0.02/0.10 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.02/0.11 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.YdPp27Qcy3 0.11/0.31 % Computer : n012.cluster.edu 0.11/0.31 % Model : x86_64 x86_64 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.31 % Memory : 8042.1875MB 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.31 % CPULimit : 960 0.11/0.31 % DateTime : Thu Jul 2 07:20:21 EDT 2020 0.11/0.31 % CPUTime : 0.11/0.31 % Running portfolio for 120 s 0.11/0.31 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.11/0.31 % Number of cores: 8 0.11/0.32 % Python version: Python 3.6.8 0.11/0.32 % Running in HO mode 0.49/0.60 % Estimated wc time : 1286 0.49/0.60 % Estimated cpu time (7 cpus) : 183.71428571428572 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.49/0.70 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.50/0.71 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.50/0.73 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.22/10.65 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 103.08/15.56 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 104.40/15.76 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 137.77/20.59 % Solved by lams/b.sh. 137.77/20.59 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.YdPp27Qcy3/e_input4bf5a6 --cpu-limit=12 --auto -s -p. 137.77/20.59 % done 124 iterations in 4.981s 137.77/20.59 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 137.77/20.59 % SZS output start Refutation 137.77/20.59 tff(cTHM250G_pme, conjecture, 137.77/20.59 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 137.77/20.59 ((~ 137.77/20.59 (((![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 (((![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xy0,Xz))) & 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xy1,Xz0) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz0))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 137.77/20.59 (![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 137.77/20.59 Xp1(Xx0,Xz))))) & 137.77/20.59 (![Xx0:a,Xy0:a]: 137.77/20.59 (((![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 137.77/20.59 (![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 137.77/20.59 Xp1(Xx0,Xy0))) | 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 137.77/20.59 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 137.77/20.59 (![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 137.77/20.59 Xp1(Xx,Xy))))) | 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 137.77/20.59 (![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 137.77/20.59 Xp1(Xx,Xy)))))). 137.77/20.59 tff(zf_stmt_0, negated_conjecture, 137.77/20.59 (~ 137.77/20.59 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 137.77/20.59 ((~ 137.77/20.59 (((![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 (((![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xy0,Xz))) & 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xy1,Xz0) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz0))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 137.77/20.59 (![Xx1:a,Xy1:a,Xz0:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 137.77/20.59 Xp1(Xx0,Xz))))) & 137.77/20.59 (![Xx0:a,Xy0:a]: 137.77/20.59 (((![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1))) & 137.77/20.59 (![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz)))) => 137.77/20.59 Xp1(Xx0,Xy0))) | 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 137.77/20.59 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx1:a,Xy1:a,Xz:a]: 137.77/20.59 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 137.77/20.59 (![Xx1:a,Xy1:a]: 137.77/20.59 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 137.77/20.59 Xp1(Xx0,Xy0)))))) => 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 137.77/20.59 (![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz)))) => 137.77/20.59 Xp1(Xx,Xy))))) | 137.77/20.59 (![Xp1:((a * a) > $o)]: 137.77/20.59 (((![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 137.77/20.59 (![Xx0:a,Xy0:a,Xz:a]: 137.77/20.59 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 137.77/20.59 Xp1(Xx,Xy))))))). 137.77/20.59 tff('0', plain, 137.77/20.59 ~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((~((((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (((!!((^[Y7 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (( 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y10 : a]: 137.77/20.59 (( 137.77/20.59 Y7(Y8, 137.77/20.59 Y9) & 137.77/20.59 Y7(Y9, 137.77/20.59 Y10)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y10))))))))))) & 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y0(Y8, 137.77/20.59 Y9) | 137.77/20.59 Y1(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y9))))))))) => 137.77/20.59 Y7(Y5, 137.77/20.59 Y6))))) & 137.77/20.59 (!!((^[Y7 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (( 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y10 : a]: 137.77/20.59 (( 137.77/20.59 Y7(Y9, 137.77/20.59 Y10) & 137.77/20.59 Y7(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y10))))))))))) & 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y0(Y8, 137.77/20.59 Y9) | 137.77/20.59 Y1(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y9))))))))) => 137.77/20.59 Y7(Y4, 137.77/20.59 Y5)))))) => 137.77/20.59 (!!((^[Y7 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (( 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y0(Y8, 137.77/20.59 Y9) | 137.77/20.59 Y1(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y9)))))))) & 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y10 : a]: 137.77/20.59 (( 137.77/20.59 Y7(Y8, 137.77/20.59 Y9) & 137.77/20.59 Y7(Y9, 137.77/20.59 Y10)) => 137.77/20.59 Y7(Y8, 137.77/20.59 Y10)))))))))))) => 137.77/20.59 Y7(Y4, 137.77/20.59 Y6))))))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (((!!((^[Y6 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (Y0(Y7, 137.77/20.59 Y8) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8)))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y6(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9)))))))))))) => 137.77/20.59 Y6(Y4, Y5))))) | 137.77/20.59 (!!((^[Y6 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y6(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9))))))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (Y1(Y7, 137.77/20.59 Y8) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8))))))))) => 137.77/20.59 Y6(Y4, Y5)))))) => 137.77/20.59 (!!((^[Y6 : (a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y6(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9))))))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y0(Y7, 137.77/20.59 Y8) | 137.77/20.59 Y1(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8))))))))) => 137.77/20.59 Y6(Y4, Y5))))))))))))) => 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y0(Y5, Y6) | 137.77/20.59 Y1(Y5, Y6)) => 137.77/20.59 Y4(Y5, Y6)))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!((^[Y7 : a]: 137.77/20.59 (( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7)))))))))))) => 137.77/20.59 Y4(Y2, Y3)))))))) | 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y1(Y5, Y6) | 137.77/20.59 Y0(Y5, Y6)) => 137.77/20.59 Y4(Y5, Y6)))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!