0.11/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.11/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.dDa4hiXWjr 0.12/0.34 % Computer : n012.cluster.edu 0.12/0.34 % Model : x86_64 x86_64 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.12/0.34 % Memory : 8042.1875MB 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.12/0.34 % CPULimit : 1200 0.12/0.34 % DateTime : Tue Jul 13 12:08:31 EDT 2021 0.12/0.34 % CPUTime : 0.12/0.34 % Running portfolio for 120 s 0.12/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.12/0.34 % Number of cores: 8 0.12/0.35 % Python version: Python 3.6.8 0.12/0.35 % Running in HO mode 0.52/0.64 % Estimated wc time : 1286 0.52/0.64 % Estimated cpu time (7 cpus) : 183.71428571428572 0.54/0.69 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.54/0.71 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 69.52/10.53 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.57/15.55 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 105.60/15.73 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 139.04/20.56 % Solved by lams/b.sh. 139.04/20.56 % Running : timeout 14 /export/starexec/sandbox2/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox2/tmp/tmp.dDa4hiXWjr/e_inpute9b998 --cpu-limit=12 --auto -s -p. 139.04/20.56 % done 42 iterations in 4.928s 139.04/20.56 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 139.04/20.56 % SZS output start Refutation 139.04/20.56 tff(cTHM251G_pme, conjecture, 139.04/20.56 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 139.04/20.56 ((~ 139.04/20.56 (((![Xx0:a,Xy0:a,Xz:a]: 139.04/20.56 (((![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: ((S(Xy0,Xw) | R(Xy0,Xw)) => Xq(Xw)))) => 139.04/20.56 Xq(Xz))) & 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 139.04/20.56 Xq(Xy0)))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: 139.04/20.56 (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xz))))) & 139.04/20.56 (![Xx0:a,Xy0:a]: 139.04/20.56 (((![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: (S(Xx0,Xw) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: ((S(Xu,Xv) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy0))) | 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: ((Xq(Xu) & R(Xu,Xv)) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: (R(Xx0,Xw) => Xq(Xw)))) => 139.04/20.56 Xq(Xy0)))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw)))) => 139.04/20.56 Xq(Xy0)))))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy))))) | 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy)))))). 139.04/20.56 tff(zf_stmt_0, negated_conjecture, 139.04/20.56 (~ 139.04/20.56 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 139.04/20.56 ((~ 139.04/20.56 (((![Xx0:a,Xy0:a,Xz:a]: 139.04/20.56 (((![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: ((S(Xy0,Xw) | R(Xy0,Xw)) => Xq(Xw)))) => 139.04/20.56 Xq(Xz))) & 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 139.04/20.56 Xq(Xy0)))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: 139.04/20.56 (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xz))))) & 139.04/20.56 (![Xx0:a,Xy0:a]: 139.04/20.56 (((![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: (S(Xx0,Xw) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: ((S(Xu,Xv) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy0))) | 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: ((Xq(Xu) & R(Xu,Xv)) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: (R(Xx0,Xw) => Xq(Xw)))) => 139.04/20.56 Xq(Xy0)))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xu:a,Xv:a]: 139.04/20.56 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 139.04/20.56 (![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw)))) => 139.04/20.56 Xq(Xy0)))))) => 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy))))) | 139.04/20.56 (![Xq:((a > $o))]: 139.04/20.56 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 139.04/20.56 (![Xu:a,Xv:a]: (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 139.04/20.56 Xq(Xy))))))). 139.04/20.56 tff('0', plain, 139.04/20.56 ~ (!!((^[Y0 : (a * a) > $o]: 139.04/20.56 (!!((^[Y1 : (a * a) > $o]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((~((((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (((!!((^[Y7 : a > $o]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y9 : a]: 139.04/20.56 (( 139.04/20.56 Y7(Y8) & 139.04/20.56 ( 139.04/20.56 Y1(Y8, 139.04/20.56 Y9) | 139.04/20.56 Y0(Y8, 139.04/20.56 Y9))) => 139.04/20.56 Y7(Y9)))))))) & 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y1(Y5, 139.04/20.56 Y8) | 139.04/20.56 Y0(Y5, 139.04/20.56 Y8)) => 139.04/20.56 Y7(Y8)))))) => 139.04/20.56 Y7(Y6))))) & 139.04/20.56 (!!((^[Y7 : a > $o]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y1(Y4, 139.04/20.56 Y8) | 139.04/20.56 Y0(Y4, 139.04/20.56 Y8)) => 139.04/20.56 Y7(Y8))))) & 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y9 : a]: 139.04/20.56 (( 139.04/20.56 Y7(Y8) & 139.04/20.56 ( 139.04/20.56 Y0(Y8, 139.04/20.56 Y9) | 139.04/20.56 Y1(Y8, 139.04/20.56 Y9))) => 139.04/20.56 Y7(Y9))))))))) => 139.04/20.56 Y7(Y5)))))) => 139.04/20.56 (!!((^[Y7 : a > $o]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y1(Y4, 139.04/20.56 Y8) | 139.04/20.56 Y0(Y4, 139.04/20.56 Y8)) => 139.04/20.56 Y7(Y8))))) & 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y9 : a]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 Y1(Y8, 139.04/20.56 Y9) | 139.04/20.56 Y0(Y8, 139.04/20.56 Y9)) & 139.04/20.56 Y7(Y8)) => 139.04/20.56 Y7(Y9))))))))) => 139.04/20.56 Y7(Y6))))))))))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (((!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 Y1(Y4, 139.04/20.56 Y7) => 139.04/20.56 Y6(Y7))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y1(Y7, 139.04/20.56 Y8) & 139.04/20.56 Y6(Y7)) => 139.04/20.56 Y6(Y8))))))))) => 139.04/20.56 Y6(Y5))))) | 139.04/20.56 (!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y6(Y7) & 139.04/20.56 Y0(Y7, 139.04/20.56 Y8)) => 139.04/20.56 Y6(Y8)))))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 Y0(Y4, 139.04/20.56 Y7) => 139.04/20.56 Y6(Y7)))))) => 139.04/20.56 Y6(Y5)))))) => 139.04/20.56 (!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y6(Y7) & 139.04/20.56 ( 139.04/20.56 Y1(Y7, 139.04/20.56 Y8) | 139.04/20.56 Y0(Y7, 139.04/20.56 Y8))) => 139.04/20.56 Y6(Y8)))))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (( 139.04/20.56 Y0(Y4, 139.04/20.56 Y7) | 139.04/20.56 Y1(Y4, 139.04/20.56 Y7)) => 139.04/20.56 Y6(Y7)))))) => 139.04/20.56 Y6(Y5))))))))))))) => 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 ((Y1(Y2, Y5) | 139.04/20.56 Y0(Y2, Y5)) => 139.04/20.56 Y4(Y5))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (((Y1(Y5, Y6) | 139.04/20.56 Y0(Y5, Y6)) & 139.04/20.56 Y4(Y5)) => 139.04/20.56 Y4(Y6))))))))) => 139.04/20.56 Y4(Y3)))))))) | 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 ((Y1(Y2, Y5) | Y0(Y2, Y5)) => 139.04/20.56 Y4(Y5))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (((Y0(Y5, Y6) | 139.04/20.56 Y1(Y5, Y6)) & 139.04/20.56 Y4(Y5)) => 139.04/20.56 Y4(Y6))))))))) => 139.04/20.56 Y4(Y3)))))))))))))))))), 139.04/20.56 inference('cnf', [status(esa)], [zf_stmt_0])). 139.04/20.56 tff('1', plain, 139.04/20.56 ~ (!!((^[Y0 : (a * a) > $o]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((~((((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (((!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y6(Y7) & 139.04/20.56 ( 139.04/20.56 Y0(Y7, 139.04/20.56 Y8) | 139.04/20.56 '#sk1'( 139.04/20.56 Y7, Y8))) => 139.04/20.56 Y6(Y8)))))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y0(Y4, 139.04/20.56 Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y4, Y7)) => 139.04/20.56 Y6(Y7)))))) => 139.04/20.56 Y6(Y5))))) & 139.04/20.56 (!