0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.13 % Command : run_portfolio.sh /export/starexec/sandbox2/benchmark/theBenchmark.p /export/starexec/sandbox2/tmp/tmp.Gzl6TwPHbg 0.13/0.33 % Computer : n014.cluster.edu 0.13/0.33 % Model : x86_64 x86_64 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.33 % Memory : 8042.1875MB 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.33 % CPULimit : 1200 0.13/0.33 % DateTime : Tue Jul 13 11:56:19 EDT 2021 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 120 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.34 % Number of cores: 8 0.13/0.34 % Python version: Python 3.6.8 0.13/0.34 % Running in HO mode 0.48/0.63 % Estimated wc time : 1286 0.48/0.63 % Estimated cpu time (7 cpus) : 183.71428571428572 0.52/0.68 % /export/starexec/sandbox2/solver/bin/lams/s6.sh running for 21s 0.52/0.69 % /export/starexec/sandbox2/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.52/0.72 % /export/starexec/sandbox2/solver/bin/lams/b.rpo.sh running for 21s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/s6.ds.sh running for 10s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/c.s.2.sh running for 68s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/c.easy.sh running for 26s 0.52/0.73 % /export/starexec/sandbox2/solver/bin/lams/old_b3.avatar.sh running for 15s 70.80/10.75 % /export/starexec/sandbox2/solver/bin/lams/old_sp2.sh running for 17s 104.10/15.54 % /export/starexec/sandbox2/solver/bin/lams/b.sh running for 31s 104.56/15.61 % Solved by lams/old_sp2.sh. 104.56/15.61 % done 1287 iterations in 4.791s 104.56/15.61 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 104.56/15.61 % SZS output start Refutation 104.56/15.61 tff(cTHM251H_pme, conjecture, 104.56/15.61 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 104.56/15.61 ((![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy))) | 104.56/15.61 ((~ 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy)))) & 104.56/15.61 (![Xx0:a,Xy0:a,Xz:a]: 104.56/15.61 (((![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy0))) & 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((R(Xy0,Xw) | S(Xy0,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xz)))) => 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw)))) => 104.56/15.61 Xq(Xz))))) & 104.56/15.61 (![Xx0:a,Xy0:a]: 104.56/15.61 (((![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((R(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: (R(Xx0,Xw) => Xq(Xw)))) => 104.56/15.61 Xq(Xy0))) | 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: (S(Xx0,Xw) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & S(Xu,Xv)) => Xq(Xv)))) => 104.56/15.61 Xq(Xy0)))) => 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw)))) => 104.56/15.61 Xq(Xy0))))))))). 104.56/15.61 tff(zf_stmt_0, negated_conjecture, 104.56/15.61 (~ 104.56/15.61 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 104.56/15.61 ((![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy))) | 104.56/15.61 ((~ 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx,Xw) | R(Xx,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy)))) & 104.56/15.61 (![Xx0:a,Xy0:a,Xz:a]: 104.56/15.61 (((![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: 104.56/15.61 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xy0))) & 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: ((R(Xy0,Xw) | S(Xy0,Xw)) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: 104.56/15.61 ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv)))) => 104.56/15.61 Xq(Xz)))) => 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw)))) => 104.56/15.61 Xq(Xz))))) & 104.56/15.61 (![Xx0:a,Xy0:a]: 104.56/15.61 (((![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((R(Xu,Xv) & Xq(Xu)) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: (R(Xx0,Xw) => Xq(Xw)))) => 104.56/15.61 Xq(Xy0))) | 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xw:a]: (S(Xx0,Xw) => Xq(Xw))) & 104.56/15.61 (![Xu:a,Xv:a]: ((Xq(Xu) & S(Xu,Xv)) => Xq(Xv)))) => 104.56/15.61 Xq(Xy0)))) => 104.56/15.61 (![Xq:((a > $o))]: 104.56/15.61 (((![Xu:a,Xv:a]: ((Xq(Xu) & (S(Xu,Xv) | R(Xu,Xv))) => Xq(Xv))) & 104.56/15.61 (![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw)))) => 104.56/15.61 Xq(Xy0)))))))))). 104.56/15.61 tff('0', plain, 104.56/15.61 ~ (!!((^[Y0 : (a * a) > $o]: 104.56/15.61 (!!((^[Y1 : (a * a) > $o]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 ((Y1(Y2, Y5) | Y0(Y2, Y5)) => 104.56/15.61 Y4(Y5))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 (Y1(Y5, Y6) | 104.56/15.61 Y0(Y5, Y6))) => 104.56/15.61 Y4(Y6))))))))) => 104.56/15.61 Y4(Y3))))) | 104.56/15.61 ((~((!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 ((Y1(Y2, Y5) | 104.56/15.61 Y0(Y2, Y5)) => 104.56/15.61 Y4(Y5))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 (Y0(Y5, Y6) | 104.56/15.61 Y1(Y5, Y6))) => 104.56/15.61 Y4(Y6))))))))) => 104.56/15.61 Y4(Y3)))))))& 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (((!!((^[Y7 : a > $o]: 104.56/15.61 ((( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y1(Y4, 104.56/15.61 Y8) | 104.56/15.61 Y0(Y4, 104.56/15.61 Y8)) => 104.56/15.61 Y7(Y8))))) & 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (!!(( 104.56/15.61 ^[Y9 : a]: 104.56/15.61 (( 104.56/15.61 Y7(Y8) & 104.56/15.61 ( 104.56/15.61 Y1(Y8, 104.56/15.61 Y9) | 104.56/15.61 Y0(Y8, 104.56/15.61 Y9))) => 104.56/15.61 Y7(Y9))))))))) => 104.56/15.61 Y7(Y5))))) & 104.56/15.61 (!!((^[Y7 : a > $o]: 104.56/15.61 ((( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y0(Y5, 104.56/15.61 Y8) | 104.56/15.61 Y1(Y5, 104.56/15.61 Y8)) => 104.56/15.61 Y7(Y8))))) & 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (!!(( 104.56/15.61 ^[Y9 : a]: 104.56/15.61 (( 104.56/15.61 Y7(Y8) & 104.56/15.61 ( 104.56/15.61 Y1(Y8, 104.56/15.61 Y9) | 104.56/15.61 Y0(Y8, 104.56/15.61 Y9))) => 104.56/15.61 Y7(Y9))))))))) => 104.56/15.61 Y7(Y6)))))) => 104.56/15.61 (!!((^[Y7 : a > $o]: 104.56/15.61 (((!!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (!!(( 104.56/15.61 ^[Y9 : a]: 104.56/15.61 (( 104.56/15.61 Y7(Y8) & 104.56/15.61 ( 104.56/15.61 Y1(Y8, 104.56/15.61 Y9) | 104.56/15.61 Y0(Y8, 104.56/15.61 Y9))) => 104.56/15.61 Y7(Y9)))))))) & 104.56/15.61 (!!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y1(Y4, 104.56/15.61 Y8) | 104.56/15.61 Y0(Y4, 104.56/15.61 Y8)) => 104.56/15.61 Y7(Y8)))))) => 104.56/15.61 Y7(Y6)))))))))))))))& 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (((!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y0(Y7, 104.56/15.61 Y8) & 104.56/15.61 Y6(Y7)) => 104.56/15.61 Y6(Y8)))))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 Y0(Y4, 104.56/15.61 Y7) => 104.56/15.61 Y6(Y7)))))) => 104.56/15.61 Y6(Y5))))) | 104.56/15.61 (!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 Y1(Y4, 104.56/15.61 Y7) => 104.56/15.61 Y6(Y7))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y6(Y7) & 104.56/15.61 Y1(Y7, 104.56/15.61 Y8)) => 104.56/15.61 Y6(Y8))))))))) => 104.56/15.61 Y6(Y5)))))) => 104.56/15.61 (!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 (!!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y6(Y7) & 104.56/15.61 ( 104.56/15.61 Y1(Y7, 104.56/15.61 Y8) | 104.56/15.61 Y0(Y7, 104.56/15.61 Y8))) => 104.56/15.61 Y6(Y8)))))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 (( 104.56/15.61 Y0(Y4, 104.56/15.61 Y7) | 104.56/15.61 Y1(Y4, 104.56/15.61 Y7)) => 104.56/15.61 Y6(Y7)))))) => 104.56/15.61 Y6(Y5)))))))))))))))))))))))))), 104.56/15.61 inference('cnf', [status(esa)], [zf_stmt_0])). 104.56/15.61 tff('1', plain, 104.56/15.61 ~ (!!((^[Y0 : (a * a) > $o]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 ((Y0(Y1, Y4) | '#sk1'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 (Y0(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2))))) | 104.56/15.61 ((~((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 ((Y0(Y1, Y4) | '#sk1'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk1'(Y4, Y5) | 104.56/15.61 Y0(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))))& 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (((!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 Y0(Y3, 104.56/15.61 Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y3, Y7)) => 104.56/15.61 Y6(Y7))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y6(Y7) & 104.56/15.61 ( 104.56/15.61 Y0(Y7, 104.56/15.61 Y8) | 104.56/15.61 '#sk1'( 104.56/15.61 Y7, Y8))) => 104.56/15.61 Y6(Y8))))))))) => 104.56/15.61 Y6(Y4))))) & 104.56/15.61 (!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 '#sk1'( 104.56/15.61 Y4, Y7) | 104.56/15.61 Y0(Y4, 104.56/15.61 Y7)) => 104.56/15.61 Y6(Y7))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 !!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y6(Y7) & 104.56/15.61 ( 104.56/15.61 Y0(Y7, 104.56/15.61 Y8) | 104.56/15.61 '#sk1'( 104.56/15.61 Y7, Y8))) => 104.56/15.61 Y6(Y8))))))))) => 104.56/15.61 Y6(Y5)))))) => 104.56/15.61 (!!((^[Y6 : a > $o]: 104.56/15.61 (((!!((^[Y7 : a]: 104.56/15.61 (!!