((^[Y7 : a]: 137.77/20.59 ((Y4(Y6, Y7) & 137.77/20.59 Y4(Y5, Y6)) => 137.77/20.59 Y4(Y5, Y7)))))))))))) => 137.77/20.59 Y4(Y2, Y3)))))))))))))))))), 137.77/20.59 inference('cnf', [status(esa)], [zf_stmt_0])). 137.77/20.59 tff('1', plain, 137.77/20.59 ~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((~((((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (((!!((^[Y6 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y6(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9))))))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 '#sk1'( 137.77/20.59 Y7, Y8) | 137.77/20.59 Y0(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8))))))))) => 137.77/20.59 Y6(Y4, Y5))))) & 137.77/20.59 (!!((^[Y6 : ( 137.77/20.59 a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y8, 137.77/20.59 Y9) & 137.77/20.59 Y6(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9))))))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 '#sk1'( 137.77/20.59 Y7, Y8) | 137.77/20.59 Y0(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8))))))))) => 137.77/20.59 Y6(Y3, Y4)))))) => 137.77/20.59 (!!((^[Y6 : (a * a) > $o]: 137.77/20.59 (((!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 '#sk1'( 137.77/20.59 Y7, Y8) | 137.77/20.59 Y0(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y8)))))))) & 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y9 : a]: 137.77/20.59 (( 137.77/20.59 Y6(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y6(Y8, 137.77/20.59 Y9)) => 137.77/20.59 Y6(Y7, 137.77/20.59 Y9)))))))))))) => 137.77/20.59 Y6(Y3, Y5))))))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (((!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 '#sk1'( 137.77/20.59 Y6, Y7) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7)))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y5(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8)))))))))))) => 137.77/20.59 Y5(Y3, Y4))))) | 137.77/20.59 (!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y5(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8))))))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 Y0(Y6, 137.77/20.59 Y7) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7))))))))) => 137.77/20.59 Y5(Y3, Y4)))))) => 137.77/20.59 (!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y5(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8))))))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (( 137.77/20.59 '#sk1'( 137.77/20.59 Y6, Y7) | 137.77/20.59 Y0(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7))))))))) => 137.77/20.59 Y5(Y3, Y4))))))))))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 Y0(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y1, Y2)))))))) | 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y0(Y4, Y5) | 137.77/20.59 '#sk1'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y5, Y6) & 137.77/20.59 Y3(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y1, Y2))))))))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['0'])). 137.77/20.59 tff('2', plain, 137.77/20.59 ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 ((~((((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (((!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y5(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8))))))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 '#sk1'( 137.77/20.59 Y6, Y7) | 137.77/20.59 '#sk2'( 137.77/20.59 Y6, Y7)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7))))))))) => 137.77/20.59 Y5(Y3, Y4))))) & 137.77/20.59 (!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 !!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y7, 137.77/20.59 Y8) & 137.77/20.59 Y5(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8))))))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 '#sk1'( 137.77/20.59 Y6, Y7) | 137.77/20.59 '#sk2'( 137.77/20.59 Y6, Y7)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7))))))))) => 137.77/20.59 Y5(Y2, Y3)))))) => 137.77/20.59 (!!((^[Y5 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (( 137.77/20.59 '#sk1'( 137.77/20.59 Y6, Y7) | 137.77/20.59 '#sk2'( 137.77/20.59 Y6, Y7)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y7)))))))) & 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y8 : a]: 137.77/20.59 (( 137.77/20.59 Y5(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y5(Y7, 137.77/20.59 Y8)) => 137.77/20.59 Y5(Y6, 137.77/20.59 Y8)))))))))))) => 137.77/20.59 Y5(Y2, Y4))))))))))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (((!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ('#sk1'(Y5, 137.77/20.59 Y6) => 137.77/20.59 Y4(Y5, Y6)))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7)))))))))))) => 137.77/20.59 Y4(Y2, Y3))))) | 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7))))))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ('#sk2'(Y5, 137.77/20.59 Y6) => 137.77/20.59 Y4(Y5, Y6))))))))) => 137.77/20.59 Y4(Y2, Y3)))))) => 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7))))))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (('#sk1'(Y5, 137.77/20.59 Y6) | 137.77/20.59 '#sk2'(Y5, 137.77/20.59 Y6)) => 137.77/20.59 Y4(Y5, Y6))))))))) => 137.77/20.59 Y4(Y2, Y3))))))))))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk2'(Y3, Y4) | '#sk1'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y4, Y5) & Y2(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['1'])). 137.77/20.59 tff('3', plain, 137.77/20.59 ~ (!!((^[Y0 : a]: 137.77/20.59 ((~((((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (((!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7))))))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (('#sk1'( 137.77/20.59 Y5, Y6) | 137.77/20.59 '#sk2'( 137.77/20.59 Y5, Y6)) => 137.77/20.59 Y4(Y5, Y6))))))))) => 137.77/20.59 Y4(Y2, Y3))))) & 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 ( 137.77/20.59 ( 137.77/20.59 Y4(Y6, 137.77/20.59 Y7) & 137.77/20.59 Y4(Y5, 137.77/20.59 Y6)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7))))))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (('#sk1'( 137.77/20.59 Y5, Y6) | 137.77/20.59 '#sk2'( 137.77/20.59 Y5, Y6)) => 137.77/20.59 Y4(Y5, Y6))))))))) => 137.77/20.59 Y4(Y1, Y2)))))) => 137.77/20.59 (!!((^[Y4 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (('#sk1'(Y5, 137.77/20.59 Y6) | 137.77/20.59 '#sk2'(Y5, 137.77/20.59 Y6)) => 137.77/20.59 Y4(Y5, Y6)))))))) & 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 (!!(( 137.77/20.59 ^[Y7 : a]: 137.77/20.59 (( 137.77/20.59 Y4(Y5, 137.77/20.59 Y6) & 137.77/20.59 Y4(Y6, 137.77/20.59 Y7)) => 137.77/20.59 Y4(Y5, 137.77/20.59 Y7)))))))))))) => 137.77/20.59 Y4(Y1, Y3))))))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (((!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ('#sk1'(Y4, Y5) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y1, Y2))))) | 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ('#sk2'(Y4, Y5) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2)))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2))))))))))))) => 137.77/20.59 (!