0.03/0.13 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.14 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.TcJl1Wj1eR 0.14/0.36 % Computer : n029.cluster.edu 0.14/0.36 % Model : x86_64 x86_64 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.36 % Memory : 8042.1875MB 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.36 % CPULimit : 1200 0.14/0.36 % DateTime : Tue Jul 13 10:32:55 EDT 2021 0.14/0.36 % CPUTime : 0.14/0.36 % Running portfolio for 120 s 0.14/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.14/0.36 % Number of cores: 8 0.14/0.36 % Python version: Python 3.6.8 0.14/0.36 % Running in HO mode 0.56/0.65 % Estimated wc time : 1286 0.56/0.65 % Estimated cpu time (7 cpus) : 183.71428571428572 0.56/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.56/0.73 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.57/0.77 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 0.57/0.78 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 69.79/10.68 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 92.37/13.87 % Solved by lams/old_sp2.sh. 92.37/13.87 % done 939 iterations in 3.126s 92.37/13.87 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 92.37/13.87 % SZS output start Refutation 92.37/13.87 tff(cTHM251D_pme, conjecture, 92.37/13.87 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 92.37/13.87 ((((![Xx0:a,Xy0:a,Xz:a]: 92.37/13.87 (((![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((R(Xy0,Xw) | S(Xy0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 92.37/13.87 Xq(Xz))) & 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 92.37/13.87 Xq(Xy0)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 92.37/13.87 Xq(Xz))))) & 92.37/13.87 (![Xx0:a,Xy0:a]: 92.37/13.87 (((![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: ((Xq(Xu) & S(Xu,Xv)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: (S(Xx0,Xw) => Xq(Xw)))) => 92.37/13.87 Xq(Xy0))) | 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: (R(Xx0,Xw) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: ((Xq(Xu) & R(Xu,Xv)) => Xq(Xv)))) => 92.37/13.87 Xq(Xy0)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy0)))))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((R(Xx,Xw) | S(Xx,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((R(Xx,Xw) | S(Xx,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy)))))). 92.37/13.87 tff(zf_stmt_0, negated_conjecture, 92.37/13.87 (~ 92.37/13.87 (![R:((a * a) > $o),S:((a * a) > $o),Xx:a,Xy:a]: 92.37/13.87 ((((![Xx0:a,Xy0:a,Xz:a]: 92.37/13.87 (((![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((R(Xy0,Xw) | S(Xy0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: 92.37/13.87 (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 92.37/13.87 Xq(Xz))) & 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((R(Xx0,Xw) | S(Xx0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: 92.37/13.87 (((R(Xu,Xv) | S(Xu,Xv)) & Xq(Xu)) => Xq(Xv)))) => 92.37/13.87 Xq(Xy0)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: 92.37/13.87 ((Xq(Xu) & (R(Xu,Xv) | S(Xu,Xv))) => Xq(Xv)))) => 92.37/13.87 Xq(Xz))))) & 92.37/13.87 (![Xx0:a,Xy0:a]: 92.37/13.87 (((![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: ((Xq(Xu) & S(Xu,Xv)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: (S(Xx0,Xw) => Xq(Xw)))) => 92.37/13.87 Xq(Xy0))) | 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xw:a]: (R(Xx0,Xw) => Xq(Xw))) & 92.37/13.87 (![Xu:a,Xv:a]: ((Xq(Xu) & R(Xu,Xv)) => Xq(Xv)))) => 92.37/13.87 Xq(Xy0)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: 92.37/13.87 (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((S(Xx0,Xw) | R(Xx0,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy0)))))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((R(Xx,Xw) | S(Xx,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy)))) => 92.37/13.87 (![Xq:((a > $o))]: 92.37/13.87 (((![Xu:a,Xv:a]: (((S(Xu,Xv) | R(Xu,Xv)) & Xq(Xu)) => Xq(Xv))) & 92.37/13.87 (![Xw:a]: ((R(Xx,Xw) | S(Xx,Xw)) => Xq(Xw)))) => 92.37/13.87 Xq(Xy))))))). 92.37/13.87 tff('0', plain, 92.37/13.87 ~ (!!((^[Y0 : (a * a) > $o]: 92.37/13.87 (!!((^[Y1 : (a * a) > $o]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((((!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (((!!((^[Y7 : a > $o]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y0(Y5, 92.37/13.87 Y8) | 92.37/13.87 Y1(Y5, 92.37/13.87 Y8)) => 92.37/13.87 Y7(Y8))))) & 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y9 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 Y0(Y8, 92.37/13.87 Y9) | 92.37/13.87 Y1(Y8, 92.37/13.87 Y9)) & 92.37/13.87 Y7(Y8)) => 92.37/13.87 Y7(Y9))))))))) => 92.37/13.87 Y7(Y6))))) & 92.37/13.87 (!!((^[Y7 : a > $o]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y0(Y4, 92.37/13.87 Y8) | 92.37/13.87 Y1(Y4, 92.37/13.87 Y8)) => 92.37/13.87 Y7(Y8))))) & 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y9 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 Y0(Y8, 92.37/13.87 Y9) | 92.37/13.87 Y1(Y8, 92.37/13.87 Y9)) & 92.37/13.87 Y7(Y8)) => 92.37/13.87 Y7(Y9))))))))) => 92.37/13.87 Y7(Y5)))))) => 92.37/13.87 (!!((^[Y7 : a > $o]: 92.37/13.87 ((( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y1(Y4, 92.37/13.87 Y8) | 92.37/13.87 Y0(Y4, 92.37/13.87 Y8)) => 92.37/13.87 Y7(Y8))))) & 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y9 : a]: 92.37/13.87 (( 92.37/13.87 Y7(Y8) & 92.37/13.87 ( 92.37/13.87 Y0(Y8, 92.37/13.87 Y9) | 92.37/13.87 Y1(Y8, 92.37/13.87 Y9))) => 92.37/13.87 Y7(Y9))))))))) => 92.37/13.87 Y7(Y6))))))))))))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (((!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y6(Y7) & 92.37/13.87 Y1(Y7, 92.37/13.87 Y8)) => 92.37/13.87 Y6(Y8)))))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (Y1(Y4, 92.37/13.87 Y7) => 92.37/13.87 Y6(Y7)))))) => 92.37/13.87 Y6(Y5))))) | 92.37/13.87 (!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 (Y0(Y4, 92.37/13.87 Y7) => 92.37/13.87 Y6(Y7))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y6(Y7) & 92.37/13.87 Y0(Y7, 92.37/13.87 Y8)) => 92.37/13.87 Y6(Y8))))))))) => 92.37/13.87 Y6(Y5)))))) => 92.37/13.87 (!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 Y1(Y7, 92.37/13.87 Y8) | 92.37/13.87 Y0(Y7, 92.37/13.87 Y8)) & 92.37/13.87 Y6(Y7)) => 92.37/13.87 Y6(Y8)))))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 ( 92.37/13.87 Y1(Y4, 92.37/13.87 Y7) | 92.37/13.87 Y0(Y4, 92.37/13.87 Y7)) => 92.37/13.87 Y6(Y7)))))) => 92.37/13.87 Y6(Y5))))))))))))) => 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (((Y1(Y5, Y6) | 92.37/13.87 Y0(Y5, Y6)) & 92.37/13.87 Y4(Y5)) => 92.37/13.87 Y4(Y6)))))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y0(Y2, Y5) | Y1(Y2, Y5)) => 92.37/13.87 Y4(Y5)))))) => 92.37/13.87 Y4(Y3)))))) => 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (((Y1(Y5, Y6) | 92.37/13.87 Y0(Y5, Y6)) & 92.37/13.87 Y4(Y5)) => 92.37/13.87 Y4(Y6)))))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y0(Y2, Y5) | Y1(Y2, Y5)) => 92.37/13.87 Y4(Y5)))))) => 92.37/13.87 Y4(Y3)))))))))))))))))), 92.37/13.87 inference('cnf', [status(esa)], [zf_stmt_0])). 92.37/13.87 tff('1', plain, 92.37/13.87 ~ (!!((^[Y0 : (a * a) > $o]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (((!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 '#sk1'( 92.37/13.87 Y4, Y7) | 92.37/13.87 Y0(Y4, 92.37/13.87 Y7)) => 92.37/13.87 Y6(Y7))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y7, Y8) | 92.37/13.87 Y0(Y7, 92.37/13.87 Y8)) & 92.37/13.87 Y6(Y7)) => 92.37/13.87 Y6(Y8))))))))) => 92.37/13.87 Y6(Y5))))) & 92.37/13.87 (!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 '#sk1'( 92.37/13.87 Y3, Y7) | 92.37/13.87 Y0(Y3, 92.37/13.87 Y7)) => 92.37/13.87 Y6(Y7))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (!!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y7, Y8) | 92.37/13.87 Y0(Y7, 92.37/13.87 Y8)) & 92.37/13.87 Y6(Y7)) => 92.37/13.87 Y6(Y8))))))))) => 92.37/13.87 Y6(Y4)))))) => 92.37/13.87 (!!((^[Y6 : a > $o]: 92.37/13.87 (((!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 ( 92.37/13.87 Y0(Y3, 92.37/13.87 Y7) | 92.37/13.87 '#sk1'( 92.37/13.87 Y3, Y7)) => 92.37/13.87 Y6(Y7))))) & 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 !!(( 92.37/13.87 ^[Y8 : a]: 92.37/13.87 (( 92.37/13.87 Y6(Y7) & 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y7, Y8) | 92.37/13.87 Y0(Y7, 92.37/13.87 Y8))) => 92.37/13.87 Y6(Y8))))))))) => 92.37/13.87 Y6(Y5))))))))))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (((!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 Y5(Y6) & 92.37/13.87 Y0(Y6, 92.37/13.87 Y7)) => 92.37/13.87 Y5(Y7)))))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (Y0(Y3, Y6) => 92.37/13.87 Y5(Y6)))))) => 92.37/13.87 Y5(Y4))))) | 92.37/13.87 (!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 ('#sk1'(Y3, Y6) => 92.37/13.87 Y5(Y6))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 Y5(Y6) & 92.37/13.87 '#sk1'( 92.37/13.87 Y6, Y7)) => 92.37/13.87 Y5(Y7))))))))) => 92.37/13.87 Y5(Y4)))))) => 92.37/13.87 (!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 ( 92.37/13.87 ( 92.37/13.87 Y0(Y6, 92.37/13.87 Y7) | 92.37/13.87 '#sk1'( 92.37/13.87 Y6, Y7)) & 92.37/13.87 Y5(Y6)) => 92.37/13.87 Y5(Y7)))))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((Y0(Y3, Y6) | 92.37/13.87 '#sk1'(Y3, Y6)) => 92.37/13.87 Y5(Y6)))))) => 92.37/13.87 Y5(Y4))))))))))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (((Y0(Y4, Y5) | 92.37/13.87 '#sk1'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5)))))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | Y0(Y1, Y4)) => 92.37/13.87 Y3(Y4)))))) => 92.37/13.87 Y3(Y2)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (((Y0(Y4, Y5) | 92.37/13.87 '#sk1'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5)))))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | Y0(Y1, Y4)) => 92.37/13.87 Y3(Y4)))))) => 92.37/13.87 Y3(Y2))))))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['0'])). 