(( 104.56/15.61 ^[Y8 : a]: 104.56/15.61 (( 104.56/15.61 Y6(Y7) & 104.56/15.61 ( 104.56/15.61 Y0(Y7, 104.56/15.61 Y8) | 104.56/15.61 '#sk1'( 104.56/15.61 Y7, Y8))) => 104.56/15.61 Y6(Y8)))))))) & 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 (( 104.56/15.61 Y0(Y3, 104.56/15.61 Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y3, Y7)) => 104.56/15.61 Y6(Y7)))))) => 104.56/15.61 Y6(Y5)))))))))))))))& 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (((!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 '#sk1'( 104.56/15.61 Y6, Y7) & 104.56/15.61 Y5(Y6)) => 104.56/15.61 Y5(Y7)))))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ('#sk1'(Y3, Y6) => 104.56/15.61 Y5(Y6)))))) => 104.56/15.61 Y5(Y4))))) | 104.56/15.61 (!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (Y0(Y3, Y6) => 104.56/15.61 Y5(Y6))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 Y5(Y6) & 104.56/15.61 Y0(Y6, 104.56/15.61 Y7)) => 104.56/15.61 Y5(Y7))))))))) => 104.56/15.61 Y5(Y4)))))) => 104.56/15.61 (!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 (( 104.56/15.61 Y5(Y6) & 104.56/15.61 ( 104.56/15.61 Y0(Y6, 104.56/15.61 Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y6, Y7))) => 104.56/15.61 Y5(Y7)))))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (('#sk1'(Y3, Y6) | 104.56/15.61 Y0(Y3, Y6)) => 104.56/15.61 Y5(Y6)))))) => 104.56/15.61 Y5(Y4))))))))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['0'])). 104.56/15.61 tff('2', plain, 104.56/15.61 ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 ((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 104.56/15.61 Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 ((~((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 104.56/15.61 Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk1'(Y3, Y4) | 104.56/15.61 '#sk2'(Y3, Y4))) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))))& 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (((!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (('#sk2'(Y2, Y6) | 104.56/15.61 '#sk1'(Y2, Y6)) => 104.56/15.61 Y5(Y6))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 Y5(Y6) & 104.56/15.61 ( 104.56/15.61 '#sk2'( 104.56/15.61 Y6, Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y6, Y7))) => 104.56/15.61 Y5(Y7))))))))) => 104.56/15.61 Y5(Y3))))) & 104.56/15.61 (!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (('#sk1'(Y3, Y6) | 104.56/15.61 '#sk2'(Y3, Y6)) => 104.56/15.61 Y5(Y6))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 ( 104.56/15.61 ( 104.56/15.61 Y5(Y6) & 104.56/15.61 ( 104.56/15.61 '#sk2'( 104.56/15.61 Y6, Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y6, Y7))) => 104.56/15.61 Y5(Y7))))))))) => 104.56/15.61 Y5(Y4)))))) => 104.56/15.61 (!!((^[Y5 : a > $o]: 104.56/15.61 (((!!((^[Y6 : a]: 104.56/15.61 (!!((^[Y7 : a]: 104.56/15.61 (( 104.56/15.61 Y5(Y6) & 104.56/15.61 ( 104.56/15.61 '#sk2'( 104.56/15.61 Y6, Y7) | 104.56/15.61 '#sk1'( 104.56/15.61 Y6, Y7))) => 104.56/15.61 Y5(Y7)))))))) & 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (('#sk2'(Y2, Y6) | 104.56/15.61 '#sk1'(Y2, Y6)) => 104.56/15.61 Y5(Y6)))))) => 104.56/15.61 Y5(Y4)))))))))))))))& 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (((!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 (('#sk1'(Y5, Y6) & 104.56/15.61 Y4(Y5)) => 104.56/15.61 Y4(Y6)))))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ('#sk1'(Y2, Y5) => 104.56/15.61 Y4(Y5)))))) => 104.56/15.61 Y4(Y3))))) | 104.56/15.61 (!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 ('#sk2'(Y2, Y5) => 104.56/15.61 Y4(Y5))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 '#sk2'(Y5, Y6)) => 104.56/15.61 Y4(Y6))))))))) => 104.56/15.61 Y4(Y3)))))) => 104.56/15.61 (!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 ('#sk2'(Y5, Y6) | 104.56/15.61 '#sk1'(Y5, Y6))) => 104.56/15.61 Y4(Y6)))))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (('#sk1'(Y2, Y5) | 104.56/15.61 '#sk2'(Y2, Y5)) => 104.56/15.61 Y4(Y5)))))) => 104.56/15.61 Y4(Y3)))))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['1'])). 104.56/15.61 tff('3', plain, 104.56/15.61 ~ (!!((^[Y0 : a]: 104.56/15.61 ((!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (('#sk2'('#sk3', Y2) | '#sk1'('#sk3', Y2)) => 104.56/15.61 Y1(Y2))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 104.56/15.61 Y1(Y3))))))))) => 104.56/15.61 Y1(Y0))))) | 104.56/15.61 ((~((!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (('#sk2'('#sk3', Y2) | '#sk1'('#sk3', Y2)) => 104.56/15.61 Y1(Y2))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3))) => 104.56/15.61 Y1(Y3))))))))) => 104.56/15.61 Y1(Y0)))))))& 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (((!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 (('#sk2'(Y1, Y5) | 104.56/15.61 '#sk1'(Y1, Y5)) => 104.56/15.61 Y4(Y5))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 ('#sk2'(Y5, 104.56/15.61 Y6) | 104.56/15.61 '#sk1'(Y5, 104.56/15.61 Y6))) => 104.56/15.61 Y4(Y6))))))))) => 104.56/15.61 Y4(Y2))))) & 104.56/15.61 (!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 (('#sk1'(Y2, Y5) | 104.56/15.61 '#sk2'(Y2, Y5)) => 104.56/15.61 Y4(Y5))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 ('#sk2'(Y5, 104.56/15.61 Y6) | 104.56/15.61 '#sk1'(Y5, 104.56/15.61 Y6))) => 104.56/15.61 Y4(Y6))))))))) => 104.56/15.61 Y4(Y3)))))) => 104.56/15.61 (!!((^[Y4 : a > $o]: 104.56/15.61 (((!!((^[Y5 : a]: 104.56/15.61 (!!((^[Y6 : a]: 104.56/15.61 ((Y4(Y5) & 104.56/15.61 ('#sk2'(Y5, Y6) | 104.56/15.61 '#sk1'(Y5, Y6))) => 104.56/15.61 Y4(Y6)))))))) & 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (('#sk2'(Y1, Y5) | 104.56/15.61 '#sk1'(Y1, Y5)) => 104.56/15.61 Y4(Y5)))))) => 104.56/15.61 Y4(Y3)))))))))))))))& 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 (('#sk1'(Y4, Y5) & 104.56/15.61 Y3(Y4)) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ('#sk1'(Y1, Y4) => Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))) | 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 ('#sk2'(Y1, Y4) => Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 '#sk2'(Y4, Y5)) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['2'])). 104.56/15.61 tff('4', plain, 104.56/15.61 ~ ((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))) | 104.56/15.61 ((~((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4')))))))& 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))& 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['3'])). 104.56/15.61 tff('5', plain, 104.56/15.61 ~ ((~((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4')))))))& 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))& 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['4'])). 104.56/15.61 tff('6', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['5'])). 104.56/15.61 tff('7', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('split', [status(esa)], ['6'])). 104.56/15.61 tff('8', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (((!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y2, Y3) & Y1(Y2)) => Y1(Y3)))))))) & 104.56/15.61 (!!((^[Y2 : a]: ('#sk1'('#sk6', Y2) => Y1(Y2)))))) => 104.56/15.61 Y1(Y0))))) | 104.56/15.61 (!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: ('#sk2'('#sk6', Y2) => Y1(Y2))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & '#sk2'(Y2, Y3)) => Y1(Y3))))))))) => 104.56/15.61 Y1(Y0)))))) => 104.56/15.61 (!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 104.56/15.61 Y1(Y3)))))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'('#sk6', Y2) | '#sk2'('#sk6', Y2)) => 104.56/15.61 Y1(Y2)))))) => 104.56/15.61 Y1(Y0)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['7'])). 104.56/15.61 tff('9', plain, 104.56/15.61 (~ (((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))) | 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11')))))) => 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'('#sk6', Y1) | '#sk2'('#sk6', Y1)) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['8'])). 104.56/15.61 tff('10', plain, 104.56/15.61 ( ((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))) | 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['9'])). 104.56/15.61 tff('11', plain, 104.56/15.61 (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))) 104.56/15.61 | (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['10'])). 104.56/15.61 tff('12', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11')))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('split', [status(esa)], ['11'])). 104.56/15.61 tff('13', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1))))))))) => 104.56/15.61 X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['12'])). 104.56/15.61 tff('14', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))) => 104.56/15.61 '#sk21'('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('triggered_bool_instantiation', [status(thm)], ['13'])). 104.56/15.61 tff('15', plain, 104.56/15.61 ((~ ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))) 104.56/15.61 | '#sk21'('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['14'])). 104.56/15.61 tff('16', plain, 104.56/15.61 (~ ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))))), 104.56/15.61 inference('split', [status(esa)], ['15'])). 104.56/15.61 tff('17', plain, 104.56/15.61 ((~ (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['16'])). 104.56/15.61 tff('18', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))), 104.56/15.61 inference('split', [status(esa)], ['17'])). 