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y3)))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.59 Y1(Y2, Y4)))))))))))) => 137.77/20.59 Y1('#sk3', Y0)))))))) | 137.77/20.59 (!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y3)))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ((Y1(Y3, Y4) & Y1(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y4)))))))))))) => 137.77/20.59 Y1('#sk3', Y0))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['2'])). 137.77/20.59 tff('4', plain, 137.77/20.59 ~ ((~((((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (((!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2))))) & 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y5, Y6) & 137.77/20.59 Y3(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y0, Y2))))))))))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => 137.77/20.59 Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))) => 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))))) | 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['3'])). 137.77/20.59 tff('5', plain, 137.77/20.59 (((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (((!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2))))) & 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y5, Y6) & 137.77/20.59 Y3(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y0, Y2))))))))))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))) => 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_or', [status(thm)], ['4'])). 137.77/20.59 tff('6', plain, 137.77/20.59 (~ ((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (((!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2))))) & 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y5, Y6) & 137.77/20.59 Y3(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y0, Y2))))))))))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['5'])). 137.77/20.59 tff('7', plain, 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (((!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y1, Y2))))) & 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y5, Y6) & 137.77/20.59 Y3(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y6))))))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5))))))))) => 137.77/20.59 Y3(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y3 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (('#sk1'(Y4, Y5) | 137.77/20.59 '#sk2'(Y4, Y5)) => 137.77/20.59 Y3(Y4, Y5)))))))) & 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 (!!((^[Y6 : a]: 137.77/20.59 ((Y3(Y4, Y5) & 137.77/20.59 Y3(Y5, Y6)) => 137.77/20.59 Y3(Y4, Y6)))))))))))) => 137.77/20.59 Y3(Y0, Y2))))))))))))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['6'])). 137.77/20.59 tff('8', plain, 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))) & 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y4, Y5) & 137.77/20.59 Y2(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2('#sk6', Y0)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2('#sk6', Y1)))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4'))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['7'])). 137.77/20.59 tff('9', plain, 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (((!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.59 Y1(Y2, Y4))))))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y3))))))))) => 137.77/20.59 Y1('#sk7', Y0))))) & 137.77/20.59 (!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ((Y1(Y3, Y4) & Y1(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y4))))))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y3))))))))) => 137.77/20.59 Y1('#sk6', '#sk7')))))) => 137.77/20.59 (!!((^[Y1 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 137.77/20.59 Y1(Y2, Y3)))))))) & 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.59 Y1(Y2, Y4)))))))))))) => 137.77/20.59 Y1('#sk6', Y0))))))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['8'])). 137.77/20.59 tff('10', plain, 137.77/20.59 (~ (((!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2))))))))) => 137.77/20.59 Y0('#sk7', '#sk8'))))) & 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y3))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2))))))))) => 137.77/20.59 Y0('#sk6', '#sk7')))))) => 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk6', '#sk8')))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4'))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['9'])). 137.77/20.59 tff('11', plain, 137.77/20.59 ( ((!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2))))))))) => 137.77/20.59 Y0('#sk7', '#sk8'))))) & 137.77/20.59 (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2))))))))) => 137.77/20.59 Y0('#sk6', '#sk7')))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['10'])). 137.77/20.59 tff('12', plain, 137.77/20.59 ( (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 137.77/20.59 Y0('#sk7', '#sk8'))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4'))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1))))))))))))), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['11'])). 137.77/20.59 tff('13', plain, 137.77/20.59 (~ '#form10' 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 define([status(thm)])). 137.77/20.59 tff('14', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( (((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 137.77/20.59 X1('#sk3', '#sk4')) 137.77/20.59 | ~ '#form10'), 137.77/20.59 inference('lazy_cnf_forall', [status(thm)], ['13'])). 137.77/20.59 tff('15', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ ((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10'), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['14'])). 137.77/20.59 tff('16', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['15'])). 137.77/20.59 tff('17', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (('#sk1'('#sk63'(X1), Y0) | '#sk2'('#sk63'(X1), Y0)) => 137.77/20.59 X1('#sk63'(X1), Y0))))) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['16'])). 137.77/20.59 tff('18', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (('#sk1'('#sk63'(X1), '#sk94'(X1)) | 137.77/20.59 '#sk2'('#sk63'(X1), '#sk94'(X1))) => 137.77/20.59 X1('#sk63'(X1), '#sk94'(X1))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['17'])). 137.77/20.59 tff('19', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( ('#sk1'('#sk63'(X1), '#sk94'(X1)) | '#sk2'('#sk63'(X1), '#sk94'(X1))) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['18'])). 137.77/20.59 tff('20', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( '#sk1'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_or', [status(thm)], ['19'])). 137.77/20.59 tff('21', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 ((X1('#sk103'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.59 X1('#sk103'(X1), Y1)))))))) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['20'])). 137.77/20.59 tff('22', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), Y0)) => 137.77/20.59 X1('#sk103'(X1), Y0))))) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['21'])). 