92.37/13.87 tff('2', plain, 92.37/13.87 ~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((((!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (((!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 (('#sk1'(Y3, 92.37/13.87 Y6) | 92.37/13.87 '#sk2'(Y3, 92.37/13.87 Y6)) => 92.37/13.87 Y5(Y6))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y6, Y7) | 92.37/13.87 '#sk2'( 92.37/13.87 Y6, Y7)) & 92.37/13.87 Y5(Y6)) => 92.37/13.87 Y5(Y7))))))))) => 92.37/13.87 Y5(Y4))))) & 92.37/13.87 (!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 (('#sk1'(Y2, 92.37/13.87 Y6) | 92.37/13.87 '#sk2'(Y2, 92.37/13.87 Y6)) => 92.37/13.87 Y5(Y6))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 (( 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y6, Y7) | 92.37/13.87 '#sk2'( 92.37/13.87 Y6, Y7)) & 92.37/13.87 Y5(Y6)) => 92.37/13.87 Y5(Y7))))))))) => 92.37/13.87 Y5(Y3)))))) => 92.37/13.87 (!!((^[Y5 : a > $o]: 92.37/13.87 (((!!((^[Y6 : a]: 92.37/13.87 (('#sk2'(Y2, Y6) | 92.37/13.87 '#sk1'(Y2, Y6)) => 92.37/13.87 Y5(Y6))))) & 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 (!!((^[Y7 : a]: 92.37/13.87 ( 92.37/13.87 ( 92.37/13.87 Y5(Y6) & 92.37/13.87 ( 92.37/13.87 '#sk1'( 92.37/13.87 Y6, Y7) | 92.37/13.87 '#sk2'( 92.37/13.87 Y6, Y7))) => 92.37/13.87 Y5(Y7))))))))) => 92.37/13.87 Y5(Y4))))))))))))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (((!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((Y4(Y5) & 92.37/13.87 '#sk2'(Y5, 92.37/13.87 Y6)) => 92.37/13.87 Y4(Y6)))))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ('#sk2'(Y2, Y5) => 92.37/13.87 Y4(Y5)))))) => 92.37/13.87 Y4(Y3))))) | 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 ('#sk1'(Y2, Y5) => 92.37/13.87 Y4(Y5))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((Y4(Y5) & 92.37/13.87 '#sk1'(Y5, 92.37/13.87 Y6)) => 92.37/13.87 Y4(Y6))))))))) => 92.37/13.87 Y4(Y3)))))) => 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((('#sk2'(Y5, 92.37/13.87 Y6) | 92.37/13.87 '#sk1'(Y5, 92.37/13.87 Y6)) & 92.37/13.87 Y4(Y5)) => 92.37/13.87 Y4(Y6)))))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (('#sk2'(Y2, Y5) | 92.37/13.87 '#sk1'(Y2, Y5)) => 92.37/13.87 Y4(Y5)))))) => 92.37/13.87 Y4(Y3))))))))))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1)))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['1'])). 92.37/13.87 tff('3', plain, 92.37/13.87 ~ (!!((^[Y0 : a]: 92.37/13.87 ((((!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (((!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (('#sk1'(Y2, Y5) | 92.37/13.87 '#sk2'(Y2, Y5)) => 92.37/13.87 Y4(Y5))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((('#sk1'(Y5, 92.37/13.87 Y6) | 92.37/13.87 '#sk2'(Y5, 92.37/13.87 Y6)) & 92.37/13.87 Y4(Y5)) => 92.37/13.87 Y4(Y6))))))))) => 92.37/13.87 Y4(Y3))))) & 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (('#sk1'(Y1, Y5) | 92.37/13.87 '#sk2'(Y1, Y5)) => 92.37/13.87 Y4(Y5))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((('#sk1'(Y5, 92.37/13.87 Y6) | 92.37/13.87 '#sk2'(Y5, 92.37/13.87 Y6)) & 92.37/13.87 Y4(Y5)) => 92.37/13.87 Y4(Y6))))))))) => 92.37/13.87 Y4(Y2)))))) => 92.37/13.87 (!!((^[Y4 : a > $o]: 92.37/13.87 (((!!((^[Y5 : a]: 92.37/13.87 (('#sk2'(Y1, Y5) | 92.37/13.87 '#sk1'(Y1, Y5)) => 92.37/13.87 Y4(Y5))))) & 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 (!!((^[Y6 : a]: 92.37/13.87 ((Y4(Y5) & 92.37/13.87 ('#sk1'(Y5, 92.37/13.87 Y6) | 92.37/13.87 '#sk2'(Y5, 92.37/13.87 Y6))) => 92.37/13.87 Y4(Y6))))))))) => 92.37/13.87 Y4(Y3))))))))))))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 '#sk2'(Y4, Y5)) => 92.37/13.87 Y3(Y5)))))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ('#sk2'(Y1, Y4) => Y3(Y4)))))) => 92.37/13.87 Y3(Y2))))) | 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 ('#sk1'(Y1, Y4) => Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 '#sk1'(Y4, Y5)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk2'(Y4, Y5) | 92.37/13.87 '#sk1'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5)))))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y1, Y4) | 92.37/13.87 '#sk1'(Y1, Y4)) => 92.37/13.87 Y3(Y4)))))) => 92.37/13.87 Y3(Y2))))))))))))) => 92.37/13.87 (!!((^[Y1 : a > $o]: 92.37/13.87 (((!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) & 92.37/13.87 Y1(Y2)) => 92.37/13.87 Y1(Y3)))))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (('#sk1'('#sk3', Y2) | '#sk2'('#sk3', Y2)) => 92.37/13.87 Y1(Y2)))))) => 92.37/13.87 Y1(Y0)))))) => 92.37/13.87 (!!((^[Y1 : a > $o]: 92.37/13.87 (((!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) & 92.37/13.87 Y1(Y2)) => 92.37/13.87 Y1(Y3)))))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (('#sk1'('#sk3', Y2) | '#sk2'('#sk3', Y2)) => 92.37/13.87 Y1(Y2)))))) => 92.37/13.87 Y1(Y0))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['2'])). 92.37/13.87 tff('4', plain, 92.37/13.87 ~ ((((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))))))))))) => 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2)))))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.87 Y0('#sk4')))))) => 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2)))))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.87 Y0('#sk4')))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['3'])). 92.37/13.87 tff('5', plain, 92.37/13.87 (((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))))))))))) => 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2)))))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.87 Y0('#sk4')))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['4'])). 92.37/13.87 tff('6', plain, 92.37/13.87 (~ ((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))))))))))) 92.37/13.87 | (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2)))))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.87 Y0('#sk4')))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['5'])). 92.37/13.87 tff('7', plain, 92.37/13.87 (~ ((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1)))))))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( ((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))))))))))))), 92.37/13.87 inference('split', [status(esa)], ['6'])). 92.37/13.87 tff('8', plain, 92.37/13.87 ((~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) 92.37/13.87 | ~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1)))))))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( ((!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))) | 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk2'(Y3, Y4) | 92.37/13.87 '#sk1'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4)))))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.87 Y2(Y3)))))) => 92.37/13.87 Y2(Y1))))))))))))))), 92.37/13.87 inference('lazy_cnf_and', [status(thm)], ['7'])). 92.37/13.87 tff('9', plain, 92.37/13.87 (~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2)))))))))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('split', [status(esa)], ['8'])). 92.37/13.87 tff('10', plain, 92.37/13.87 (~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (((!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (('#sk1'(Y0, Y3) | '#sk2'(Y0, Y3)) => 92.37/13.87 Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk1'(Y3, Y4) | 92.37/13.87 '#sk2'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1))))) & 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (('#sk1'('#sk13', Y3) | 92.37/13.87 '#sk2'('#sk13', Y3)) => 92.37/13.87 Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((('#sk1'(Y3, Y4) | 92.37/13.87 '#sk2'(Y3, Y4)) & 92.37/13.87 Y2(Y3)) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y0)))))) => 92.37/13.87 (!!((^[Y2 : a > $o]: 92.37/13.87 (((!!((^[Y3 : a]: 92.37/13.87 (('#sk2'('#sk13', Y3) | 92.37/13.87 '#sk1'('#sk13', Y3)) => 92.37/13.87 Y2(Y3))))) & 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 ((Y2(Y3) & 92.37/13.87 ('#sk1'(Y3, Y4) | 92.37/13.87 '#sk2'(Y3, Y4))) => 92.37/13.87 Y2(Y4))))))))) => 92.37/13.87 Y2(Y1))))))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['9'])). 92.37/13.87 tff('11', plain, 92.37/13.87 (~ (!!((^[Y0 : a]: 92.37/13.87 (((!!((^[Y1 : a > $o]: 92.37/13.87 (((!!((^[Y2 : a]: 92.37/13.87 (('#sk1'('#sk19', Y2) | '#sk2'('#sk19', Y2)) => 92.37/13.87 Y1(Y2))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) & 92.37/13.87 Y1(Y2)) => 92.37/13.87 Y1(Y3))))))))) => 92.37/13.87 Y1(Y0))))) & 92.37/13.87 (!!((^[Y1 : a > $o]: 92.37/13.87 (((!!((^[Y2 : a]: 92.37/13.87 (('#sk1'('#sk13', Y2) | '#sk2'('#sk13', Y2)) => 92.37/13.87 Y1(Y2))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3)) & 92.37/13.87 Y1(Y2)) => 92.37/13.87 Y1(Y3))))))))) => 92.37/13.87 Y1('#sk19')))))) => 92.37/13.87 (!!((^[Y1 : a > $o]: 92.37/13.87 (((!!((^[Y2 : a]: 92.37/13.87 (('#sk2'('#sk13', Y2) | '#sk1'('#sk13', Y2)) => 92.37/13.87 Y1(Y2))))) & 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (!!((^[Y3 : a]: 92.37/13.87 ((Y1(Y2) & 92.37/13.87 ('#sk1'(Y2, Y3) | '#sk2'(Y2, Y3))) => 92.37/13.87 Y1(Y3))))))))) => 92.37/13.87 Y1(Y0)))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['10'])). 92.37/13.87 tff('12', plain, 92.37/13.87 (~ (((!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk19', Y1) | '#sk2'('#sk19', Y1)) => 92.37/13.87 Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk26'))))) & 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk13', Y1) | '#sk2'('#sk13', Y1)) => 92.37/13.87 Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk19')))))) => 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk2'('#sk13', Y1) | '#sk1'('#sk13', Y1)) => 92.37/13.87 Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk26'))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['11'])). 92.37/13.87 tff('13', plain, 92.37/13.87 ( ((!