0.03/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.12/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.DHY3Cs0NaO true 0.13/0.34 % Computer : n023.cluster.edu 0.13/0.34 % Model : x86_64 x86_64 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.13/0.34 % Memory : 8042.1875MB 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.13/0.34 % CPULimit : 1440 0.13/0.34 % WCLimit : 180 0.13/0.34 % DateTime : Mon Jul 3 05:01:06 EDT 2023 0.13/0.34 % CPUTime : 0.13/0.34 % Running portfolio for 1440 s 0.13/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.13/0.35 % Number of cores: 8 0.13/0.35 % Python version: Python 3.6.8 0.13/0.35 % Running in HO mode 0.54/0.67 % Total configuration time : 828 0.54/0.67 % Estimated wc time : 1656 0.54/0.67 % Estimated cpu time (8 cpus) : 207.0 0.54/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.73 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.55/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 0.55/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 51.42/7.19 % Solved by lams/20_acsne_simpl.sh. 51.42/7.19 % done 858 iterations in 6.286s 51.42/7.19 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 51.42/7.19 % SZS output start Refutation 51.42/7.19 thf(a_type, type, a: $tType). 51.42/7.19 thf('#sk60_type', type, '#sk60': (a > $o) > a). 51.42/7.19 thf('#form254_type', type, '#form254': (a > $o) > $o). 51.42/7.19 thf('#sk6_type', type, '#sk6': a). 51.42/7.19 thf('#sk143_type', type, '#sk143': (a > $o) > a). 51.42/7.19 thf('#form19_type', type, '#form19': $o). 51.42/7.19 thf('#sk97_type', type, '#sk97': (a > $o) > a). 51.42/7.19 thf('#sk5_type', type, '#sk5': a > $o). 51.42/7.19 thf('#form14_type', type, '#form14': $o). 51.42/7.19 thf('#sk255_type', type, '#sk255': (a > $o) > a). 51.42/7.19 thf('#sk4_type', type, '#sk4': a). 51.42/7.19 thf('#form117_type', type, '#form117': (a > $o) > $o). 51.42/7.19 thf('#sk56_type', type, '#sk56': (a > $o) > a). 51.42/7.19 thf('#sk15_type', type, '#sk15': a). 51.42/7.19 thf('#form9_type', type, '#form9': $o). 51.42/7.19 thf('#sk138_type', type, '#sk138': (a > $o) > a). 51.42/7.19 thf('#sk23_type', type, '#sk23': a). 51.42/7.19 thf('#form96_type', type, '#form96': (a > $o) > $o). 51.42/7.19 thf('#sk107_type', type, '#sk107': (a > $o) > a). 51.42/7.19 thf('#sk8_type', type, '#sk8': a > $o). 51.42/7.19 thf('#form264_type', type, '#form264': (a > $o) > $o). 51.42/7.19 thf('#sk43_type', type, '#sk43': a > $o). 51.42/7.19 thf('#sk187_type', type, '#sk187': (a > $o) > a). 51.42/7.19 thf('#sk118_type', type, '#sk118': (a > $o) > a). 51.42/7.19 thf('#sk265_type', type, '#sk265': (a > $o) > a). 51.42/7.19 thf('#sk3_type', type, '#sk3': a). 51.42/7.19 thf('#sk7_type', type, '#sk7': a). 51.42/7.19 thf('#sk1_type', type, '#sk1': a > a > $o). 51.42/7.19 thf('#sk42_type', type, '#sk42': (a > $o) > a). 51.42/7.19 thf('#sk50_type', type, '#sk50': (a > $o) > a). 51.42/7.19 thf('#sk2_type', type, '#sk2': a > a > $o). 51.42/7.19 thf('#sk65_type', type, '#sk65': (a > $o) > a). 51.42/7.19 thf('#sk10_type', type, '#sk10': a). 51.42/7.19 thf(cTHM251H_pme, conjecture, 51.42/7.19 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 51.42/7.19 ( ( ( ![Xx0:a,Xy0:a]: 51.42/7.19 ( ( ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 51.42/7.19 ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) | 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) ) => 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) ) ) & 51.42/7.19 ( ![Xx0:a,Xy0:a,Xz:a]: 51.42/7.19 ( ( ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) & 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xz ) ) ) ) => 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xz ) ) ) ) ) & 51.42/7.19 ( ~( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy ) ) ) ) ) | 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy ) ) ) ))). 51.42/7.19 thf(zf_stmt_0, negated_conjecture, 51.42/7.19 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 51.42/7.19 ( ( ( ![Xx0:a,Xy0:a]: 51.42/7.19 ( ( ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xw:a]: ( ( R @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) & 51.42/7.19 ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( R @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) | 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( S @ Xu @ Xv ) ) => ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: ( ( S @ Xx0 @ Xw ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) ) => 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx0 @ Xw ) | ( R @ Xx0 @ Xw ) ) => 51.42/7.19 ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) ) ) & 51.42/7.19 ( ![Xx0:a,Xy0:a,Xz:a]: 51.42/7.19 ( ( ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & 51.42/7.19 ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 51.42/7.19 ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy0 ) ) ) & 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & 51.42/7.19 ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xy0 @ Xw ) | ( R @ Xy0 @ Xw ) ) => 51.42/7.19 ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xz ) ) ) ) => 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( R @ Xx0 @ Xw ) | ( S @ Xx0 @ Xw ) ) => 51.42/7.19 ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xz ) ) ) ) ) & 51.42/7.19 ( ~( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( Xq @ Xu ) & ( ( S @ Xu @ Xv ) | ( R @ Xu @ Xv ) ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy ) ) ) ) ) | 51.42/7.19 ( ![Xq:( a > $o )]: 51.42/7.19 ( ( ( ![Xu:a,Xv:a]: 51.42/7.19 ( ( ( ( R @ Xu @ Xv ) | ( S @ Xu @ Xv ) ) & ( Xq @ Xu ) ) => 51.42/7.19 ( Xq @ Xv ) ) ) & 51.42/7.19 ( ![Xw:a]: 51.42/7.19 ( ( ( S @ Xx @ Xw ) | ( R @ Xx @ Xw ) ) => ( Xq @ Xw ) ) ) ) => 51.42/7.19 ( Xq @ Xy ) ) ) ) )), 51.42/7.19 inference('cnf.neg', [status(esa)], [cTHM251H_pme])). 51.42/7.19 thf(zip_derived_cl0, plain, 51.42/7.19 (~ (((!!) @ (^[Y0 : a > a > $o]: 51.42/7.19 (((!!) @ (^[Y1 : a > a > $o]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ 51.42/7.19 Y7) => 51.42/7.19 (Y6 @ Y7)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y6 @ 51.42/7.19 Y7) & 51.42/7.19 (Y0 @ 51.42/7.19 Y7 @ Y8))) => 51.42/7.19 (Y6 @ Y8))))))))))) => 51.42/7.19 (Y6 @ Y5)))))) | 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y6 @ 51.42/7.19 Y7) & 51.42/7.19 (Y1 @ 51.42/7.19 Y7 @ Y8))) => 51.42/7.19 (Y6 @ Y8))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y4 @ 51.42/7.19 Y7) => 51.42/7.19 (Y6 @ Y7)))))))) => 51.42/7.19 (Y6 @ Y5)))))))) => 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y7 @ 51.42/7.19 Y8) | 51.42/7.19 (Y0 @ 51.42/7.19 Y7 @ Y8))) & 51.42/7.19 (Y6 @ Y7))) => 51.42/7.19 (Y6 @ Y8))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y4 @ 51.42/7.19 Y7) | 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ Y7))) => 51.42/7.19 (Y6 @ Y7)))))))) => 51.42/7.19 (Y6 @ Y5)))))))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y9 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y7 @ 51.42/7.19 Y8) & 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y8 @ 51.42/7.19 Y9) | 51.42/7.19 (Y0 @ 51.42/7.19 Y8 @ Y9))))) => 51.42/7.19 (Y7 @ Y9))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ 51.42/7.19 Y8) | 51.42/7.19 (Y1 @ 51.42/7.19 Y4 @ Y8))) => 51.42/7.19 (Y7 @ Y8)))))))) => 51.42/7.19 (Y7 @ Y5)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y9 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y8 @ 51.42/7.19 Y9) | 51.42/7.19 (Y0 @ 51.42/7.19 Y8 @ Y9))) & 51.42/7.19 (Y7 @ Y8))) => 51.42/7.19 (Y7 @ Y9))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y5 @ 51.42/7.19 Y8) | 51.42/7.19 (Y0 @ 51.42/7.19 Y5 @ Y8))) => 51.42/7.19 (Y7 @ Y8)))))))) => 51.42/7.19 (Y7 @ Y6)))))))) => 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y9 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y8 @ 51.42/7.19 Y9) | 51.42/7.19 (Y0 @ 51.42/7.19 Y8 @ Y9))) & 51.42/7.19 (Y7 @ Y8))) => 51.42/7.19 (Y7 @ Y9))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ 51.42/7.19 Y8) | 51.42/7.19 (Y1 @ 51.42/7.19 Y4 @ Y8))) => 51.42/7.19 (Y7 @ Y8)))))))) => 51.42/7.19 (Y7 @ Y6))))))))))))))))) & 51.42/7.19 (((~) @ (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y4 @ 51.42/7.19 Y5) & 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 (Y0 @ 51.42/7.19 Y5 @ Y6))))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) | 51.42/7.19 (Y0 @ 51.42/7.19 Y2 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3)))))))))) | 51.42/7.19 (((!!) @ (^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 (Y1 @ 51.42/7.19 Y5 @ Y6))) & 51.42/7.19 (Y4 @ Y5))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y1 @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) | 51.42/7.19 (Y0 @ 51.42/7.19 Y2 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3))))))))))))))))))))), 51.42/7.19 inference('cnf', [status(esa)], [zf_stmt_0])). 