0.14/0.14 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.14/0.15 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.wqzj1vDEd2 0.16/0.37 % Computer : n015.cluster.edu 0.16/0.37 % Model : x86_64 x86_64 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.37 % Memory : 8042.1875MB 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64 0.23/0.37 % CPULimit : 1200 0.23/0.37 % DateTime : Tue Jul 13 12:12:05 EDT 2021 0.23/0.37 % CPUTime : 0.23/0.37 % Running portfolio for 120 s 0.23/0.37 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.23/0.38 % Number of cores: 8 0.23/0.38 % Python version: Python 3.6.8 0.23/0.38 % Running in HO mode 0.56/0.67 % Estimated wc time : 1286 0.56/0.67 % Estimated cpu time (7 cpus) : 183.71428571428572 0.61/0.74 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.61/0.75 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.61/0.76 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.61/0.77 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.62/0.79 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.62/0.79 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.62/0.80 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 71.05/10.80 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.92/15.71 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.44/15.77 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 138.59/20.53 % Solved by lams/b.sh. 138.59/20.53 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.wqzj1vDEd2/e_input9e9bed --cpu-limit=12 --auto -s -p. 138.59/20.53 % done 107 iterations in 4.781s 138.59/20.53 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 138.59/20.53 % SZS output start Refutation 138.59/20.53 tff(cTHM250H_pme, conjecture, 138.59/20.53 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 138.59/20.53 (((~ 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 138.59/20.53 (![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 138.59/20.53 Xp1(Xx,Xy)))) & 138.59/20.53 (![Xx0:a,Xy0:a]: 138.59/20.53 (((![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 138.59/20.53 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xy0))) | 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 138.59/20.53 (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xy0)))) => 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xy1,Xz) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz)))) => 138.59/20.53 Xp1(Xx0,Xy0))))) & 138.59/20.53 (![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 (((![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 138.59/20.53 Xp1(Xx0,Xy0))) & 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xy1,Xz0) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz0)))) => 138.59/20.53 Xp1(Xy0,Xz)))) => 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 138.59/20.53 (![Xx1:a,Xy1:a]: ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xz)))))) | 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz))) & 138.59/20.53 (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0)))) => 138.59/20.53 Xp1(Xx,Xy)))))). 138.59/20.53 tff(zf_stmt_0, negated_conjecture, 138.59/20.53 (~ 138.59/20.53 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 138.59/20.53 (((~ 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx0:a,Xy0:a]: ((R(Xx0,Xy0) | S(Xx0,Xy0)) => Xp1(Xx0,Xy0))) & 138.59/20.53 (![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 ((Xp1(Xy0,Xz) & Xp1(Xx0,Xy0)) => Xp1(Xx0,Xz)))) => 138.59/20.53 Xp1(Xx,Xy)))) & 138.59/20.53 (![Xx0:a,Xy0:a]: 138.59/20.53 (((![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 138.59/20.53 (![Xx1:a,Xy1:a]: (S(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xy0))) | 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz)) => Xp1(Xx1,Xz))) & 138.59/20.53 (![Xx1:a,Xy1:a]: (R(Xx1,Xy1) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xy0)))) => 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: 138.59/20.53 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz:a]: 138.59/20.53 ((Xp1(Xy1,Xz) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz)))) => 138.59/20.53 Xp1(Xx0,Xy0))))) & 138.59/20.53 (![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 (((![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: 138.59/20.53 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0)))) => 138.59/20.53 Xp1(Xx0,Xy0))) & 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a]: 138.59/20.53 ((S(Xx1,Xy1) | R(Xx1,Xy1)) => Xp1(Xx1,Xy1))) & 138.59/20.53 (![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xy1,Xz0) & Xp1(Xx1,Xy1)) => Xp1(Xx1,Xz0)))) => 138.59/20.53 Xp1(Xy0,Xz)))) => 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx1:a,Xy1:a,Xz0:a]: 138.59/20.53 ((Xp1(Xx1,Xy1) & Xp1(Xy1,Xz0)) => Xp1(Xx1,Xz0))) & 138.59/20.53 (![Xx1:a,Xy1:a]: 138.59/20.53 ((R(Xx1,Xy1) | S(Xx1,Xy1)) => Xp1(Xx1,Xy1)))) => 138.59/20.53 Xp1(Xx0,Xz)))))) | 138.59/20.53 (![Xp1:((a * a) > $o)]: 138.59/20.53 (((![Xx0:a,Xy0:a,Xz:a]: 138.59/20.53 ((Xp1(Xx0,Xy0) & Xp1(Xy0,Xz)) => Xp1(Xx0,Xz))) & 138.59/20.53 (![Xx0:a,Xy0:a]: ((S(Xx0,Xy0) | R(Xx0,Xy0)) => Xp1(Xx0,Xy0)))) => 138.59/20.53 Xp1(Xx,Xy))))))). 138.59/20.53 tff('0', plain, 138.59/20.53 ~ (!!((^[Y0 : (a * a) > $o]: 138.59/20.53 (!!((^[Y1 : (a * a) > $o]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (((~((!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y0(Y5, Y6) | 138.59/20.53 Y1(Y5, Y6)) => 138.59/20.53 Y4(Y5, Y6)))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (( 138.59/20.53 Y4(Y6, 138.59/20.53 Y7) & 138.59/20.53 Y4(Y5, 138.59/20.53 Y6)) => 138.59/20.53 Y4(Y5, 138.59/20.53 Y7)))))))))))) => 138.59/20.53 Y4(Y2, Y3)))))))& 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (((!!((^[Y6 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y6(Y7, 138.59/20.53 Y8) & 138.59/20.53 Y6(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y9))))))))))) & 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (Y1(Y7, 138.59/20.53 Y8) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y8))))))))) => 138.59/20.53 Y6(Y4, Y5))))) | 138.59/20.53 (!!((^[Y6 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y6(Y7, 138.59/20.53 Y8) & 138.59/20.53 Y6(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y9))))))))))) & 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (Y0(Y7, 138.59/20.53 Y8) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y8))))))))) => 138.59/20.53 Y6(Y4, Y5)))))) => 138.59/20.53 (!!((^[Y6 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y7 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 138.59/20.53 Y0(Y7, 138.59/20.53 Y8) | 138.59/20.53 Y1(Y7, 138.59/20.53 Y8)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y8)))))))) & 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y6(Y8, 138.59/20.53 Y9) & 138.59/20.53 Y6(Y7, 138.59/20.53 Y8)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y9)))))))))))) => 138.59/20.53 Y6(Y4, Y5))))))))))))& 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (((!!