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk19', Y1) | '#sk2'('#sk19', Y1)) => Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk26'))))) & 92.37/13.87 (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk13', Y1) | '#sk2'('#sk13', Y1)) => Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk19'))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['12'])). 92.37/13.87 tff('14', plain, 92.37/13.87 ( (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk13', Y1) | '#sk2'('#sk13', Y1)) => Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk19')))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_and', [status(thm)], ['13'])). 92.37/13.87 tff('15', plain, 92.37/13.87 (![X1 : a > $o]: 92.37/13.87 (((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => X1(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.87 X1(Y1))))))))) => 92.37/13.87 X1('#sk19'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_forall', [status(thm)], ['14'])). 92.37/13.87 tff('16', plain, 92.37/13.87 ( (((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1))))))))) => 92.37/13.87 '#sk46'('#sk19'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('triggered_bool_instantiation', [status(thm)], ['15'])). 92.37/13.87 tff('17', plain, 92.37/13.87 ((~ ((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1))))))))) 92.37/13.87 | '#sk46'('#sk19'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['16'])). 92.37/13.87 tff('18', plain, 92.37/13.87 (~ ((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1)))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( ((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1))))))))))), 92.37/13.87 inference('split', [status(esa)], ['17'])). 92.37/13.87 tff('19', plain, 92.37/13.87 ((~ (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) 92.37/13.87 | ~ (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1)))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( ((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.87 '#sk46'(Y1))))))))))), 92.37/13.87 inference('lazy_cnf_and', [status(thm)], ['18'])). 92.37/13.87 tff('20', plain, 92.37/13.87 (~ (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0)))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))))), 92.37/13.87 inference('split', [status(esa)], ['19'])). 92.37/13.87 tff('21', plain, 92.37/13.87 (~ (('#sk1'('#sk13', '#sk135'('#sk46')) | 92.37/13.87 '#sk2'('#sk13', '#sk135'('#sk46'))) => 92.37/13.87 '#sk46'('#sk135'('#sk46')))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['20'])). 92.37/13.87 tff('22', plain, 92.37/13.87 ( ('#sk1'('#sk13', '#sk135'('#sk46')) | 92.37/13.87 '#sk2'('#sk13', '#sk135'('#sk46')))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['21'])). 92.37/13.87 tff('23', plain, 92.37/13.87 (( '#sk1'('#sk13', '#sk135'('#sk46')) 92.37/13.87 | '#sk2'('#sk13', '#sk135'('#sk46')))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))))), 92.37/13.87 inference('lazy_cnf_or', [status(thm)], ['22'])). 92.37/13.87 tff('24', plain, 92.37/13.87 ( '#sk2'('#sk13', '#sk135'('#sk46'))) 92.37/13.87 <= (( '#sk2'('#sk13', '#sk135'('#sk46')))), 92.37/13.87 inference('split', [status(esa)], ['23'])). 92.37/13.87 tff('25', plain, 92.37/13.87 (~ (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk2'('#sk13', Y1) | '#sk1'('#sk13', Y1)) => Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((Y0(Y1) & ('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2))) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk26')))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['12'])). 92.37/13.87 tff('26', plain, 92.37/13.87 (~ (((!!((^[Y0 : a]: 92.37/13.87 (('#sk2'('#sk13', Y0) | '#sk1'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk46'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 92.37/13.87 '#sk46'(Y1))))))))) => 92.37/13.87 '#sk46'('#sk26'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_exists', [status(thm)], ['25'])). 92.37/13.87 tff('27', plain, 92.37/13.87 ( ((!!((^[Y0 : a]: 92.37/13.87 (('#sk2'('#sk13', Y0) | '#sk1'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (('#sk46'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 92.37/13.87 '#sk46'(Y1)))))))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['26'])). 92.37/13.87 tff('28', plain, 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk2'('#sk13', Y0) | '#sk1'('#sk13', Y0)) => '#sk46'(Y0)))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_and', [status(thm)], ['27'])). 92.37/13.87 tff('29', plain, 92.37/13.87 (![X1 : a]: (('#sk2'('#sk13', X1) | '#sk1'('#sk13', X1)) => '#sk46'(X1))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_forall', [status(thm)], ['28'])). 92.37/13.87 tff('30', plain, 92.37/13.87 (![X1 : a]: 92.37/13.87 (~ ('#sk2'('#sk13', X1) | '#sk1'('#sk13', X1)) | '#sk46'(X1))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['29'])). 92.37/13.87 tff('31', plain, 92.37/13.87 (![X1 : a]: (~ '#sk2'('#sk13', X1) | '#sk46'(X1))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_or', [status(thm)], ['30'])). 92.37/13.87 tff('32', plain, 92.37/13.87 ( '#sk46'('#sk135'('#sk46'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2)))))))))))))))) & 92.37/13.87 ( '#sk2'('#sk13', '#sk135'('#sk46')))), 92.37/13.87 inference('sup-', [status(thm)], ['24', '31'])). 92.37/13.87 tff('33', plain, 92.37/13.87 (~ '#sk46'('#sk135'('#sk46'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.87 '#sk46'(Y0))))))), 92.37/13.87 inference('lazy_cnf_imply', [status(thm)], ['21'])). 92.37/13.87 tff('34', plain, 92.37/13.87 ~ ( '#sk2'('#sk13', '#sk135'('#sk46'))) | 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0)))))) | 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2)))))))))))))))), 92.37/13.87 inference('sup-', [status(thm)], ['32', '33'])). 92.37/13.87 tff('35', plain, 92.37/13.87 ( (!!((^[Y0 : a > $o]: 92.37/13.87 (((!!((^[Y1 : a]: 92.37/13.87 (('#sk1'('#sk19', Y1) | '#sk2'('#sk19', Y1)) => Y0(Y1))))) & 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 ((('#sk1'(Y1, Y2) | '#sk2'(Y1, Y2)) & Y0(Y1)) => 92.37/13.87 Y0(Y2))))))))) => 92.37/13.87 Y0('#sk26')))))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk2'(Y0, Y4) | 92.37/13.87 '#sk1'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((Y3(Y4) & 92.37/13.87 ('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5))) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))))))))))))))), 92.37/13.87 inference('lazy_cnf_and', [status(thm)], ['13'])). 92.37/13.87 tff('36', plain, 92.37/13.87 (![X1 : a > $o]: 92.37/13.87 (((!!((^[Y0 : a]: 92.37/13.87 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => X1(Y0))))) & 92.37/13.87 (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.87 X1(Y1))))))))) => 92.37/13.87 X1('#sk26'))) 92.37/13.87 <= (~ 92.37/13.87 ( (!!((^[Y0 : a]: 92.37/13.87 (!!((^[Y1 : a]: 92.37/13.87 (!!((^[Y2 : a]: 92.37/13.87 (((!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y1, Y4) | 92.37/13.87 '#sk2'(Y1, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y2))))) & 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.87 (((!!((^[Y4 : a]: 92.37/13.87 (('#sk1'(Y0, Y4) | 92.37/13.87 '#sk2'(Y0, Y4)) => 92.37/13.87 Y3(Y4))))) & 92.37/13.87 (!!((^[Y4 : a]: 92.37/13.87 (!!((^[Y5 : a]: 92.37/13.87 ((('#sk1'(Y4, Y5) | 92.37/13.87 '#sk2'(Y4, Y5)) & 92.37/13.87 Y3(Y4)) => 92.37/13.87 Y3(Y5))))))))) => 92.37/13.87 Y3(Y1)))))) => 92.37/13.87 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['35'])). 92.37/13.88 tff('37', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))) => 92.37/13.88 '#sk46'('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('triggered_bool_instantiation', [status(thm)], ['36'])). 92.37/13.88 tff('38', plain, 92.37/13.88 (~ '#sk46'('#sk26')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['26'])). 92.37/13.88 tff('39', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))) => 92.37/13.88 $false)) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('demod', [status(thm)], ['37', '38'])). 92.37/13.88 tff('40', plain, 92.37/13.88 ( (~(((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('simplify boolean subterms', [status(thm)], ['39'])). 92.37/13.88 tff('41', plain, 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('simplify nested equalities', [status(thm)], ['40'])). 92.37/13.88 tff('42', plain, 92.37/13.88 ((~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['41'])). 92.37/13.88 tff('43', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('split', [status(esa)], ['42'])). 92.37/13.88 tff('44', plain, 92.37/13.88 (~ (('#sk1'('#sk19', '#sk114'('#sk46')) | 92.37/13.88 '#sk2'('#sk19', '#sk114'('#sk46'))) => 92.37/13.88 '#sk46'('#sk114'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['43'])). 92.37/13.88 tff('45', plain, 92.37/13.88 ( ('#sk1'('#sk19', '#sk114'('#sk46')) | 92.37/13.88 '#sk2'('#sk19', '#sk114'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['44'])). 92.37/13.88 tff('46', plain, 92.37/13.88 (( '#sk1'('#sk19', '#sk114'('#sk46')) 92.37/13.88 | '#sk2'('#sk19', '#sk114'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['45'])). 92.37/13.88 tff('47', plain, 92.37/13.88 ( '#sk2'('#sk19', '#sk114'('#sk46'))) | 92.37/13.88 ( '#sk1'('#sk19', '#sk114'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0)))))), 92.37/13.88 inference('split', [status(esa)], ['46'])). 92.37/13.88 tff('48', plain, 92.37/13.88 ( '#sk2'('#sk19', '#sk114'('#sk46'))) 92.37/13.88 <= (( '#sk2'('#sk19', '#sk114'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['46'])). 92.37/13.88 tff('49', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk46'(Y0) & ('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1))) => 92.37/13.88 '#sk46'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['27'])). 