104.56/15.61 tff('19', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1))))))))) => 104.56/15.61 X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['12'])). 104.56/15.61 tff('20', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1))))))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['19'])). 104.56/15.61 tff('21', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => X1(Y0))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['20'])). 104.56/15.61 tff('22', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ ('#sk2'('#sk6', '#sk90'(X1)) => X1('#sk90'(X1))) 104.56/15.61 | X1('#sk11') 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['21'])). 104.56/15.61 tff('23', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 ( '#sk2'('#sk6', '#sk90'(X1)) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['22'])). 104.56/15.61 tff('24', plain, 104.56/15.61 ![X1 : a > $o]: 104.56/15.61 ( '#form138'(X1) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1))))))))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('25', plain, 104.56/15.61 (~ '#form138'('#sk21')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))), 104.56/15.61 inference('renaming', [status(thm)], ['18', '24'])). 104.56/15.61 tff('26', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0)))))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('split', [status(esa)], ['17'])). 104.56/15.61 tff('27', plain, 104.56/15.61 (~ ('#sk2'('#sk6', '#sk90'('#sk21')) => '#sk21'('#sk90'('#sk21')))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['26'])). 104.56/15.61 tff('28', plain, 104.56/15.61 ( '#sk2'('#sk6', '#sk90'('#sk21'))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['27'])). 104.56/15.61 tff('29', plain, 104.56/15.61 (~ (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'('#sk6', Y1) | '#sk2'('#sk6', Y1)) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11')))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['9'])). 104.56/15.61 tff('30', plain, 104.56/15.61 (~ (((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk6', Y0) | '#sk2'('#sk6', Y0)) => '#sk21'(Y0)))))) => 104.56/15.61 '#sk21'('#sk11'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['29'])). 104.56/15.61 tff('31', plain, 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk21'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk6', Y0) | '#sk2'('#sk6', Y0)) => '#sk21'(Y0))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['30'])). 104.56/15.61 tff('32', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk6', Y0) | '#sk2'('#sk6', Y0)) => '#sk21'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['31'])). 104.56/15.61 tff('33', plain, 104.56/15.61 (![X1 : a]: (('#sk1'('#sk6', X1) | '#sk2'('#sk6', X1)) => '#sk21'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['32'])). 104.56/15.61 tff('34', plain, 104.56/15.61 (![X1 : a]: (~ ('#sk1'('#sk6', X1) | '#sk2'('#sk6', X1)) | '#sk21'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['33'])). 104.56/15.61 tff('35', plain, 104.56/15.61 (![X1 : a]: (~ '#sk2'('#sk6', X1) | '#sk21'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['34'])). 104.56/15.61 tff('36', plain, 104.56/15.61 ( '#sk21'('#sk90'('#sk21'))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0)))))) & 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['28', '35'])). 104.56/15.61 tff('37', plain, 104.56/15.61 (~ '#sk21'('#sk90'('#sk21'))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['27'])). 104.56/15.61 tff('38', plain, 104.56/15.61 ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0)))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['36', '37'])). 104.56/15.61 tff('39', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11')))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('split', [status(esa)], ['11'])). 104.56/15.61 tff('40', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0)))))) => 104.56/15.61 X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['39'])). 104.56/15.61 tff('41', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0)))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['40'])). 104.56/15.61 tff('42', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['41'])). 104.56/15.61 tff('43', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk94'(X1), Y0) & X1('#sk94'(X1))) => X1(Y0))))) 104.56/15.61 | X1('#sk11') 104.56/15.61 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0))))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['42'])). 104.56/15.61 tff('44', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (~ (('#sk1'('#sk94'(X1), '#sk117'(X1)) & X1('#sk94'(X1))) => 104.56/15.61 X1('#sk117'(X1))) 104.56/15.61 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0))))) 104.56/15.61 | X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['43'])). 104.56/15.61 tff('45', plain, 104.56/15.61 ![X1 : a > $o]: 104.56/15.61 ( '#form147'(X1) | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0)))))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('46', plain, 104.56/15.61 ![X1 : a > $o]: 104.56/15.61 (~ ('#sk1'('#sk6', '#sk178'(X1)) => X1('#sk178'(X1))) | '#form147'(X1)), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['45'])). 104.56/15.61 tff('47', plain, 104.56/15.61 ![X1 : a > $o]: ( '#sk1'('#sk6', '#sk178'(X1)) | '#form147'(X1)), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['46'])). 104.56/15.61 tff('48', plain, 104.56/15.61 (![X1 : a]: (~ '#sk1'('#sk6', X1) | '#sk21'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['34'])). 104.56/15.61 tff('49', plain, 104.56/15.61 (![X0 : a > $o]: ( '#form147'(X0) | '#sk21'('#sk178'(X0)))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['47', '48'])). 104.56/15.61 tff('50', plain, ![X1 : a > $o]: (~ X1('#sk178'(X1)) | '#form147'(X1)), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['46'])). 104.56/15.61 tff('51', plain, 104.56/15.61 (( '#form147'((^[Y0 : a]: '#sk21'(Y0))) 104.56/15.61 | '#form147'((^[Y0 : a]: '#sk21'((^[Y1 : a]: Y1)(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['49', '50'])). 104.56/15.61 tff('52', plain, 104.56/15.61 (( '#form147'('#sk21') | '#form147'('#sk21'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('ho_norm', [status(thm)], ['51'])). 104.56/15.61 tff('53', plain, 104.56/15.61 ( '#form147'('#sk21')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1)))))))))))))), 104.56/15.61 inference('simplify', [status(thm)], ['52'])). 104.56/15.61 tff('54', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & X1(Y0)) => X1(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0)))))) => 104.56/15.61 X1('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['39'])). 104.56/15.61 tff('55', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))) => 104.56/15.61 '#sk21'('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('triggered_bool_instantiation', [status(thm)], ['54'])). 104.56/15.61 tff('56', plain, 104.56/15.61 ((~ ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))) 104.56/15.61 | '#sk21'('#sk11'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk11'))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['55'])). 104.56/15.61 tff('57', plain, 104.56/15.61 (~ ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))))), 104.56/15.61 inference('split', [status(esa)], ['56'])). 104.56/15.61 tff('58', plain, 104.56/15.61 ((~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['57'])). 104.56/15.61 tff('59', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('split', [status(esa)], ['58'])). 104.56/15.61 tff('60', plain, 104.56/15.61 ![X1 : a > $o]: 104.56/15.61 ( '#form147'(X1) | ~ (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => X1(Y0)))))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('61', plain, 104.56/15.61 (~ '#form147'('#sk21')) 104.56/15.61 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.61 inference('renaming', [status(thm)], ['59', '60'])). 104.56/15.61 tff('62', plain, 104.56/15.61 ( (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))) | 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['53', '61'])). 104.56/15.61 tff('63', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('split', [status(esa)], ['6'])). 104.56/15.61 tff('64', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (((!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (('#sk2'('#sk7', Y3) | 104.56/15.61 '#sk1'('#sk7', Y3)) => 104.56/15.61 Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y0))))) & 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.61 Y2(Y3))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4))))))))) => 104.56/15.61 Y2(Y1)))))) => 104.56/15.61 (!!((^[Y2 : a > $o]: 104.56/15.61 (((!!((^[Y3 : a]: 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 ((Y2(Y3) & 104.56/15.61 ('#sk2'(Y3, Y4) | 104.56/15.61 '#sk1'(Y3, Y4))) => 104.56/15.61 Y2(Y4)))))))) & 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 (('#sk2'('#sk7', Y3) | 104.56/15.61 '#sk1'('#sk7', Y3)) => 104.56/15.61 Y2(Y3)))))) => 104.56/15.61 Y2(Y1))))))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['63'])). 104.56/15.61 tff('65', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (((!