137.77/20.59 tff('23', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) => 137.77/20.59 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1))), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['22'])). 137.77/20.59 tff('24', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['23'])). 137.77/20.59 tff('25', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( (X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['23'])). 137.77/20.59 tff('26', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( X1('#sk151'(X1), '#sk274'(X1)) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1))), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['25'])). 137.77/20.59 tff('27', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( X1('#sk103'(X1), '#sk151'(X1)) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | '#sk1'('#sk63'(X1), '#sk94'(X1))), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['25'])). 137.77/20.59 tff('28', plain, 137.77/20.59 ~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4'))))), 137.77/20.59 inference('lazy_cnf_or', [status(thm)], ['4'])). 137.77/20.59 tff('29', plain, 137.77/20.59 ~ (((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk5'(Y1, Y2) & '#sk5'(Y0, Y1)) => 137.77/20.59 '#sk5'(Y0, Y2)))))))))))) => 137.77/20.59 '#sk5'('#sk3', '#sk4')), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['28'])). 137.77/20.59 tff('30', plain, 137.77/20.59 ((!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))) & 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk5'(Y1, Y2) & '#sk5'(Y0, Y1)) => 137.77/20.59 '#sk5'(Y0, Y2)))))))))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['29'])). 137.77/20.59 tff('31', plain, 137.77/20.59 (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['30'])). 137.77/20.59 tff('32', plain, 137.77/20.59 ![X1 : a]: 137.77/20.59 (!!((^[Y0 : a]: (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk5'(X1, Y0))))), 137.77/20.59 inference('lazy_cnf_forall', [status(thm)], ['31'])). 137.77/20.59 tff('33', plain, 137.77/20.59 ![X1 : a, X2 : a]: (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk5'(X1, X2)), 137.77/20.59 inference('lazy_cnf_forall', [status(thm)], ['32'])). 137.77/20.59 tff('34', plain, 137.77/20.59 ![X1 : a, X2 : a]: 137.77/20.59 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk5'(X1, X2)), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['33'])). 137.77/20.59 tff('35', plain, ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X1, X2)), 137.77/20.59 inference('lazy_cnf_or', [status(thm)], ['34'])). 137.77/20.59 tff('36', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ X1('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['18'])). 137.77/20.59 tff('37', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( '#form197'(X1) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 define([status(thm)])). 137.77/20.59 tff('38', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 ((X1('#sk103'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.59 X1('#sk103'(X1), Y1)))))))) 137.77/20.59 | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['37'])). 137.77/20.59 tff('39', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ (!!((^[Y0 : a]: 137.77/20.59 ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), Y0)) => 137.77/20.59 X1('#sk103'(X1), Y0))))) 137.77/20.59 | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['38'])). 137.77/20.59 tff('40', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) => 137.77/20.59 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.59 | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_exists', [status(thm)], ['39'])). 137.77/20.59 tff('41', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ X1('#sk103'(X1), '#sk274'(X1)) | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['40'])). 137.77/20.59 tff('42', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( (X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) 137.77/20.59 | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['40'])). 137.77/20.59 tff('43', plain, 137.77/20.59 ![X1 : (a * a) > $o]: ( X1('#sk151'(X1), '#sk274'(X1)) | '#form197'(X1)), 137.77/20.59 inference('lazy_cnf_and', [status(thm)], ['42'])). 137.77/20.59 tff('44', plain, ~ '#sk5'('#sk3', '#sk4'), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['29'])). 137.77/20.59 tff('45', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X1, X2)), 137.77/20.59 inference('lazy_cnf_or', [status(thm)], ['34'])). 137.77/20.59 tff('46', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ X1('#sk63'(X1), '#sk94'(X1)) 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ '#form10' 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['18'])). 137.77/20.59 tff('47', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 ( '#form197'(X1) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.59 define([status(thm)])). 137.77/20.59 tff('48', plain, 137.77/20.59 ![X1 : (a * a) > $o]: 137.77/20.59 (~ '#form197'(X1) 137.77/20.59 | ~ '#form10' 137.77/20.59 | X1('#sk3', '#sk4') 137.77/20.59 | ~ X1('#sk63'(X1), '#sk94'(X1))), 137.77/20.59 inference('renaming', [status(thm)], ['46', '47'])). 137.77/20.59 tff('49', plain, 137.77/20.59 (~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk6', '#sk8'))))) 137.77/20.59 | ~ (!!((^[Y0 : a]: 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5)))))))))))) => 137.77/20.59 Y2(Y0, Y1))))) | 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))) => 137.77/20.59 (!!((^[Y2 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (!!((^[Y5 : a]: 137.77/20.59 ((Y2(Y3, Y4) & 137.77/20.59 Y2(Y4, Y5)) => 137.77/20.59 Y2(Y3, Y5))))))))))) & 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 (!!((^[Y4 : a]: 137.77/20.59 (('#sk1'(Y3, Y4) | 137.77/20.59 '#sk2'(Y3, Y4)) => 137.77/20.59 Y2(Y3, Y4))))))))) => 137.77/20.59 Y2(Y0, Y1)))))))))))) 137.77/20.59 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.59 Y0(Y1, Y3)))))))))))) => 137.77/20.59 Y0('#sk3', '#sk4')))))), 137.77/20.59 inference('lazy_cnf_imply', [status(thm)], ['10'])). 137.77/20.59 tff('50', plain, 137.77/20.59 (~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.59 (((!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.59 Y0(Y1, Y2)))))))) & 137.77/20.59 (!!((^[Y1 : a]: 137.77/20.59 (!!((^[Y2 : a]: 137.77/20.59 (!!((^[Y3 : a]: 137.77/20.59 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk6', '#sk8'))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))))))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4')))))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['10'])). 137.77/20.60 tff('51', plain, 137.77/20.60 ( '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('52', plain, 137.77/20.60 (~ '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4'))))) 137.77/20.60 | ~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk6', '#sk8')))))), 137.77/20.60 inference('renaming', [status(thm)], ['49', '51'])). 137.77/20.60 tff('53', plain, 137.77/20.60 (~ '#form10' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('54', plain, 137.77/20.60 ( '#form10' 137.77/20.60 | ~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk6', '#sk8'))))) 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('renaming', [status(thm)], ['52', '53'])). 