51.42/7.19 thf(zip_derived_cl1, plain, 51.42/7.19 (~ (((!!) @ (^[Y0 : a > a > $o]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ 51.42/7.19 Y6) => 51.42/7.19 (Y5 @ Y6)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y5 @ 51.42/7.19 Y6) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y6 @ Y7))) => 51.42/7.19 (Y5 @ Y7))))))))))) => 51.42/7.19 (Y5 @ Y4)))))) | 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y5 @ 51.42/7.19 Y6) & 51.42/7.19 (Y0 @ 51.42/7.19 Y6 @ Y7))) => 51.42/7.19 (Y5 @ Y7))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y3 @ 51.42/7.19 Y6) => 51.42/7.19 (Y5 @ Y6)))))))) => 51.42/7.19 (Y5 @ Y4)))))))) => 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y6 @ 51.42/7.19 Y7) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y6 @ Y7))) & 51.42/7.19 (Y5 @ Y6))) => 51.42/7.19 (Y5 @ Y7))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y3 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y6))) => 51.42/7.19 (Y5 @ Y6)))))))) => 51.42/7.19 (Y5 @ Y4)))))))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y6 @ 51.42/7.19 Y7) & 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y7 @ 51.42/7.19 Y8) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y7 @ Y8))))) => 51.42/7.19 (Y6 @ Y8))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ 51.42/7.19 Y7) | 51.42/7.19 (Y0 @ 51.42/7.19 Y3 @ Y7))) => 51.42/7.19 (Y6 @ Y7)))))))) => 51.42/7.19 (Y6 @ Y4)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y7 @ 51.42/7.19 Y8) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y7 @ Y8))) & 51.42/7.19 (Y6 @ Y7))) => 51.42/7.19 (Y6 @ Y8))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ 51.42/7.19 Y7) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y7))) => 51.42/7.19 (Y6 @ Y7)))))))) => 51.42/7.19 (Y6 @ Y5)))))))) => 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y8 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y7 @ 51.42/7.19 Y8) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y7 @ Y8))) & 51.42/7.19 (Y6 @ Y7))) => 51.42/7.19 (Y6 @ Y8))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ 51.42/7.19 Y7) | 51.42/7.19 (Y0 @ 51.42/7.19 Y3 @ Y7))) => 51.42/7.19 (Y6 @ Y7)))))))) => 51.42/7.19 (Y6 @ Y5))))))))))))))))) & 51.42/7.19 (((~) @ (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y0 @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))))) | 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 (Y0 @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((( 51.42/7.19 (Y0 @ 51.42/7.19 Y1 @ Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))))))))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 51.42/7.19 thf(zip_derived_cl2, plain, 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) => 51.42/7.19 (Y4 @ Y5)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y4 @ 51.42/7.19 Y5) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y5 @ Y6))) => 51.42/7.19 (Y4 @ Y6))))))))))) => 51.42/7.19 (Y4 @ Y3)))))) | 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y4 @ 51.42/7.19 Y5) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y5 @ Y6))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3)))))))) => 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (((( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y5 @ Y6))) & 51.42/7.19 (Y4 @ Y5))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3)))))))))))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y5 @ 51.42/7.19 Y6) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y6 @ 51.42/7.19 Y7) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y6 @ Y7))))) => 51.42/7.19 (Y5 @ Y7))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ Y6))) => 51.42/7.19 (Y5 @ Y6)))))))) => 51.42/7.19 (Y5 @ Y3)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y6 @ 51.42/7.19 Y7) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y6 @ Y7))) & 51.42/7.19 (Y5 @ Y6))) => 51.42/7.19 (Y5 @ Y7))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y6))) => 51.42/7.19 (Y5 @ Y6)))))))) => 51.42/7.19 (Y5 @ Y4)))))))) => 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y5 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y7 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y6 @ 51.42/7.19 Y7) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y6 @ Y7))) & 51.42/7.19 (Y5 @ Y6))) => 51.42/7.19 (Y5 @ Y7))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ Y6))) => 51.42/7.19 (Y5 @ Y6)))))))) => 51.42/7.19 (Y5 @ Y4))))))))))))))))) & 51.42/7.19 (((~) @ (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y3 : a]: 51.42/7.19 ((((('#sk2' @ 51.42/7.19 Y0 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ Y3))) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))))) | 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ Y4))) & 51.42/7.19 (Y2 @ Y3))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((((('#sk2' @ 51.42/7.19 Y0 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ Y3))) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1))))))))))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 51.42/7.19 thf(zip_derived_cl3, plain, 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) => 51.42/7.19 (Y3 @ Y4)))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) => 51.42/7.19 (Y3 @ Y5))))))))))) => 51.42/7.19 (Y3 @ Y2)))))) | 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ Y5))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y4 @ 51.42/7.19 Y5) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y5 @ Y6))))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y2)))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y5 @ Y6))) & 51.42/7.19 (Y4 @ Y5))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3)))))))) => 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a > $o]: 51.42/7.19 (((( 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y6 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y5 @ 51.42/7.19 Y6) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y5 @ Y6))) & 51.42/7.19 (Y4 @ Y5))) => 51.42/7.19 (Y4 @ Y6))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ Y5))) => 51.42/7.19 (Y4 @ Y5)))))))) => 51.42/7.19 (Y4 @ Y3))))))))))))))))) & 51.42/7.19 (((~) @ (((!!) @ (^[Y1 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y3 : a]: 51.42/7.19 (((((Y1 @ 51.42/7.19 Y2) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ Y3))))) => 51.42/7.19 (Y1 @ Y3))))))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((('#sk2' @ 51.42/7.19 '#sk3' @ Y2) | 51.42/7.19 ('#sk1' @ 51.42/7.19 '#sk3' @ Y2))) => 51.42/7.19 (Y1 @ Y2)))))))) => 51.42/7.19 (Y1 @ Y0)))))))))) | 51.42/7.19 (((!!) @ (^[Y1 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((((((('#sk1' @ 51.42/7.19 Y2 @ Y3) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ Y3))) & 51.42/7.19 (Y1 @ Y2))) => 51.42/7.19 (Y1 @ Y3))))))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y2) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y2))) => 51.42/7.19 (Y1 @ Y2)))))))) => 51.42/7.19 (Y1 @ Y0)))))))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 51.42/7.19 thf(zip_derived_cl4, plain, 51.42/7.19 (~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y3) => 51.42/7.19 (Y2 @ Y3)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))))) => 51.42/7.19 (Y2 @ Y1)))))) | 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ 51.42/7.19 Y3) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))) => 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) & 51.42/7.19 (Y2 @ Y3))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ Y3))) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) & 51.42/7.19 (((~) @ (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ 51.42/7.19 Y1 @ Y2) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))))) | 51.42/7.19 (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((((('#sk1' @ Y1 @ Y2) | 51.42/7.19 ('#sk2' @ Y1 @ Y2))) & 51.42/7.19 (Y0 @ Y1))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4'))))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 51.42/7.19 thf(zip_derived_cl6, plain, 51.42/7.19 (~ (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((((('#sk1' @ Y1 @ Y2) | 51.42/7.19 ('#sk2' @ Y1 @ Y2))) & 51.42/7.19 (Y0 @ Y1))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4'))))))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 51.42/7.19 thf(zip_derived_cl8, plain, 51.42/7.19 (~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 51.42/7.19 Y1))) & 51.42/7.19 ('#sk5' @ Y0))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))))) => 51.42/7.19 ('#sk5' @ '#sk4')))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl6])). 