92.37/13.88 tff('50', plain, 92.37/13.88 (![X1 : a]: 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk46'(X1) & ('#sk1'(X1, Y0) | '#sk2'(X1, Y0))) => 92.37/13.88 '#sk46'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['49'])). 92.37/13.88 tff('51', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 (('#sk46'(X1) & ('#sk1'(X1, X2) | '#sk2'(X1, X2))) => '#sk46'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['50'])). 92.37/13.88 tff('52', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 (~ ('#sk46'(X1) & ('#sk1'(X1, X2) | '#sk2'(X1, X2))) | '#sk46'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['51'])). 92.37/13.88 tff('53', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 (~ '#sk46'(X1) | ~ ('#sk1'(X1, X2) | '#sk2'(X1, X2)) | '#sk46'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['52'])). 92.37/13.88 tff('54', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk46'(X2) | ~ '#sk46'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['53'])). 92.37/13.88 tff('55', plain, 92.37/13.88 ((~ '#sk46'('#sk19') | '#sk46'('#sk114'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk2'('#sk19', '#sk114'('#sk46')))), 92.37/13.88 inference('sup-', [status(thm)], ['48', '54'])). 92.37/13.88 tff('56', plain, 92.37/13.88 ~ ( '#sk2'('#sk19', '#sk114'('#sk46'))) | ~ ( '#sk46'('#sk19')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) | 92.37/13.88 ( '#sk46'('#sk114'('#sk46'))), inference('split', [status(esa)], ['55'])). 92.37/13.88 tff('57', plain, 92.37/13.88 ( '#sk1'('#sk19', '#sk114'('#sk46'))) 92.37/13.88 <= (( '#sk1'('#sk19', '#sk114'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['46'])). 92.37/13.88 tff('58', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk46'(X2) | ~ '#sk46'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['53'])). 92.37/13.88 tff('59', plain, 92.37/13.88 ((~ '#sk46'('#sk19') | '#sk46'('#sk114'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk1'('#sk19', '#sk114'('#sk46')))), 92.37/13.88 inference('sup-', [status(thm)], ['57', '58'])). 92.37/13.88 tff('60', plain, 92.37/13.88 ~ ( '#sk1'('#sk19', '#sk114'('#sk46'))) | ~ ( '#sk46'('#sk19')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) | 92.37/13.88 ( '#sk46'('#sk114'('#sk46'))), inference('split', [status(esa)], ['59'])). 92.37/13.88 tff('61', plain, 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0)))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['42'])). 92.37/13.88 tff('62', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))) => 92.37/13.88 X1('#sk19'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['14'])). 92.37/13.88 tff('63', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))) 92.37/13.88 | X1('#sk19'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['62'])). 92.37/13.88 tff('64', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => X1(Y0))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) 92.37/13.88 | X1('#sk19'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['63'])). 92.37/13.88 tff('65', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form118'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('66', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((('#sk1'('#sk17'(X1), Y0) | '#sk2'('#sk17'(X1), Y0)) & 92.37/13.88 X1('#sk17'(X1))) => 92.37/13.88 X1(Y0))))) 92.37/13.88 | '#form118'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['65'])). 92.37/13.88 tff('67', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ ((('#sk1'('#sk17'(X1), '#sk25'(X1)) | 92.37/13.88 '#sk2'('#sk17'(X1), '#sk25'(X1))) & 92.37/13.88 X1('#sk17'(X1))) => 92.37/13.88 X1('#sk25'(X1))) 92.37/13.88 | '#form118'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['66'])). 92.37/13.88 tff('68', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( (('#sk1'('#sk17'(X1), '#sk25'(X1)) | '#sk2'('#sk17'(X1), '#sk25'(X1))) & 92.37/13.88 X1('#sk17'(X1))) 92.37/13.88 | '#form118'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['67'])). 92.37/13.88 tff('69', plain, ![X1 : a > $o]: ( X1('#sk17'(X1)) | '#form118'(X1)), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['68'])). 92.37/13.88 tff('70', plain, 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk4')))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('split', [status(esa)], ['6'])). 92.37/13.88 tff('71', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))) => 92.37/13.88 X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['70'])). 92.37/13.88 tff('72', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0)))))) => 92.37/13.88 '#sk46'('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('triggered_bool_instantiation', [status(thm)], ['71'])). 92.37/13.88 tff('73', plain, 92.37/13.88 ((~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0)))))) 92.37/13.88 | '#sk46'('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['72'])). 92.37/13.88 tff('74', plain, 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0)))))))), 92.37/13.88 inference('split', [status(esa)], ['73'])). 92.37/13.88 tff('75', plain, 92.37/13.88 ((~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk46'(Y0)))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['74'])). 92.37/13.88 tff('76', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('split', [status(esa)], ['75'])). 92.37/13.88 tff('77', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((('#sk2'('#sk17'('#sk46'), Y0) | '#sk1'('#sk17'('#sk46'), Y0)) & 92.37/13.88 '#sk46'('#sk17'('#sk46'))) => 92.37/13.88 '#sk46'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['76'])). 92.37/13.88 tff('78', plain, 92.37/13.88 (~ ((('#sk2'('#sk17'('#sk46'), '#sk501') | 92.37/13.88 '#sk1'('#sk17'('#sk46'), '#sk501')) & 92.37/13.88 '#sk46'('#sk17'('#sk46'))) => 92.37/13.88 '#sk46'('#sk501'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['77'])). 92.37/13.88 tff('79', plain, 92.37/13.88 ( (('#sk2'('#sk17'('#sk46'), '#sk501') | 92.37/13.88 '#sk1'('#sk17'('#sk46'), '#sk501')) & 92.37/13.88 '#sk46'('#sk17'('#sk46')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['78'])). 92.37/13.88 tff('80', plain, 92.37/13.88 ( ('#sk2'('#sk17'('#sk46'), '#sk501') | 92.37/13.88 '#sk1'('#sk17'('#sk46'), '#sk501'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['79'])). 92.37/13.88 tff('81', plain, 92.37/13.88 (( '#sk2'('#sk17'('#sk46'), '#sk501') 92.37/13.88 | '#sk1'('#sk17'('#sk46'), '#sk501'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['80'])). 92.37/13.88 tff('82', plain, 92.37/13.88 ( '#sk1'('#sk17'('#sk46'), '#sk501')) 92.37/13.88 <= (( '#sk1'('#sk17'('#sk46'), '#sk501'))), 92.37/13.88 inference('split', [status(esa)], ['81'])). 92.37/13.88 tff('83', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk46'(X2) | ~ '#sk46'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['53'])). 92.37/13.88 tff('84', plain, 92.37/13.88 ((~ '#sk46'('#sk17'('#sk46')) | '#sk46'('#sk501'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk1'('#sk17'('#sk46'), '#sk501'))), 92.37/13.88 inference('sup-', [status(thm)], ['82', '83'])). 92.37/13.88 tff('85', plain, 92.37/13.88 (~ '#sk46'('#sk17'('#sk46'))) <= (~ ( '#sk46'('#sk17'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['84'])). 92.37/13.88 tff('86', plain, ( '#form118'('#sk46')) <= (~ ( '#sk46'('#sk17'('#sk46')))), 92.37/13.88 inference('sup-', [status(thm)], ['69', '85'])). 92.37/13.88 tff('87', plain, 92.37/13.88 ( '#sk46'('#sk114'('#sk46'))) <= (( '#sk46'('#sk114'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['59'])). 92.37/13.88 tff('88', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))) => 92.37/13.88 X1('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['35'])). 92.37/13.88 tff('89', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))) 92.37/13.88 | X1('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['88'])). 92.37/13.88 tff('90', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => X1(Y0))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) 92.37/13.88 | X1('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['89'])). 92.37/13.88 tff('91', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (('#sk1'('#sk19', '#sk114'(X1)) | '#sk2'('#sk19', '#sk114'(X1))) => 92.37/13.88 X1('#sk114'(X1))) 92.37/13.88 | X1('#sk26') 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['90'])). 92.37/13.88 tff('92', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form118'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1))))))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('93', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ '#form118'((^[Y0 : a]: X1(Y0))) 92.37/13.88 | X1('#sk26') 92.37/13.88 | ~ (('#sk1'('#sk19', '#sk114'(X1)) | '#sk2'('#sk19', '#sk114'(X1))) => 92.37/13.88 X1('#sk114'(X1))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('renaming', [status(thm)], ['91', '92'])). 92.37/13.88 tff('94', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ '#form118'(X1) 92.37/13.88 | X1('#sk26') 92.37/13.88 | ~ (('#sk1'('#sk19', '#sk114'(X1)) | '#sk2'('#sk19', '#sk114'(X1))) => 92.37/13.88 X1('#sk114'(X1))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('ho_norm', [status(thm)], ['93'])). 92.37/13.88 tff('95', plain, 92.37/13.88 (![X1 : a > $o]: (~ X1('#sk114'(X1)) | X1('#sk26') | ~ '#form118'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['94'])). 92.37/13.88 tff('96', plain, 92.37/13.88 ((~ '#form118'((^[Y0 : a]: '#sk46'((^[Y1 : a]: Y1)(Y0)))) 92.37/13.88 | (^[Y0 : a]: '#sk46'((^[Y1 : a]: Y1)(Y0)))('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk46'('#sk114'('#sk46')))), 92.37/13.88 inference('sup-', [status(thm)], ['87', '95'])). 92.37/13.88 tff('97', plain, 92.37/13.88 ((~ '#form118'('#sk46') | '#sk46'('#sk26'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk46'('#sk114'('#sk46')))), 92.37/13.88 inference('ho_norm', [status(thm)], ['96'])). 92.37/13.88 tff('98', plain, 92.37/13.88 (~ '#sk46'('#sk26')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['26'])). 