((^[Y7 : ( 138.59/20.53 a * a) > $o]: 138.59/20.53 ((( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y1(Y8, 138.59/20.53 Y9) | 138.59/20.53 Y0(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y9)))))))) & 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y10 : a]: 138.59/20.53 (( 138.59/20.53 Y7(Y8, 138.59/20.53 Y9) & 138.59/20.53 Y7(Y9, 138.59/20.53 Y10)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y10)))))))))))) => 138.59/20.53 Y7(Y4, Y5))))) & 138.59/20.53 (!!((^[Y7 : ( 138.59/20.53 a * a) > $o]: 138.59/20.53 ((( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y1(Y8, 138.59/20.53 Y9) | 138.59/20.53 Y0(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y9)))))))) & 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y10 : a]: 138.59/20.53 (( 138.59/20.53 Y7(Y9, 138.59/20.53 Y10) & 138.59/20.53 Y7(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y10)))))))))))) => 138.59/20.53 Y7(Y5, Y6)))))) => 138.59/20.53 (!!((^[Y7 : ( 138.59/20.53 a * a) > $o]: 138.59/20.53 (((!!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y10 : a]: 138.59/20.53 (( 138.59/20.53 Y7(Y8, 138.59/20.53 Y9) & 138.59/20.53 Y7(Y9, 138.59/20.53 Y10)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y10))))))))))) & 138.59/20.53 (!!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y0(Y8, 138.59/20.53 Y9) | 138.59/20.53 Y1(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y7(Y8, 138.59/20.53 Y9))))))))) => 138.59/20.53 Y7(Y4, Y6)))))))))))))))) | 138.59/20.53 (!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ((Y4(Y5, Y6) & 138.59/20.53 Y4(Y6, Y7)) => 138.59/20.53 Y4(Y5, Y7))))))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y1(Y5, Y6) | 138.59/20.53 Y0(Y5, Y6)) => 138.59/20.53 Y4(Y5, Y6))))))))) => 138.59/20.53 Y4(Y2, Y3)))))))))))))))))), 138.59/20.53 inference('cnf', [status(esa)], [zf_stmt_0])). 138.59/20.53 tff('1', plain, 138.59/20.53 ~ (!!((^[Y0 : (a * a) > $o]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (((~((!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk1'(Y4, Y5) | 138.59/20.53 Y0(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5)))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y5, Y6) & 138.59/20.53 Y3(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y6)))))))))))) => 138.59/20.53 Y3(Y1, Y2)))))))& 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (((!!((^[Y5 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 138.59/20.53 Y5(Y6, 138.59/20.53 Y7) & 138.59/20.53 Y5(Y7, 138.59/20.53 Y8)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y8))))))))))) & 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 Y0(Y6, 138.59/20.53 Y7) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y7))))))))) => 138.59/20.53 Y5(Y3, Y4))))) | 138.59/20.53 (!!((^[Y5 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 138.59/20.53 Y5(Y6, 138.59/20.53 Y7) & 138.59/20.53 Y5(Y7, 138.59/20.53 Y8)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y8))))))))))) & 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 '#sk1'( 138.59/20.53 Y6, Y7) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y7))))))))) => 138.59/20.53 Y5(Y3, Y4)))))) => 138.59/20.53 (!!((^[Y5 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (( 138.59/20.53 '#sk1'( 138.59/20.53 Y6, Y7) | 138.59/20.53 Y0(Y6, 138.59/20.53 Y7)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y7)))))))) & 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 138.59/20.53 Y5(Y7, 138.59/20.53 Y8) & 138.59/20.53 Y5(Y6, 138.59/20.53 Y7)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y8)))))))))))) => 138.59/20.53 Y5(Y3, Y4))))))))))))& 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (((!!((^[Y6 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 138.59/20.53 Y0(Y7, 138.59/20.53 Y8) | 138.59/20.53 '#sk1'( 138.59/20.53 Y7, Y8)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y8)))))))) & 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (!!(( 138.59/20.53 ^[Y9 : a]: 138.59/20.53 (( 138.59/20.53 Y6(Y7, 138.59/20.53 Y8) & 138.59/20.53 Y6(Y8, 138.59/20.53 Y9)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y9)))))))))))) => 138.59/20.53 Y6(Y3, Y4))))) & 138.59/20.53 (!!((^[Y6 : (a * a) 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Y0(Y7, 138.59/20.53 Y8)) => 138.59/20.53 Y6(Y7, 138.59/20.53 Y8))))))))) => 138.59/20.53 Y6(Y3, Y5)))))))))))))))) | 138.59/20.53 (!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y4, Y5) & 138.59/20.53 Y3(Y5, Y6)) => 138.59/20.53 Y3(Y4, Y6))))))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y0(Y4, Y5) | 138.59/20.53 '#sk1'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5))))))))) => 138.59/20.53 Y3(Y1, Y2))))))))))))))), 138.59/20.53 inference('lazy_cnf_exists', [status(thm)], ['0'])). 138.59/20.53 tff('2', plain, 138.59/20.53 ~ (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (((~((!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (('#sk1'(Y3, Y4) | 138.59/20.53 '#sk2'(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y4)))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y4, Y5) & 138.59/20.53 Y2(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y5)))))))))))) => 138.59/20.53 Y2(Y0, Y1)))))))& 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (((!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 ( 138.59/20.53 Y4(Y5, 138.59/20.53 Y6) & 138.59/20.53 Y4(Y6, 138.59/20.53 Y7)) => 138.59/20.53 Y4(Y5, 138.59/20.53 Y7))))))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ('#sk2'(Y5, Y6) => 138.59/20.53 Y4(Y5, Y6))))))))) => 138.59/20.53 Y4(Y2, Y3))))) | 138.59/20.53 (!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 ( 138.59/20.53 Y4(Y5, 138.59/20.53 Y6) & 138.59/20.53 Y4(Y6, 138.59/20.53 Y7)) => 138.59/20.53 Y4(Y5, 138.59/20.53 Y7))))))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ('#sk1'(Y5, Y6) => 138.59/20.53 Y4(Y5, Y6))))))))) => 138.59/20.53 Y4(Y2, Y3)))))) => 138.59/20.53 (!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (('#sk1'(Y5, Y6) | 138.59/20.53 '#sk2'(Y5, Y6)) => 138.59/20.53 Y4(Y5, Y6)))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (( 138.59/20.53 Y4(Y6, 138.59/20.53 Y7) & 138.59/20.53 Y4(Y5, 138.59/20.53 Y6)) => 138.59/20.53 Y4(Y5, 138.59/20.53 Y7)))))))))))) => 138.59/20.53 Y4(Y2, Y3))))))))))))& 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (((!!((^[Y5 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 ( 138.59/20.53 '#sk2'( 138.59/20.53 Y6, Y7) | 138.59/20.53 '#sk1'( 138.59/20.53 Y6, Y7)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y7)))))))) & 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 !!(( 138.59/20.53 ^[Y8 : a]: 138.59/20.53 (( 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Y8))))))))))) & 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 (( 138.59/20.53 '#sk1'( 138.59/20.53 Y6, Y7) | 138.59/20.53 '#sk2'( 138.59/20.53 Y6, Y7)) => 138.59/20.53 Y5(Y6, 138.59/20.53 Y7))))))))) => 138.59/20.53 Y5(Y2, Y4)))))))))))))))) | 138.59/20.53 (!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (('#sk2'(Y3, Y4) | '#sk1'(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y4))))))))) => 138.59/20.53 Y2(Y0, Y1)))))))))))), 138.59/20.53 inference('lazy_cnf_exists', [status(thm)], ['1'])). 