51.42/7.19 thf(zip_derived_cl10, plain, 51.42/7.19 ( (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 51.42/7.19 ('#sk5' @ Y0))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0))))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 51.42/7.19 thf(zip_derived_cl13, plain, 51.42/7.19 ( (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) & 51.42/7.19 ('#sk5' @ Y0))) => 51.42/7.19 ('#sk5' @ Y1)))))))))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 51.42/7.19 thf(zip_derived_cl17, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) & 51.42/7.19 ('#sk5' @ X2))) => 51.42/7.19 ('#sk5' @ Y0))))))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 51.42/7.19 thf(zip_derived_cl21, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 ((((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) => 51.42/7.19 ('#sk5' @ X4)))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl17])). 51.42/7.19 thf(zip_derived_cl29, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) & ('#sk5' @ X2))) 51.42/7.19 | ('#sk5' @ X4))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 51.42/7.19 thf(zip_derived_cl39, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 51.42/7.19 | ~ ('#sk5' @ X2) 51.42/7.19 | ('#sk5' @ X4))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl29])). 51.42/7.19 thf(zip_derived_cl49, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 51.42/7.19 thf(zip_derived_cl50, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X4) | ~ ('#sk5' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl39])). 51.42/7.19 thf(zip_derived_cl5, plain, 51.42/7.19 (~ (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 ((('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y3) => 51.42/7.19 (Y2 @ Y3)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))))) => 51.42/7.19 (Y2 @ Y1)))))) | 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((('#sk2' @ 51.42/7.19 Y0 @ 51.42/7.19 Y3) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))) => 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) & 51.42/7.19 (Y2 @ Y3))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((((('#sk2' @ 51.42/7.19 Y0 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ Y3))) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) & 51.42/7.19 (((~) @ (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ 51.42/7.19 Y1 @ Y2) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4'))))))))))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 51.42/7.19 thf(zip_derived_cl7, plain, 51.42/7.19 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 ((('#sk1' @ 51.42/7.19 Y0 @ Y3) => 51.42/7.19 (Y2 @ Y3)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))))) => 51.42/7.19 (Y2 @ Y1)))))) | 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 (Y2 @ 51.42/7.19 Y3) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ Y4))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((('#sk2' @ 51.42/7.19 Y0 @ Y3) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))) => 51.42/7.19 (((!!) @ (^[Y2 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y3 : a]: 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (((( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y3 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y3 @ Y4))) & 51.42/7.19 (Y2 @ Y3))) => 51.42/7.19 (Y2 @ Y4))))))))) & 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((((('#sk2' @ 51.42/7.19 Y0 @ Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ Y3))) => 51.42/7.19 (Y2 @ Y3)))))))) => 51.42/7.19 (Y2 @ Y1)))))))))))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl5])). 51.42/7.19 thf(zip_derived_cl9, plain, 51.42/7.19 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((((((!!) @ (^[Y1 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 ((('#sk1' @ '#sk6' @ 51.42/7.19 Y2) => (Y1 @ Y2)))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((((Y1 @ 51.42/7.19 Y2) & 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ Y3))) => 51.42/7.19 (Y1 @ Y3))))))))))) => 51.42/7.19 (Y1 @ Y0)))))) | 51.42/7.19 (((!!) @ (^[Y1 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 (((((Y1 @ 51.42/7.19 Y2) & 51.42/7.19 ('#sk2' @ 51.42/7.19 Y2 @ Y3))) => 51.42/7.19 (Y1 @ Y3))))))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ 51.42/7.19 Y2) => (Y1 @ Y2)))))))) => 51.42/7.19 (Y1 @ Y0)))))))) => 51.42/7.19 (((!!) @ (^[Y1 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y2 : a]: 51.42/7.19 (((!!) @ (^[Y3 : a]: 51.42/7.19 ((((((('#sk2' @ 51.42/7.19 Y2 @ 51.42/7.19 Y3) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y2 @ Y3))) & 51.42/7.19 (Y1 @ Y2))) => 51.42/7.19 (Y1 @ Y3))))))))) & 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ 51.42/7.19 Y2) | ('#sk1' @ 51.42/7.19 '#sk6' @ Y2))) => 51.42/7.19 (Y1 @ Y2)))))))) => 51.42/7.19 (Y1 @ Y0))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl7])). 51.42/7.19 thf(zip_derived_cl12, plain, 51.42/7.19 ((~ (((((((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ('#sk1' @ Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) | 51.42/7.19 (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ('#sk2' @ Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))) => 51.42/7.19 (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))) & 51.42/7.19 (Y0 @ Y1))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk6' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl9])). 51.42/7.19 thf(zip_derived_cl15, plain, 51.42/7.19 (( (((((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk1' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) | 51.42/7.19 (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 51.42/7.19 thf(zip_derived_cl19, plain, 51.42/7.19 (( (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk1' @ '#sk6' @ Y1) => (Y0 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk1' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl15])). 51.42/7.19 thf(zip_derived_cl23, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))))) => 51.42/7.19 (X2 @ '#sk7'))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 51.42/7.19 thf(zip_derived_cl32, plain, 51.42/7.19 ((~ ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl33, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))))) => 51.42/7.19 (X2 @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))) => 51.42/7.19 (X2 @ '#sk4'))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 51.42/7.19 thf(zip_derived_cl35, plain, 51.42/7.19 (( (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))))) => 51.42/7.19 ('#sk5' @ '#sk4'))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('triggered_bool_instantiation', [status(thm)], 51.42/7.19 [zip_derived_cl33])). 51.42/7.19 thf(zip_derived_cl11, plain, (~ ('#sk5' @ '#sk4')), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl8])). 51.42/7.19 thf(zip_derived_cl262, plain, 51.42/7.19 (( (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))))) => 51.42/7.19 ($false))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('demod', [status(thm)], [zip_derived_cl35, zip_derived_cl11])). 51.42/7.19 thf(zip_derived_cl263, plain, 51.42/7.19 (( (((~) @ (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | 51.42/7.19 ('#sk1' @ Y0 @ Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ 51.42/7.19 Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))))))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl262])). 