1))) 133.79/20.62 | ~ '#form349'(X1) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | X1('#sk11', '#sk20')), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['210'])). 133.79/20.62 tff('222', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#sk2'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | '#sk1'('#sk37'(X1), '#sk52'(X1)) 133.79/20.62 | X1('#sk11', '#sk20') 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54' 133.79/20.62 | ~ '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_or', [status(thm)], ['221'])). 133.79/20.62 tff('223', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( '#form349'(X1) 133.79/20.62 | ~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 133.79/20.62 define([status(thm)])). 133.79/20.62 tff('224', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 ((X1(Y0, Y1) & X1('#sk106'(X1), Y0)) => 133.79/20.62 X1('#sk106'(X1), Y1)))))))) 133.79/20.62 | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['223'])). 133.79/20.62 tff('225', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ (!!((^[Y0 : a]: 133.79/20.62 ((X1('#sk149'(X1), Y0) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.62 X1('#sk106'(X1), Y0))))) 133.79/20.62 | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['224'])). 133.79/20.62 tff('226', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ ((X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) => 133.79/20.62 X1('#sk106'(X1), '#sk228'(X1))) 133.79/20.62 | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_exists', [status(thm)], ['225'])). 133.79/20.62 tff('227', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 (~ X1('#sk106'(X1), '#sk228'(X1)) | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['226'])). 133.79/20.62 tff('228', plain, 133.79/20.62 ![X1 : (a * a) > $o]: 133.79/20.62 ( (X1('#sk149'(X1), '#sk228'(X1)) & X1('#sk106'(X1), '#sk149'(X1))) 133.79/20.62 | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['226'])). 133.79/20.62 tff('229', plain, 133.79/20.62 ![X1 : (a * a) > $o]: ( X1('#sk106'(X1), '#sk149'(X1)) | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['228'])). 133.79/20.62 tff('230', plain, 133.79/20.62 ![X1 : (a * a) > $o]: ( X1('#sk149'(X1), '#sk228'(X1)) | '#form349'(X1)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['228'])). 133.79/20.62 tff('231', plain, 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (!!((^[Y2 : a]: 133.79/20.62 (('#sk73'(Y0, Y1) & '#sk73'(Y1, Y2)) => 133.79/20.62 '#sk73'(Y0, Y2))))))))))) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['214'])). 133.79/20.62 tff('232', plain, 133.79/20.62 ![X1 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (!!((^[Y1 : a]: 133.79/20.62 (('#sk73'(X1, Y0) & '#sk73'(Y0, Y1)) => '#sk73'(X1, Y1)))))))) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['231'])). 133.79/20.62 tff('233', plain, 133.79/20.62 ![X1 : a, X2 : a]: 133.79/20.62 ( (!!((^[Y0 : a]: 133.79/20.62 (('#sk73'(X1, X2) & '#sk73'(X2, Y0)) => '#sk73'(X1, Y0))))) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['232'])). 133.79/20.62 tff('234', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 ( (('#sk73'(X1, X2) & '#sk73'(X2, X3)) => '#sk73'(X1, X3)) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38'), 133.79/20.62 inference('lazy_cnf_forall', [status(thm)], ['233'])). 133.79/20.62 tff('235', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ ('#sk73'(X1, X2) & '#sk73'(X2, X3)) 133.79/20.62 | '#sk73'(X1, X3) 133.79/20.62 | '#form38' 133.79/20.62 | '#form9' 133.79/20.62 | '#form54'), 133.79/20.62 inference('lazy_cnf_imply', [status(thm)], ['234'])). 133.79/20.62 tff('236', plain, 133.79/20.62 ![X1 : a, X2 : a, X3 : a]: 133.79/20.62 (~ '#sk73'(X1, X2) 133.79/20.62 | ~ '#sk73'(X2, X3) 133.79/20.62 | '#form54' 133.79/20.62 | '#form9' 133.79/20.62 | '#form38' 133.79/20.62 | '#sk73'(X1, X3)), 133.79/20.62 inference('lazy_cnf_and', [status(thm)], ['235'])). 133.79/20.62 tff('237', plain, $false, 133.79/20.62 inference('eprover', [status(thm)], 133.79/20.62 ['22', '24', '32', '38', '39', '41', '42', '48', '49', '50', 133.79/20.62 '63', '78', '103', '107', '111', '112', '114', '116', '122', 133.79/20.62 '123', '129', '141', '146', '150', '154', '155', '162', 133.79/20.62 '167', '168', '169', '170', '176', '183', '197', '211', 133.79/20.62 '213', '219', '220', '222', '227', '229', '230', '236'])). 133.79/20.62 133.79/20.62 % SZS output end Refutation 133.79/20.62 133.79/20.62 133.79/20.62 % Terminating... 134.37/20.73 % Runner terminated. 134.37/20.75 % Zipperpin 1.5 exiting 134.37/20.77 EOF