138.59/20.53 tff('3', plain, 138.59/20.53 ~ (!!((^[Y0 : a]: 138.59/20.53 (((~((!!((^[Y1 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 138.59/20.53 Y1(Y2, Y3)))))))) & 138.59/20.53 (!!((^[Y2 : a]: 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(!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk1'(Y4, Y5) | 138.59/20.53 '#sk2'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5)))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y5, Y6) & 138.59/20.53 Y3(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y6)))))))))))) => 138.59/20.53 Y3(Y1, Y2))))))))))))& 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (((!!((^[Y4 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (('#sk2'(Y5, Y6) | 138.59/20.53 '#sk1'(Y5, Y6)) => 138.59/20.53 Y4(Y5, Y6)))))))) & 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 (!!((^[Y7 : a]: 138.59/20.53 ( 138.59/20.53 ( 138.59/20.53 Y4(Y5, 138.59/20.53 Y6) & 138.59/20.53 Y4(Y6, 138.59/20.53 Y7)) => 138.59/20.53 Y4(Y5, 138.59/20.53 Y7)))))))))))) => 138.59/20.53 Y4(Y1, Y2))))) & 138.59/20.53 (!!((^[Y4 : (a * a) > 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(!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 138.59/20.53 Y1(Y2, Y4))))))))))) & 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 138.59/20.53 Y1(Y2, Y3))))))))) => 138.59/20.53 Y1('#sk3', Y0))))))))), 138.59/20.53 inference('lazy_cnf_exists', [status(thm)], ['2'])). 138.59/20.53 tff('4', plain, 138.59/20.53 ~ (((~((!!((^[Y0 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.53 Y0(Y1, Y2)))))))) & 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 138.59/20.53 Y0(Y1, Y3)))))))))))) => 138.59/20.53 Y0('#sk3', '#sk4')))))))& 138.59/20.53 (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & 138.59/20.53 Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.53 Y2(Y0, Y1))))) | 138.59/20.53 (!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & 138.59/20.53 Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.53 Y2(Y0, Y1)))))) => 138.59/20.53 (!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (('#sk1'(Y3, Y4) | 138.59/20.53 '#sk2'(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y4)))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y4, Y5) & 138.59/20.53 Y2(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y5)))))))))))) => 138.59/20.53 Y2(Y0, Y1))))))))))))& 138.59/20.53 (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk2'(Y4, Y5) | 138.59/20.53 '#sk1'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5)))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y4, Y5) & 138.59/20.53 Y3(Y5, Y6)) => 138.59/20.53 Y3(Y4, Y6)))))))))))) => 138.59/20.53 Y3(Y0, Y1))))) & 138.59/20.53 (!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk2'(Y4, Y5) | 138.59/20.53 '#sk1'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5)))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y5, Y6) & 138.59/20.53 Y3(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y6)))))))))))) => 138.59/20.53 Y3(Y1, Y2)))))) => 138.59/20.53 (!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y4, Y5) & 138.59/20.53 Y3(Y5, Y6)) => 138.59/20.53 Y3(Y4, Y6))))))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk1'(Y4, Y5) | 138.59/20.53 '#sk2'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5))))))))) => 138.59/20.53 Y3(Y0, Y2)))))))))))))))) | 138.59/20.53 (!!((^[Y0 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 138.59/20.53 Y0(Y1, Y2))))))))) => 138.59/20.53 Y0('#sk3', '#sk4')))))), 138.59/20.53 inference('lazy_cnf_exists', [status(thm)], ['3'])). 138.59/20.53 tff('5', plain, 138.59/20.53 ~ ((~((!!((^[Y0 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.53 Y0(Y1, Y2)))))))) & 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 138.59/20.53 Y0(Y1, Y3)))))))))))) => 138.59/20.53 Y0('#sk3', '#sk4')))))))& 138.59/20.53 (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & 138.59/20.53 Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.53 Y2(Y0, Y1))))) | 138.59/20.53 (!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & 138.59/20.53 Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.53 Y2(Y0, Y1)))))) => 138.59/20.53 (!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (('#sk1'(Y3, Y4) | 138.59/20.53 '#sk2'(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y4)))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y4, Y5) & Y2(Y3, Y4)) => 138.59/20.53 Y2(Y3, Y5)))))))))))) => 138.59/20.53 Y2(Y0, Y1))))))))))))& 138.59/20.53 (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (('#sk2'(Y4, Y5) | 138.59/20.53 '#sk1'(Y4, Y5)) => 138.59/20.53 Y3(Y4, Y5)))))))) & 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 (!!((^[Y6 : a]: 138.59/20.53 ((Y3(Y4, Y5) & 138.59/20.53 Y3(Y5, Y6)) => 138.59/20.53 Y3(Y4, Y6)))))))))))) => 138.59/20.53 Y3(Y0, Y1))))) & 138.59/20.53 (!!((^[Y3 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 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(!!((^[Y1 : a]: 138.59/20.53 (!!((^[Y2 : a]: 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 138.59/20.53 Y0('#sk3', '#sk4'))))) 138.59/20.53 | ~ (!!((^[Y0 : a]: 138.59/20.53 (!!((^[Y1 : a]: 138.59/20.53 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.53 (((!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 (!!((^[Y5 : a]: 138.59/20.53 ((Y2(Y3, Y4) & 138.59/20.53 Y2(Y4, Y5)) => 138.59/20.53 Y2(Y3, Y5))))))))))) & 138.59/20.53 (!!((^[Y3 : a]: 138.59/20.53 (!!((^[Y4 : a]: 138.59/20.53 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * 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a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) => 138.59/20.54 X1('#sk3', '#sk4')) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1))))))))))))), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['6'])). 138.59/20.54 tff('8', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2)))))))))))))))), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['7'])). 138.59/20.54 tff('9', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => X1(Y0, Y1)))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | X1('#sk3', '#sk4')), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['8'])). 138.59/20.54 tff('10', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (('#sk1'('#sk30'(X1), Y0) | '#sk2'('#sk30'(X1), Y0)) => 138.59/20.54 X1('#sk30'(X1), Y0))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['9'])). 138.59/20.54 tff('11', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (('#sk1'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk2'('#sk30'(X1), '#sk44'(X1))) => 138.59/20.54 X1('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | X1('#sk3', '#sk4')), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['10'])). 138.59/20.54 tff('12', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['11'])). 138.59/20.54 tff('13', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( ('#sk1'('#sk30'(X1), '#sk44'(X1)) | '#sk2'('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['11'])). 