51.42/7.19 thf(zip_derived_cl264, plain, 51.42/7.19 ((~ (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('simplify nested equalities', [status(thm)], 51.42/7.19 [zip_derived_cl263])). 51.42/7.19 thf(zip_derived_cl265, plain, 51.42/7.19 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0)))))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl264])). 51.42/7.19 thf(zip_derived_cl33, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))))) => 51.42/7.19 (X2 @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))) => 51.42/7.19 (X2 @ '#sk4'))) 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl32])). 51.42/7.19 thf(zip_derived_cl45, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))))) => 51.42/7.19 (X2 @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))) 51.42/7.19 | (X2 @ '#sk4') 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl33])). 51.42/7.19 thf(zip_derived_cl53, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))))) => 51.42/7.19 (X2 @ Y1))))))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | (X2 @ '#sk4'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl45])). 51.42/7.19 thf(zip_derived_cl60, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((((X2 @ ('#sk42' @ X2)) & 51.42/7.19 ((('#sk2' @ ('#sk42' @ X2) @ Y0) | ('#sk1' @ 51.42/7.19 ('#sk42' @ X2) @ Y0))))) => 51.42/7.19 (X2 @ Y0)))))) 51.42/7.19 | (X2 @ '#sk4') 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl53])). 51.42/7.19 thf(zip_derived_cl71, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((((X2 @ ('#sk42' @ X2)) & 51.42/7.19 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.19 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) => 51.42/7.19 (X2 @ ('#sk56' @ X2)))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | (X2 @ '#sk4'))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl60])). 51.42/7.19 thf(zip_derived_cl87, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (X2 @ ('#sk56' @ X2)) 51.42/7.19 | (X2 @ '#sk4') 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl71])). 51.42/7.19 thf(zip_derived_cl101, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form96' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl266, plain, 51.42/7.19 ((~ ('#form96' @ '#sk5') 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk5' @ Y0) & 51.42/7.19 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))))) => 51.42/7.19 ('#sk5' @ Y1))))))))))), 51.42/7.19 inference('renaming', [status(thm)], 51.42/7.19 [zip_derived_cl265, zip_derived_cl101])). 51.42/7.19 thf(zip_derived_cl267, plain, 51.42/7.19 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk5' @ ('#sk42' @ '#sk5')) & 51.42/7.19 ((('#sk2' @ ('#sk42' @ '#sk5') @ Y0) | ('#sk1' @ 51.42/7.19 ('#sk42' @ '#sk5') @ Y0))))) => 51.42/7.19 ('#sk5' @ Y0)))))) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ ('#form96' @ '#sk5'))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])). 51.42/7.19 thf(zip_derived_cl268, plain, 51.42/7.19 ((~ ((((('#sk5' @ ('#sk42' @ '#sk5')) & 51.42/7.19 ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 51.42/7.19 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))))) => 51.42/7.19 ('#sk5' @ ('#sk56' @ '#sk5')))) 51.42/7.19 | ~ ('#form96' @ '#sk5') 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl267])). 51.42/7.19 thf(zip_derived_cl270, plain, 51.42/7.19 ((~ ('#sk5' @ ('#sk56' @ '#sk5')) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ ('#form96' @ '#sk5'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl268])). 51.42/7.19 thf(zip_derived_cl269, plain, 51.42/7.19 (( ((('#sk5' @ ('#sk42' @ '#sk5')) & 51.42/7.19 ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 51.42/7.19 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))))) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ ('#form96' @ '#sk5'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl268])). 51.42/7.19 thf(zip_derived_cl271, plain, 51.42/7.19 (( ('#sk5' @ ('#sk42' @ '#sk5')) | ~ ('#form96' @ '#sk5') | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl269])). 51.42/7.19 thf(zip_derived_cl272, plain, 51.42/7.19 (( ((('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) | ('#sk1' @ 51.42/7.19 ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')))) 51.42/7.19 | ~ ('#form96' @ '#sk5') 51.42/7.19 | ~ ('#form14'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl269])). 51.42/7.19 thf(zip_derived_cl273, plain, 51.42/7.19 (( ('#sk2' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 51.42/7.19 | ('#sk1' @ ('#sk42' @ '#sk5') @ ('#sk56' @ '#sk5')) 51.42/7.19 | ~ ('#form14') 51.42/7.19 | ~ ('#form96' @ '#sk5'))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl272])). 51.42/7.19 thf(zip_derived_cl23, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))))) => 51.42/7.19 (X2 @ '#sk7'))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 51.42/7.19 thf(zip_derived_cl32, plain, 51.42/7.19 ((~ ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl36, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))))) => 51.42/7.19 (X2 @ '#sk7'))))), 51.42/7.19 inference('renaming', [status(thm)], [zip_derived_cl23, zip_derived_cl32])). 51.42/7.19 thf(zip_derived_cl40, plain, 51.42/7.19 ((~ ('#form19') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl41, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) => 51.42/7.19 (X2 @ '#sk7'))) 51.42/7.19 | ~ ('#form19'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl40])). 51.42/7.19 thf(zip_derived_cl52, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl41])). 51.42/7.19 thf(zip_derived_cl59, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk2' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ '#sk7'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl52])). 51.42/7.19 thf(zip_derived_cl70, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ 51.42/7.19 Y0))) => 51.42/7.19 (X2 @ Y0)))))) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl59])). 51.42/7.19 thf(zip_derived_cl85, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (((((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ 51.42/7.19 ('#sk65' @ X2)))) => 51.42/7.19 (X2 @ ('#sk65' @ X2)))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ '#sk7'))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl70])). 51.42/7.19 thf(zip_derived_cl98, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (X2 @ ('#sk65' @ X2)) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 51.42/7.19 thf(zip_derived_cl98, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ (X2 @ ('#sk65' @ X2)) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 51.42/7.19 thf(zip_derived_cl113, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form117' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl115, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ('#form117' @ X2) 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ (X2 @ ('#sk65' @ X2)))), 51.42/7.19 inference('renaming', [status(thm)], 51.42/7.19 [zip_derived_cl98, zip_derived_cl113])). 51.42/7.19 thf(zip_derived_cl101, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form96' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl102, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ((((('#sk2' @ '#sk3' @ ('#sk97' @ X2)) | ('#sk1' @ '#sk3' @ 51.42/7.19 ('#sk97' @ X2)))) => 51.42/7.19 (X2 @ ('#sk97' @ X2)))) 51.42/7.19 | ('#form96' @ X2))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl101])). 51.42/7.19 thf(zip_derived_cl118, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ((('#sk2' @ '#sk3' @ ('#sk97' @ X2)) | ('#sk1' @ '#sk3' @ 51.42/7.19 ('#sk97' @ X2)))) 51.42/7.19 | ('#form96' @ X2))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 51.42/7.19 thf(zip_derived_cl135, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#sk2' @ '#sk3' @ ('#sk97' @ X2)) 51.42/7.19 | ('#sk1' @ '#sk3' @ ('#sk97' @ X2)) 51.42/7.19 | ('#form96' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl118])). 51.42/7.19 thf(zip_derived_cl119, plain, 51.42/7.19 (![X2 : a > $o]: (~ (X2 @ ('#sk97' @ X2)) | ('#form96' @ X2))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl102])). 