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y0(Y3, 139.04/20.56 Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y3, Y7)) => 139.04/20.56 Y6(Y7))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 !!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 Y6(Y7) & 139.04/20.56 ( 139.04/20.56 '#sk1'( 139.04/20.56 Y7, Y8) | 139.04/20.56 Y0(Y7, 139.04/20.56 Y8))) => 139.04/20.56 Y6(Y8))))))))) => 139.04/20.56 Y6(Y4)))))) => 139.04/20.56 (!!((^[Y6 : a > $o]: 139.04/20.56 (((!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (( 139.04/20.56 Y0(Y3, 139.04/20.56 Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y3, Y7)) => 139.04/20.56 Y6(Y7))))) & 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y8 : a]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 Y0(Y7, 139.04/20.56 Y8) | 139.04/20.56 '#sk1'( 139.04/20.56 Y7, Y8)) & 139.04/20.56 Y6(Y7)) => 139.04/20.56 Y6(Y8))))))))) => 139.04/20.56 Y6(Y5))))))))))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (((!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (Y0(Y3, Y6) => 139.04/20.56 Y5(Y6))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y0(Y6, 139.04/20.56 Y7) & 139.04/20.56 Y5(Y6)) => 139.04/20.56 Y5(Y7))))))))) => 139.04/20.56 Y5(Y4))))) | 139.04/20.56 (!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y5(Y6) & 139.04/20.56 '#sk1'( 139.04/20.56 Y6, Y7)) => 139.04/20.56 Y5(Y7)))))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ('#sk1'(Y3, 139.04/20.56 Y6) => 139.04/20.56 Y5(Y6)))))) => 139.04/20.56 Y5(Y4)))))) => 139.04/20.56 (!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (( 139.04/20.56 Y5(Y6) & 139.04/20.56 ( 139.04/20.56 Y0(Y6, 139.04/20.56 Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y6, Y7))) => 139.04/20.56 Y5(Y7)))))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (('#sk1'(Y3, 139.04/20.56 Y6) | 139.04/20.56 Y0(Y3, Y6)) => 139.04/20.56 Y5(Y6)))))) => 139.04/20.56 Y5(Y4))))))))))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 ((Y0(Y1, Y4) | '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (((Y0(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2)))))))) | 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 ((Y0(Y1, Y4) | '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((('#sk1'(Y4, Y5) | 139.04/20.56 Y0(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))))))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['0'])). 139.04/20.56 tff('2', plain, 139.04/20.56 ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((~((((!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (((!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y5(Y6) & 139.04/20.56 ( 139.04/20.56 '#sk2'( 139.04/20.56 Y6, Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y6, Y7))) => 139.04/20.56 Y5(Y7)))))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (('#sk2'( 139.04/20.56 Y3, Y6) | 139.04/20.56 '#sk1'( 139.04/20.56 Y3, Y6)) => 139.04/20.56 Y5(Y6)))))) => 139.04/20.56 Y5(Y4))))) & 139.04/20.56 (!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (('#sk2'( 139.04/20.56 Y2, Y6) | 139.04/20.56 '#sk1'( 139.04/20.56 Y2, Y6)) => 139.04/20.56 Y5(Y6))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 ( 139.04/20.56 ( 139.04/20.56 Y5(Y6) & 139.04/20.56 ( 139.04/20.56 '#sk1'( 139.04/20.56 Y6, Y7) | 139.04/20.56 '#sk2'( 139.04/20.56 Y6, Y7))) => 139.04/20.56 Y5(Y7))))))))) => 139.04/20.56 Y5(Y3)))))) => 139.04/20.56 (!!((^[Y5 : a > $o]: 139.04/20.56 (((!!((^[Y6 : a]: 139.04/20.56 (('#sk2'(Y2, 139.04/20.56 Y6) | 139.04/20.56 '#sk1'(Y2, 139.04/20.56 Y6)) => 139.04/20.56 Y5(Y6))))) & 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (!!(( 139.04/20.56 ^[Y7 : a]: 139.04/20.56 (( 139.04/20.56 ( 139.04/20.56 '#sk2'( 139.04/20.56 Y6, Y7) | 139.04/20.56 '#sk1'( 139.04/20.56 Y6, Y7)) & 139.04/20.56 Y5(Y6)) => 139.04/20.56 Y5(Y7))))))))) => 139.04/20.56 Y5(Y4))))))))))))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (((!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 ('#sk2'(Y2, Y5) => 139.04/20.56 Y4(Y5))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 (('#sk2'( 139.04/20.56 Y5, Y6) & 139.04/20.56 Y4(Y5)) => 139.04/20.56 Y4(Y6))))))))) => 139.04/20.56 Y4(Y3))))) | 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ((Y4(Y5) & 139.04/20.56 '#sk1'( 139.04/20.56 Y5, Y6)) => 139.04/20.56 Y4(Y6)))))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ('#sk1'(Y2, Y5) => 139.04/20.56 Y4(Y5)))))) => 139.04/20.56 Y4(Y3)))))) => 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ((Y4(Y5) & 139.04/20.56 ('#sk2'( 139.04/20.56 Y5, Y6) | 139.04/20.56 '#sk1'( 139.04/20.56 Y5, Y6))) => 139.04/20.56 Y4(Y6)))))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (('#sk1'(Y2, Y5) | 139.04/20.56 '#sk2'(Y2, Y5)) => 139.04/20.56 Y4(Y5)))))) => 139.04/20.56 Y4(Y3))))))))))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 139.04/20.56 Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4)) & 139.04/20.56 Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1)))))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 139.04/20.56 Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((('#sk1'(Y3, Y4) | 139.04/20.56 '#sk2'(Y3, Y4)) & 139.04/20.56 Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1)))))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['1'])). 139.04/20.56 tff('3', plain, 139.04/20.56 ~ (!!((^[Y0 : a]: 139.04/20.56 ((~((((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (((!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ((Y4(Y5) & 139.04/20.56 ('#sk2'( 139.04/20.56 Y5, Y6) | 139.04/20.56 '#sk1'( 139.04/20.56 Y5, Y6))) => 139.04/20.56 Y4(Y6)))))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (('#sk2'(Y2, Y5) | 139.04/20.56 '#sk1'(Y2, Y5)) => 139.04/20.56 Y4(Y5)))))) => 139.04/20.56 Y4(Y3))))) & 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 (('#sk2'(Y1, Y5) | 139.04/20.56 '#sk1'(Y1, Y5)) => 139.04/20.56 Y4(Y5))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ((Y4(Y5) & 139.04/20.56 ('#sk1'( 139.04/20.56 Y5, Y6) | 139.04/20.56 '#sk2'( 139.04/20.56 Y5, Y6))) => 139.04/20.56 Y4(Y6))))))))) => 139.04/20.56 Y4(Y2)))))) => 139.04/20.56 (!!((^[Y4 : a > $o]: 139.04/20.56 (((!!((^[Y5 : a]: 139.04/20.56 (('#sk2'(Y1, Y5) | 139.04/20.56 '#sk1'(Y1, Y5)) => 139.04/20.56 Y4(Y5))))) & 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (!!((^[Y6 : a]: 139.04/20.56 ((('#sk2'( 139.04/20.56 Y5, Y6) | 139.04/20.56 '#sk1'( 139.04/20.56 Y5, Y6)) & 139.04/20.56 Y4(Y5)) => 139.04/20.56 Y4(Y6))))))))) => 139.04/20.56 Y4(Y3))))))))))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (((!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 ('#sk2'(Y1, Y4) => Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 (('#sk2'(Y4, Y5) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))) | 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 '#sk1'(Y4, Y5)) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ('#sk1'(Y1, Y4) => Y3(Y4)))))) => 139.04/20.56 Y3(Y2)))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5))) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk1'(Y1, Y4) | 139.04/20.56 '#sk2'(Y1, Y4)) => 139.04/20.56 Y3(Y4)))))) => 139.04/20.56 Y3(Y2))))))))))))) => 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (('#sk2'('#sk3', Y2) | '#sk1'('#sk3', Y2)) => 139.04/20.56 Y1(Y2))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) & 139.04/20.56 Y1(Y2)) => 139.04/20.56 Y1(Y3))))))))) => 139.04/20.56 Y1(Y0)))))))) | 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (('#sk2'('#sk3', Y2) | '#sk1'('#sk3', Y2)) => 139.04/20.56 Y1(Y2))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) & 139.04/20.56 Y1(Y2)) => 139.04/20.56 Y1(Y3))))))))) => 139.04/20.56 Y1(Y0))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['2'])). 