138.59/20.54 tff('14', plain, 138.59/20.54 ( '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('15', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1))), 138.59/20.54 inference('renaming', [status(thm)], ['12', '14'])). 138.59/20.54 tff('16', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( ('#sk1'('#sk30'(X1), '#sk44'(X1)) | '#sk2'('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['11'])). 138.59/20.54 tff('17', plain, 138.59/20.54 ( '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('18', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ('#sk1'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk2'('#sk30'(X1), '#sk44'(X1)))), 138.59/20.54 inference('renaming', [status(thm)], ['16', '17'])). 138.59/20.54 tff('19', plain, 138.59/20.54 ( '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2)))))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('20', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form102' 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ '#form77'), 138.59/20.54 inference('renaming', [status(thm)], ['15', '19'])). 138.59/20.54 tff('21', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1('#sk140'(X1), Y0)) => 138.59/20.54 X1('#sk140'(X1), Y1)))))))) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['20'])). 138.59/20.54 tff('22', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 ((X1('#sk168'(X1), Y0) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), Y0))))) 138.59/20.54 | ~ '#form102' 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['21'])). 138.59/20.54 tff('23', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), '#sk201'(X1))) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['22'])). 138.59/20.54 tff('24', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | ~ '#form102' 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['23'])). 138.59/20.54 tff('25', plain, 138.59/20.54 ~ (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk3', '#sk4'))))), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['4'])). 138.59/20.54 tff('26', plain, 138.59/20.54 ~ (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 138.59/20.54 '#sk5'(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1))))))))) => 138.59/20.54 '#sk5'('#sk3', '#sk4')), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['25'])). 138.59/20.54 tff('27', plain, 138.59/20.54 ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 138.59/20.54 '#sk5'(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1))))))))), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['26'])). 138.59/20.54 tff('28', plain, 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk5'(Y0, Y1) & '#sk5'(Y1, Y2)) => 138.59/20.54 '#sk5'(Y0, Y2))))))))))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['27'])). 138.59/20.54 tff('29', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk5'(X1, Y0) & '#sk5'(Y0, Y1)) => '#sk5'(X1, Y1)))))))), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['28'])). 138.59/20.54 tff('30', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 (!!((^[Y0 : a]: (('#sk5'(X1, X2) & '#sk5'(X2, Y0)) => '#sk5'(X1, Y0))))), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['29'])). 138.59/20.54 tff('31', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (('#sk5'(X1, X2) & '#sk5'(X2, X3)) => '#sk5'(X1, X3)), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['30'])). 138.59/20.54 tff('32', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ ('#sk5'(X1, X2) & '#sk5'(X2, X3)) | '#sk5'(X1, X3)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['31'])). 138.59/20.54 tff('33', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ '#sk5'(X1, X2) | ~ '#sk5'(X2, X3) | '#sk5'(X1, X3)), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['32'])). 138.59/20.54 tff('34', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2))))))))))))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ('#sk1'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk2'('#sk30'(X1), '#sk44'(X1)))), 138.59/20.54 inference('renaming', [status(thm)], ['16', '17'])). 138.59/20.54 tff('35', plain, 138.59/20.54 ( '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2)))))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('36', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form102' 138.59/20.54 | ('#sk1'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk2'('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ '#form77'), 138.59/20.54 inference('renaming', [status(thm)], ['34', '35'])). 138.59/20.54 tff('37', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['36'])). 138.59/20.54 tff('38', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1('#sk140'(X1), Y0)) => 138.59/20.54 X1('#sk140'(X1), Y1)))))))) 138.59/20.54 | ~ '#form102' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77' 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['37'])). 138.59/20.54 tff('39', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 ((X1('#sk168'(X1), Y0) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), Y0))))) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['38'])). 138.59/20.54 tff('40', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), '#sk201'(X1))) 138.59/20.54 | ~ '#form102' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77' 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['39'])). 138.59/20.54 tff('41', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['40'])). 138.59/20.54 tff('42', plain, ~ '#sk5'('#sk3', '#sk4'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['26'])). 138.59/20.54 tff('43', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) 138.59/20.54 | ~ '#form102' 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['23'])). 138.59/20.54 tff('44', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk140'(X1), '#sk168'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['43'])). 138.59/20.54 tff('45', plain, 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => '#sk5'(Y0, Y1)))))))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['27'])). 138.59/20.54 tff('46', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 (!!((^[Y0 : a]: (('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) => '#sk5'(X1, Y0))))), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['45'])). 138.59/20.54 tff('47', plain, 138.59/20.54 ![X1 : a, X2 : a]: (('#sk2'(X1, X2) | '#sk1'(X1, X2)) => '#sk5'(X1, X2)), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['46'])). 138.59/20.54 tff('48', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk5'(X1, X2)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['47'])). 138.59/20.54 tff('49', plain, ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['48'])). 138.59/20.54 tff('50', plain, ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['48'])). 138.59/20.54 tff('51', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['40'])). 138.59/20.54 tff('52', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk140'(X1), '#sk168'(X1)) 138.59/20.54 | ~ '#form102' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77' 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['51'])). 