137.77/20.60 tff('55', plain, 137.77/20.60 (~ (((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk12'(Y0, Y1)))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk12'(Y0, Y1) & '#sk12'(Y1, Y2)) => 137.77/20.60 '#sk12'(Y0, Y2)))))))))))) => 137.77/20.60 '#sk12'('#sk6', '#sk8')) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['54'])). 137.77/20.60 tff('56', plain, (~ '#sk12'('#sk6', '#sk8') | '#form10' | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['55'])). 137.77/20.60 tff('57', plain, 137.77/20.60 ![X1 : (a * a) > $o]: ( X1('#sk103'(X1), '#sk151'(X1)) | '#form197'(X1)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['42'])). 137.77/20.60 tff('58', plain, 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk5'(Y1, Y2) & '#sk5'(Y0, Y1)) => 137.77/20.60 '#sk5'(Y0, Y2))))))))))), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['30'])). 137.77/20.60 tff('59', plain, 137.77/20.60 ![X1 : a]: 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk5'(Y0, Y1) & '#sk5'(X1, Y0)) => '#sk5'(X1, Y1)))))))), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['58'])). 137.77/20.60 tff('60', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 (!!((^[Y0 : a]: (('#sk5'(X2, Y0) & '#sk5'(X1, X2)) => '#sk5'(X1, Y0))))), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['59'])). 137.77/20.60 tff('61', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (('#sk5'(X2, X3) & '#sk5'(X1, X2)) => '#sk5'(X1, X3)), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['60'])). 137.77/20.60 tff('62', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ ('#sk5'(X2, X3) & '#sk5'(X1, X2)) | '#sk5'(X1, X3)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['61'])). 137.77/20.60 tff('63', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ '#sk5'(X2, X3) | ~ '#sk5'(X1, X2) | '#sk5'(X1, X3)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['62'])). 137.77/20.60 tff('64', plain, 137.77/20.60 ( (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk6', '#sk7'))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4'))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['11'])). 137.77/20.60 tff('65', plain, 137.77/20.60 (~ '#form10' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('66', plain, 137.77/20.60 ( '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))))))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk6', '#sk7')))))), 137.77/20.60 inference('renaming', [status(thm)], ['64', '65'])). 137.77/20.60 tff('67', plain, 137.77/20.60 ( '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('68', plain, 137.77/20.60 (~ '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk6', '#sk7'))))) 137.77/20.60 | '#form10'), 137.77/20.60 inference('renaming', [status(thm)], ['66', '67'])). 137.77/20.60 tff('69', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) => 137.77/20.60 X1('#sk6', '#sk7')) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['68'])). 137.77/20.60 tff('70', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['69'])). 137.77/20.60 tff('71', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['70'])). 137.77/20.60 tff('72', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1('#sk103'(X1), Y0)) => 137.77/20.60 X1('#sk103'(X1), Y1)))))))) 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['71'])). 137.77/20.60 tff('73', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk151'(X1), Y0) & X1('#sk103'(X1), '#sk151'(X1))) => 137.77/20.60 X1('#sk103'(X1), Y0))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7')), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['72'])). 137.77/20.60 tff('74', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk151'(X1), Y0) & X1('#sk103'(X1), '#sk151'(X1))) => 137.77/20.60 X1('#sk103'(X1), Y0))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7')), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['72'])). 137.77/20.60 tff('75', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form210'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('76', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form210'(X1) 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk151'(X1), Y0) & X1('#sk103'(X1), '#sk151'(X1))) => 137.77/20.60 X1('#sk103'(X1), Y0)))))), 137.77/20.60 inference('renaming', [status(thm)], ['73', '75'])). 137.77/20.60 tff('77', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((X1('#sk151'(X1), '#sk274'(X1)) & X1('#sk103'(X1), '#sk151'(X1))) => 137.77/20.60 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['76'])). 137.77/20.60 tff('78', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.60 | ~ '#form210'(X1) 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['77'])). 137.77/20.60 tff('79', plain, 137.77/20.60 ( (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk7', '#sk8'))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4'))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['11'])). 137.77/20.60 tff('80', plain, 137.77/20.60 (~ '#form10' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk3', '#sk4')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('81', plain, 137.77/20.60 ( '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))))))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk7', '#sk8')))))), 137.77/20.60 inference('renaming', [status(thm)], ['79', '80'])). 137.77/20.60 tff('82', plain, 137.77/20.60 ( '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('83', plain, 137.77/20.60 (~ '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk7', '#sk8'))))) 137.77/20.60 | '#form10'), 137.77/20.60 inference('renaming', [status(thm)], ['81', '82'])). 137.77/20.60 tff('84', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) => 137.77/20.60 X1('#sk7', '#sk8')) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['83'])). 137.77/20.60 tff('85', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))) 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['84'])). 137.77/20.60 tff('86', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['85'])). 137.77/20.60 tff('87', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 ((X1('#sk80'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.60 X1('#sk80'(X1), Y1)))))))) 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['86'])). 137.77/20.60 tff('88', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk80'(X1), '#sk122'(X1)) & X1('#sk122'(X1), Y0)) => 137.77/20.60 X1('#sk80'(X1), Y0))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8')), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['87'])). 137.77/20.60 tff('89', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((X1('#sk80'(X1), '#sk122'(X1)) & X1('#sk122'(X1), '#sk172'(X1))) => 137.77/20.60 X1('#sk80'(X1), '#sk172'(X1))) 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['88'])). 137.77/20.60 tff('90', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form210'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('91', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form210'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ ((X1('#sk80'(X1), '#sk122'(X1)) & X1('#sk122'(X1), '#sk172'(X1))) => 137.77/20.60 X1('#sk80'(X1), '#sk172'(X1)))), 137.77/20.60 inference('renaming', [status(thm)], ['89', '90'])). 