139.04/20.56 tff('4', plain, 139.04/20.56 ~ ((~((((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (((!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5))) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y1, Y4) | 139.04/20.56 '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4)))))) => 139.04/20.56 Y3(Y2))))) & 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk1'(Y4, Y5) | 139.04/20.56 '#sk2'(Y4, Y5))) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y1)))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))))))))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))) => 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 139.04/20.56 Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 139.04/20.56 Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))))) | 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['3'])). 139.04/20.56 tff('5', plain, 139.04/20.56 (((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (((!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5))) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y1, Y4) | 139.04/20.56 '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4)))))) => 139.04/20.56 Y3(Y2))))) & 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk1'(Y4, Y5) | 139.04/20.56 '#sk2'(Y4, Y5))) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y1)))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))))))))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))) => 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['4'])). 139.04/20.56 tff('6', plain, 139.04/20.56 (~ ((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (((!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5))) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y1, Y4) | 139.04/20.56 '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4)))))) => 139.04/20.56 Y3(Y2))))) & 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk1'(Y4, Y5) | 139.04/20.56 '#sk2'(Y4, Y5))) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y1)))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))))))))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['5'])). 139.04/20.56 tff('7', plain, 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (((!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5))) => 139.04/20.56 Y3(Y5)))))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y1, Y4) | 139.04/20.56 '#sk1'(Y1, Y4)) => 139.04/20.56 Y3(Y4)))))) => 139.04/20.56 Y3(Y2))))) & 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((Y3(Y4) & 139.04/20.56 ('#sk1'(Y4, Y5) | 139.04/20.56 '#sk2'(Y4, Y5))) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y1)))))) => 139.04/20.56 (!!((^[Y3 : a > $o]: 139.04/20.56 (((!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y0, Y4) | 139.04/20.56 '#sk1'(Y0, Y4)) => 139.04/20.56 Y3(Y4))))) & 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (!!((^[Y5 : a]: 139.04/20.56 ((('#sk2'(Y4, Y5) | 139.04/20.56 '#sk1'(Y4, Y5)) & 139.04/20.56 Y3(Y4)) => 139.04/20.56 Y3(Y5))))))))) => 139.04/20.56 Y3(Y2))))))))))))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['6'])). 139.04/20.56 tff('8', plain, 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))) & 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (('#sk2'('#sk6', Y3) | 139.04/20.56 '#sk1'('#sk6', Y3)) => 139.04/20.56 Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk1'(Y3, Y4) | 139.04/20.56 '#sk2'(Y3, Y4))) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y0)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (('#sk2'('#sk6', Y3) | 139.04/20.56 '#sk1'('#sk6', Y3)) => 139.04/20.56 Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4)) & 139.04/20.56 Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['7'])). 139.04/20.56 tff('9', plain, 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (((!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((Y1(Y2) & 139.04/20.56 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 139.04/20.56 Y1(Y3)))))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (('#sk2'('#sk7', Y2) | '#sk1'('#sk7', Y2)) => 139.04/20.56 Y1(Y2)))))) => 139.04/20.56 Y1(Y0))))) & 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (('#sk2'('#sk6', Y2) | '#sk1'('#sk6', Y2)) => 139.04/20.56 Y1(Y2))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((Y1(Y2) & 139.04/20.56 ('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3))) => 139.04/20.56 Y1(Y3))))))))) => 139.04/20.56 Y1('#sk7')))))) => 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (('#sk2'('#sk6', Y2) | '#sk1'('#sk6', Y2)) => 139.04/20.56 Y1(Y2))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) & 139.04/20.56 Y1(Y2)) => 139.04/20.56 Y1(Y3))))))))) => 139.04/20.56 Y1(Y0))))))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['8'])). 139.04/20.56 tff('10', plain, 139.04/20.56 (~ (((!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8'))))) & 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk7')))))) => 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk8')))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['9'])). 139.04/20.56 tff('11', plain, 139.04/20.56 ( ((!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8'))))) & 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk7')))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['10'])). 139.04/20.56 tff('12', plain, 139.04/20.56 ( (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['11'])). 139.04/20.56 tff('13', plain, 139.04/20.56 (~ '#form10' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('14', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1))))))))) => 139.04/20.56 X1('#sk4')) 139.04/20.56 | ~ '#form10'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['13'])). 139.04/20.56 tff('15', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1))))))))) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['14'])). 139.04/20.56 tff('16', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => X1(Y0))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['15'])). 139.04/20.56 tff('17', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk3', '#sk33'(X1)) | '#sk1'('#sk3', '#sk33'(X1))) => 139.04/20.56 X1('#sk33'(X1))) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['16'])). 139.04/20.56 tff('18', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk3', '#sk33'(X1)) | '#sk1'('#sk3', '#sk33'(X1))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['17'])). 139.04/20.56 tff('19', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1))))))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['18'])). 139.04/20.56 tff('20', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((('#sk2'('#sk40'(X1), Y0) | '#sk1'('#sk40'(X1), Y0)) & 139.04/20.56 X1('#sk40'(X1))) => 139.04/20.56 X1(Y0))))) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4') 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['19'])). 139.04/20.56 tff('21', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((('#sk2'('#sk40'(X1), '#sk58'(X1)) | 139.04/20.56 '#sk1'('#sk40'(X1), '#sk58'(X1))) & 139.04/20.56 X1('#sk40'(X1))) => 139.04/20.56 X1('#sk58'(X1))) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['20'])). 139.04/20.56 tff('22', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk58'(X1)) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4') 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['21'])). 139.04/20.56 tff('23', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1))) & 139.04/20.56 X1('#sk40'(X1))) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4') 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['21'])). 