138.59/20.54 tff('53', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk168'(X1), '#sk201'(X1)) 138.59/20.54 | ~ '#form77' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['43'])). 138.59/20.54 tff('54', plain, 138.59/20.54 ( '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk2'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1))))) | 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ('#sk1'(Y3, Y4) => Y2(Y3, Y4))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('55', plain, 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (((!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 138.59/20.54 Y1(Y2, Y4))))))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ('#sk2'(Y2, Y3) => Y1(Y2, Y3))))))))) => 138.59/20.54 Y1('#sk103', Y0))))) | 138.59/20.54 (!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 138.59/20.54 Y1(Y2, Y4))))))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ('#sk1'(Y2, Y3) => Y1(Y2, Y3))))))))) => 138.59/20.54 Y1('#sk103', Y0)))))) => 138.59/20.54 (!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y3)))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y3, Y4) & Y1(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y4)))))))))))) => 138.59/20.54 Y1('#sk103', Y0))))))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['54'])). 138.59/20.54 tff('56', plain, 138.59/20.54 (~ (((!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) | 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))) => 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['55'])). 138.59/20.54 tff('57', plain, 138.59/20.54 ( ((!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) | 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['56'])). 138.59/20.54 tff('58', plain, 138.59/20.54 ( (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk2'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['57'])). 138.59/20.54 tff('59', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) => 138.59/20.54 X1('#sk103', '#sk129')) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['58'])). 138.59/20.54 tff('60', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['59'])). 138.59/20.54 tff('61', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['60'])). 138.59/20.54 tff('62', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 ((X1('#sk140'(X1), Y0) & X1(Y0, Y1)) => 138.59/20.54 X1('#sk140'(X1), Y1)))))))) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['61'])). 138.59/20.54 tff('63', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 ((X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), Y0)) => 138.59/20.54 X1('#sk140'(X1), Y0))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['62'])). 138.59/20.54 tff('64', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) => 138.59/20.54 X1('#sk140'(X1), '#sk201'(X1))) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['63'])). 138.59/20.54 tff('65', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['64'])). 138.59/20.54 tff('66', plain, 138.59/20.54 (~ '#form525' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('67', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1))))))))) => 138.59/20.54 X1('#sk103', '#sk129')) 138.59/20.54 | ~ '#form525'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['66'])). 138.59/20.54 tff('68', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1))))))))) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form525'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['67'])). 138.59/20.54 tff('69', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | ~ '#form525' 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['68'])). 138.59/20.54 tff('70', plain, 138.59/20.54 ( '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (((!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y0, Y1))))) & 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk2'(Y4, Y5) | 138.59/20.54 '#sk1'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5)))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y5, Y6) & 138.59/20.54 Y3(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y6)))))))))))) => 138.59/20.54 Y3(Y1, Y2)))))) => 138.59/20.54 (!!((^[Y3 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (!!((^[Y6 : a]: 138.59/20.54 ((Y3(Y4, Y5) & 138.59/20.54 Y3(Y5, Y6)) => 138.59/20.54 Y3(Y4, Y6))))))))))) & 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 (('#sk1'(Y4, Y5) | 138.59/20.54 '#sk2'(Y4, Y5)) => 138.59/20.54 Y3(Y4, Y5))))))))) => 138.59/20.54 Y3(Y0, Y2)))))))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('71', plain, 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (((!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk2'(Y3, Y4) | 138.59/20.54 '#sk1'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & 138.59/20.54 Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2('#sk128', Y0))))) & 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk2'(Y3, Y4) | 138.59/20.54 '#sk1'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4)))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y4, Y5) & 138.59/20.54 Y2(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y5)))))))))))) => 138.59/20.54 Y2(Y0, Y1)))))) => 138.59/20.54 (!!((^[Y2 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (!!((^[Y5 : a]: 138.59/20.54 ((Y2(Y3, Y4) & Y2(Y4, Y5)) => 138.59/20.54 Y2(Y3, Y5))))))))))) & 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 (('#sk1'(Y3, Y4) | 138.59/20.54 '#sk2'(Y3, Y4)) => 138.59/20.54 Y2(Y3, Y4))))))))) => 138.59/20.54 Y2('#sk128', Y1)))))))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['70'])). 138.59/20.54 tff('72', plain, 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (((!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y3)))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 138.59/20.54 Y1(Y2, Y4)))))))))))) => 138.59/20.54 Y1('#sk128', '#sk155'))))) & 138.59/20.54 (!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y3)))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y3, Y4) & Y1(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y4)))))))))))) => 138.59/20.54 Y1('#sk155', Y0)))))) => 138.59/20.54 (!!((^[Y1 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (!!((^[Y4 : a]: 138.59/20.54 ((Y1(Y2, Y3) & Y1(Y3, Y4)) => 138.59/20.54 Y1(Y2, Y4))))))))))) & 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 (('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) => 138.59/20.54 Y1(Y2, Y3))))))))) => 138.59/20.54 Y1('#sk128', Y0))))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['71'])). 138.59/20.54 tff('73', plain, 138.59/20.54 (~ (((!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk128', '#sk155'))))) & 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk155', '#sk185')))))) => 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk128', '#sk185')))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['72'])). 138.59/20.54 tff('74', plain, 138.59/20.54 ( ((!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk128', '#sk155'))))) & 138.59/20.54 (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk155', '#sk185')))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['73'])). 