137.77/20.60 tff('92', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form210'(X1) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ ((X1('#sk80'(X1), '#sk122'(X1)) & X1('#sk122'(X1), '#sk172'(X1))) => 137.77/20.60 X1('#sk80'(X1), '#sk172'(X1)))), 137.77/20.60 inference('ho_norm', [status(thm)], ['91'])). 137.77/20.60 tff('93', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk80'(X1), '#sk172'(X1)) 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['92'])). 137.77/20.60 tff('94', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (X1('#sk151'(X1), '#sk274'(X1)) & X1('#sk103'(X1), '#sk151'(X1))) 137.77/20.60 | ~ '#form210'(X1) 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['77'])). 137.77/20.60 tff('95', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk103'(X1), '#sk151'(X1)) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['94'])). 137.77/20.60 tff('96', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk151'(X1), '#sk274'(X1)) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk6', '#sk7') 137.77/20.60 | ~ '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['94'])). 137.77/20.60 tff('97', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (X1('#sk80'(X1), '#sk122'(X1)) & X1('#sk122'(X1), '#sk172'(X1))) 137.77/20.60 | X1('#sk7', '#sk8') 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['92'])). 137.77/20.60 tff('98', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk80'(X1), '#sk122'(X1)) 137.77/20.60 | ~ '#form210'(X1) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['97'])). 137.77/20.60 tff('99', plain, 137.77/20.60 ( ((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk12'(Y0, Y1)))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk12'(Y0, Y1) & '#sk12'(Y1, Y2)) => 137.77/20.60 '#sk12'(Y0, Y2)))))))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['55'])). 137.77/20.60 tff('100', plain, 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk12'(Y0, Y1) & '#sk12'(Y1, Y2)) => 137.77/20.60 '#sk12'(Y0, Y2))))))))))) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['99'])). 137.77/20.60 tff('101', plain, 137.77/20.60 ![X1 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk12'(X1, Y0) & '#sk12'(Y0, Y1)) => '#sk12'(X1, Y1)))))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['100'])). 137.77/20.60 tff('102', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (('#sk12'(X1, X2) & '#sk12'(X2, Y0)) => '#sk12'(X1, Y0))))) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['101'])). 137.77/20.60 tff('103', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 ( (('#sk12'(X1, X2) & '#sk12'(X2, X3)) => '#sk12'(X1, X3)) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['102'])). 137.77/20.60 tff('104', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ ('#sk12'(X1, X2) & '#sk12'(X2, X3)) 137.77/20.60 | '#sk12'(X1, X3) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['103'])). 137.77/20.60 tff('105', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ '#sk12'(X1, X2) 137.77/20.60 | ~ '#sk12'(X2, X3) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#sk12'(X1, X3)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['104'])). 137.77/20.60 tff('106', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form210'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('107', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (('#sk1'('#sk63'(X1), Y0) | '#sk2'('#sk63'(X1), Y0)) => 137.77/20.60 X1('#sk63'(X1), Y0))))) 137.77/20.60 | '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['106'])). 137.77/20.60 tff('108', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (('#sk1'('#sk63'(X1), '#sk94'(X1)) | 137.77/20.60 '#sk2'('#sk63'(X1), '#sk94'(X1))) => 137.77/20.60 X1('#sk63'(X1), '#sk94'(X1))) 137.77/20.60 | '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['107'])). 137.77/20.60 tff('109', plain, 137.77/20.60 ![X1 : (a * a) > $o]: (~ X1('#sk63'(X1), '#sk94'(X1)) | '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['108'])). 137.77/20.60 tff('110', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk122'(X1), '#sk172'(X1)) 137.77/20.60 | ~ '#form210'(X1) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9' 137.77/20.60 | X1('#sk7', '#sk8')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['97'])). 137.77/20.60 tff('111', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( ('#sk1'('#sk63'(X1), '#sk94'(X1)) | '#sk2'('#sk63'(X1), '#sk94'(X1))) 137.77/20.60 | '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['108'])). 137.77/20.60 tff('112', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#sk1'('#sk63'(X1), '#sk94'(X1)) 137.77/20.60 | '#sk2'('#sk63'(X1), '#sk94'(X1)) 137.77/20.60 | '#form210'(X1)), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['111'])). 137.77/20.60 tff('113', plain, 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk12'(Y0, Y1)))))))) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['99'])). 137.77/20.60 tff('114', plain, 137.77/20.60 ![X1 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk12'(X1, Y0))))) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['113'])). 137.77/20.60 tff('115', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk12'(X1, X2)) 137.77/20.60 | ~ '#form9' 137.77/20.60 | '#form10'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['114'])). 137.77/20.60 tff('116', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) 137.77/20.60 | '#sk12'(X1, X2) 137.77/20.60 | '#form10' 137.77/20.60 | ~ '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['115'])). 137.77/20.60 tff('117', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 (~ '#sk1'(X1, X2) | ~ '#form9' | '#form10' | '#sk12'(X1, X2)), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['116'])). 137.77/20.60 tff('118', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 (~ '#sk2'(X1, X2) | ~ '#form9' | '#form10' | '#sk12'(X1, X2)), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['116'])). 137.77/20.60 tff('119', plain, 137.77/20.60 ( '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (((!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk1'(Y3, Y4) => Y2(Y3, Y4)))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5)))))))))))) => 137.77/20.60 Y2(Y0, Y1))))) | 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1)))))) => 137.77/20.60 (!!((^[Y2 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (!!((^[Y5 : a]: 137.77/20.60 ((Y2(Y3, Y4) & 137.77/20.60 Y2(Y4, Y5)) => 137.77/20.60 Y2(Y3, Y5))))))))))) & 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 (('#sk1'(Y3, Y4) | 137.77/20.60 '#sk2'(Y3, Y4)) => 137.77/20.60 Y2(Y3, Y4))))))))) => 137.77/20.60 Y2(Y0, Y1))))))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('120', plain, 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (((!!((^[Y1 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ('#sk1'(Y2, Y3) => Y1(Y2, Y3)))))))) & 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.60 Y1(Y2, Y4)))))))))))) => 137.77/20.60 Y1('#sk11', Y0))))) | 137.77/20.60 (!!((^[Y1 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.60 Y1(Y2, Y4))))))))))) & 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 137.77/20.60 Y1('#sk11', Y0)))))) => 137.77/20.60 (!!