92.37/13.88 tff('99', plain, 92.37/13.88 (~ '#form118'('#sk46')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk46'('#sk114'('#sk46')))), 92.37/13.88 inference('demod', [status(thm)], ['97', '98'])). 92.37/13.88 tff('100', plain, 92.37/13.88 ( '#sk46'('#sk17'('#sk46'))) | ~ ( '#sk46'('#sk114'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['86', '99'])). 92.37/13.88 tff('101', plain, 92.37/13.88 ( '#sk46'('#sk114'('#sk46'))) <= (( '#sk46'('#sk114'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['59'])). 92.37/13.88 tff('102', plain, 92.37/13.88 (~ '#sk46'('#sk114'('#sk46'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['44'])). 92.37/13.88 tff('103', plain, 92.37/13.88 ~ ( '#sk46'('#sk114'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk19', Y0) | '#sk2'('#sk19', Y0)) => '#sk46'(Y0)))))), 92.37/13.88 inference('sup-', [status(thm)], ['101', '102'])). 92.37/13.88 tff('104', plain, 92.37/13.88 ~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))) | 92.37/13.88 ( '#sk46'('#sk19')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['17'])). 92.37/13.88 tff('105', plain, 92.37/13.88 ( '#sk2'('#sk17'('#sk46'), '#sk501')) 92.37/13.88 <= (( '#sk2'('#sk17'('#sk46'), '#sk501'))), 92.37/13.88 inference('split', [status(esa)], ['81'])). 92.37/13.88 tff('106', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk46'(X2) | ~ '#sk46'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['53'])). 92.37/13.88 tff('107', plain, 92.37/13.88 ((~ '#sk46'('#sk17'('#sk46')) | '#sk46'('#sk501'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk2'('#sk17'('#sk46'), '#sk501'))), 92.37/13.88 inference('sup-', [status(thm)], ['105', '106'])). 92.37/13.88 tff('108', plain, 92.37/13.88 ~ ( '#sk2'('#sk17'('#sk46'), '#sk501')) | ( '#sk46'('#sk501')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) | 92.37/13.88 ~ ( '#sk46'('#sk17'('#sk46'))), 92.37/13.88 inference('split', [status(esa)], ['107'])). 92.37/13.88 tff('109', plain, 92.37/13.88 ~ ( '#sk1'('#sk17'('#sk46'), '#sk501')) | ( '#sk46'('#sk501')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) | 92.37/13.88 ~ ( '#sk46'('#sk17'('#sk46'))), inference('split', [status(esa)], ['84'])). 92.37/13.88 tff('110', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))) => 92.37/13.88 X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['70'])). 92.37/13.88 tff('111', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))) 92.37/13.88 | X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['110'])). 92.37/13.88 tff('112', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0))))) 92.37/13.88 | X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['111'])). 92.37/13.88 tff('113', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((('#sk2'('#sk17'(X1), Y0) | '#sk1'('#sk17'(X1), Y0)) & 92.37/13.88 X1('#sk17'(X1))) => 92.37/13.88 X1(Y0))))) 92.37/13.88 | X1('#sk4') 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['112'])). 92.37/13.88 tff('114', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((('#sk2'('#sk17'(X1), '#sk25'(X1)) | 92.37/13.88 '#sk1'('#sk17'(X1), '#sk25'(X1))) & 92.37/13.88 X1('#sk17'(X1))) => 92.37/13.88 X1('#sk25'(X1))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0))))) 92.37/13.88 | X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['113'])). 92.37/13.88 tff('115', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form34'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('116', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ (('#sk1'('#sk3', '#sk45'(X1)) | '#sk2'('#sk3', '#sk45'(X1))) => 92.37/13.88 X1('#sk45'(X1))) 92.37/13.88 | '#form34'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['115'])). 92.37/13.88 tff('117', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( ('#sk1'('#sk3', '#sk45'(X1)) | '#sk2'('#sk3', '#sk45'(X1))) 92.37/13.88 | '#form34'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['116'])). 92.37/13.88 tff('118', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#sk1'('#sk3', '#sk45'(X1)) 92.37/13.88 | '#sk2'('#sk3', '#sk45'(X1)) 92.37/13.88 | '#form34'(X1)), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['117'])). 92.37/13.88 tff('119', plain, 92.37/13.88 ~ (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['4'])). 92.37/13.88 tff('120', plain, 92.37/13.88 ~ (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))) => 92.37/13.88 '#sk5'('#sk4')), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['119'])). 92.37/13.88 tff('121', plain, 92.37/13.88 ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['120'])). 92.37/13.88 tff('122', plain, 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['121'])). 92.37/13.88 tff('123', plain, 92.37/13.88 ![X1 : a]: (('#sk1'('#sk3', X1) | '#sk2'('#sk3', X1)) => '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['122'])). 92.37/13.88 tff('124', plain, 92.37/13.88 ![X1 : a]: (~ ('#sk1'('#sk3', X1) | '#sk2'('#sk3', X1)) | '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['123'])). 92.37/13.88 tff('125', plain, ![X1 : a]: (~ '#sk2'('#sk3', X1) | '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['124'])). 92.37/13.88 tff('126', plain, 92.37/13.88 ![X0 : a > $o]: 92.37/13.88 ( '#form34'(X0) | '#sk1'('#sk3', '#sk45'(X0)) | '#sk5'('#sk45'(X0))), 92.37/13.88 inference('sup-', [status(thm)], ['118', '125'])). 92.37/13.88 tff('127', plain, ![X1 : a]: (~ '#sk1'('#sk3', X1) | '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['124'])). 92.37/13.88 tff('128', plain, ![X0 : a > $o]: ( '#sk5'('#sk45'(X0)) | '#form34'(X0)), 92.37/13.88 inference('clc', [status(thm)], ['126', '127'])). 92.37/13.88 tff('129', plain, ![X1 : a > $o]: (~ X1('#sk45'(X1)) | '#form34'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['116'])). 92.37/13.88 tff('130', plain, 92.37/13.88 ( '#form34'((^[Y0 : a]: '#sk5'(Y0))) 92.37/13.88 | '#form34'((^[Y0 : a]: '#sk5'((^[Y1 : a]: Y1)(Y0))))), 92.37/13.88 inference('sup-', [status(thm)], ['128', '129'])). 92.37/13.88 tff('131', plain, ( '#form34'('#sk5') | '#form34'('#sk5')), 92.37/13.88 inference('ho_norm', [status(thm)], ['130'])). 92.37/13.88 tff('132', plain, '#form34'('#sk5'), 92.37/13.88 inference('simplify', [status(thm)], ['131'])). 92.37/13.88 tff('133', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & X1(Y0)) => 92.37/13.88 X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))) => 92.37/13.88 X1('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['70'])). 92.37/13.88 tff('134', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))) => 92.37/13.88 '#sk5'('#sk4'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('triggered_bool_instantiation', [status(thm)], ['133'])). 92.37/13.88 tff('135', plain, ~ '#sk5'('#sk4'), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['120'])). 92.37/13.88 tff('136', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))) => 92.37/13.88 $false)) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('demod', [status(thm)], ['134', '135'])). 92.37/13.88 tff('137', plain, 92.37/13.88 ( (~(((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('simplify boolean subterms', [status(thm)], ['136'])). 92.37/13.88 tff('138', plain, 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('simplify nested equalities', [status(thm)], ['137'])). 92.37/13.88 tff('139', plain, 92.37/13.88 ((~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & 92.37/13.88 Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk4'))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['138'])). 92.37/13.88 tff('140', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))))), 92.37/13.88 inference('split', [status(esa)], ['139'])). 92.37/13.88 tff('141', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form34'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => X1(Y0)))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('142', plain, 92.37/13.88 (~ '#form34'('#sk5')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0))))))), 92.37/13.88 inference('renaming', [status(thm)], ['140', '141'])). 92.37/13.88 tff('143', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))), 92.37/13.88 inference('sup-', [status(thm)], ['132', '142'])). 92.37/13.88 tff('144', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('split', [status(esa)], ['139'])). 92.37/13.88 tff('145', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((('#sk2'('#sk17'('#sk5'), Y0) | '#sk1'('#sk17'('#sk5'), Y0)) & 92.37/13.88 '#sk5'('#sk17'('#sk5'))) => 92.37/13.88 '#sk5'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['144'])). 92.37/13.88 tff('146', plain, 92.37/13.88 (~ ((('#sk2'('#sk17'('#sk5'), '#sk407') | 92.37/13.88 '#sk1'('#sk17'('#sk5'), '#sk407')) & 92.37/13.88 '#sk5'('#sk17'('#sk5'))) => 92.37/13.88 '#sk5'('#sk407'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['145'])). 92.37/13.88 tff('147', plain, 92.37/13.88 ( (('#sk2'('#sk17'('#sk5'), '#sk407') | '#sk1'('#sk17'('#sk5'), '#sk407')) & 92.37/13.88 '#sk5'('#sk17'('#sk5')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['146'])). 92.37/13.88 tff('148', plain, 92.37/13.88 ( ('#sk2'('#sk17'('#sk5'), '#sk407') | '#sk1'('#sk17'('#sk5'), '#sk407'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['147'])). 92.37/13.88 tff('149', plain, 92.37/13.88 (( '#sk2'('#sk17'('#sk5'), '#sk407') | '#sk1'('#sk17'('#sk5'), '#sk407'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['148'])). 92.37/13.88 tff('150', plain, 92.37/13.88 ( '#sk1'('#sk17'('#sk5'), '#sk407')) 92.37/13.88 <= (( '#sk1'('#sk17'('#sk5'), '#sk407'))), 92.37/13.88 inference('split', [status(esa)], ['149'])). 92.37/13.88 tff('151', plain, 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['121'])). 92.37/13.88 tff('152', plain, 92.37/13.88 ![X1 : a]: 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 ((('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) & '#sk5'(X1)) => '#sk5'(Y0))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['151'])). 