139.04/20.56 tff('24', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk40'(X1)) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['23'])). 139.04/20.56 tff('25', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1))) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['23'])). 139.04/20.56 tff('26', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4') 139.04/20.56 | '#sk1'('#sk3', '#sk33'(X1)) 139.04/20.56 | '#sk2'('#sk3', '#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['25'])). 139.04/20.56 tff('27', plain, 139.04/20.56 ~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['4'])). 139.04/20.56 tff('28', plain, 139.04/20.56 ~ (((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk5'(Y0)) => 139.04/20.56 '#sk5'(Y1))))))))) => 139.04/20.56 '#sk5'('#sk4')), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['27'])). 139.04/20.56 tff('29', plain, 139.04/20.56 ((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk5'(Y0)) => 139.04/20.56 '#sk5'(Y1))))))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['28'])). 139.04/20.56 tff('30', plain, 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['29'])). 139.04/20.56 tff('31', plain, 139.04/20.56 ![X1 : a]: (('#sk2'('#sk3', X1) | '#sk1'('#sk3', X1)) => '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['30'])). 139.04/20.56 tff('32', plain, 139.04/20.56 ![X1 : a]: (~ ('#sk2'('#sk3', X1) | '#sk1'('#sk3', X1)) | '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['31'])). 139.04/20.56 tff('33', plain, ![X1 : a]: (~ '#sk2'('#sk3', X1) | '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['32'])). 139.04/20.56 tff('34', plain, ![X1 : a]: (~ '#sk1'('#sk3', X1) | '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['32'])). 139.04/20.56 tff('35', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk33'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['17'])). 139.04/20.56 tff('36', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((('#sk2'('#sk40'(X1), Y0) | '#sk1'('#sk40'(X1), Y0)) & 139.04/20.56 X1('#sk40'(X1))) => 139.04/20.56 X1(Y0))))) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10' 139.04/20.56 | ~ X1('#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['35'])). 139.04/20.56 tff('37', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((('#sk2'('#sk40'(X1), '#sk58'(X1)) | 139.04/20.56 '#sk1'('#sk40'(X1), '#sk58'(X1))) & 139.04/20.56 X1('#sk40'(X1))) => 139.04/20.56 X1('#sk58'(X1))) 139.04/20.56 | ~ X1('#sk33'(X1)) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['36'])). 139.04/20.56 tff('38', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk58'(X1)) | X1('#sk4') | ~ '#form10' | ~ X1('#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['37'])). 139.04/20.56 tff('39', plain, ~ '#sk5'('#sk4'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['28'])). 139.04/20.56 tff('40', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1))) & 139.04/20.56 X1('#sk40'(X1))) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10' 139.04/20.56 | ~ X1('#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['37'])). 139.04/20.56 tff('41', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk40'(X1)) | ~ X1('#sk33'(X1)) | ~ '#form10' | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['40'])). 139.04/20.56 tff('42', plain, 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk5'(Y0)) => 139.04/20.56 '#sk5'(Y1)))))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['29'])). 139.04/20.56 tff('43', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 ((('#sk1'(X1, Y0) | '#sk2'(X1, Y0)) & '#sk5'(X1)) => '#sk5'(Y0))))), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['42'])). 139.04/20.56 tff('44', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 ((('#sk1'(X1, X2) | '#sk2'(X1, X2)) & '#sk5'(X1)) => '#sk5'(X2)), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['43'])). 139.04/20.56 tff('45', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ (('#sk1'(X1, X2) | '#sk2'(X1, X2)) & '#sk5'(X1)) | '#sk5'(X2)), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['44'])). 139.04/20.56 tff('46', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | ~ '#sk5'(X1) | '#sk5'(X2)), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['45'])). 139.04/20.56 tff('47', plain, 139.04/20.56 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['46'])). 139.04/20.56 tff('48', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1))) 139.04/20.56 | ~ X1('#sk33'(X1)) 139.04/20.56 | ~ '#form10' 139.04/20.56 | X1('#sk4')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['40'])). 139.04/20.56 tff('49', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | X1('#sk4') 139.04/20.56 | ~ '#form10' 139.04/20.56 | ~ X1('#sk33'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['48'])). 139.04/20.56 tff('50', plain, 139.04/20.56 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['46'])). 139.04/20.56 tff('51', plain, 139.04/20.56 (~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['10'])). 139.04/20.56 tff('52', plain, 139.04/20.56 ( '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('53', plain, 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (((!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: ('#sk2'('#sk11', Y2) => Y1(Y2))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk2'(Y2, Y3) & Y1(Y2)) => Y1(Y3))))))))) => 139.04/20.56 Y1(Y0))))) | 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((Y1(Y2) & '#sk1'(Y2, Y3)) => Y1(Y3)))))))) & 139.04/20.56 (!!((^[Y2 : a]: ('#sk1'('#sk11', Y2) => Y1(Y2)))))) => 139.04/20.56 Y1(Y0)))))) => 139.04/20.56 (!!((^[Y1 : a > $o]: 139.04/20.56 (((!!((^[Y2 : a]: 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 ((Y1(Y2) & 139.04/20.56 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 139.04/20.56 Y1(Y3)))))))) & 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (('#sk1'('#sk11', Y2) | '#sk2'('#sk11', Y2)) => 139.04/20.56 Y1(Y2)))))) => 139.04/20.56 Y1(Y0))))))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['52'])). 139.04/20.56 tff('54', plain, 139.04/20.56 (~ (((!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: ('#sk2'('#sk11', Y1) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 (('#sk2'(Y1, Y2) & Y0(Y1)) => Y0(Y2))))))))) => 139.04/20.56 Y0('#sk13'))))) | 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))) => 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk1'('#sk11', Y1) | '#sk2'('#sk11', Y1)) => 139.04/20.56 Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['53'])). 139.04/20.56 tff('55', plain, 139.04/20.56 ( ((!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: ('#sk2'('#sk11', Y1) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: (('#sk2'(Y1, Y2) & Y0(Y1)) => Y0(Y2))))))))) => 139.04/20.56 Y0('#sk13'))))) | 139.04/20.56 (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['54'])). 139.04/20.56 tff('56', plain, 139.04/20.56 ( (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: ('#sk2'('#sk11', Y1) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: (('#sk2'(Y1, Y2) & Y0(Y1)) => Y0(Y2))))))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['55'])). 139.04/20.56 tff('57', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (((!!((^[Y0 : a]: ('#sk2'('#sk11', Y0) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1))))))))) => 139.04/20.56 X1('#sk13')) 139.04/20.56 | '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['56'])). 139.04/20.56 tff('58', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((!!((^[Y0 : a]: ('#sk2'('#sk11', Y0) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1))))))))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['57'])). 