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (('#sk2'('#sk7', Y2) | '#sk1'('#sk7', Y2)) => 104.56/15.61 Y1(Y2))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 104.56/15.61 Y1(Y3))))))))) => 104.56/15.61 Y1('#sk12'))))) & 104.56/15.61 (!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (('#sk1'('#sk12', Y2) | '#sk2'('#sk12', Y2)) => 104.56/15.61 Y1(Y2))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 104.56/15.61 Y1(Y3))))))))) => 104.56/15.61 Y1(Y0)))))) => 104.56/15.61 (!!((^[Y1 : a > $o]: 104.56/15.61 (((!!((^[Y2 : a]: 104.56/15.61 (!!((^[Y3 : a]: 104.56/15.61 ((Y1(Y2) & 104.56/15.61 ('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3))) => 104.56/15.61 Y1(Y3)))))))) & 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (('#sk2'('#sk7', Y2) | '#sk1'('#sk7', Y2)) => 104.56/15.61 Y1(Y2)))))) => 104.56/15.61 Y1(Y0)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['64'])). 104.56/15.61 tff('66', plain, 104.56/15.61 (~ (((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk12'))))) & 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk1'('#sk12', Y1) | '#sk2'('#sk12', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk16')))))) => 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk16'))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['65'])). 104.56/15.61 tff('67', plain, 104.56/15.61 ( ((!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk12'))))) & 104.56/15.61 (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk1'('#sk12', Y1) | '#sk2'('#sk12', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk16'))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['66'])). 104.56/15.61 tff('68', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk12')))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['67'])). 104.56/15.61 tff('69', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 X1(Y1))))))))) => 104.56/15.61 X1('#sk12'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['68'])). 104.56/15.61 tff('70', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) => 104.56/15.61 '#sk27'('#sk12'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('triggered_bool_instantiation', [status(thm)], ['69'])). 104.56/15.61 tff('71', plain, 104.56/15.61 ((~ ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) 104.56/15.61 | '#sk27'('#sk12'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['70'])). 104.56/15.61 tff('72', plain, 104.56/15.61 (~ ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))))), 104.56/15.61 inference('split', [status(esa)], ['71'])). 104.56/15.61 tff('73', plain, 104.56/15.61 ((~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['72'])). 104.56/15.61 tff('74', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('split', [status(esa)], ['73'])). 104.56/15.61 tff('75', plain, 104.56/15.61 (~ (('#sk2'('#sk7', '#sk122'('#sk27')) | 104.56/15.61 '#sk1'('#sk7', '#sk122'('#sk27'))) => 104.56/15.61 '#sk27'('#sk122'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['74'])). 104.56/15.61 tff('76', plain, 104.56/15.61 ( ('#sk2'('#sk7', '#sk122'('#sk27')) | '#sk1'('#sk7', '#sk122'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['75'])). 104.56/15.61 tff('77', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4')))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('split', [status(esa)], ['6'])). 104.56/15.61 tff('78', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 ((X1(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 X1(Y1))))))))) => 104.56/15.61 X1('#sk4'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['77'])). 104.56/15.61 tff('79', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1))))))))) => 104.56/15.61 '#sk5'('#sk4'))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('triggered_bool_instantiation', [status(thm)], ['78'])). 104.56/15.61 tff('80', plain, 104.56/15.61 ~ (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['4'])). 104.56/15.61 tff('81', plain, 104.56/15.61 ~ (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1))))))))) => 104.56/15.61 '#sk5'('#sk4')), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['80'])). 104.56/15.61 tff('82', plain, ~ '#sk5'('#sk4'), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['81'])). 104.56/15.61 tff('83', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1))))))))) => 104.56/15.61 $false)) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('demod', [status(thm)], ['79', '82'])). 104.56/15.61 tff('84', plain, 104.56/15.61 ( (~(((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1)))))))))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('simplify boolean subterms', [status(thm)], ['83'])). 104.56/15.61 tff('85', plain, 104.56/15.61 (~ ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1)))))))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('simplify nested equalities', [status(thm)], ['84'])). 104.56/15.61 tff('86', plain, 104.56/15.61 ((~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1)))))))))) 104.56/15.61 <= (( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => 104.56/15.61 Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & 104.56/15.61 ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk4'))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['85'])). 104.56/15.61 tff('87', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('split', [status(esa)], ['86'])). 104.56/15.61 tff('88', plain, 104.56/15.61 (~ (('#sk2'('#sk3', '#sk20'('#sk5')) | '#sk1'('#sk3', '#sk20'('#sk5'))) => 104.56/15.61 '#sk5'('#sk20'('#sk5')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['87'])). 104.56/15.61 tff('89', plain, 104.56/15.61 ( ('#sk2'('#sk3', '#sk20'('#sk5')) | '#sk1'('#sk3', '#sk20'('#sk5')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['88'])). 104.56/15.61 tff('90', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 (~ '#form189'(X1, X2) | ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('91', plain, 104.56/15.61 ( '#form189'('#sk7', '#sk122'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('renaming', [status(thm)], ['76', '90'])). 104.56/15.61 tff('92', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 (~ '#form189'(X1, X2) | ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('93', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 ( '#sk2'(X1, X2) | '#sk1'(X1, X2) | ~ '#form189'(X1, X2)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['92'])). 104.56/15.61 tff('94', plain, 104.56/15.61 (( '#sk1'('#sk7', '#sk122'('#sk27')) | '#sk2'('#sk7', '#sk122'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('sup-', [status(thm)], ['91', '93'])). 104.56/15.61 tff('95', plain, 104.56/15.61 ( '#sk1'('#sk7', '#sk122'('#sk27'))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) | 104.56/15.61 ( '#sk2'('#sk7', '#sk122'('#sk27'))), 104.56/15.61 inference('split', [status(esa)], ['94'])). 104.56/15.61 tff('96', plain, 104.56/15.61 ( '#sk2'('#sk7', '#sk122'('#sk27'))) 104.56/15.61 <= (( '#sk2'('#sk7', '#sk122'('#sk27')))), 104.56/15.61 inference('split', [status(esa)], ['94'])). 104.56/15.61 tff('97', plain, 104.56/15.61 (~ (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2)))))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk2'('#sk7', Y1) | '#sk1'('#sk7', Y1)) => Y0(Y1)))))) => 104.56/15.61 Y0('#sk16')))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['66'])). 104.56/15.61 tff('98', plain, 104.56/15.61 (~ (((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) => 104.56/15.61 '#sk27'('#sk16'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['97'])). 104.56/15.61 tff('99', plain, 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['98'])). 104.56/15.61 tff('100', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['99'])). 104.56/15.61 tff('101', plain, 104.56/15.61 (![X1 : a]: (('#sk2'('#sk7', X1) | '#sk1'('#sk7', X1)) => '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['100'])). 104.56/15.61 tff('102', plain, 104.56/15.61 (![X1 : a]: (~ ('#sk2'('#sk7', X1) | '#sk1'('#sk7', X1)) | '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['101'])). 104.56/15.61 tff('103', plain, 104.56/15.61 (![X1 : a]: (~ '#sk2'('#sk7', X1) | '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['102'])). 104.56/15.61 tff('104', plain, 104.56/15.61 ( '#sk27'('#sk122'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) & 104.56/15.61 ( '#sk2'('#sk7', '#sk122'('#sk27')))), 104.56/15.61 inference('sup-', [status(thm)], ['96', '103'])). 104.56/15.61 tff('105', plain, 104.56/15.61 (~ '#sk27'('#sk122'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['75'])). 104.56/15.61 tff('106', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) | 104.56/15.61 ~ ( '#sk2'('#sk7', '#sk122'('#sk27'))), 104.56/15.61 inference('sup-', [status(thm)], ['104', '105'])). 104.56/15.61 tff('107', plain, 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) | 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) | 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))), 104.56/15.61 inference('split', [status(esa)], ['73'])). 104.56/15.61 tff('108', plain, 104.56/15.61 ( '#sk27'('#sk12')) | 104.56/15.61 ~ 104.56/15.61 ( ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))), 104.56/15.61 inference('split', [status(esa)], ['71'])). 