((^[Y1 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (!!((^[Y4 : a]: 137.77/20.60 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 137.77/20.60 Y1(Y2, Y4))))))))))) & 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 137.77/20.60 Y1(Y2, Y3))))))))) => 137.77/20.60 Y1('#sk11', Y0))))))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['119'])). 137.77/20.60 tff('121', plain, 137.77/20.60 (~ (((!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) | 137.77/20.60 (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))) => 137.77/20.60 (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['120'])). 137.77/20.60 tff('122', plain, 137.77/20.60 ( ((!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) | 137.77/20.60 (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['121'])). 137.77/20.60 tff('123', plain, 137.77/20.60 ( (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2)))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['122'])). 137.77/20.60 tff('124', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 137.77/20.60 X1('#sk11', '#sk13')) 137.77/20.60 | '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['123'])). 137.77/20.60 tff('125', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['124'])). 137.77/20.60 tff('126', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['125'])). 137.77/20.60 tff('127', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: ('#sk1'('#sk219'(X1), Y0) => X1('#sk219'(X1), Y0))))) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['126'])). 137.77/20.60 tff('128', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ('#sk1'('#sk219'(X1), '#sk290'(X1)) => 137.77/20.60 X1('#sk219'(X1), '#sk290'(X1))) 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | '#form9' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['127'])). 137.77/20.60 tff('129', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['128'])). 137.77/20.60 tff('130', plain, 137.77/20.60 (~ '#form468' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('131', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) => 137.77/20.60 X1('#sk11', '#sk13')) 137.77/20.60 | ~ '#form468'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['130'])). 137.77/20.60 tff('132', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['131'])). 137.77/20.60 tff('133', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['132'])). 137.77/20.60 tff('134', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 ((X1('#sk103'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.60 X1('#sk103'(X1), Y1)))))))) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['133'])). 137.77/20.60 tff('135', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), Y0)) => 137.77/20.60 X1('#sk103'(X1), Y0))))) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['134'])). 137.77/20.60 tff('136', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) => 137.77/20.60 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['135'])). 137.77/20.60 tff('137', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['136'])). 137.77/20.60 tff('138', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['136'])). 137.77/20.60 tff('139', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form895'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('140', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form895'(X1) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468' 137.77/20.60 | ~ X1('#sk103'(X1), '#sk274'(X1))), 137.77/20.60 inference('renaming', [status(thm)], ['137', '139'])). 137.77/20.60 tff('141', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13')), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['136'])). 137.77/20.60 tff('142', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk103'(X1), '#sk151'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['141'])). 137.77/20.60 tff('143', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form895'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('144', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form895'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | X1('#sk103'(X1), '#sk151'(X1))), 137.77/20.60 inference('renaming', [status(thm)], ['142', '143'])). 137.77/20.60 tff('145', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form895'(X1) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | X1('#sk103'(X1), '#sk151'(X1))), 137.77/20.60 inference('ho_norm', [status(thm)], ['144'])). 137.77/20.60 tff('146', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form895'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('147', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: ('#sk2'('#sk918'(X1), Y0) => X1('#sk918'(X1), Y0))))) 137.77/20.60 | '#form895'(X1)), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['146'])). 137.77/20.60 tff('148', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ('#sk2'('#sk918'(X1), '#sk950'(X1)) => 137.77/20.60 X1('#sk918'(X1), '#sk950'(X1))) 137.77/20.60 | '#form895'(X1)), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['147'])). 137.77/20.60 tff('149', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk918'(X1), '#sk950'(X1)) | '#form895'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['148'])). 137.77/20.60 tff('150', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk151'(X1), '#sk274'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['141'])). 137.77/20.60 tff('151', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form895'(X1) 137.77/20.60 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('152', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form895'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | X1('#sk151'(X1), '#sk274'(X1))), 137.77/20.60 inference('renaming', [status(thm)], ['150', '151'])). 137.77/20.60 tff('153', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ '#form895'(X1) 137.77/20.60 | ~ '#form468' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | X1('#sk151'(X1), '#sk274'(X1))), 137.77/20.60 inference('ho_norm', [status(thm)], ['152'])). 137.77/20.60 tff('154', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#sk2'('#sk918'(X1), '#sk950'(X1)) | '#form895'(X1)), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['148'])). 137.77/20.60 tff('155', plain, 137.77/20.60 (~ (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 137.77/20.60 Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['121'])). 137.77/20.60 tff('156', plain, 137.77/20.60 (~ (((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk46'(Y0, Y1) & '#sk46'(Y1, Y2)) => 137.77/20.60 '#sk46'(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk46'(Y0, Y1))))))))) => 137.77/20.60 '#sk46'('#sk11', '#sk13')) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['155'])). 137.77/20.60 tff('157', plain, 137.77/20.60 ( ((!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk46'(Y0, Y1) & '#sk46'(Y1, Y2)) => 137.77/20.60 '#sk46'(Y0, Y2))))))))))) & 137.77/20.60 (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk46'(Y0, Y1))))))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['156'])). 