139.04/20.56 tff('59', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: ('#sk2'('#sk11', Y0) => X1(Y0))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 139.04/20.56 | '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['58'])). 139.04/20.56 tff('60', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ('#sk2'('#sk11', '#sk100'(X1)) => X1('#sk100'(X1))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['59'])). 139.04/20.56 tff('61', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk100'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 139.04/20.56 | '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['60'])). 139.04/20.56 tff('62', plain, 139.04/20.56 (~ '#form183' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('63', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0)))))) => 139.04/20.56 X1('#sk13')) 139.04/20.56 | ~ '#form183'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['62'])). 139.04/20.56 tff('64', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0)))))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['63'])). 139.04/20.56 tff('65', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0))))) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['64'])). 139.04/20.56 tff('66', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((X1('#sk363'(X1)) & '#sk1'('#sk363'(X1), Y0)) => X1(Y0))))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183' 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['65'])). 139.04/20.56 tff('67', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((X1('#sk363'(X1)) & '#sk1'('#sk363'(X1), '#sk381'(X1))) => 139.04/20.56 X1('#sk381'(X1))) 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0))))) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['66'])). 139.04/20.56 tff('68', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk381'(X1)) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183' 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['67'])). 139.04/20.56 tff('69', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ('#sk1'('#sk11', '#sk393'(X1)) => X1('#sk393'(X1))) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ X1('#sk381'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['68'])). 139.04/20.56 tff('70', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk11', '#sk393'(X1)) 139.04/20.56 | ~ X1('#sk381'(X1)) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['69'])). 139.04/20.56 tff('71', plain, 139.04/20.56 (~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk1'('#sk11', Y1) | '#sk2'('#sk11', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['54'])). 139.04/20.56 tff('72', plain, 139.04/20.56 (~ (((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk26'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 '#sk26'(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (('#sk1'('#sk11', Y0) | '#sk2'('#sk11', Y0)) => '#sk26'(Y0)))))) => 139.04/20.56 '#sk26'('#sk13')) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['71'])). 139.04/20.56 tff('73', plain, 139.04/20.56 ( ((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk26'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 '#sk26'(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (('#sk1'('#sk11', Y0) | '#sk2'('#sk11', Y0)) => '#sk26'(Y0)))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['72'])). 139.04/20.56 tff('74', plain, 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 (('#sk1'('#sk11', Y0) | '#sk2'('#sk11', Y0)) => '#sk26'(Y0))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['73'])). 139.04/20.56 tff('75', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 ( (('#sk1'('#sk11', X1) | '#sk2'('#sk11', X1)) => '#sk26'(X1)) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['74'])). 139.04/20.56 tff('76', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 (~ ('#sk1'('#sk11', X1) | '#sk2'('#sk11', X1)) 139.04/20.56 | '#sk26'(X1) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['75'])). 139.04/20.56 tff('77', plain, 139.04/20.56 ![X1 : a]: (~ '#sk1'('#sk11', X1) | '#form9' | '#sk26'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['76'])). 139.04/20.56 tff('78', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk393'(X1)) | ~ X1('#sk381'(X1)) | X1('#sk13') | ~ '#form183'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['69'])). 139.04/20.56 tff('79', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (X1('#sk363'(X1)) & '#sk1'('#sk363'(X1), '#sk381'(X1))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183' 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['67'])). 139.04/20.56 tff('80', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk363'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0))))) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['79'])). 139.04/20.56 tff('81', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ('#sk1'('#sk11', '#sk393'(X1)) => X1('#sk393'(X1))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk363'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['80'])). 139.04/20.56 tff('82', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk11', '#sk393'(X1)) 139.04/20.56 | X1('#sk363'(X1)) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['81'])). 139.04/20.56 tff('83', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk363'(X1), '#sk381'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk11', Y0) => X1(Y0))))) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['79'])). 139.04/20.56 tff('84', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ('#sk1'('#sk11', '#sk393'(X1)) => X1('#sk393'(X1))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ '#form183' 139.04/20.56 | '#sk1'('#sk363'(X1), '#sk381'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['83'])). 139.04/20.56 tff('85', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk11', '#sk393'(X1)) 139.04/20.56 | '#sk1'('#sk363'(X1), '#sk381'(X1)) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['84'])). 139.04/20.56 tff('86', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk393'(X1)) | X1('#sk363'(X1)) | ~ '#form183' | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['81'])). 139.04/20.56 tff('87', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk393'(X1)) 139.04/20.56 | '#sk1'('#sk363'(X1), '#sk381'(X1)) 139.04/20.56 | ~ '#form183' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['84'])). 139.04/20.56 tff('88', plain, 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk26'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 '#sk26'(Y1)))))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['73'])). 139.04/20.56 tff('89', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 (('#sk26'(X1) & ('#sk2'(X1, Y0) | '#sk1'(X1, Y0))) => 139.04/20.56 '#sk26'(Y0))))) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['88'])). 139.04/20.56 tff('90', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 ( (('#sk26'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) => '#sk26'(X2)) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['89'])). 139.04/20.56 tff('91', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ ('#sk26'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) 139.04/20.56 | '#sk26'(X2) 139.04/20.56 | '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['90'])). 139.04/20.56 tff('92', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ '#sk26'(X1) 139.04/20.56 | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) 139.04/20.56 | '#form9' 139.04/20.56 | '#sk26'(X2)), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['91'])). 