138.59/20.54 tff('75', plain, 138.59/20.54 ( (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk155', '#sk185'))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['74'])). 138.59/20.54 tff('76', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) => 138.59/20.54 X1('#sk155', '#sk185')) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['75'])). 138.59/20.54 tff('77', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))) 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['76'])). 138.59/20.54 tff('78', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2))))))))))) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk155', '#sk185')), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['77'])). 138.59/20.54 tff('79', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (('#sk2'('#sk30'(X1), Y0) | '#sk1'('#sk30'(X1), Y0)) => 138.59/20.54 X1('#sk30'(X1), Y0))))) 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['78'])). 138.59/20.54 tff('80', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form465'(X1) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('81', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form465'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form525' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1))))))))), 138.59/20.54 inference('renaming', [status(thm)], ['69', '80'])). 138.59/20.54 tff('82', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form465'(X1) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form525' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk1'(Y0, Y1) => X1(Y0, Y1))))))))), 138.59/20.54 inference('ho_norm', [status(thm)], ['81'])). 138.59/20.54 tff('83', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: ('#sk1'('#sk862'(X1), Y0) => X1('#sk862'(X1), Y0))))) 138.59/20.54 | ~ '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['82'])). 138.59/20.54 tff('84', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ('#sk1'('#sk862'(X1), '#sk870'(X1)) => 138.59/20.54 X1('#sk862'(X1), '#sk870'(X1))) 138.59/20.54 | ~ '#form465'(X1) 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form525'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['83'])). 138.59/20.54 tff('85', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk862'(X1), '#sk870'(X1)) 138.59/20.54 | ~ '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['84'])). 138.59/20.54 tff('86', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk168'(X1), '#sk201'(X1)) 138.59/20.54 | ~ '#form102' 138.59/20.54 | X1('#sk3', '#sk4') 138.59/20.54 | ~ '#form77' 138.59/20.54 | '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['51'])). 138.59/20.54 tff('87', plain, 138.59/20.54 (~ (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y2, Y3) & Y0(Y1, Y2)) => Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['56'])). 138.59/20.54 tff('88', plain, 138.59/20.54 (~ (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk186'(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk186'(Y1, Y2) & '#sk186'(Y0, Y1)) => 138.59/20.54 '#sk186'(Y0, Y2)))))))))))) => 138.59/20.54 '#sk186'('#sk103', '#sk129')) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['87'])). 138.59/20.54 tff('89', plain, 138.59/20.54 ( ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk186'(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk186'(Y1, Y2) & '#sk186'(Y0, Y1)) => 138.59/20.54 '#sk186'(Y0, Y2)))))))))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['88'])). 138.59/20.54 tff('90', plain, 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk186'(Y0, Y1)))))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['89'])). 138.59/20.54 tff('91', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk186'(X1, Y0))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['90'])). 138.59/20.54 tff('92', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk186'(X1, X2)) | '#form77'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['91'])). 138.59/20.54 tff('93', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk186'(X1, X2) | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['92'])). 138.59/20.54 tff('94', plain, 138.59/20.54 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form77' | '#sk186'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['93'])). 138.59/20.54 tff('95', plain, 138.59/20.54 (~ (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) => 138.59/20.54 Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk128', '#sk185'))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['73'])). 138.59/20.54 tff('96', plain, 138.59/20.54 (~ (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk256'(Y0, Y1) & '#sk256'(Y1, Y2)) => 138.59/20.54 '#sk256'(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk256'(Y0, Y1))))))))) => 138.59/20.54 '#sk256'('#sk128', '#sk185')) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['95'])). 138.59/20.54 tff('97', plain, (~ '#sk256'('#sk128', '#sk185') | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['96'])). 138.59/20.54 tff('98', plain, 138.59/20.54 ( (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) => Y0(Y1, Y2)))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => Y0(Y1, Y3)))))))))))) => 138.59/20.54 Y0('#sk128', '#sk155'))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['74'])). 138.59/20.54 tff('99', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) => 138.59/20.54 X1('#sk128', '#sk155')) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['98'])). 138.59/20.54 tff('100', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))) 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['99'])). 138.59/20.54 tff('101', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) => X1(Y0, Y1)))))))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk128', '#sk155')), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['100'])). 138.59/20.54 tff('102', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (('#sk2'('#sk30'(X1), Y0) | '#sk1'('#sk30'(X1), Y0)) => 138.59/20.54 X1('#sk30'(X1), Y0))))) 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['101'])). 138.59/20.54 tff('103', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (('#sk2'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk1'('#sk30'(X1), '#sk44'(X1))) => 138.59/20.54 X1('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1(Y1, Y2)) => X1(Y0, Y2))))))))))) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk128', '#sk155')), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['102'])). 138.59/20.54 tff('104', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form465'(X1) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('105', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form465'((^[Y0 : a,Y1 : a]: X1(Y0, Y1))) 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | '#form102' 138.59/20.54 | ~ (('#sk2'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk1'('#sk30'(X1), '#sk44'(X1))) => 138.59/20.54 X1('#sk30'(X1), '#sk44'(X1)))), 138.59/20.54 inference('renaming', [status(thm)], ['103', '104'])). 