137.77/20.60 tff('158', plain, 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk46'(Y0, Y1)))))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['157'])). 137.77/20.60 tff('159', plain, 137.77/20.60 ![X1 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk46'(X1, Y0))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['158'])). 137.77/20.60 tff('160', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk46'(X1, X2)) | '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['159'])). 137.77/20.60 tff('161', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk46'(X1, X2) | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['160'])). 137.77/20.60 tff('162', plain, 137.77/20.60 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form9' | '#sk46'(X1, X2)), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['161'])). 137.77/20.60 tff('163', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['128'])). 137.77/20.60 tff('164', plain, 137.77/20.60 (~ '#form468' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('165', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('renaming', [status(thm)], ['163', '164'])). 137.77/20.60 tff('166', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 ((X1('#sk103'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.60 X1('#sk103'(X1), Y1)))))))) 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['165'])). 137.77/20.60 tff('167', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), Y0)) => 137.77/20.60 X1('#sk103'(X1), Y0))))) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['166'])). 137.77/20.60 tff('168', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) => 137.77/20.60 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['167'])). 137.77/20.60 tff('169', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['168'])). 137.77/20.60 tff('170', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13'))))) 137.77/20.60 | '#form9' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['128'])). 137.77/20.60 tff('171', plain, 137.77/20.60 (~ '#form468' 137.77/20.60 | (!!((^[Y0 : (a * a) > $o]: 137.77/20.60 (((!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (!!((^[Y3 : a]: 137.77/20.60 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 137.77/20.60 Y0(Y1, Y3))))))))))) & 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 137.77/20.60 Y0('#sk11', '#sk13')))))), 137.77/20.60 define([status(thm)])). 137.77/20.60 tff('172', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( '#form468' 137.77/20.60 | ~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('renaming', [status(thm)], ['170', '171'])). 137.77/20.60 tff('173', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 ((X1('#sk103'(X1), Y0) & X1(Y0, Y1)) => 137.77/20.60 X1('#sk103'(X1), Y1)))))))) 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['172'])). 137.77/20.60 tff('174', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ (!!((^[Y0 : a]: 137.77/20.60 ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), Y0)) => 137.77/20.60 X1('#sk103'(X1), Y0))))) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['173'])). 137.77/20.60 tff('175', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ ((X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) => 137.77/20.60 X1('#sk103'(X1), '#sk274'(X1))) 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_exists', [status(thm)], ['174'])). 137.77/20.60 tff('176', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 (~ X1('#sk103'(X1), '#sk274'(X1)) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['175'])). 137.77/20.60 tff('177', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['168'])). 137.77/20.60 tff('178', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk103'(X1), '#sk151'(X1)) 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['177'])). 137.77/20.60 tff('179', plain, 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (!!((^[Y2 : a]: 137.77/20.60 (('#sk46'(Y0, Y1) & '#sk46'(Y1, Y2)) => 137.77/20.60 '#sk46'(Y0, Y2))))))))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['157'])). 137.77/20.60 tff('180', plain, 137.77/20.60 ![X1 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (!!((^[Y1 : a]: 137.77/20.60 (('#sk46'(X1, Y0) & '#sk46'(Y0, Y1)) => '#sk46'(X1, Y1)))))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['179'])). 137.77/20.60 tff('181', plain, 137.77/20.60 ![X1 : a, X2 : a]: 137.77/20.60 ( (!!((^[Y0 : a]: 137.77/20.60 (('#sk46'(X1, X2) & '#sk46'(X2, Y0)) => '#sk46'(X1, Y0))))) 137.77/20.60 | '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['180'])). 137.77/20.60 tff('182', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 ( (('#sk46'(X1, X2) & '#sk46'(X2, X3)) => '#sk46'(X1, X3)) | '#form9'), 137.77/20.60 inference('lazy_cnf_forall', [status(thm)], ['181'])). 137.77/20.60 tff('183', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ ('#sk46'(X1, X2) & '#sk46'(X2, X3)) | '#sk46'(X1, X3) | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['182'])). 137.77/20.60 tff('184', plain, 137.77/20.60 ![X1 : a, X2 : a, X3 : a]: 137.77/20.60 (~ '#sk46'(X1, X2) | ~ '#sk46'(X2, X3) | '#form9' | '#sk46'(X1, X3)), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['183'])). 137.77/20.60 tff('185', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( (X1('#sk103'(X1), '#sk151'(X1)) & X1('#sk151'(X1), '#sk274'(X1))) 137.77/20.60 | '#form468' 137.77/20.60 | '#form9' 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1))), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['175'])). 137.77/20.60 tff('186', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk103'(X1), '#sk151'(X1)) 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['185'])). 137.77/20.60 tff('187', plain, (~ '#sk46'('#sk11', '#sk13') | '#form9'), 137.77/20.60 inference('lazy_cnf_imply', [status(thm)], ['156'])). 137.77/20.60 tff('188', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk151'(X1), '#sk274'(X1)) 137.77/20.60 | ~ X1('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['177'])). 137.77/20.60 tff('189', plain, 137.77/20.60 ![X1 : (a * a) > $o]: 137.77/20.60 ( X1('#sk151'(X1), '#sk274'(X1)) 137.77/20.60 | '#sk1'('#sk219'(X1), '#sk290'(X1)) 137.77/20.60 | X1('#sk11', '#sk13') 137.77/20.60 | '#form9' 137.77/20.60 | '#form468'), 137.77/20.60 inference('lazy_cnf_and', [status(thm)], ['185'])). 137.77/20.60 tff('190', plain, 137.77/20.60 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form9' | '#sk46'(X1, X2)), 137.77/20.60 inference('lazy_cnf_or', [status(thm)], ['161'])). 137.77/20.60 tff('191', plain, $false, 137.77/20.60 inference('eprover', [status(thm)], 137.77/20.60 ['24', '26', '27', '35', '41', '43', '44', '45', '48', '56', 137.77/20.60 '57', '63', '78', '93', '95', '96', '98', '105', '109', 137.77/20.60 '110', '112', '117', '118', '140', '145', '149', '153', 137.77/20.60 '154', '162', '169', '176', '178', '184', '186', '187', 137.77/20.60 '188', '189', '190'])). 137.77/20.60 137.77/20.60 % SZS output end Refutation 137.77/20.60 137.77/20.60 137.77/20.60 % Terminating... 137.77/20.60 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 138.13/20.68 % Runner terminated. 138.13/20.69 % Zipperpin 1.5 exiting 138.13/20.71 EOF