104.56/15.61 tff('109', plain, 104.56/15.61 ( (!!((^[Y0 : a > $o]: 104.56/15.61 (((!!((^[Y1 : a]: 104.56/15.61 (('#sk1'('#sk12', Y1) | '#sk2'('#sk12', Y1)) => Y0(Y1))))) & 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 ((Y0(Y1) & ('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2))) => 104.56/15.61 Y0(Y2))))))))) => 104.56/15.61 Y0('#sk16')))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['67'])). 104.56/15.61 tff('110', plain, 104.56/15.61 (![X1 : a > $o]: 104.56/15.61 (((!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => X1(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 X1(Y1))))))))) => 104.56/15.61 X1('#sk16'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['109'])). 104.56/15.61 tff('111', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) => 104.56/15.61 '#sk27'('#sk16'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('triggered_bool_instantiation', [status(thm)], ['110'])). 104.56/15.61 tff('112', plain, 104.56/15.61 (~ '#sk27'('#sk16')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['98'])). 104.56/15.61 tff('113', plain, 104.56/15.61 ( (((!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) => 104.56/15.61 $false)) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('demod', [status(thm)], ['111', '112'])). 104.56/15.61 tff('114', plain, 104.56/15.61 ( (~(((!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('simplify boolean subterms', [status(thm)], ['113'])). 104.56/15.61 tff('115', plain, 104.56/15.61 (~ ((!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('simplify nested equalities', [status(thm)], ['114'])). 104.56/15.61 tff('116', plain, 104.56/15.61 ((~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0))))) 104.56/15.61 | ~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['115'])). 104.56/15.61 tff('117', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => 104.56/15.61 '#sk27'(Y0))))))), 104.56/15.61 inference('split', [status(esa)], ['116'])). 104.56/15.61 tff('118', plain, 104.56/15.61 (~ (('#sk1'('#sk12', '#sk127'('#sk27')) | 104.56/15.61 '#sk2'('#sk12', '#sk127'('#sk27'))) => 104.56/15.61 '#sk27'('#sk127'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => 104.56/15.61 '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['117'])). 104.56/15.61 tff('119', plain, 104.56/15.61 ( ('#sk1'('#sk12', '#sk127'('#sk27')) | 104.56/15.61 '#sk2'('#sk12', '#sk127'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => 104.56/15.61 '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['118'])). 104.56/15.61 tff('120', plain, 104.56/15.61 (( '#sk1'('#sk12', '#sk127'('#sk27')) 104.56/15.61 | '#sk2'('#sk12', '#sk127'('#sk27')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => 104.56/15.61 '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['119'])). 104.56/15.61 tff('121', plain, 104.56/15.61 ( '#sk1'('#sk12', '#sk127'('#sk27'))) 104.56/15.61 <= (( '#sk1'('#sk12', '#sk127'('#sk27')))), 104.56/15.61 inference('split', [status(esa)], ['120'])). 104.56/15.61 tff('122', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['99'])). 104.56/15.61 tff('123', plain, 104.56/15.61 (![X1 : a]: 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk27'(X1) & ('#sk2'(X1, Y0) | '#sk1'(X1, Y0))) => 104.56/15.61 '#sk27'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['122'])). 104.56/15.61 tff('124', plain, 104.56/15.61 (![X1 : a, X2 : a]: 104.56/15.61 (('#sk27'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) => '#sk27'(X2))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['123'])). 104.56/15.61 tff('125', plain, 104.56/15.61 (![X1 : a, X2 : a]: 104.56/15.61 (~ ('#sk27'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) | '#sk27'(X2))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['124'])). 104.56/15.61 tff('126', plain, 104.56/15.61 (![X1 : a, X2 : a]: 104.56/15.61 (~ '#sk27'(X1) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk27'(X2))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['125'])). 104.56/15.61 tff('127', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 ( '#form189'(X1, X2) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('128', plain, 104.56/15.61 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#form189'(X1, X2)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['127'])). 104.56/15.61 tff('129', plain, 104.56/15.61 (![X1 : a, X2 : a]: 104.56/15.61 (~ '#sk27'(X1) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk27'(X2))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['125'])). 104.56/15.61 tff('130', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 ( '#form189'(X1, X2) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('131', plain, 104.56/15.61 (![X1 : a, X2 : a]: (~ '#form189'(X1, X2) | '#sk27'(X2) | ~ '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('renaming', [status(thm)], ['129', '130'])). 104.56/15.61 tff('132', plain, 104.56/15.61 (![X0 : a, X1 : a]: (~ '#sk1'(X1, X0) | ~ '#sk27'(X1) | '#sk27'(X0))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['128', '131'])). 104.56/15.61 tff('133', plain, 104.56/15.61 (( '#sk27'('#sk127'('#sk27')) | ~ '#sk27'('#sk12'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) & 104.56/15.61 ( '#sk1'('#sk12', '#sk127'('#sk27')))), 104.56/15.61 inference('sup-', [status(thm)], ['121', '132'])). 104.56/15.61 tff('134', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) | 104.56/15.61 ~ ( '#sk1'('#sk12', '#sk127'('#sk27'))) | ~ ( '#sk27'('#sk12')) | 104.56/15.61 ( '#sk27'('#sk127'('#sk27'))), inference('split', [status(esa)], ['133'])). 104.56/15.61 tff('135', plain, 104.56/15.61 ( '#sk2'('#sk12', '#sk127'('#sk27'))) 104.56/15.61 <= (( '#sk2'('#sk12', '#sk127'('#sk27')))), 104.56/15.61 inference('split', [status(esa)], ['120'])). 104.56/15.61 tff('136', plain, 104.56/15.61 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#form189'(X1, X2)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['127'])). 104.56/15.61 tff('137', plain, 104.56/15.61 (![X1 : a, X2 : a]: (~ '#form189'(X1, X2) | '#sk27'(X2) | ~ '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('renaming', [status(thm)], ['129', '130'])). 104.56/15.61 tff('138', plain, 104.56/15.61 (![X0 : a, X1 : a]: (~ '#sk2'(X1, X0) | ~ '#sk27'(X1) | '#sk27'(X0))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['136', '137'])). 104.56/15.61 tff('139', plain, 104.56/15.61 (( '#sk27'('#sk127'('#sk27')) | ~ '#sk27'('#sk12'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) & 104.56/15.61 ( '#sk2'('#sk12', '#sk127'('#sk27')))), 104.56/15.61 inference('sup-', [status(thm)], ['135', '138'])). 104.56/15.61 tff('140', plain, 104.56/15.61 ( '#sk27'('#sk127'('#sk27'))) | 104.56/15.61 ~ ( '#sk2'('#sk12', '#sk127'('#sk27'))) | ~ ( '#sk27'('#sk12')) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))), 104.56/15.61 inference('split', [status(esa)], ['139'])). 104.56/15.61 tff('141', plain, 104.56/15.61 ( '#sk1'('#sk12', '#sk127'('#sk27'))) | 104.56/15.61 ( '#sk2'('#sk12', '#sk127'('#sk27'))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0)))))), 104.56/15.61 inference('split', [status(esa)], ['120'])). 104.56/15.61 tff('142', plain, 104.56/15.61 ( '#sk27'('#sk127'('#sk27'))) <= (( '#sk27'('#sk127'('#sk27')))), 104.56/15.61 inference('split', [status(esa)], ['139'])). 104.56/15.61 tff('143', plain, 104.56/15.61 (~ '#sk27'('#sk127'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => 104.56/15.61 '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['118'])). 104.56/15.61 tff('144', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0)))))) | 104.56/15.61 ~ ( '#sk27'('#sk127'('#sk27'))), 104.56/15.61 inference('sup-', [status(thm)], ['142', '143'])). 104.56/15.61 tff('145', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) | 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) | 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk1'('#sk12', Y0) | '#sk2'('#sk12', Y0)) => '#sk27'(Y0)))))), 104.56/15.61 inference('split', [status(esa)], ['116'])). 104.56/15.61 tff('146', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('split', [status(esa)], ['73'])). 104.56/15.61 tff('147', plain, 104.56/15.61 (~ (!!((^[Y0 : a]: 104.56/15.61 (('#sk27'('#sk437') & 104.56/15.61 ('#sk2'('#sk437', Y0) | '#sk1'('#sk437', Y0))) => 104.56/15.61 '#sk27'(Y0)))))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['146'])). 104.56/15.61 tff('148', plain, 104.56/15.61 (~ (('#sk27'('#sk437') & 104.56/15.61 ('#sk2'('#sk437', '#sk438') | '#sk1'('#sk437', '#sk438'))) => 104.56/15.61 '#sk27'('#sk438'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_exists', [status(thm)], ['147'])). 104.56/15.61 tff('149', plain, 104.56/15.61 ( ('#sk27'('#sk437') & 104.56/15.61 ('#sk2'('#sk437', '#sk438') | '#sk1'('#sk437', '#sk438')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['148'])). 104.56/15.61 tff('150', plain, 104.56/15.61 ( ('#sk2'('#sk437', '#sk438') | '#sk1'('#sk437', '#sk438'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['149'])). 104.56/15.61 tff('151', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 (~ '#form189'(X1, X2) | ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('152', plain, 104.56/15.61 ( '#form189'('#sk437', '#sk438')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('renaming', [status(thm)], ['150', '151'])). 