51.42/7.19 thf(zip_derived_cl16, plain, 51.42/7.19 ((~ (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))) & 51.42/7.19 (Y0 @ Y1))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk6' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl12])). 51.42/7.19 thf(zip_derived_cl20, plain, 51.42/7.19 ((~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 51.42/7.19 thf(zip_derived_cl20, plain, 51.42/7.19 ((~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl16])). 51.42/7.19 thf(zip_derived_cl26, plain, 51.42/7.19 (( ('#form9') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl28, plain, 51.42/7.19 ((~ ('#form9') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))))), 51.42/7.19 inference('renaming', [status(thm)], [zip_derived_cl20, zip_derived_cl26])). 51.42/7.19 thf(zip_derived_cl32, plain, 51.42/7.19 ((~ ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl37, plain, 51.42/7.19 (( ('#form14') 51.42/7.19 | ~ (((((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.19 Y0 @ Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))) 51.42/7.19 | ~ ('#form9'))), 51.42/7.19 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl32])). 51.42/7.19 thf(zip_derived_cl47, plain, 51.42/7.19 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 51.42/7.19 thf(zip_derived_cl46, plain, 51.42/7.19 (( (((((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.19 Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))))) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 51.42/7.19 thf(zip_derived_cl54, plain, 51.42/7.19 (( (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 51.42/7.19 ('#sk8' @ Y0))) => 51.42/7.19 ('#sk8' @ Y1))))))))) 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#form9'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 51.42/7.19 thf(zip_derived_cl61, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 ( (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 51.42/7.19 ('#sk8' @ X2))) => 51.42/7.19 ('#sk8' @ Y0)))))) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl54])). 51.42/7.19 thf(zip_derived_cl72, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) => 51.42/7.19 ('#sk8' @ X4))) 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#form9'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl61])). 51.42/7.19 thf(zip_derived_cl88, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk8' @ X2))) 51.42/7.19 | ('#sk8' @ X4) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl72])). 51.42/7.19 thf(zip_derived_cl104, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 51.42/7.19 | ~ ('#sk8' @ X2) 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#sk8' @ X4))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl88])). 51.42/7.19 thf(zip_derived_cl120, plain, 51.42/7.19 (![X2 : a, X4 : a]: 51.42/7.19 (~ ('#sk2' @ X2 @ X4) 51.42/7.19 | ('#sk8' @ X4) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#sk8' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 51.42/7.19 thf(zip_derived_cl14, plain, 51.42/7.19 ( (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y0) | ('#sk1' @ '#sk3' @ Y0))) => 51.42/7.19 ('#sk5' @ Y0))))))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl10])). 51.42/7.19 thf(zip_derived_cl18, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) => ('#sk5' @ 51.42/7.19 X2)))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl14])). 51.42/7.19 thf(zip_derived_cl22, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 (~ ((('#sk2' @ '#sk3' @ X2) | ('#sk1' @ '#sk3' @ X2))) 51.42/7.19 | ('#sk5' @ X2))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl18])). 51.42/7.19 thf(zip_derived_cl31, plain, 51.42/7.19 (![X2 : a]: (~ ('#sk1' @ '#sk3' @ X2) | ('#sk5' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 51.42/7.19 thf(zip_derived_cl30, plain, 51.42/7.19 (![X2 : a]: (~ ('#sk2' @ '#sk3' @ X2) | ('#sk5' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 51.42/7.19 thf(zip_derived_cl97, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((X2 @ ('#sk50' @ X2)) & ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl85])). 51.42/7.19 thf(zip_derived_cl111, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (X2 @ ('#sk50' @ X2)) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ '#sk7'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])). 51.42/7.19 thf(zip_derived_cl113, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form117' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl128, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ('#form117' @ (^[Y0 : a]: (X2 @ Y0))) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ ('#sk50' @ X2)))), 51.42/7.19 inference('renaming', [status(thm)], 51.42/7.19 [zip_derived_cl111, zip_derived_cl113])). 51.42/7.19 thf(zip_derived_cl145, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ('#form117' @ X2) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ ('#sk50' @ X2)))), 51.42/7.19 inference('ho_norm', [status(thm)], [zip_derived_cl128])). 51.42/7.19 thf(zip_derived_cl113, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form117' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl114, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ((('#sk2' @ '#sk6' @ ('#sk118' @ X2)) => (X2 @ ('#sk118' @ X2)))) 51.42/7.19 | ('#form117' @ X2))), 51.42/7.19 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl113])). 51.42/7.19 thf(zip_derived_cl130, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#sk2' @ '#sk6' @ ('#sk118' @ X2)) | ('#form117' @ X2))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 51.42/7.19 thf(zip_derived_cl131, plain, 51.42/7.19 (![X2 : a > $o]: (~ (X2 @ ('#sk118' @ X2)) | ('#form117' @ X2))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl114])). 51.42/7.19 thf(zip_derived_cl112, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))) 51.42/7.19 | ~ ('#form19') 51.42/7.19 | (X2 @ '#sk7'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl97])). 51.42/7.19 thf(zip_derived_cl113, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( ('#form117' @ X2) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: ((('#sk2' @ '#sk6' @ Y0) => (X2 @ Y0)))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl129, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ('#form117' @ (^[Y0 : a]: (X2 @ Y0))) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))), 51.42/7.19 inference('renaming', [status(thm)], 51.42/7.19 [zip_derived_cl112, zip_derived_cl113])). 51.42/7.19 thf(zip_derived_cl146, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 (~ ('#form117' @ X2) 51.42/7.19 | (X2 @ '#sk7') 51.42/7.19 | ~ ('#form19') 51.42/7.19 | ('#sk2' @ ('#sk50' @ X2) @ ('#sk65' @ X2)))), 51.42/7.19 inference('ho_norm', [status(thm)], [zip_derived_cl129])). 51.42/7.19 thf(zip_derived_cl55, plain, 51.42/7.19 (( (((!!) @ (^[Y0 : a]: 51.42/7.19 ((((('#sk2' @ '#sk6' @ Y0) | ('#sk1' @ '#sk6' @ Y0))) => 51.42/7.19 ('#sk8' @ Y0)))))) 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#form9'))), 51.42/7.19 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl46])). 51.42/7.19 thf(zip_derived_cl62, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 ( ((((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) => ('#sk8' @ 51.42/7.19 X2))) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14'))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl55])). 51.42/7.19 thf(zip_derived_cl73, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 (~ ((('#sk2' @ '#sk6' @ X2) | ('#sk1' @ '#sk6' @ X2))) 51.42/7.19 | ('#sk8' @ X2) 51.42/7.19 | ('#form14') 51.42/7.19 | ~ ('#form9'))), 51.42/7.19 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])). 51.42/7.19 thf(zip_derived_cl89, plain, 51.42/7.19 (![X2 : a]: 51.42/7.19 (~ ('#sk2' @ '#sk6' @ X2) 51.42/7.19 | ~ ('#form9') 51.42/7.19 | ('#form14') 51.42/7.19 | ('#sk8' @ X2))), 51.42/7.19 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 51.42/7.19 thf(zip_derived_cl23, plain, 51.42/7.19 (![X2 : a > $o]: 51.42/7.19 ( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => (X2 @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((((X2 @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 (X2 @ Y1))))))))))) => 51.42/7.19 (X2 @ '#sk7'))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | 51.42/7.19 ('#sk1' @ '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])). 