92.37/13.88 tff('153', plain, 92.37/13.88 ![X1 : a, X2 : a]: 92.37/13.88 ((('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk5'(X1)) => '#sk5'(X2)), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['152'])). 92.37/13.88 tff('154', plain, 92.37/13.88 ![X1 : a, X2 : a]: 92.37/13.88 (~ (('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk5'(X1)) | '#sk5'(X2)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['153'])). 92.37/13.88 tff('155', plain, 92.37/13.88 ![X1 : a, X2 : a]: 92.37/13.88 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | ~ '#sk5'(X1) | '#sk5'(X2)), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['154'])). 92.37/13.88 tff('156', plain, 92.37/13.88 ![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['155'])). 92.37/13.88 tff('157', plain, 92.37/13.88 ((~ '#sk5'('#sk17'('#sk5')) | '#sk5'('#sk407'))) 92.37/13.88 <= (( '#sk1'('#sk17'('#sk5'), '#sk407'))), 92.37/13.88 inference('sup-', [status(thm)], ['150', '156'])). 92.37/13.88 tff('158', plain, 92.37/13.88 ( '#sk5'('#sk407')) | ~ ( '#sk5'('#sk17'('#sk5'))) | 92.37/13.88 ~ ( '#sk1'('#sk17'('#sk5'), '#sk407')), 92.37/13.88 inference('split', [status(esa)], ['157'])). 92.37/13.88 tff('159', plain, 92.37/13.88 ( '#sk2'('#sk17'('#sk5'), '#sk407')) 92.37/13.88 <= (( '#sk2'('#sk17'('#sk5'), '#sk407'))), 92.37/13.88 inference('split', [status(esa)], ['149'])). 92.37/13.88 tff('160', plain, 92.37/13.88 ![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk5'(X2) | ~ '#sk5'(X1)), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['155'])). 92.37/13.88 tff('161', plain, 92.37/13.88 ((~ '#sk5'('#sk17'('#sk5')) | '#sk5'('#sk407'))) 92.37/13.88 <= (( '#sk2'('#sk17'('#sk5'), '#sk407'))), 92.37/13.88 inference('sup-', [status(thm)], ['159', '160'])). 92.37/13.88 tff('162', plain, 92.37/13.88 ( '#sk5'('#sk407')) | ~ ( '#sk5'('#sk17'('#sk5'))) | 92.37/13.88 ~ ( '#sk2'('#sk17'('#sk5'), '#sk407')), 92.37/13.88 inference('split', [status(esa)], ['161'])). 92.37/13.88 tff('163', plain, 92.37/13.88 ( '#sk5'('#sk17'('#sk5'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['147'])). 92.37/13.88 tff('164', plain, 92.37/13.88 (~ '#sk5'('#sk17'('#sk5'))) <= (~ ( '#sk5'('#sk17'('#sk5')))), 92.37/13.88 inference('split', [status(esa)], ['161'])). 92.37/13.88 tff('165', plain, 92.37/13.88 ( '#sk5'('#sk17'('#sk5'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['163', '164'])). 92.37/13.88 tff('166', plain, ( '#sk5'('#sk407')) <= (( '#sk5'('#sk407'))), 92.37/13.88 inference('split', [status(esa)], ['161'])). 92.37/13.88 tff('167', plain, 92.37/13.88 (~ '#sk5'('#sk407')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['146'])). 92.37/13.88 tff('168', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1))))))))) | 92.37/13.88 ~ ( '#sk5'('#sk407')), inference('sup-', [status(thm)], ['166', '167'])). 92.37/13.88 tff('169', plain, 92.37/13.88 ( '#sk1'('#sk17'('#sk5'), '#sk407')) | 92.37/13.88 ( '#sk2'('#sk17'('#sk5'), '#sk407')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1))))))))), 92.37/13.88 inference('split', [status(esa)], ['149'])). 92.37/13.88 tff('170', plain, 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk4')))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk5'(Y0)) => 92.37/13.88 '#sk5'(Y1))))))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk3', Y0) | '#sk2'('#sk3', Y0)) => '#sk5'(Y0)))))), 92.37/13.88 inference('split', [status(esa)], ['139'])). 92.37/13.88 tff('171', plain, 92.37/13.88 ~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))) | 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk1'('#sk3', Y1) | '#sk2'('#sk3', Y1)) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk4')))))), 92.37/13.88 inference('split', [status(esa)], ['6'])). 92.37/13.88 tff('172', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['8'])). 92.37/13.88 tff('173', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (((!!((^[Y1 : a > $o]: 92.37/13.88 (((!!((^[Y2 : a]: 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ((Y1(Y2) & '#sk2'(Y2, Y3)) => Y1(Y3)))))))) & 92.37/13.88 (!!((^[Y2 : a]: ('#sk2'('#sk12', Y2) => Y1(Y2)))))) => 92.37/13.88 Y1(Y0))))) | 92.37/13.88 (!!((^[Y1 : a > $o]: 92.37/13.88 (((!!((^[Y2 : a]: ('#sk1'('#sk12', Y2) => Y1(Y2))))) & 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ((Y1(Y2) & '#sk1'(Y2, Y3)) => Y1(Y3))))))))) => 92.37/13.88 Y1(Y0)))))) => 92.37/13.88 (!!((^[Y1 : a > $o]: 92.37/13.88 (((!!((^[Y2 : a]: 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ((('#sk2'(Y2, Y3) | '#sk1'(Y2, Y3)) & 92.37/13.88 Y1(Y2)) => 92.37/13.88 Y1(Y3)))))))) & 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (('#sk2'('#sk12', Y2) | '#sk1'('#sk12', Y2)) => 92.37/13.88 Y1(Y2)))))) => 92.37/13.88 Y1(Y0)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['172'])). 92.37/13.88 tff('174', plain, 92.37/13.88 (~ (((!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))) | 92.37/13.88 (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18')))))) => 92.37/13.88 (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk2'('#sk12', Y1) | '#sk1'('#sk12', Y1)) => 92.37/13.88 Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['173'])). 92.37/13.88 tff('175', plain, 92.37/13.88 ( ((!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))) | 92.37/13.88 (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['174'])). 92.37/13.88 tff('176', plain, 92.37/13.88 (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))) 92.37/13.88 | (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['175'])). 92.37/13.88 tff('177', plain, 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18')))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('split', [status(esa)], ['176'])). 92.37/13.88 tff('178', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1))))))))) => 92.37/13.88 X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['177'])). 92.37/13.88 tff('179', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1))))))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['178'])). 92.37/13.88 tff('180', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => X1(Y0))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['179'])). 92.37/13.88 tff('181', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ('#sk1'('#sk12', '#sk106'(X1)) => X1('#sk106'(X1))) 92.37/13.88 | X1('#sk18') 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['180'])). 92.37/13.88 tff('182', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 ( '#sk1'('#sk12', '#sk106'(X1)) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1)))))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['181'])). 92.37/13.88 tff('183', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form142'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1))))))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('184', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((X1('#sk174'(X1)) & '#sk1'('#sk174'(X1), Y0)) => X1(Y0))))) 92.37/13.88 | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['183'])). 92.37/13.88 tff('185', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ ((X1('#sk174'(X1)) & '#sk1'('#sk174'(X1), '#sk208'(X1))) => 92.37/13.88 X1('#sk208'(X1))) 92.37/13.88 | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['184'])). 92.37/13.88 tff('186', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( (X1('#sk174'(X1)) & '#sk1'('#sk174'(X1), '#sk208'(X1))) 92.37/13.88 | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['185'])). 92.37/13.88 tff('187', plain, ![X1 : a > $o]: ( X1('#sk174'(X1)) | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['186'])). 92.37/13.88 tff('188', plain, 92.37/13.88 ![X1 : a > $o]: ( '#sk1'('#sk174'(X1), '#sk208'(X1)) | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['186'])). 92.37/13.88 tff('189', plain, 92.37/13.88 (~ (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((('#sk2'(Y1, Y2) | '#sk1'(Y1, Y2)) & Y0(Y1)) => 92.37/13.88 Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk2'('#sk12', Y1) | '#sk1'('#sk12', Y1)) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18')))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['174'])). 92.37/13.88 tff('190', plain, 92.37/13.88 (~ (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk35'(Y0)) => 92.37/13.88 '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk2'('#sk12', Y0) | '#sk1'('#sk12', Y0)) => '#sk35'(Y0)))))) => 92.37/13.88 '#sk35'('#sk18'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['189'])). 92.37/13.88 tff('191', plain, 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk35'(Y0)) => 92.37/13.88 '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (('#sk2'('#sk12', Y0) | '#sk1'('#sk12', Y0)) => '#sk35'(Y0))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['190'])). 92.37/13.88 tff('192', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk35'(Y0)) => 92.37/13.88 '#sk35'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['191'])). 92.37/13.88 tff('193', plain, 92.37/13.88 (![X1 : a]: 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 ((('#sk2'(X1, Y0) | '#sk1'(X1, Y0)) & '#sk35'(X1)) => 92.37/13.88 '#sk35'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['192'])). 92.37/13.88 tff('194', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 ((('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk35'(X1)) => '#sk35'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['193'])). 92.37/13.88 tff('195', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 (~ (('#sk2'(X1, X2) | '#sk1'(X1, X2)) & '#sk35'(X1)) | '#sk35'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['194'])). 92.37/13.88 tff('196', plain, 92.37/13.88 (![X1 : a, X2 : a]: 92.37/13.88 (~ ('#sk2'(X1, X2) | '#sk1'(X1, X2)) | ~ '#sk35'(X1) | '#sk35'(X2))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['195'])). 