139.04/20.56 tff('93', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ '#sk1'(X1, X2) | '#sk26'(X2) | '#form9' | ~ '#sk26'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['92'])). 139.04/20.56 tff('94', plain, 139.04/20.56 ( (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['11'])). 139.04/20.56 tff('95', plain, 139.04/20.56 (~ '#form10' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('96', plain, 139.04/20.56 ( '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8')))))), 139.04/20.56 inference('renaming', [status(thm)], ['94', '95'])). 139.04/20.56 tff('97', plain, 139.04/20.56 ( '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('98', plain, 139.04/20.56 (~ '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 139.04/20.56 Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | '#form10'), 139.04/20.56 inference('renaming', [status(thm)], ['96', '97'])). 139.04/20.56 tff('99', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))) => 139.04/20.56 X1('#sk8')) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['98'])). 139.04/20.56 tff('100', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['99'])). 139.04/20.56 tff('101', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['100'])). 139.04/20.56 tff('102', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk2'('#sk40'(X1), Y0) | '#sk1'('#sk40'(X1), Y0))) => 139.04/20.56 X1(Y0))))) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['101'])). 139.04/20.56 tff('103', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk2'('#sk40'(X1), '#sk58'(X1)) | 139.04/20.56 '#sk1'('#sk40'(X1), '#sk58'(X1)))) => 139.04/20.56 X1('#sk58'(X1))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['102'])). 139.04/20.56 tff('104', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk58'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['103'])). 139.04/20.56 tff('105', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) => 139.04/20.56 X1('#sk109'(X1))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ X1('#sk58'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['104'])). 139.04/20.56 tff('106', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk109'(X1)) 139.04/20.56 | ~ X1('#sk58'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['105'])). 139.04/20.56 tff('107', plain, 139.04/20.56 (~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['10'])). 139.04/20.56 tff('108', plain, 139.04/20.56 ( '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('109', plain, 139.04/20.56 (~ '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk8')))))), 139.04/20.56 inference('renaming', [status(thm)], ['107', '108'])). 139.04/20.56 tff('110', plain, 139.04/20.56 (~ '#form10' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('111', plain, 139.04/20.56 ( '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk8'))))) 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('renaming', [status(thm)], ['109', '110'])). 139.04/20.56 tff('112', plain, 139.04/20.56 (~ (((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => '#sk12'(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk12'(Y0)) => 139.04/20.56 '#sk12'(Y1))))))))) => 139.04/20.56 '#sk12'('#sk8')) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['111'])). 139.04/20.56 tff('113', plain, (~ '#sk12'('#sk8') | '#form10' | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['112'])). 139.04/20.56 tff('114', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (X1('#sk40'(X1)) & 139.04/20.56 ('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1)))) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['103'])). 139.04/20.56 tff('115', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk40'(X1), '#sk58'(X1)) | '#sk1'('#sk40'(X1), '#sk58'(X1))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['114'])). 139.04/20.56 tff('116', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['115'])). 139.04/20.56 tff('117', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#form193'(X1) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('118', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) => 139.04/20.56 X1('#sk109'(X1))) 139.04/20.56 | '#form193'(X1)), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['117'])). 139.04/20.56 tff('119', plain, ![X1 : a > $o]: (~ X1('#sk109'(X1)) | '#form193'(X1)), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['118'])). 139.04/20.56 tff('120', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk40'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['114'])). 139.04/20.56 tff('121', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) => 139.04/20.56 X1('#sk109'(X1))) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | X1('#sk40'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['120'])). 139.04/20.56 tff('122', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk109'(X1)) 139.04/20.56 | X1('#sk40'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['121'])). 139.04/20.56 tff('123', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) 139.04/20.56 | ~ X1('#sk58'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['105'])). 139.04/20.56 tff('124', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk7', '#sk109'(X1)) 139.04/20.56 | '#sk1'('#sk7', '#sk109'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ X1('#sk58'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['123'])). 139.04/20.56 tff('125', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) 139.04/20.56 | '#form193'(X1)), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['118'])). 139.04/20.56 tff('126', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk7', '#sk109'(X1)) 139.04/20.56 | '#sk1'('#sk7', '#sk109'(X1)) 139.04/20.56 | '#form193'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['125'])). 139.04/20.56 tff('127', plain, 139.04/20.56 ( (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk7'))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4'))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['11'])). 139.04/20.56 tff('128', plain, 139.04/20.56 (~ '#form10' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk4')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('129', plain, 139.04/20.56 ( '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))))))))) 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk7')))))), 139.04/20.56 inference('renaming', [status(thm)], ['127', '128'])). 139.04/20.56 tff('130', plain, 139.04/20.56 ( '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (((!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 (('#sk2'(Y3, Y4) & Y2(Y3)) => 139.04/20.56 Y2(Y4))))))))) => 139.04/20.56 Y2(Y1))))) | 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 139.04/20.56 Y2(Y1)))))) => 139.04/20.56 (!!((^[Y2 : a > $o]: 139.04/20.56 (((!!((^[Y3 : a]: 139.04/20.56 (!!((^[Y4 : a]: 139.04/20.56 ((Y2(Y3) & 139.04/20.56 ('#sk2'(Y3, Y4) | 139.04/20.56 '#sk1'(Y3, Y4))) => 139.04/20.56 Y2(Y4)))))))) & 139.04/20.56 (!!((^[Y3 : a]: 139.04/20.56 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 139.04/20.56 Y2(Y3)))))) => 139.04/20.56 Y2(Y1))))))))))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('131', plain, 139.04/20.56 (~ '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (('#sk2'('#sk6', Y1) | '#sk1'('#sk6', Y1)) => Y0(Y1))))) & 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 139.04/20.56 Y0(Y2))))))))) => 139.04/20.56 Y0('#sk7'))))) 139.04/20.56 | '#form10'), 139.04/20.56 inference('renaming', [status(thm)], ['129', '130'])). 139.04/20.56 tff('132', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1))))))))) => 139.04/20.56 X1('#sk7')) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['131'])). 