104.56/15.61 tff('153', plain, 104.56/15.61 (![X1 : a, X2 : a]: (~ '#form189'(X1, X2) | '#sk27'(X2) | ~ '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('renaming', [status(thm)], ['129', '130'])). 104.56/15.61 tff('154', plain, 104.56/15.61 ((~ '#sk27'('#sk437') | '#sk27'('#sk438'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) & 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['152', '153'])). 104.56/15.61 tff('155', plain, 104.56/15.61 ( '#sk27'('#sk437')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['149'])). 104.56/15.61 tff('156', plain, 104.56/15.61 ( '#sk27'('#sk438')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) & 104.56/15.61 ~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('demod', [status(thm)], ['154', '155'])). 104.56/15.61 tff('157', plain, 104.56/15.61 (~ '#sk27'('#sk438')) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1)))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['148'])). 104.56/15.61 tff('158', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk27'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.61 '#sk27'(Y1))))))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))), 104.56/15.61 inference('sup-', [status(thm)], ['156', '157'])). 104.56/15.61 tff('159', plain, 104.56/15.61 ( '#sk1'('#sk7', '#sk122'('#sk27'))) 104.56/15.61 <= (( '#sk1'('#sk7', '#sk122'('#sk27')))), 104.56/15.61 inference('split', [status(esa)], ['94'])). 104.56/15.61 tff('160', plain, 104.56/15.61 (![X1 : a]: (~ '#sk1'('#sk7', X1) | '#sk27'(X1))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2))))))))))))))))), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['102'])). 104.56/15.61 tff('161', plain, 104.56/15.61 ( '#sk27'('#sk122'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) & 104.56/15.61 ( '#sk1'('#sk7', '#sk122'('#sk27')))), 104.56/15.61 inference('sup-', [status(thm)], ['159', '160'])). 104.56/15.61 tff('162', plain, 104.56/15.61 (~ '#sk27'('#sk122'('#sk27'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['75'])). 104.56/15.61 tff('163', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk27'(Y0)))))) | 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (!!((^[Y2 : a]: 104.56/15.61 (((!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | 104.56/15.61 '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y1))))) & 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (('#sk1'(Y1, Y4) | 104.56/15.61 '#sk2'(Y1, Y4)) => 104.56/15.61 Y3(Y4))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5))))))))) => 104.56/15.61 Y3(Y2)))))) => 104.56/15.61 (!!((^[Y3 : a > $o]: 104.56/15.61 (((!!((^[Y4 : a]: 104.56/15.61 (!!((^[Y5 : a]: 104.56/15.61 ((Y3(Y4) & 104.56/15.61 ('#sk2'(Y4, Y5) | 104.56/15.61 '#sk1'(Y4, Y5))) => 104.56/15.61 Y3(Y5)))))))) & 104.56/15.61 (!!((^[Y4 : a]: 104.56/15.61 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.61 Y3(Y4)))))) => 104.56/15.61 Y3(Y2)))))))))))))))) | 104.56/15.61 ~ ( '#sk1'('#sk7', '#sk122'('#sk27'))), 104.56/15.61 inference('sup-', [status(thm)], ['161', '162'])). 104.56/15.61 tff('164', plain, 104.56/15.61 ( ('#sk2'('#sk3', '#sk20'('#sk5')) | '#sk1'('#sk3', '#sk20'('#sk5')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['88'])). 104.56/15.61 tff('165', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 (~ '#form189'(X1, X2) | ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.61 define([status(thm)])). 104.56/15.61 tff('166', plain, 104.56/15.61 ( '#form189'('#sk3', '#sk20'('#sk5'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('renaming', [status(thm)], ['164', '165'])). 104.56/15.61 tff('167', plain, 104.56/15.61 ![X1 : a, X2 : a]: 104.56/15.61 ( '#sk2'(X1, X2) | '#sk1'(X1, X2) | ~ '#form189'(X1, X2)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['92'])). 104.56/15.61 tff('168', plain, 104.56/15.61 (( '#sk1'('#sk3', '#sk20'('#sk5')) | '#sk2'('#sk3', '#sk20'('#sk5')))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('sup-', [status(thm)], ['166', '167'])). 104.56/15.61 tff('169', plain, 104.56/15.61 ( '#sk2'('#sk3', '#sk20'('#sk5'))) 104.56/15.61 <= (( '#sk2'('#sk3', '#sk20'('#sk5')))), 104.56/15.61 inference('split', [status(esa)], ['168'])). 104.56/15.61 tff('170', plain, 104.56/15.61 ((!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))) & 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (!!((^[Y1 : a]: 104.56/15.61 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.61 '#sk5'(Y1))))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['81'])). 104.56/15.61 tff('171', plain, 104.56/15.61 (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))), 104.56/15.61 inference('lazy_cnf_and', [status(thm)], ['170'])). 104.56/15.61 tff('172', plain, 104.56/15.61 ![X1 : a]: (('#sk2'('#sk3', X1) | '#sk1'('#sk3', X1)) => '#sk5'(X1)), 104.56/15.61 inference('lazy_cnf_forall', [status(thm)], ['171'])). 104.56/15.61 tff('173', plain, 104.56/15.61 ![X1 : a]: (~ ('#sk2'('#sk3', X1) | '#sk1'('#sk3', X1)) | '#sk5'(X1)), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['172'])). 104.56/15.61 tff('174', plain, ![X1 : a]: (~ '#sk2'('#sk3', X1) | '#sk5'(X1)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['173'])). 104.56/15.61 tff('175', plain, 104.56/15.61 ( '#sk5'('#sk20'('#sk5'))) <= (( '#sk2'('#sk3', '#sk20'('#sk5')))), 104.56/15.61 inference('sup-', [status(thm)], ['169', '174'])). 104.56/15.61 tff('176', plain, 104.56/15.61 (~ '#sk5'('#sk20'('#sk5'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['88'])). 104.56/15.61 tff('177', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0)))))) | 104.56/15.61 ~ ( '#sk2'('#sk3', '#sk20'('#sk5'))), 104.56/15.61 inference('sup-', [status(thm)], ['175', '176'])). 104.56/15.61 tff('178', plain, 104.56/15.61 ( '#sk1'('#sk3', '#sk20'('#sk5'))) 104.56/15.61 <= (( '#sk1'('#sk3', '#sk20'('#sk5')))), 104.56/15.61 inference('split', [status(esa)], ['168'])). 104.56/15.61 tff('179', plain, ![X1 : a]: (~ '#sk1'('#sk3', X1) | '#sk5'(X1)), 104.56/15.61 inference('lazy_cnf_or', [status(thm)], ['173'])). 104.56/15.61 tff('180', plain, 104.56/15.61 ( '#sk5'('#sk20'('#sk5'))) <= (( '#sk1'('#sk3', '#sk20'('#sk5')))), 104.56/15.61 inference('sup-', [status(thm)], ['178', '179'])). 104.56/15.61 tff('181', plain, 104.56/15.61 (~ '#sk5'('#sk20'('#sk5'))) 104.56/15.61 <= (~ 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0))))))), 104.56/15.61 inference('lazy_cnf_imply', [status(thm)], ['88'])). 104.56/15.61 tff('182', plain, 104.56/15.61 ( (!!((^[Y0 : a]: 104.56/15.61 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0)))))) | 104.56/15.62 ~ ( '#sk1'('#sk3', '#sk20'('#sk5'))), 104.56/15.62 inference('sup-', [status(thm)], ['180', '181'])). 104.56/15.62 tff('183', plain, 104.56/15.62 ( '#sk2'('#sk3', '#sk20'('#sk5'))) | 104.56/15.62 ( '#sk1'('#sk3', '#sk20'('#sk5'))) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0)))))), 104.56/15.62 inference('split', [status(esa)], ['168'])). 104.56/15.62 tff('184', plain, 104.56/15.62 (![X1 : a > $o]: 104.56/15.62 (((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => X1(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 ((X1(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 X1(Y1))))))))) => 104.56/15.62 X1('#sk12'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 (((!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y1))))) & 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y1, Y4) | 104.56/15.62 '#sk2'(Y1, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y2)))))) => 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5)))))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4)))))) => 104.56/15.62 Y3(Y2))))))))))))))))), 104.56/15.62 inference('lazy_cnf_forall', [status(thm)], ['68'])). 104.56/15.62 tff('185', plain, 104.56/15.62 ( (((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))) => 104.56/15.62 '#sk5'('#sk12'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 (((!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y1))))) & 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y1, Y4) | 104.56/15.62 '#sk2'(Y1, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y2)))))) => 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5)))))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4)))))) => 104.56/15.62 Y3(Y2))))))))))))))))), 104.56/15.62 inference('triggered_bool_instantiation', [status(thm)], ['184'])). 104.56/15.62 tff('186', plain, 104.56/15.62 ((~ ((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))) 104.56/15.62 | '#sk5'('#sk12'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 (((!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y1))))) & 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y1, Y4) | 104.56/15.62 '#sk2'(Y1, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y2)))))) => 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5)))))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4)))))) => 104.56/15.62 Y3(Y2))))))))))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['185'])). 