92.37/13.88 tff('197', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk1'(X1, X2) | '#sk35'(X2) | ~ '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['196'])). 92.37/13.88 tff('198', plain, 92.37/13.88 (![X0 : a > $o]: 92.37/13.88 ( '#form142'(X0) | ~ '#sk35'('#sk174'(X0)) | '#sk35'('#sk208'(X0)))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['188', '197'])). 92.37/13.88 tff('199', plain, ![X1 : a > $o]: (~ X1('#sk208'(X1)) | '#form142'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['185'])). 92.37/13.88 tff('200', plain, 92.37/13.88 ((~ '#sk35'('#sk174'((^[Y0 : a]: '#sk35'(Y0)))) 92.37/13.88 | '#form142'((^[Y0 : a]: '#sk35'(Y0))) 92.37/13.88 | '#form142'((^[Y0 : a]: '#sk35'((^[Y1 : a]: Y1)(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['198', '199'])). 92.37/13.88 tff('201', plain, 92.37/13.88 ((~ '#sk35'('#sk174'('#sk35')) 92.37/13.88 | '#form142'('#sk35') 92.37/13.88 | '#form142'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('ho_norm', [status(thm)], ['200'])). 92.37/13.88 tff('202', plain, 92.37/13.88 (( '#form142'('#sk35') | ~ '#sk35'('#sk174'('#sk35')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('simplify', [status(thm)], ['201'])). 92.37/13.88 tff('203', plain, 92.37/13.88 (~ '#sk35'('#sk174'('#sk35'))) <= (~ ( '#sk35'('#sk174'('#sk35')))), 92.37/13.88 inference('split', [status(esa)], ['202'])). 92.37/13.88 tff('204', plain, 92.37/13.88 ( '#form142'('#sk35')) <= (~ ( '#sk35'('#sk174'('#sk35')))), 92.37/13.88 inference('sup-', [status(thm)], ['187', '203'])). 92.37/13.88 tff('205', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => X1(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1))))))))) => 92.37/13.88 X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['177'])). 92.37/13.88 tff('206', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))) => 92.37/13.88 '#sk35'('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('triggered_bool_instantiation', [status(thm)], ['205'])). 92.37/13.88 tff('207', plain, 92.37/13.88 ((~ ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))) 92.37/13.88 | '#sk35'('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['206'])). 92.37/13.88 tff('208', plain, 92.37/13.88 (~ ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))))), 92.37/13.88 inference('split', [status(esa)], ['207'])). 92.37/13.88 tff('209', plain, 92.37/13.88 ((~ (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['208'])). 92.37/13.88 tff('210', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('split', [status(esa)], ['209'])). 92.37/13.88 tff('211', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form142'(X1) 92.37/13.88 | ~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk1'(Y0, Y1)) => X1(Y1))))))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('212', plain, 92.37/13.88 (~ '#form142'('#sk35')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('renaming', [status(thm)], ['210', '211'])). 92.37/13.88 tff('213', plain, 92.37/13.88 ( '#sk35'('#sk174'('#sk35'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['204', '212'])). 92.37/13.88 tff('214', plain, ( '#form142'('#sk35')) <= (( '#form142'('#sk35'))), 92.37/13.88 inference('split', [status(esa)], ['202'])). 92.37/13.88 tff('215', plain, 92.37/13.88 (~ '#form142'('#sk35')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('renaming', [status(thm)], ['210', '211'])). 92.37/13.88 tff('216', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))) | 92.37/13.88 ~ ( '#form142'('#sk35')), 92.37/13.88 inference('sup-', [status(thm)], ['214', '215'])). 92.37/13.88 tff('217', plain, 92.37/13.88 ( ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))) | 92.37/13.88 ~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0)))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1))))))))), 92.37/13.88 inference('split', [status(esa)], ['209'])). 92.37/13.88 tff('218', plain, 92.37/13.88 ( '#sk35'('#sk18')) | 92.37/13.88 ~ 92.37/13.88 ( ((!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk1'(Y0, Y1)) => '#sk35'(Y1)))))))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18')))))), 92.37/13.88 inference('split', [status(esa)], ['207'])). 92.37/13.88 tff('219', plain, 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: ('#sk1'('#sk12', Y1) => Y0(Y1))))) & 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk1'(Y1, Y2)) => Y0(Y2))))))))) => 92.37/13.88 Y0('#sk18')))))) | 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18')))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['176'])). 92.37/13.88 tff('220', plain, 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18')))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('split', [status(esa)], ['176'])). 92.37/13.88 tff('221', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0)))))) => 92.37/13.88 X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['220'])). 92.37/13.88 tff('222', plain, 92.37/13.88 ( (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))) => 92.37/13.88 '#sk35'('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('triggered_bool_instantiation', [status(thm)], ['221'])). 92.37/13.88 tff('223', plain, 92.37/13.88 ((~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))) 92.37/13.88 | '#sk35'('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['222'])). 92.37/13.88 tff('224', plain, 92.37/13.88 ( '#sk35'('#sk18')) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18')))))) | 92.37/13.88 ~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('split', [status(esa)], ['223'])). 92.37/13.88 tff('225', plain, 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))))), 92.37/13.88 inference('split', [status(esa)], ['223'])). 92.37/13.88 tff('226', plain, 92.37/13.88 ((~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))) 92.37/13.88 <= (~ 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['225'])). 92.37/13.88 tff('227', plain, 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1))))))))) | 92.37/13.88 ~ ( (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))), 92.37/13.88 inference('split', [status(esa)], ['226'])). 92.37/13.88 tff('228', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1))))))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('split', [status(esa)], ['226'])). 92.37/13.88 tff('229', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (('#sk35'('#sk110'('#sk35')) & '#sk2'('#sk110'('#sk35'), Y0)) => 92.37/13.88 '#sk35'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['228'])). 92.37/13.88 tff('230', plain, 92.37/13.88 (~ (('#sk35'('#sk110'('#sk35')) & 92.37/13.88 '#sk2'('#sk110'('#sk35'), '#sk127'('#sk35'))) => 92.37/13.88 '#sk35'('#sk127'('#sk35')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['229'])). 92.37/13.88 tff('231', plain, 92.37/13.88 ( ('#sk35'('#sk110'('#sk35')) & 92.37/13.88 '#sk2'('#sk110'('#sk35'), '#sk127'('#sk35')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['230'])). 92.37/13.88 tff('232', plain, 92.37/13.88 ( '#sk2'('#sk110'('#sk35'), '#sk127'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['231'])). 92.37/13.88 tff('233', plain, 92.37/13.88 (![X1 : a, X2 : a]: (~ '#sk2'(X1, X2) | '#sk35'(X2) | ~ '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['196'])). 92.37/13.88 tff('234', plain, 92.37/13.88 ((~ '#sk35'('#sk110'('#sk35')) | '#sk35'('#sk127'('#sk35')))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1))))))))) & 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['232', '233'])). 92.37/13.88 tff('235', plain, 92.37/13.88 ( '#sk35'('#sk110'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['231'])). 92.37/13.88 tff('236', plain, 92.37/13.88 ( '#sk35'('#sk127'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1))))))))) & 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('demod', [status(thm)], ['234', '235'])). 92.37/13.88 tff('237', plain, 92.37/13.88 (~ '#sk35'('#sk127'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['230'])). 92.37/13.88 tff('238', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: (('#sk35'(Y0) & '#sk2'(Y0, Y1)) => '#sk35'(Y1))))))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['236', '237'])). 92.37/13.88 tff('239', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0)))))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('split', [status(esa)], ['209'])). 92.37/13.88 tff('240', plain, 92.37/13.88 (~ ('#sk1'('#sk12', '#sk106'('#sk35')) => '#sk35'('#sk106'('#sk35')))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['239'])). 92.37/13.88 tff('241', plain, 92.37/13.88 ( '#sk1'('#sk12', '#sk106'('#sk35'))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['240'])). 92.37/13.88 tff('242', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk2'('#sk12', Y0) | '#sk1'('#sk12', Y0)) => '#sk35'(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['191'])). 92.37/13.88 tff('243', plain, 92.37/13.88 (![X1 : a]: (('#sk2'('#sk12', X1) | '#sk1'('#sk12', X1)) => '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['242'])). 92.37/13.88 tff('244', plain, 92.37/13.88 (![X1 : a]: 92.37/13.88 (~ ('#sk2'('#sk12', X1) | '#sk1'('#sk12', X1)) | '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['243'])). 92.37/13.88 tff('245', plain, 92.37/13.88 (![X1 : a]: (~ '#sk1'('#sk12', X1) | '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['244'])). 92.37/13.88 tff('246', plain, 92.37/13.88 ( '#sk35'('#sk106'('#sk35'))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0)))))) & 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['241', '245'])). 92.37/13.88 tff('247', plain, 92.37/13.88 (~ '#sk35'('#sk106'('#sk35'))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['240'])). 92.37/13.88 tff('248', plain, 92.37/13.88 ( (!!((^[Y0 : a]: ('#sk1'('#sk12', Y0) => '#sk35'(Y0)))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['246', '247'])). 