139.04/20.56 tff('133', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => X1(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1))))))))) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['132'])). 139.04/20.56 tff('134', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => X1(Y0))))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['133'])). 139.04/20.56 tff('135', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk6', '#sk49'(X1)) | '#sk1'('#sk6', '#sk49'(X1))) => 139.04/20.56 X1('#sk49'(X1))) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1))))))))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['134'])). 139.04/20.56 tff('136', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk6', '#sk49'(X1)) | '#sk1'('#sk6', '#sk49'(X1))) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['135'])). 139.04/20.56 tff('137', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1))))))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['136'])). 139.04/20.56 tff('138', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), Y0) | '#sk2'('#sk40'(X1), Y0))) => 139.04/20.56 X1(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7') 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['137'])). 139.04/20.56 tff('139', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), '#sk58'(X1)) | 139.04/20.56 '#sk2'('#sk40'(X1), '#sk58'(X1)))) => 139.04/20.56 X1('#sk58'(X1))) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['138'])). 139.04/20.56 tff('140', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk58'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7') 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['139'])). 139.04/20.56 tff('141', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk7', '#sk109'(X1)) | '#sk1'('#sk7', '#sk109'(X1))) 139.04/20.56 | X1('#sk40'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['121'])). 139.04/20.56 tff('142', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk7', '#sk109'(X1)) 139.04/20.56 | '#sk1'('#sk7', '#sk109'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | X1('#sk40'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['141'])). 139.04/20.56 tff('143', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | X1('#sk8') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['115'])). 139.04/20.56 tff('144', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#form193'(X1) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0)))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('145', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ '#form193'(X1) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk8') 139.04/20.56 | '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk2'('#sk40'(X1), '#sk58'(X1))), 139.04/20.56 inference('renaming', [status(thm)], ['143', '144'])). 139.04/20.56 tff('146', plain, 139.04/20.56 ( ((!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => '#sk12'(Y0))))) & 139.04/20.56 (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk12'(Y0)) => 139.04/20.56 '#sk12'(Y1))))))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['112'])). 139.04/20.56 tff('147', plain, 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk6', Y0) | '#sk1'('#sk6', Y0)) => '#sk12'(Y0))))) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['146'])). 139.04/20.56 tff('148', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 ( (('#sk2'('#sk6', X1) | '#sk1'('#sk6', X1)) => '#sk12'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['147'])). 139.04/20.56 tff('149', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 (~ ('#sk2'('#sk6', X1) | '#sk1'('#sk6', X1)) 139.04/20.56 | '#sk12'(X1) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['148'])). 139.04/20.56 tff('150', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 (~ '#sk1'('#sk6', X1) | '#form10' | ~ '#form9' | '#sk12'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['149'])). 139.04/20.56 tff('151', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), '#sk58'(X1)) | '#sk2'('#sk40'(X1), '#sk58'(X1)))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7') 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['139'])). 139.04/20.56 tff('152', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk40'(X1)) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['151'])). 139.04/20.56 tff('153', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk1'('#sk40'(X1), '#sk58'(X1)) | '#sk2'('#sk40'(X1), '#sk58'(X1))) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['151'])). 139.04/20.56 tff('154', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7') 139.04/20.56 | '#sk1'('#sk6', '#sk49'(X1)) 139.04/20.56 | '#sk2'('#sk6', '#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['153'])). 139.04/20.56 tff('155', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk49'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 139.04/20.56 X1(Y1)))))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['135'])). 139.04/20.56 tff('156', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), Y0) | '#sk2'('#sk40'(X1), Y0))) => 139.04/20.56 X1(Y0))))) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ X1('#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['155'])). 139.04/20.56 tff('157', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ ((X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), '#sk58'(X1)) | 139.04/20.56 '#sk2'('#sk40'(X1), '#sk58'(X1)))) => 139.04/20.56 X1('#sk58'(X1))) 139.04/20.56 | ~ X1('#sk49'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['156'])). 139.04/20.56 tff('158', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk58'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ X1('#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['157'])). 139.04/20.56 tff('159', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 (~ '#sk2'('#sk6', X1) | '#form10' | ~ '#form9' | '#sk12'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['149'])). 139.04/20.56 tff('160', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( (X1('#sk40'(X1)) & 139.04/20.56 ('#sk1'('#sk40'(X1), '#sk58'(X1)) | '#sk2'('#sk40'(X1), '#sk58'(X1)))) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ X1('#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['157'])). 139.04/20.56 tff('161', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk40'(X1)) 139.04/20.56 | ~ X1('#sk49'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['160'])). 139.04/20.56 tff('162', plain, 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: 139.04/20.56 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk12'(Y0)) => 139.04/20.56 '#sk12'(Y1)))))))) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['146'])). 139.04/20.56 tff('163', plain, 139.04/20.56 ![X1 : a]: 139.04/20.56 ( (!!((^[Y0 : a]: 139.04/20.56 ((('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) & '#sk12'(X1)) => 139.04/20.56 '#sk12'(Y0))))) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['162'])). 139.04/20.56 tff('164', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 ( ((('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk12'(X1)) => '#sk12'(X2)) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10'), 139.04/20.56 inference('lazy_cnf_forall', [status(thm)], ['163'])). 139.04/20.56 tff('165', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ (('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk12'(X1)) 139.04/20.56 | '#sk12'(X2) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9'), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['164'])). 139.04/20.56 tff('166', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) 139.04/20.56 | ~ '#sk12'(X1) 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | '#sk12'(X2)), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['165'])). 