138.59/20.54 tff('106', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form465'(X1) 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | '#form102' 138.59/20.54 | ~ (('#sk2'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk1'('#sk30'(X1), '#sk44'(X1))) => 138.59/20.54 X1('#sk30'(X1), '#sk44'(X1)))), 138.59/20.54 inference('ho_norm', [status(thm)], ['105'])). 138.59/20.54 tff('107', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['106'])). 138.59/20.54 tff('108', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk1'('#sk862'(X1), '#sk870'(X1)) 138.59/20.54 | ~ '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['84'])). 138.59/20.54 tff('109', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (('#sk2'('#sk30'(X1), Y0) | '#sk1'('#sk30'(X1), Y0)) => 138.59/20.54 X1('#sk30'(X1), Y0))))) 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | '#form102' 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['78'])). 138.59/20.54 tff('110', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form465'(X1) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('111', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ '#form465'(X1) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (('#sk2'('#sk30'(X1), Y0) | '#sk1'('#sk30'(X1), Y0)) => 138.59/20.54 X1('#sk30'(X1), Y0)))))), 138.59/20.54 inference('renaming', [status(thm)], ['109', '110'])). 138.59/20.54 tff('112', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (('#sk2'('#sk30'(X1), '#sk44'(X1)) | 138.59/20.54 '#sk1'('#sk30'(X1), '#sk44'(X1))) => 138.59/20.54 X1('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | '#form102' 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['111'])). 138.59/20.54 tff('113', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form465'(X1) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk155', '#sk185')), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['112'])). 138.59/20.54 tff('114', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( ('#sk2'('#sk30'(X1), '#sk44'(X1)) | '#sk1'('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['106'])). 138.59/20.54 tff('115', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | ~ '#form465'(X1) 138.59/20.54 | X1('#sk128', '#sk155') 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['114'])). 138.59/20.54 tff('116', plain, 138.59/20.54 ( ((!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk256'(Y0, Y1) & '#sk256'(Y1, Y2)) => 138.59/20.54 '#sk256'(Y0, Y2))))))))))) & 138.59/20.54 (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk256'(Y0, Y1))))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['96'])). 138.59/20.54 tff('117', plain, 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) => '#sk256'(Y0, Y1)))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['116'])). 138.59/20.54 tff('118', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) => '#sk256'(X1, Y0))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['117'])). 138.59/20.54 tff('119', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 ( (('#sk1'(X1, X2) | '#sk2'(X1, X2)) => '#sk256'(X1, X2)) | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['118'])). 138.59/20.54 tff('120', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk256'(X1, X2) | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['119'])). 138.59/20.54 tff('121', plain, 138.59/20.54 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form102' | '#sk256'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['120'])). 138.59/20.54 tff('122', plain, 138.59/20.54 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form102' | '#sk256'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['120'])). 138.59/20.54 tff('123', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['64'])). 138.59/20.54 tff('124', plain, 138.59/20.54 (~ '#form525' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('125', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | ~ X1('#sk140'(X1), '#sk201'(X1))), 138.59/20.54 inference('renaming', [status(thm)], ['123', '124'])). 138.59/20.54 tff('126', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: ('#sk2'('#sk594'(X1), Y0) => X1('#sk594'(X1), Y0))))) 138.59/20.54 | ~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['125'])). 138.59/20.54 tff('127', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ('#sk2'('#sk594'(X1), '#sk658'(X1)) => 138.59/20.54 X1('#sk594'(X1), '#sk658'(X1))) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | ~ X1('#sk140'(X1), '#sk201'(X1))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['126'])). 138.59/20.54 tff('128', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk594'(X1), '#sk658'(X1)) 138.59/20.54 | ~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['127'])). 138.59/20.54 tff('129', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk2'('#sk594'(X1), '#sk658'(X1)) 138.59/20.54 | ~ X1('#sk140'(X1), '#sk201'(X1)) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['127'])). 138.59/20.54 tff('130', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( ('#sk2'('#sk30'(X1), '#sk44'(X1)) | '#sk1'('#sk30'(X1), '#sk44'(X1))) 138.59/20.54 | ~ '#form465'(X1) 138.59/20.54 | '#form102' 138.59/20.54 | X1('#sk155', '#sk185')), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['112'])). 138.59/20.54 tff('131', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk2'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | '#sk1'('#sk30'(X1), '#sk44'(X1)) 138.59/20.54 | X1('#sk155', '#sk185') 138.59/20.54 | '#form102' 138.59/20.54 | ~ '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['130'])). 138.59/20.54 tff('132', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form465'(X1) 138.59/20.54 | ~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 ((X1(Y1, Y2) & X1(Y0, Y1)) => X1(Y0, Y2)))))))))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('133', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 ((X1(Y0, Y1) & X1('#sk140'(X1), Y0)) => 138.59/20.54 X1('#sk140'(X1), Y1)))))))) 138.59/20.54 | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['132'])). 138.59/20.54 tff('134', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: 138.59/20.54 ((X1('#sk168'(X1), Y0) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), Y0))))) 138.59/20.54 | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['133'])). 138.59/20.54 tff('135', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ((X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) => 138.59/20.54 X1('#sk140'(X1), '#sk201'(X1))) 138.59/20.54 | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['134'])). 138.59/20.54 tff('136', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk140'(X1), '#sk201'(X1)) | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['135'])). 138.59/20.54 tff('137', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (X1('#sk168'(X1), '#sk201'(X1)) & X1('#sk140'(X1), '#sk168'(X1))) 138.59/20.54 | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['135'])). 138.59/20.54 tff('138', plain, 138.59/20.54 ![X1 : (a * a) > $o]: ( X1('#sk140'(X1), '#sk168'(X1)) | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['137'])). 