92.37/13.88 tff('249', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0)))))) => 92.37/13.88 X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_forall', [status(thm)], ['220'])). 92.37/13.88 tff('250', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) & 92.37/13.88 (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0)))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['249'])). 92.37/13.88 tff('251', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: ((X1(Y0) & '#sk2'(Y0, Y1)) => X1(Y1)))))))) 92.37/13.88 | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['250'])). 92.37/13.88 tff('252', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ (!!((^[Y0 : a]: 92.37/13.88 ((X1('#sk110'(X1)) & '#sk2'('#sk110'(X1), Y0)) => X1(Y0))))) 92.37/13.88 | X1('#sk18') 92.37/13.88 | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0))))))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['251'])). 92.37/13.88 tff('253', plain, 92.37/13.88 (![X1 : a > $o]: 92.37/13.88 (~ ((X1('#sk110'(X1)) & '#sk2'('#sk110'(X1), '#sk127'(X1))) => 92.37/13.88 X1('#sk127'(X1))) 92.37/13.88 | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0))))) 92.37/13.88 | X1('#sk18'))) 92.37/13.88 <= (( (!!((^[Y0 : a > $o]: 92.37/13.88 (((!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 ((Y0(Y1) & '#sk2'(Y1, Y2)) => Y0(Y2)))))))) & 92.37/13.88 (!!((^[Y1 : a]: ('#sk2'('#sk12', Y1) => Y0(Y1)))))) => 92.37/13.88 Y0('#sk18'))))))), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['252'])). 92.37/13.88 tff('254', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form151'(X1) | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0)))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('255', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 (~ ('#sk2'('#sk12', '#sk186'(X1)) => X1('#sk186'(X1))) 92.37/13.88 | '#form151'(X1)), 92.37/13.88 inference('lazy_cnf_exists', [status(thm)], ['254'])). 92.37/13.88 tff('256', plain, 92.37/13.88 ![X1 : a > $o]: ( '#sk2'('#sk12', '#sk186'(X1)) | '#form151'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['255'])). 92.37/13.88 tff('257', plain, 92.37/13.88 (![X1 : a]: (~ '#sk2'('#sk12', X1) | '#sk35'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['244'])). 92.37/13.88 tff('258', plain, 92.37/13.88 (![X0 : a > $o]: ( '#form151'(X0) | '#sk35'('#sk186'(X0)))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['256', '257'])). 92.37/13.88 tff('259', plain, ![X1 : a > $o]: (~ X1('#sk186'(X1)) | '#form151'(X1)), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['255'])). 92.37/13.88 tff('260', plain, 92.37/13.88 (( '#form151'((^[Y0 : a]: '#sk35'(Y0))) 92.37/13.88 | '#form151'((^[Y0 : a]: '#sk35'((^[Y1 : a]: Y1)(Y0)))))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['258', '259'])). 92.37/13.88 tff('261', plain, 92.37/13.88 (( '#form151'('#sk35') | '#form151'('#sk35'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('ho_norm', [status(thm)], ['260'])). 92.37/13.88 tff('262', plain, 92.37/13.88 ( '#form151'('#sk35')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('simplify', [status(thm)], ['261'])). 92.37/13.88 tff('263', plain, 92.37/13.88 (~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('split', [status(esa)], ['226'])). 92.37/13.88 tff('264', plain, 92.37/13.88 ![X1 : a > $o]: 92.37/13.88 ( '#form151'(X1) | ~ (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => X1(Y0)))))), 92.37/13.88 define([status(thm)])). 92.37/13.88 tff('265', plain, 92.37/13.88 (~ '#form151'('#sk35')) 92.37/13.88 <= (~ ( (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0))))))), 92.37/13.88 inference('renaming', [status(thm)], ['263', '264'])). 92.37/13.88 tff('266', plain, 92.37/13.88 ( (!!((^[Y0 : a]: ('#sk2'('#sk12', Y0) => '#sk35'(Y0)))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['262', '265'])). 92.37/13.88 tff('267', plain, ( '#sk35'('#sk18')) <= (( '#sk35'('#sk18'))), 92.37/13.88 inference('split', [status(esa)], ['207'])). 92.37/13.88 tff('268', plain, 92.37/13.88 (~ '#sk35'('#sk18')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['190'])). 92.37/13.88 tff('269', plain, 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))) | 92.37/13.88 ~ ( '#sk35'('#sk18')), inference('sup-', [status(thm)], ['267', '268'])). 92.37/13.88 tff('270', plain, 92.37/13.88 ( '#form142'('#sk35')) | ~ ( '#sk35'('#sk174'('#sk35'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['202'])). 92.37/13.88 tff('271', plain, 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))))))))))) | 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (((!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk2'(Y3, Y4)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: ('#sk2'(Y0, Y3) => Y2(Y3)))))) => 92.37/13.88 Y2(Y1))))) | 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: ('#sk1'(Y0, Y3) => Y2(Y3))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((Y2(Y3) & '#sk1'(Y3, Y4)) => 92.37/13.88 Y2(Y4))))))))) => 92.37/13.88 Y2(Y1)))))) => 92.37/13.88 (!!((^[Y2 : a > $o]: 92.37/13.88 (((!!((^[Y3 : a]: 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 ((('#sk2'(Y3, Y4) | 92.37/13.88 '#sk1'(Y3, Y4)) & 92.37/13.88 Y2(Y3)) => 92.37/13.88 Y2(Y4)))))))) & 92.37/13.88 (!!((^[Y3 : a]: 92.37/13.88 (('#sk2'(Y0, Y3) | '#sk1'(Y0, Y3)) => 92.37/13.88 Y2(Y3)))))) => 92.37/13.88 Y2(Y1)))))))))))))), 92.37/13.88 inference('split', [status(esa)], ['8'])). 92.37/13.88 tff('272', plain, ( '#sk46'('#sk501')) <= (( '#sk46'('#sk501'))), 92.37/13.88 inference('split', [status(esa)], ['84'])). 92.37/13.88 tff('273', plain, 92.37/13.88 (~ '#sk46'('#sk501')) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['78'])). 92.37/13.88 tff('274', plain, 92.37/13.88 ~ ( '#sk46'('#sk501')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['272', '273'])). 92.37/13.88 tff('275', plain, 92.37/13.88 ( '#sk46'('#sk17'('#sk46'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('lazy_cnf_and', [status(thm)], ['79'])). 92.37/13.88 tff('276', plain, 92.37/13.88 (~ '#sk46'('#sk17'('#sk46'))) <= (~ ( '#sk46'('#sk17'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['84'])). 92.37/13.88 tff('277', plain, 92.37/13.88 ( '#sk46'('#sk17'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['275', '276'])). 92.37/13.88 tff('278', plain, 92.37/13.88 ( '#sk2'('#sk17'('#sk46'), '#sk501')) | 92.37/13.88 ( '#sk1'('#sk17'('#sk46'), '#sk501')) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))), 92.37/13.88 inference('split', [status(esa)], ['81'])). 92.37/13.88 tff('279', plain, 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0)))))) | 92.37/13.88 ~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk2'(Y0, Y1) | '#sk1'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1))))))))) | 92.37/13.88 ( ((!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0))))) & 92.37/13.88 (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 ((('#sk1'(Y0, Y1) | '#sk2'(Y0, Y1)) & '#sk46'(Y0)) => 92.37/13.88 '#sk46'(Y1)))))))))), 92.37/13.88 inference('split', [status(esa)], ['19'])). 92.37/13.88 tff('280', plain, 92.37/13.88 ( '#sk1'('#sk13', '#sk135'('#sk46'))) 92.37/13.88 <= (( '#sk1'('#sk13', '#sk135'('#sk46')))), 92.37/13.88 inference('split', [status(esa)], ['23'])). 92.37/13.88 tff('281', plain, 92.37/13.88 (![X1 : a]: (~ '#sk1'('#sk13', X1) | '#sk46'(X1))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))))))))))))))), 92.37/13.88 inference('lazy_cnf_or', [status(thm)], ['30'])). 92.37/13.88 tff('282', plain, 92.37/13.88 ( '#sk46'('#sk135'('#sk46'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | 92.37/13.88 '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))) & 92.37/13.88 ( '#sk1'('#sk13', '#sk135'('#sk46')))), 92.37/13.88 inference('sup-', [status(thm)], ['280', '281'])). 92.37/13.88 tff('283', plain, 92.37/13.88 (~ '#sk46'('#sk135'('#sk46'))) 92.37/13.88 <= (~ 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => 92.37/13.88 '#sk46'(Y0))))))), 92.37/13.88 inference('lazy_cnf_imply', [status(thm)], ['21'])). 92.37/13.88 tff('284', plain, 92.37/13.88 ~ ( '#sk1'('#sk13', '#sk135'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0)))))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (!!((^[Y1 : a]: 92.37/13.88 (!!((^[Y2 : a]: 92.37/13.88 (((!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y1, Y4) | 92.37/13.88 '#sk2'(Y1, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2))))) & 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk1'(Y0, Y4) | 92.37/13.88 '#sk2'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5)) & 92.37/13.88 Y3(Y4)) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y1)))))) => 92.37/13.88 (!!((^[Y3 : a > $o]: 92.37/13.88 (((!!((^[Y4 : a]: 92.37/13.88 (('#sk2'(Y0, Y4) | '#sk1'(Y0, Y4)) => 92.37/13.88 Y3(Y4))))) & 92.37/13.88 (!!((^[Y4 : a]: 92.37/13.88 (!!((^[Y5 : a]: 92.37/13.88 ((Y3(Y4) & 92.37/13.88 ('#sk1'(Y4, Y5) | 92.37/13.88 '#sk2'(Y4, Y5))) => 92.37/13.88 Y3(Y5))))))))) => 92.37/13.88 Y3(Y2)))))))))))))))), 92.37/13.88 inference('sup-', [status(thm)], ['282', '283'])). 92.37/13.88 tff('285', plain, 92.37/13.88 ( '#sk1'('#sk13', '#sk135'('#sk46'))) | 92.37/13.88 ( '#sk2'('#sk13', '#sk135'('#sk46'))) | 92.37/13.88 ( (!!((^[Y0 : a]: 92.37/13.88 (('#sk1'('#sk13', Y0) | '#sk2'('#sk13', Y0)) => '#sk46'(Y0)))))), 92.37/13.88 inference('split', [status(esa)], ['23'])). 92.37/13.88 tff('286', plain, $false, 92.37/13.88 inference('sat_resolution*', [status(thm)], 92.37/13.88 ['34', '47', '56', '60', '61', '100', '103', '104', '108', 92.37/13.88 '109', '143', '158', '162', '165', '168', '169', '170', 92.37/13.88 '171', '213', '216', '217', '218', '219', '224', '227', 92.37/13.88 '238', '248', '266', '269', '270', '271', '274', '277', 92.37/13.88 '278', '279', '284', '285'])). 92.37/13.88 92.37/13.88 % SZS output end Refutation 92.37/13.88 92.37/13.88 92.37/13.88 % Terminating... 93.05/14.01 % Runner terminated. 93.07/14.02 % Zipperpin 1.5 exiting 93.07/14.02 EOF