139.04/20.56 tff('167', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ '#sk1'(X1, X2) 139.04/20.56 | '#sk12'(X2) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | ~ '#sk12'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['166'])). 139.04/20.56 tff('168', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk1'('#sk40'(X1), '#sk58'(X1)) | '#sk2'('#sk40'(X1), '#sk58'(X1))) 139.04/20.56 | ~ X1('#sk49'(X1)) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | X1('#sk7')), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['160'])). 139.04/20.56 tff('169', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk1'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | '#sk2'('#sk40'(X1), '#sk58'(X1)) 139.04/20.56 | X1('#sk7') 139.04/20.56 | ~ '#form9' 139.04/20.56 | '#form10' 139.04/20.56 | ~ X1('#sk49'(X1))), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['168'])). 139.04/20.56 tff('170', plain, 139.04/20.56 ![X1 : a, X2 : a]: 139.04/20.56 (~ '#sk2'(X1, X2) 139.04/20.56 | '#sk12'(X2) 139.04/20.56 | '#form10' 139.04/20.56 | ~ '#form9' 139.04/20.56 | ~ '#sk12'(X1)), 139.04/20.56 inference('lazy_cnf_or', [status(thm)], ['166'])). 139.04/20.56 tff('171', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 139.04/20.56 | '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['60'])). 139.04/20.56 tff('172', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk179'(X1), Y0) & X1('#sk179'(X1))) => X1(Y0))))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | '#form9' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['171'])). 139.04/20.56 tff('173', plain, 139.04/20.56 (~ '#form183' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('174', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#form183' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | '#form9' 139.04/20.56 | X1('#sk13') 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk179'(X1), Y0) & X1('#sk179'(X1))) => X1(Y0)))))), 139.04/20.56 inference('renaming', [status(thm)], ['172', '173'])). 139.04/20.56 tff('175', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk179'(X1), '#sk289'(X1)) & X1('#sk179'(X1))) => 139.04/20.56 X1('#sk289'(X1))) 139.04/20.56 | X1('#sk13') 139.04/20.56 | '#form9' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | '#form183'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['174'])). 139.04/20.56 tff('176', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk179'(X1), '#sk289'(X1)) & X1('#sk179'(X1))) 139.04/20.56 | '#form183' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | '#form9' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['175'])). 139.04/20.56 tff('177', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( X1('#sk179'(X1)) 139.04/20.56 | X1('#sk13') 139.04/20.56 | '#form9' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | '#form183'), 139.04/20.56 inference('lazy_cnf_and', [status(thm)], ['176'])). 139.04/20.56 tff('178', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk289'(X1)) 139.04/20.56 | '#form183' 139.04/20.56 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.56 | '#form9' 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['175'])). 139.04/20.56 tff('179', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ X1('#sk100'(X1)) 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 139.04/20.56 | '#form9' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: 139.04/20.56 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13'))))) 139.04/20.56 | X1('#sk13')), 139.04/20.56 inference('lazy_cnf_imply', [status(thm)], ['60'])). 139.04/20.56 tff('180', plain, 139.04/20.56 (~ '#form183' 139.04/20.56 | (!!((^[Y0 : a > $o]: 139.04/20.56 (((!!((^[Y1 : a]: 139.04/20.56 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2)))))))) & 139.04/20.56 (!!((^[Y1 : a]: ('#sk1'('#sk11', Y1) => Y0(Y1)))))) => 139.04/20.56 Y0('#sk13')))))), 139.04/20.56 define([status(thm)])). 139.04/20.56 tff('181', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( '#form183' 139.04/20.56 | X1('#sk13') 139.04/20.56 | '#form9' 139.04/20.56 | ~ (!!((^[Y0 : a]: 139.04/20.56 (!!((^[Y1 : a]: (('#sk2'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 139.04/20.56 | ~ X1('#sk100'(X1))), 139.04/20.56 inference('renaming', [status(thm)], ['179', '180'])). 139.04/20.56 tff('182', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (!!((^[Y0 : a]: 139.04/20.56 (('#sk2'('#sk179'(X1), Y0) & X1('#sk179'(X1))) => X1(Y0))))) 139.04/20.56 | ~ X1('#sk100'(X1)) 139.04/20.56 | '#form9' 139.04/20.56 | X1('#sk13') 139.04/20.56 | '#form183'), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['181'])). 139.04/20.56 tff('183', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 (~ (('#sk2'('#sk179'(X1), '#sk289'(X1)) & X1('#sk179'(X1))) => 139.04/20.56 X1('#sk289'(X1))) 139.04/20.56 | '#form183' 139.04/20.56 | X1('#sk13') 139.04/20.56 | '#form9' 139.04/20.56 | ~ X1('#sk100'(X1))), 139.04/20.56 inference('lazy_cnf_exists', [status(thm)], ['182'])). 139.04/20.56 tff('184', plain, 139.04/20.56 ![X1 : a > $o]: 139.04/20.56 ( ('#sk2'('#sk179'(X1), '#sk289'(X1)) & X1('#sk179'(X1))) 139.04/20.56 | ~ X1('#sk100'(X1)) 139.04/20.56 | '#form9' 139.04/20.56 | X1('#sk13') 139.04/20.57 | '#form183'), 139.04/20.57 inference('lazy_cnf_imply', [status(thm)], ['183'])). 139.04/20.57 tff('185', plain, 139.04/20.57 ![X1 : a > $o]: 139.04/20.57 ( X1('#sk179'(X1)) 139.04/20.57 | '#form183' 139.04/20.57 | X1('#sk13') 139.04/20.57 | '#form9' 139.04/20.57 | ~ X1('#sk100'(X1))), 139.04/20.57 inference('lazy_cnf_and', [status(thm)], ['184'])). 139.04/20.57 tff('186', plain, 139.04/20.57 ![X1 : a > $o]: 139.04/20.57 (~ X1('#sk289'(X1)) 139.04/20.57 | ~ X1('#sk100'(X1)) 139.04/20.57 | '#form9' 139.04/20.57 | X1('#sk13') 139.04/20.57 | '#form183'), 139.04/20.57 inference('lazy_cnf_imply', [status(thm)], ['183'])). 139.04/20.57 tff('187', plain, 139.04/20.57 ![X1 : a > $o]: 139.04/20.57 ( '#sk2'('#sk179'(X1), '#sk289'(X1)) 139.04/20.57 | X1('#sk13') 139.04/20.57 | '#form9' 139.04/20.57 | '#sk2'('#sk11', '#sk100'(X1)) 139.04/20.57 | '#form183'), 139.04/20.57 inference('lazy_cnf_and', [status(thm)], ['176'])). 139.04/20.57 tff('188', plain, (~ '#sk26'('#sk13') | '#form9'), 139.04/20.57 inference('lazy_cnf_imply', [status(thm)], ['72'])). 139.04/20.57 tff('189', plain, 139.04/20.57 ![X1 : a]: (~ '#sk2'('#sk11', X1) | '#form9' | '#sk26'(X1)), 139.04/20.57 inference('lazy_cnf_or', [status(thm)], ['76'])). 139.04/20.57 tff('190', plain, 139.04/20.57 ![X1 : a > $o]: 139.04/20.57 ( '#sk2'('#sk179'(X1), '#sk289'(X1)) 139.04/20.57 | '#form183' 139.04/20.57 | X1('#sk13') 139.04/20.57 | '#form9' 139.04/20.57 | ~ X1('#sk100'(X1))), 139.04/20.57 inference('lazy_cnf_and', [status(thm)], ['184'])). 139.04/20.57 tff('191', plain, 139.04/20.57 ![X1 : a, X2 : a]: 139.04/20.57 (~ '#sk2'(X1, X2) | '#sk26'(X2) | '#form9' | ~ '#sk26'(X1)), 139.04/20.57 inference('lazy_cnf_or', [status(thm)], ['92'])). 139.04/20.57 tff('192', plain, $false, 139.04/20.57 inference('eprover', [status(thm)], 139.04/20.57 ['22', '24', '26', '33', '34', '38', '39', '41', '47', '49', 139.04/20.57 '50', '70', '77', '78', '82', '85', '86', '87', '93', '106', 139.04/20.57 '113', '119', '122', '124', '126', '140', '142', '145', 139.04/20.57 '150', '152', '154', '158', '159', '161', '167', '169', 139.04/20.57 '170', '177', '178', '185', '186', '187', '188', '189', 139.04/20.57 '190', '191'])). 139.04/20.57 139.04/20.57 % SZS output end Refutation 139.04/20.57 139.04/20.57 139.04/20.57 % /export/starexec/sandbox2/solver/bin/lams/b.lsimp.sh running for 17s 139.04/20.57 % Terminating... 139.91/20.70 % Runner terminated. 139.91/20.71 % Zipperpin 1.5 exiting 139.91/20.72 EOF