51.42/7.19 thf(zip_derived_cl24, plain, 51.42/7.19 (( (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 ('#sk8' @ Y1))))))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 inference('triggered_bool_instantiation', [status(thm)], 51.42/7.19 [zip_derived_cl23])). 51.42/7.19 thf(zip_derived_cl32, plain, 51.42/7.19 ((~ ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & 51.42/7.19 ((('#sk2' @ Y1 @ Y2) | 51.42/7.19 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk2' @ '#sk3' @ Y1) | ('#sk1' @ 51.42/7.19 '#sk3' @ Y1))) => 51.42/7.19 (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk4')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl202, plain, 51.42/7.19 (( ('#form14') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 ('#sk8' @ Y1))))))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))))), 51.42/7.19 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl32])). 51.42/7.19 thf(zip_derived_cl40, plain, 51.42/7.19 ((~ ('#form19') 51.42/7.19 | (((!!) @ (^[Y0 : a > $o]: 51.42/7.19 (((((((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((Y0 @ Y1) & ('#sk2' @ 51.42/7.19 Y1 @ Y2))) => 51.42/7.19 (Y0 @ Y2))))))))) & 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((('#sk2' @ '#sk6' @ Y1) => (Y0 @ Y1)))))))) => 51.42/7.19 (Y0 @ '#sk7')))))))), 51.42/7.19 define([status(thm)])). 51.42/7.19 thf(zip_derived_cl203, plain, 51.42/7.19 (( ('#form19') 51.42/7.19 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.19 (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.19 ('#sk8' @ Y1))))))))))) => 51.42/7.19 ('#sk8' @ '#sk7'))) 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (Y3 @ 51.42/7.19 Y4) & 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y1)))))) & 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y1 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y1 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2)))))))) => 51.42/7.19 (((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (!!) @ ( 51.42/7.19 ^[Y5 : a]: 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 (( 51.42/7.19 ('#sk2' @ 51.42/7.19 Y4 @ 51.42/7.19 Y5) | 51.42/7.19 ('#sk1' @ 51.42/7.19 Y4 @ Y5))) & 51.42/7.19 (Y3 @ Y4))) => 51.42/7.19 (Y3 @ Y5))))))))) & 51.42/7.19 (((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 ( 51.42/7.19 ( 51.42/7.19 (( 51.42/7.19 ('#sk1' @ 51.42/7.19 Y0 @ 51.42/7.19 Y4) | 51.42/7.19 ('#sk2' @ 51.42/7.19 Y0 @ Y4))) => 51.42/7.19 (Y3 @ Y4)))))))) => 51.42/7.19 (Y3 @ Y2))))))))))))))))) 51.42/7.19 | ('#form14'))), 51.42/7.19 inference('renaming', [status(thm)], 51.42/7.19 [zip_derived_cl202, zip_derived_cl40])). 51.42/7.19 thf(zip_derived_cl26, plain, 51.42/7.19 (( ('#form9') 51.42/7.19 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.19 (((!!) @ (^[Y1 : a]: 51.42/7.19 (((!!) @ (^[Y2 : a]: 51.42/7.19 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.19 (((((((!!) @ ( 51.42/7.19 ^[Y4 : a]: 51.42/7.19 (( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (Y3 @ 51.42/7.20 Y4) & 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk1' @ 51.42/7.20 Y0 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk2' @ 51.42/7.20 Y0 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y1)))))) & 51.42/7.20 (((!!) @ (^[Y3 : a > $o]: 51.42/7.20 (((((((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))) & 51.42/7.20 (Y3 @ Y4))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y1 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y1 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y2)))))))) => 51.42/7.20 (((!!) @ (^[Y3 : a > $o]: 51.42/7.20 (((((((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))) & 51.42/7.20 (Y3 @ Y4))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (( 51.42/7.20 ('#sk1' @ 51.42/7.20 Y0 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk2' @ 51.42/7.20 Y0 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y2))))))))))))))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl204, plain, 51.42/7.20 ((~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | (((((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))))) => 51.42/7.20 ('#sk8' @ '#sk7'))) 51.42/7.20 | ('#form19'))), 51.42/7.20 inference('renaming', [status(thm)], 51.42/7.20 [zip_derived_cl203, zip_derived_cl26])). 51.42/7.20 thf(zip_derived_cl205, plain, 51.42/7.20 ((~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))))) 51.42/7.20 | ('#sk8' @ '#sk7') 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl204])). 51.42/7.20 thf(zip_derived_cl47, plain, 51.42/7.20 ((~ ('#sk8' @ '#sk7') | ~ ('#form9') | ('#form14'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl37])). 51.42/7.20 thf(zip_derived_cl206, plain, 51.42/7.20 ((~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ~ (((((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))))))), 51.42/7.20 inference('clc', [status(thm)], [zip_derived_cl205, zip_derived_cl47])). 51.42/7.20 thf(zip_derived_cl207, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: ((('#sk1' @ '#sk6' @ Y0) => ('#sk8' @ Y0)))))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl206])). 51.42/7.20 thf(zip_derived_cl208, plain, 51.42/7.20 ((~ ((('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) => ('#sk8' @ 51.42/7.20 ('#sk60' @ '#sk8')))) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl207])). 51.42/7.20 thf(zip_derived_cl210, plain, 51.42/7.20 ((~ ('#sk8' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl208])). 51.42/7.20 thf(zip_derived_cl212, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ 51.42/7.20 ('#sk107' @ '#sk8') @ Y0))) => 51.42/7.20 ('#sk8' @ Y0)))))) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl210])). 51.42/7.20 thf(zip_derived_cl214, plain, 51.42/7.20 ((~ ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 51.42/7.20 ('#sk143' @ '#sk8')))) => 51.42/7.20 ('#sk8' @ ('#sk143' @ '#sk8')))) 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl212])). 51.42/7.20 thf(zip_derived_cl218, plain, 51.42/7.20 ((~ ('#sk8' @ ('#sk143' @ '#sk8')) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 51.42/7.20 thf(zip_derived_cl217, plain, 51.42/7.20 (( ((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 51.42/7.20 ('#sk143' @ '#sk8')))) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl214])). 51.42/7.20 thf(zip_derived_cl221, plain, 51.42/7.20 (( ('#sk8' @ ('#sk107' @ '#sk8')) 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 51.42/7.20 thf(zip_derived_cl222, plain, 51.42/7.20 (( ('#sk1' @ ('#sk107' @ '#sk8') @ ('#sk143' @ '#sk8')) 51.42/7.20 | ~ ('#sk8' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 51.42/7.20 thf(zip_derived_cl209, plain, 51.42/7.20 (( ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk8' @ Y0) & ('#sk1' @ Y0 @ Y1))) => 51.42/7.20 ('#sk8' @ Y1))))))))) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl208])). 51.42/7.20 thf(zip_derived_cl211, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ 51.42/7.20 ('#sk107' @ '#sk8') @ Y0))) => 51.42/7.20 ('#sk8' @ Y0)))))) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl209])). 51.42/7.20 thf(zip_derived_cl213, plain, 51.42/7.20 ((~ ((((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 51.42/7.20 ('#sk143' @ '#sk8')))) => 51.42/7.20 ('#sk8' @ ('#sk143' @ '#sk8')))) 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl211])). 51.42/7.20 thf(zip_derived_cl216, plain, 51.42/7.20 ((~ ('#sk8' @ ('#sk143' @ '#sk8')) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])). 51.42/7.20 thf(zip_derived_cl215, plain, 51.42/7.20 (( ((('#sk8' @ ('#sk107' @ '#sk8')) & ('#sk1' @ ('#sk107' @ '#sk8') @ 51.42/7.20 ('#sk143' @ '#sk8')))) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#form19') 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl213])). 51.42/7.20 thf(zip_derived_cl219, plain, 51.42/7.20 (( ('#sk8' @ ('#sk107' @ '#sk8')) 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl215])). 51.42/7.20 thf(zip_derived_cl220, plain, 51.42/7.20 (( ('#sk1' @ ('#sk107' @ '#sk8') @ ('#sk143' @ '#sk8')) 51.42/7.20 | ('#sk1' @ '#sk6' @ ('#sk60' @ '#sk8')) 51.42/7.20 | ('#form19') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl215])). 