104.56/15.62 tff('187', plain, 104.56/15.62 (~ ((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))) 104.56/15.62 <= (~ 104.56/15.62 ( ((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))))), 104.56/15.62 inference('split', [status(esa)], ['186'])). 104.56/15.62 tff('188', plain, 104.56/15.62 ((~ (!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) 104.56/15.62 | ~ (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))) 104.56/15.62 <= (~ 104.56/15.62 ( ((!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk7', Y0) | '#sk1'('#sk7', Y0)) => '#sk5'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['187'])). 104.56/15.62 tff('189', plain, 104.56/15.62 (~ (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('split', [status(esa)], ['188'])). 104.56/15.62 tff('190', plain, 104.56/15.62 (~ (!!((^[Y0 : a]: 104.56/15.62 (('#sk5'('#sk441') & 104.56/15.62 ('#sk2'('#sk441', Y0) | '#sk1'('#sk441', Y0))) => 104.56/15.62 '#sk5'(Y0)))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['189'])). 104.56/15.62 tff('191', plain, 104.56/15.62 (~ (('#sk5'('#sk441') & 104.56/15.62 ('#sk2'('#sk441', '#sk442') | '#sk1'('#sk441', '#sk442'))) => 104.56/15.62 '#sk5'('#sk442'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['190'])). 104.56/15.62 tff('192', plain, 104.56/15.62 ( ('#sk5'('#sk441') & 104.56/15.62 ('#sk2'('#sk441', '#sk442') | '#sk1'('#sk441', '#sk442')))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['191'])). 104.56/15.62 tff('193', plain, 104.56/15.62 ( ('#sk2'('#sk441', '#sk442') | '#sk1'('#sk441', '#sk442'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['192'])). 104.56/15.62 tff('194', plain, 104.56/15.62 ![X1 : a, X2 : a]: 104.56/15.62 (~ '#form189'(X1, X2) | ('#sk2'(X1, X2) | '#sk1'(X1, X2))), 104.56/15.62 define([status(thm)])). 104.56/15.62 tff('195', plain, 104.56/15.62 ( '#form189'('#sk441', '#sk442')) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('renaming', [status(thm)], ['193', '194'])). 104.56/15.62 tff('196', plain, 104.56/15.62 ![X1 : a, X2 : a]: 104.56/15.62 ( '#sk2'(X1, X2) | '#sk1'(X1, X2) | ~ '#form189'(X1, X2)), 104.56/15.62 inference('lazy_cnf_or', [status(thm)], ['92'])). 104.56/15.62 tff('197', plain, 104.56/15.62 (( '#sk1'('#sk441', '#sk442') | '#sk2'('#sk441', '#sk442'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('sup-', [status(thm)], ['195', '196'])). 104.56/15.62 tff('198', plain, 104.56/15.62 ( '#sk2'('#sk441', '#sk442')) | ( '#sk1'('#sk441', '#sk442')) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))), 104.56/15.62 inference('split', [status(esa)], ['197'])). 104.56/15.62 tff('199', plain, 104.56/15.62 ( '#sk1'('#sk441', '#sk442')) <= (( '#sk1'('#sk441', '#sk442'))), 104.56/15.62 inference('split', [status(esa)], ['197'])). 104.56/15.62 tff('200', plain, 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['170'])). 104.56/15.62 tff('201', plain, 104.56/15.62 ![X1 : a]: 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (('#sk5'(X1) & ('#sk2'(X1, Y0) | '#sk1'(X1, Y0))) => '#sk5'(Y0))))), 104.56/15.62 inference('lazy_cnf_forall', [status(thm)], ['200'])). 104.56/15.62 tff('202', plain, 104.56/15.62 ![X1 : a, X2 : a]: 104.56/15.62 (('#sk5'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) => '#sk5'(X2)), 104.56/15.62 inference('lazy_cnf_forall', [status(thm)], ['201'])). 104.56/15.62 tff('203', plain, 104.56/15.62 ![X1 : a, X2 : a]: 104.56/15.62 (~ ('#sk5'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) | '#sk5'(X2)), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['202'])). 104.56/15.62 tff('204', plain, 104.56/15.62 ![X1 : a, X2 : a]: 104.56/15.62 (~ '#sk5'(X1) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk5'(X2)), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['203'])). 104.56/15.62 tff('205', plain, 104.56/15.62 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 104.56/15.62 inference('lazy_cnf_or', [status(thm)], ['204'])). 104.56/15.62 tff('206', plain, 104.56/15.62 ((~ '#sk5'('#sk441') | '#sk5'('#sk442'))) 104.56/15.62 <= (( '#sk1'('#sk441', '#sk442'))), 104.56/15.62 inference('sup-', [status(thm)], ['199', '205'])). 104.56/15.62 tff('207', plain, ( '#sk5'('#sk442')) <= (( '#sk5'('#sk442'))), 104.56/15.62 inference('split', [status(esa)], ['206'])). 104.56/15.62 tff('208', plain, 104.56/15.62 (~ '#sk5'('#sk442')) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['191'])). 104.56/15.62 tff('209', plain, 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))) | 104.56/15.62 ~ ( '#sk5'('#sk442')), inference('sup-', [status(thm)], ['207', '208'])). 104.56/15.62 tff('210', plain, 104.56/15.62 ( '#sk5'('#sk441')) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['192'])). 104.56/15.62 tff('211', plain, (~ '#sk5'('#sk441')) <= (~ ( '#sk5'('#sk441'))), 104.56/15.62 inference('split', [status(esa)], ['206'])). 104.56/15.62 tff('212', plain, 104.56/15.62 ( '#sk5'('#sk441')) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))), 104.56/15.62 inference('sup-', [status(thm)], ['210', '211'])). 104.56/15.62 tff('213', plain, 104.56/15.62 ( '#sk5'('#sk442')) | ~ ( '#sk5'('#sk441')) | 104.56/15.62 ~ ( '#sk1'('#sk441', '#sk442')), 104.56/15.62 inference('split', [status(esa)], ['206'])). 104.56/15.62 tff('214', plain, 104.56/15.62 ( '#sk2'('#sk441', '#sk442')) <= (( '#sk2'('#sk441', '#sk442'))), 104.56/15.62 inference('split', [status(esa)], ['197'])). 104.56/15.62 tff('215', plain, 104.56/15.62 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 104.56/15.62 inference('lazy_cnf_or', [status(thm)], ['204'])). 104.56/15.62 tff('216', plain, 104.56/15.62 ((~ '#sk5'('#sk441') | '#sk5'('#sk442'))) 104.56/15.62 <= (( '#sk2'('#sk441', '#sk442'))), 104.56/15.62 inference('sup-', [status(thm)], ['214', '215'])). 104.56/15.62 tff('217', plain, 104.56/15.62 ( '#sk5'('#sk442')) | ~ ( '#sk2'('#sk441', '#sk442')) | 104.56/15.62 ~ ( '#sk5'('#sk441')), inference('split', [status(esa)], ['216'])). 104.56/15.62 tff('218', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: 104.56/15.62 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.62 Y0(Y2))))))))) => 104.56/15.62 Y0('#sk4')))))) | 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk5'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 104.56/15.62 '#sk5'(Y1))))))))) | 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (('#sk2'('#sk3', Y0) | '#sk1'('#sk3', Y0)) => '#sk5'(Y0)))))), 104.56/15.62 inference('split', [status(esa)], ['86'])). 104.56/15.62 tff('219', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))))))))))) | 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: 104.56/15.62 (('#sk2'('#sk3', Y1) | '#sk1'('#sk3', Y1)) => Y0(Y1))))) & 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 104.56/15.62 Y0(Y2))))))))) => 104.56/15.62 Y0('#sk4')))))) | 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: 104.56/15.62 (((!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | 104.56/15.62 '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y1))))) & 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y1, Y4) | 104.56/15.62 '#sk2'(Y1, Y4)) => 104.56/15.62 Y3(Y4))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5))))))))) => 104.56/15.62 Y3(Y2)))))) => 104.56/15.62 (!!((^[Y3 : a > $o]: 104.56/15.62 (((!!((^[Y4 : a]: 104.56/15.62 (!!((^[Y5 : a]: 104.56/15.62 ((Y3(Y4) & 104.56/15.62 ('#sk2'(Y4, Y5) | 104.56/15.62 '#sk1'(Y4, Y5))) => 104.56/15.62 Y3(Y5)))))))) & 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 104.56/15.62 Y3(Y4)))))) => 104.56/15.62 Y3(Y2)))))))))))))))), 104.56/15.62 inference('split', [status(esa)], ['6'])). 104.56/15.62 tff('220', plain, 104.56/15.62 (~ (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1))))))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('split', [status(esa)], ['58'])). 104.56/15.62 tff('221', plain, 104.56/15.62 (~ (!!((^[Y0 : a]: 104.56/15.62 (('#sk1'('#sk94'('#sk21'), Y0) & '#sk21'('#sk94'('#sk21'))) => 104.56/15.62 '#sk21'(Y0)))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['220'])). 104.56/15.62 tff('222', plain, 104.56/15.62 (~ (('#sk1'('#sk94'('#sk21'), '#sk117'('#sk21')) & 104.56/15.62 '#sk21'('#sk94'('#sk21'))) => 104.56/15.62 '#sk21'('#sk117'('#sk21')))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['221'])). 104.56/15.62 tff('223', plain, 104.56/15.62 ( ('#sk1'('#sk94'('#sk21'), '#sk117'('#sk21')) & 104.56/15.62 '#sk21'('#sk94'('#sk21')))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['222'])). 104.56/15.62 tff('224', plain, 104.56/15.62 ( '#sk1'('#sk94'('#sk21'), '#sk117'('#sk21'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['223'])). 104.56/15.62 tff('225', plain, 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk21'(Y0) & ('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1))) => 104.56/15.62 '#sk21'(Y1))))))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['31'])). 104.56/15.62 tff('226', plain, 104.56/15.62 (![X1 : a]: 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (('#sk21'(X1) & ('#sk2'(X1, Y0) | '#sk1'(X1, Y0))) => 104.56/15.62 '#sk21'(Y0)))))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_forall', [status(thm)], ['225'])). 104.56/15.62 tff('227', plain, 104.56/15.62 (![X1 : a, X2 : a]: 104.56/15.62 (('#sk21'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) => '#sk21'(X2))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_forall', [status(thm)], ['226'])). 