138.59/20.54 tff('139', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | '#form77' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129'))))) 138.59/20.54 | X1('#sk103', '#sk129')), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['64'])). 138.59/20.54 tff('140', plain, 138.59/20.54 (~ '#form525' 138.59/20.54 | (!!((^[Y0 : (a * a) > $o]: 138.59/20.54 (((!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (!!((^[Y3 : a]: 138.59/20.54 ((Y0(Y1, Y2) & Y0(Y2, Y3)) => 138.59/20.54 Y0(Y1, Y3))))))))))) & 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: ('#sk1'(Y1, Y2) => Y0(Y1, Y2))))))))) => 138.59/20.54 Y0('#sk103', '#sk129')))))), 138.59/20.54 define([status(thm)])). 138.59/20.54 tff('141', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | ~ (!!((^[Y0 : a]: (!!((^[Y1 : a]: ('#sk2'(Y0, Y1) => X1(Y0, Y1)))))))) 138.59/20.54 | (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1)))), 138.59/20.54 inference('renaming', [status(thm)], ['139', '140'])). 138.59/20.54 tff('142', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ (!!((^[Y0 : a]: ('#sk2'('#sk594'(X1), Y0) => X1('#sk594'(X1), Y0))))) 138.59/20.54 | (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['141'])). 138.59/20.54 tff('143', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ ('#sk2'('#sk594'(X1), '#sk658'(X1)) => 138.59/20.54 X1('#sk594'(X1), '#sk658'(X1))) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1)))), 138.59/20.54 inference('lazy_cnf_exists', [status(thm)], ['142'])). 138.59/20.54 tff('144', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 (~ X1('#sk594'(X1), '#sk658'(X1)) 138.59/20.54 | (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['143'])). 138.59/20.54 tff('145', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk168'(X1), '#sk201'(X1)) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | ~ X1('#sk594'(X1), '#sk658'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['144'])). 138.59/20.54 tff('146', plain, 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk186'(Y1, Y2) & '#sk186'(Y0, Y1)) => 138.59/20.54 '#sk186'(Y0, Y2))))))))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['89'])). 138.59/20.54 tff('147', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk186'(Y0, Y1) & '#sk186'(X1, Y0)) => 138.59/20.54 '#sk186'(X1, Y1)))))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['146'])). 138.59/20.54 tff('148', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (('#sk186'(X2, Y0) & '#sk186'(X1, X2)) => '#sk186'(X1, Y0))))) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['147'])). 138.59/20.54 tff('149', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 ( (('#sk186'(X2, X3) & '#sk186'(X1, X2)) => '#sk186'(X1, X3)) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['148'])). 138.59/20.54 tff('150', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ ('#sk186'(X2, X3) & '#sk186'(X1, X2)) 138.59/20.54 | '#sk186'(X1, X3) 138.59/20.54 | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['149'])). 138.59/20.54 tff('151', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ '#sk186'(X2, X3) 138.59/20.54 | ~ '#sk186'(X1, X2) 138.59/20.54 | '#form77' 138.59/20.54 | '#sk186'(X1, X3)), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['150'])). 138.59/20.54 tff('152', plain, 138.59/20.54 ![X1 : (a * a) > $o]: ( X1('#sk168'(X1), '#sk201'(X1)) | '#form465'(X1)), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['137'])). 138.59/20.54 tff('153', plain, 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (!!((^[Y2 : a]: 138.59/20.54 (('#sk256'(Y0, Y1) & '#sk256'(Y1, Y2)) => 138.59/20.54 '#sk256'(Y0, Y2))))))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['116'])). 138.59/20.54 tff('154', plain, 138.59/20.54 ![X1 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (!!((^[Y1 : a]: 138.59/20.54 (('#sk256'(X1, Y0) & '#sk256'(Y0, Y1)) => 138.59/20.54 '#sk256'(X1, Y1)))))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['153'])). 138.59/20.54 tff('155', plain, 138.59/20.54 ![X1 : a, X2 : a]: 138.59/20.54 ( (!!((^[Y0 : a]: 138.59/20.54 (('#sk256'(X1, X2) & '#sk256'(X2, Y0)) => '#sk256'(X1, Y0))))) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['154'])). 138.59/20.54 tff('156', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 ( (('#sk256'(X1, X2) & '#sk256'(X2, X3)) => '#sk256'(X1, X3)) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_forall', [status(thm)], ['155'])). 138.59/20.54 tff('157', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ ('#sk256'(X1, X2) & '#sk256'(X2, X3)) 138.59/20.54 | '#sk256'(X1, X3) 138.59/20.54 | '#form102'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['156'])). 138.59/20.54 tff('158', plain, 138.59/20.54 ![X1 : a, X2 : a, X3 : a]: 138.59/20.54 (~ '#sk256'(X1, X2) 138.59/20.54 | ~ '#sk256'(X2, X3) 138.59/20.54 | '#form102' 138.59/20.54 | '#sk256'(X1, X3)), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['157'])). 138.59/20.54 tff('159', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( '#sk2'('#sk594'(X1), '#sk658'(X1)) 138.59/20.54 | (X1('#sk140'(X1), '#sk168'(X1)) & X1('#sk168'(X1), '#sk201'(X1))) 138.59/20.54 | '#form77' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form525'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['143'])). 138.59/20.54 tff('160', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk168'(X1), '#sk201'(X1)) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | '#sk2'('#sk594'(X1), '#sk658'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['159'])). 138.59/20.54 tff('161', plain, (~ '#sk186'('#sk103', '#sk129') | '#form77'), 138.59/20.54 inference('lazy_cnf_imply', [status(thm)], ['88'])). 138.59/20.54 tff('162', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk140'(X1), '#sk168'(X1)) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | ~ X1('#sk594'(X1), '#sk658'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['144'])). 138.59/20.54 tff('163', plain, 138.59/20.54 ![X1 : (a * a) > $o]: 138.59/20.54 ( X1('#sk140'(X1), '#sk168'(X1)) 138.59/20.54 | '#form525' 138.59/20.54 | X1('#sk103', '#sk129') 138.59/20.54 | '#form77' 138.59/20.54 | '#sk2'('#sk594'(X1), '#sk658'(X1))), 138.59/20.54 inference('lazy_cnf_and', [status(thm)], ['159'])). 138.59/20.54 tff('164', plain, 138.59/20.54 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form77' | '#sk186'(X1, X2)), 138.59/20.54 inference('lazy_cnf_or', [status(thm)], ['93'])). 138.59/20.54 tff('165', plain, $false, 138.59/20.54 inference('eprover', [status(thm)], 138.59/20.54 ['24', '33', '41', '42', '44', '49', '50', '52', '53', '85', 138.59/20.54 '86', '94', '97', '107', '108', '113', '115', '121', '122', 138.59/20.54 '128', '129', '131', '136', '138', '145', '151', '152', 138.59/20.54 '158', '160', '161', '162', '163', '164'])). 138.59/20.54 138.59/20.54 % SZS output end Refutation 138.59/20.54 138.59/20.54 138.59/20.54 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 138.59/20.54 % Terminating... 139.21/20.71 % Runner terminated. 139.22/20.72 % Zipperpin 1.5 exiting 139.22/20.74 EOF