51.42/7.20 thf(zip_derived_cl90, plain, 51.42/7.20 (![X2 : a]: 51.42/7.20 (~ ('#sk1' @ '#sk6' @ X2) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ('#sk8' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl73])). 51.42/7.20 thf(zip_derived_cl26, plain, 51.42/7.20 (( ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 (((((((!!) @ (^[Y3 : a > $o]: 51.42/7.20 (((((((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (Y3 @ 51.42/7.20 Y4) & 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk1' @ 51.42/7.20 Y0 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk2' @ 51.42/7.20 Y0 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y1)))))) & 51.42/7.20 (((!!) @ (^[Y3 : a > $o]: 51.42/7.20 (((((((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))) & 51.42/7.20 (Y3 @ Y4))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y1 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y1 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y2)))))))) => 51.42/7.20 (((!!) @ (^[Y3 : a > $o]: 51.42/7.20 (((((((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (!!) @ ( 51.42/7.20 ^[Y5 : a]: 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y4 @ 51.42/7.20 Y5) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y4 @ Y5))) & 51.42/7.20 (Y3 @ Y4))) => 51.42/7.20 (Y3 @ Y5))))))))) & 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (( 51.42/7.20 ('#sk1' @ 51.42/7.20 Y0 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk2' @ 51.42/7.20 Y0 @ Y4))) => 51.42/7.20 (Y3 @ Y4)))))))) => 51.42/7.20 (Y3 @ Y2))))))))))))))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl27, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 (((((((!!) @ (^[Y2 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y3 : a]: 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (( 51.42/7.20 (Y2 @ 51.42/7.20 Y3) & 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y3 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y3 @ Y4))))) => 51.42/7.20 (Y2 @ Y4))))))))) & 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 ((((('#sk1' @ 51.42/7.20 '#sk10' @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk2' @ 51.42/7.20 '#sk10' @ 51.42/7.20 Y3))) => 51.42/7.20 (Y2 @ Y3)))))))) => 51.42/7.20 (Y2 @ Y0)))))) & 51.42/7.20 (((!!) @ (^[Y2 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y3 : a]: 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 ( 51.42/7.20 ( 51.42/7.20 (( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y3 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y3 @ Y4))) & 51.42/7.20 (Y2 @ Y3))) => 51.42/7.20 (Y2 @ Y4))))))))) & 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 ((((('#sk2' @ 51.42/7.20 Y0 @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y0 @ Y3))) => 51.42/7.20 (Y2 @ Y3)))))))) => 51.42/7.20 (Y2 @ Y1)))))))) => 51.42/7.20 (((!!) @ (^[Y2 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y3 : a]: 51.42/7.20 (((!!) @ ( 51.42/7.20 ^[Y4 : a]: 51.42/7.20 (((( 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y3 @ 51.42/7.20 Y4) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y3 @ Y4))) & 51.42/7.20 (Y2 @ Y3))) => 51.42/7.20 (Y2 @ Y4))))))))) & 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 ((((('#sk1' @ 51.42/7.20 '#sk10' @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk2' @ 51.42/7.20 '#sk10' @ 51.42/7.20 Y3))) => 51.42/7.20 (Y2 @ Y3)))))))) => 51.42/7.20 (Y2 @ Y1)))))))))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl26])). 51.42/7.20 thf(zip_derived_cl38, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((((((!!) @ (^[Y1 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y2 : a]: 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 (((((Y1 @ 51.42/7.20 Y2) & 51.42/7.20 (( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y2 @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y2 @ Y3))))) => 51.42/7.20 (Y1 @ Y3))))))))) & 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ 51.42/7.20 Y2) | ('#sk2' @ 51.42/7.20 '#sk10' @ Y2))) => 51.42/7.20 (Y1 @ Y2)))))))) => 51.42/7.20 (Y1 @ '#sk15')))))) & 51.42/7.20 (((!!) @ (^[Y1 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y2 : a]: 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 (((((( 51.42/7.20 ('#sk2' @ 51.42/7.20 Y2 @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y2 @ Y3))) & 51.42/7.20 (Y1 @ Y2))) => 51.42/7.20 (Y1 @ Y3))))))))) & 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ 51.42/7.20 Y2) | ('#sk1' @ 51.42/7.20 '#sk15' @ Y2))) => 51.42/7.20 (Y1 @ Y2)))))))) => 51.42/7.20 (Y1 @ Y0)))))))) => 51.42/7.20 (((!!) @ (^[Y1 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y2 : a]: 51.42/7.20 (((!!) @ (^[Y3 : a]: 51.42/7.20 ((((((('#sk2' @ 51.42/7.20 Y2 @ 51.42/7.20 Y3) | 51.42/7.20 ('#sk1' @ 51.42/7.20 Y2 @ Y3))) & 51.42/7.20 (Y1 @ Y2))) => 51.42/7.20 (Y1 @ Y3))))))))) & 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ 51.42/7.20 Y2) | ('#sk2' @ 51.42/7.20 '#sk10' @ Y2))) => 51.42/7.20 (Y1 @ Y2)))))))) => 51.42/7.20 (Y1 @ Y0))))))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl27])). 51.42/7.20 thf(zip_derived_cl48, plain, 51.42/7.20 ((~ (((((((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 (((((Y0 @ Y1) & 51.42/7.20 ((('#sk2' @ Y1 @ 51.42/7.20 Y2) | ('#sk1' @ 51.42/7.20 Y1 @ Y2))))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y1) | 51.42/7.20 ('#sk2' @ '#sk10' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk15')))))) & 51.42/7.20 (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((((('#sk2' @ Y1 @ 51.42/7.20 Y2) | ('#sk1' @ 51.42/7.20 Y1 @ Y2))) & 51.42/7.20 (Y0 @ Y1))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y1) | 51.42/7.20 ('#sk1' @ '#sk15' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk23')))))))) => 51.42/7.20 (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))) & 51.42/7.20 (Y0 @ Y1))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y1) | 51.42/7.20 ('#sk2' @ '#sk10' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk23')))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl38])). 51.42/7.20 thf(zip_derived_cl56, plain, 51.42/7.20 (( (((((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 (((((Y0 @ Y1) & 51.42/7.20 ((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 51.42/7.20 '#sk10' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk15')))))) & 51.42/7.20 (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))) & 51.42/7.20 (Y0 @ Y1))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 51.42/7.20 '#sk15' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk23')))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 51.42/7.20 thf(zip_derived_cl64, plain, 51.42/7.20 (( (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))) & 51.42/7.20 (Y0 @ Y1))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y1) | ('#sk1' @ 51.42/7.20 '#sk15' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk23')))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 51.42/7.20 thf(zip_derived_cl78, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))) & 51.42/7.20 (X2 @ Y0))) => 51.42/7.20 (X2 @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 51.42/7.20 Y0))) => 51.42/7.20 (X2 @ Y0)))))))) => 51.42/7.20 (X2 @ '#sk23'))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 51.42/7.20 thf(zip_derived_cl79, plain, 51.42/7.20 (( (((((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))))) => 51.42/7.20 ('#sk43' @ '#sk23'))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('triggered_bool_instantiation', [status(thm)], 51.42/7.20 [zip_derived_cl78])). 51.42/7.20 thf(zip_derived_cl334, plain, 51.42/7.20 ((~ (((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))))) 51.42/7.20 | ('#sk43' @ '#sk23') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])). 51.42/7.20 thf(zip_derived_cl57, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 ((((((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))) & 51.42/7.20 (Y0 @ Y1))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 51.42/7.20 '#sk10' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk23')))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl48])). 51.42/7.20 thf(zip_derived_cl68, plain, 51.42/7.20 ((~ (((((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))))) => 51.42/7.20 ('#sk43' @ '#sk23'))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl57])). 