104.56/15.62 tff('228', plain, 104.56/15.62 (![X1 : a, X2 : a]: 104.56/15.62 (~ ('#sk21'(X1) & ('#sk2'(X1, X2) | '#sk1'(X1, X2))) | '#sk21'(X2))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['227'])). 104.56/15.62 tff('229', plain, 104.56/15.62 (![X1 : a, X2 : a]: 104.56/15.62 (~ '#sk21'(X1) | ~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | '#sk21'(X2))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['228'])). 104.56/15.62 tff('230', plain, 104.56/15.62 (![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk21'(X2) | ~ '#sk21'(X1))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_or', [status(thm)], ['229'])). 104.56/15.62 tff('231', plain, 104.56/15.62 ((~ '#sk21'('#sk94'('#sk21')) | '#sk21'('#sk117'('#sk21')))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1))))))))) & 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('sup-', [status(thm)], ['224', '230'])). 104.56/15.62 tff('232', plain, 104.56/15.62 ( '#sk21'('#sk94'('#sk21'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['223'])). 104.56/15.62 tff('233', plain, 104.56/15.62 ( '#sk21'('#sk117'('#sk21'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1))))))))) & 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('demod', [status(thm)], ['231', '232'])). 104.56/15.62 tff('234', plain, 104.56/15.62 (~ '#sk21'('#sk117'('#sk21'))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['222'])). 104.56/15.62 tff('235', plain, 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1))))))))) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))))))))))), 104.56/15.62 inference('sup-', [status(thm)], ['233', '234'])). 104.56/15.62 tff('236', plain, 104.56/15.62 ( ((!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.62 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))) | 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1))))))))) | 104.56/15.62 ~ ( (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0)))))), 104.56/15.62 inference('split', [status(esa)], ['58'])). 104.56/15.62 tff('237', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.62 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.62 Y0('#sk11')))))) | 104.56/15.62 ( '#sk21'('#sk11')) | 104.56/15.62 ~ 104.56/15.62 ( ((!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk1'(Y0, Y1) & '#sk21'(Y0)) => '#sk21'(Y1)))))))) & 104.56/15.62 (!!((^[Y0 : a]: ('#sk1'('#sk6', Y0) => '#sk21'(Y0))))))), 104.56/15.62 inference('split', [status(esa)], ['56'])). 104.56/15.62 tff('238', plain, 104.56/15.62 ~ 104.56/15.62 ( ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))) | 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.62 Y0('#sk11')))))) | 104.56/15.62 ( '#sk21'('#sk11')), inference('split', [status(esa)], ['15'])). 104.56/15.62 tff('239', plain, ( '#sk21'('#sk11')) <= (( '#sk21'('#sk11'))), 104.56/15.62 inference('split', [status(esa)], ['15'])). 104.56/15.62 tff('240', plain, 104.56/15.62 (~ '#sk21'('#sk11')) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['30'])). 104.56/15.62 tff('241', plain, 104.56/15.62 ~ ( '#sk21'('#sk11')) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))))))))))), 104.56/15.62 inference('sup-', [status(thm)], ['239', '240'])). 104.56/15.62 tff('242', plain, 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: ('#sk2'('#sk6', Y1) => Y0(Y1))))) & 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2))))))))) => 104.56/15.62 Y0('#sk11')))))) | 104.56/15.62 ( (!!((^[Y0 : a > $o]: 104.56/15.62 (((!!((^[Y1 : a]: 104.56/15.62 (!!((^[Y2 : a]: (('#sk1'(Y1, Y2) & Y0(Y1)) => Y0(Y2)))))))) & 104.56/15.62 (!!((^[Y1 : a]: ('#sk1'('#sk6', Y1) => Y0(Y1)))))) => 104.56/15.62 Y0('#sk11')))))) | 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))))))))))), 104.56/15.62 inference('split', [status(esa)], ['11'])). 104.56/15.62 tff('243', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))) | 104.56/15.62 ( ((!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0))))) & 104.56/15.62 (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1)))))))))) | 104.56/15.62 ~ ( (!!((^[Y0 : a]: ('#sk2'('#sk6', Y0) => '#sk21'(Y0)))))), 104.56/15.62 inference('split', [status(esa)], ['17'])). 104.56/15.62 tff('244', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: (('#sk21'(Y0) & '#sk2'(Y0, Y1)) => '#sk21'(Y1))))))))), 104.56/15.62 inference('sat_resolution*', [status(thm)], 104.56/15.62 ['38', '62', '95', '106', '107', '108', '134', '140', '141', 104.56/15.62 '144', '145', '158', '163', '177', '182', '183', '198', 104.56/15.62 '209', '212', '213', '217', '218', '219', '235', '236', 104.56/15.62 '237', '238', '241', '242', '243'])). 104.56/15.62 tff('245', plain, ~ '#form138'('#sk21'), 104.56/15.62 inference('simpl_trail', [status(thm)], ['25', '244'])). 104.56/15.62 tff('246', plain, 104.56/15.62 ![X1 : a > $o]: 104.56/15.62 ( '#form138'(X1) 104.56/15.62 | ~ (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1))))))))), 104.56/15.62 define([status(thm)])). 104.56/15.62 tff('247', plain, 104.56/15.62 ![X1 : a > $o]: 104.56/15.62 (~ (!!((^[Y0 : a]: 104.56/15.62 ((X1('#sk166'(X1)) & '#sk2'('#sk166'(X1), Y0)) => X1(Y0))))) 104.56/15.62 | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['246'])). 104.56/15.62 tff('248', plain, 104.56/15.62 ![X1 : a > $o]: 104.56/15.62 (~ ((X1('#sk166'(X1)) & '#sk2'('#sk166'(X1), '#sk194'(X1))) => 104.56/15.62 X1('#sk194'(X1))) 104.56/15.62 | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_exists', [status(thm)], ['247'])). 104.56/15.62 tff('249', plain, 104.56/15.62 ![X1 : a > $o]: 104.56/15.62 ( (X1('#sk166'(X1)) & '#sk2'('#sk166'(X1), '#sk194'(X1))) 104.56/15.62 | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['248'])). 104.56/15.62 tff('250', plain, ![X1 : a > $o]: ( X1('#sk166'(X1)) | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['249'])). 104.56/15.62 tff('251', plain, 104.56/15.62 ![X1 : a > $o]: ( '#sk2'('#sk166'(X1), '#sk194'(X1)) | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_and', [status(thm)], ['249'])). 104.56/15.62 tff('252', plain, 104.56/15.62 (![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk21'(X2) | ~ '#sk21'(X1))) 104.56/15.62 <= (~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1)))))))))))))), 104.56/15.62 inference('lazy_cnf_or', [status(thm)], ['229'])). 104.56/15.62 tff('253', plain, 104.56/15.62 ~ 104.56/15.62 ( (!!((^[Y0 : a]: 104.56/15.62 (!!((^[Y1 : a]: 104.56/15.62 (((!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 (('#sk1'(Y3, Y4) & Y2(Y3)) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))) | 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 104.56/15.62 Y2(Y4))))))))) => 104.56/15.62 Y2(Y1)))))) => 104.56/15.62 (!!((^[Y2 : a > $o]: 104.56/15.62 (((!!((^[Y3 : a]: 104.56/15.62 (!!((^[Y4 : a]: 104.56/15.62 ((Y2(Y3) & 104.56/15.62 ('#sk2'(Y3, Y4) | 104.56/15.62 '#sk1'(Y3, Y4))) => 104.56/15.62 Y2(Y4)))))))) & 104.56/15.62 (!!((^[Y3 : a]: 104.56/15.62 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 104.56/15.62 Y2(Y3)))))) => 104.56/15.62 Y2(Y1))))))))))))), 104.56/15.62 inference('sat_resolution*', [status(thm)], 104.56/15.62 ['95', '106', '107', '108', '134', '140', '141', '144', '145', 104.56/15.62 '158', '163', '177', '182', '183', '198', '209', '212', 104.56/15.62 '213', '217', '218', '219'])). 104.56/15.62 tff('254', plain, 104.56/15.62 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk21'(X2) | ~ '#sk21'(X1)), 104.56/15.62 inference('simpl_trail', [status(thm)], ['252', '253'])). 104.56/15.62 tff('255', plain, 104.56/15.62 ![X0 : a > $o]: 104.56/15.62 ( '#form138'(X0) | ~ '#sk21'('#sk166'(X0)) | '#sk21'('#sk194'(X0))), 104.56/15.62 inference('sup-', [status(thm)], ['251', '254'])). 104.56/15.62 tff('256', plain, ![X1 : a > $o]: (~ X1('#sk194'(X1)) | '#form138'(X1)), 104.56/15.62 inference('lazy_cnf_imply', [status(thm)], ['248'])). 104.56/15.62 tff('257', plain, 104.56/15.62 (~ '#sk21'('#sk166'((^[Y0 : a]: '#sk21'(Y0)))) 104.56/15.62 | '#form138'((^[Y0 : a]: '#sk21'(Y0))) 104.56/15.62 | '#form138'((^[Y0 : a]: '#sk21'((^[Y1 : a]: Y1)(Y0))))), 104.56/15.62 inference('sup-', [status(thm)], ['255', '256'])). 104.56/15.62 tff('258', plain, 104.56/15.62 (~ '#sk21'('#sk166'('#sk21')) 104.56/15.62 | '#form138'('#sk21') 104.56/15.62 | '#form138'('#sk21')), 104.56/15.62 inference('ho_norm', [status(thm)], ['257'])). 104.56/15.62 tff('259', plain, ~ '#form138'('#sk21'), 104.56/15.62 inference('simpl_trail', [status(thm)], ['25', '244'])). 104.56/15.62 tff('260', plain, ~ '#form138'('#sk21'), 104.56/15.62 inference('simpl_trail', [status(thm)], ['25', '244'])). 104.56/15.62 tff('261', plain, ~ '#sk21'('#sk166'('#sk21')), 104.56/15.62 inference('demod', [status(thm)], ['258', '259', '260'])). 104.56/15.62 tff('262', plain, '#form138'('#sk21'), 104.56/15.62 inference('sup-', [status(thm)], ['250', '261'])). 104.56/15.62 tff('263', plain, $false, inference('demod', [status(thm)], ['245', '262'])). 104.56/15.62 104.56/15.62 % SZS output end Refutation 104.56/15.62 104.56/15.62 104.56/15.62 % /export/starexec/sandbox2/solver/bin/lams/sh1.sh running for 26s 104.56/15.62 % Terminating... 104.56/15.67 % Runner terminated. 104.58/15.69 % Zipperpin 1.5 exiting 104.58/15.69 EOF