51.42/7.20 thf(zip_derived_cl83, plain, ((~ ('#sk43' @ '#sk23') | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 51.42/7.20 thf(zip_derived_cl335, plain, 51.42/7.20 (( ('#form9') 51.42/7.20 | ~ (((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))))))), 51.42/7.20 inference('clc', [status(thm)], [zip_derived_cl334, zip_derived_cl83])). 51.42/7.20 thf(zip_derived_cl336, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl335])). 51.42/7.20 thf(zip_derived_cl78, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))) & 51.42/7.20 (X2 @ Y0))) => 51.42/7.20 (X2 @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ 51.42/7.20 Y0))) => 51.42/7.20 (X2 @ Y0)))))))) => 51.42/7.20 (X2 @ '#sk23'))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl64])). 51.42/7.20 thf(zip_derived_cl92, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))) & 51.42/7.20 (X2 @ Y0))) => 51.42/7.20 (X2 @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))) 51.42/7.20 | (X2 @ '#sk23') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl78])). 51.42/7.20 thf(zip_derived_cl106, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))) & 51.42/7.20 (X2 @ Y0))) => 51.42/7.20 (X2 @ Y1))))))))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk23'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl92])). 51.42/7.20 thf(zip_derived_cl123, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((((('#sk2' @ ('#sk138' @ X2) @ Y0) | ('#sk1' @ 51.42/7.20 ('#sk138' @ X2) @ Y0))) & 51.42/7.20 (X2 @ ('#sk138' @ X2)))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | (X2 @ '#sk23') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl106])). 51.42/7.20 thf(zip_derived_cl137, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ((((((('#sk2' @ ('#sk138' @ X2) @ ('#sk187' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk138' @ X2) @ ('#sk187' @ X2)))) & 51.42/7.20 (X2 @ ('#sk138' @ X2)))) => 51.42/7.20 (X2 @ ('#sk187' @ X2)))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk23'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl123])). 51.42/7.20 thf(zip_derived_cl150, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (X2 @ ('#sk187' @ X2)) 51.42/7.20 | (X2 @ '#sk23') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl137])). 51.42/7.20 thf(zip_derived_cl163, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form264' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl337, plain, 51.42/7.20 ((~ ('#form264' @ '#sk43') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))))), 51.42/7.20 inference('renaming', [status(thm)], 51.42/7.20 [zip_derived_cl336, zip_derived_cl163])). 51.42/7.20 thf(zip_derived_cl338, plain, 51.42/7.20 ((~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((((('#sk2' @ ('#sk138' @ '#sk43') @ Y0) | ('#sk1' @ 51.42/7.20 ('#sk138' @ '#sk43') @ Y0))) & 51.42/7.20 ('#sk43' @ ('#sk138' @ '#sk43')))) => 51.42/7.20 ('#sk43' @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#form264' @ '#sk43'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl337])). 51.42/7.20 thf(zip_derived_cl339, plain, 51.42/7.20 ((~ ((((((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | 51.42/7.20 ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) & 51.42/7.20 ('#sk43' @ ('#sk138' @ '#sk43')))) => 51.42/7.20 ('#sk43' @ ('#sk187' @ '#sk43')))) 51.42/7.20 | ~ ('#form264' @ '#sk43') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl338])). 51.42/7.20 thf(zip_derived_cl341, plain, 51.42/7.20 ((~ ('#sk43' @ ('#sk187' @ '#sk43')) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#form264' @ '#sk43'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 51.42/7.20 thf(zip_derived_cl121, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 (~ ('#sk1' @ X2 @ X4) 51.42/7.20 | ('#sk8' @ X4) 51.42/7.20 | ~ ('#form9') 51.42/7.20 | ('#form14') 51.42/7.20 | ~ ('#sk8' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl104])). 51.42/7.20 thf(zip_derived_cl340, plain, 51.42/7.20 (( ((((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | 51.42/7.20 ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) & 51.42/7.20 ('#sk43' @ ('#sk138' @ '#sk43')))) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#form264' @ '#sk43'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl339])). 51.42/7.20 thf(zip_derived_cl343, plain, 51.42/7.20 (( ('#sk43' @ ('#sk138' @ '#sk43')) 51.42/7.20 | ~ ('#form264' @ '#sk43') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl340])). 51.42/7.20 thf(zip_derived_cl342, plain, 51.42/7.20 (( ((('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) | ('#sk1' @ 51.42/7.20 ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')))) 51.42/7.20 | ~ ('#form264' @ '#sk43') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl340])). 51.42/7.20 thf(zip_derived_cl344, plain, 51.42/7.20 (( ('#sk2' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) 51.42/7.20 | ('#sk1' @ ('#sk138' @ '#sk43') @ ('#sk187' @ '#sk43')) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#form264' @ '#sk43'))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl342])). 51.42/7.20 thf(zip_derived_cl163, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form264' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk2' @ '#sk15' @ Y0) | ('#sk1' @ '#sk15' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl164, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ((((('#sk2' @ '#sk15' @ ('#sk265' @ X2)) | ('#sk1' @ '#sk15' @ 51.42/7.20 ('#sk265' @ X2)))) => 51.42/7.20 (X2 @ ('#sk265' @ X2)))) 51.42/7.20 | ('#form264' @ X2))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl163])). 51.42/7.20 thf(zip_derived_cl175, plain, 51.42/7.20 (![X2 : a > $o]: (~ (X2 @ ('#sk265' @ X2)) | ('#form264' @ X2))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 51.42/7.20 thf(zip_derived_cl174, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ((('#sk2' @ '#sk15' @ ('#sk265' @ X2)) | ('#sk1' @ '#sk15' @ 51.42/7.20 ('#sk265' @ X2)))) 51.42/7.20 | ('#form264' @ X2))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])). 51.42/7.20 thf(zip_derived_cl183, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#sk2' @ '#sk15' @ ('#sk265' @ X2)) 51.42/7.20 | ('#sk1' @ '#sk15' @ ('#sk265' @ X2)) 51.42/7.20 | ('#form264' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl174])). 51.42/7.20 thf(zip_derived_cl63, plain, 51.42/7.20 (( (((!!) @ (^[Y0 : a > $o]: 51.42/7.20 (((((((!!) @ (^[Y1 : a]: 51.42/7.20 (((!!) @ (^[Y2 : a]: 51.42/7.20 (((((Y0 @ Y1) & 51.42/7.20 ((('#sk2' @ Y1 @ Y2) | 51.42/7.20 ('#sk1' @ Y1 @ Y2))))) => 51.42/7.20 (Y0 @ Y2))))))))) & 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y1) | ('#sk2' @ 51.42/7.20 '#sk10' @ Y1))) => 51.42/7.20 (Y0 @ Y1)))))))) => 51.42/7.20 (Y0 @ '#sk15')))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl56])). 51.42/7.20 thf(zip_derived_cl74, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( (((((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 (((((X2 @ Y0) & 51.42/7.20 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))))) => 51.42/7.20 (X2 @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ 51.42/7.20 Y0))) => 51.42/7.20 (X2 @ Y0)))))))) => 51.42/7.20 (X2 @ '#sk15'))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 51.42/7.20 thf(zip_derived_cl91, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 (((((X2 @ Y0) & 51.42/7.20 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 51.42/7.20 Y0 @ Y1))))) => 51.42/7.20 (X2 @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl74])). 51.42/7.20 thf(zip_derived_cl105, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 (((((X2 @ Y0) & 51.42/7.20 ((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))))) => 51.42/7.20 (X2 @ Y1))))))))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl91])). 51.42/7.20 thf(zip_derived_cl122, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((!!) @ (^[Y0 : a]: 51.42/7.20 (((((X2 @ ('#sk42' @ X2)) & 51.42/7.20 ((('#sk2' @ ('#sk42' @ X2) @ Y0) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ Y0))))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 51.42/7.20 thf(zip_derived_cl136, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (((((X2 @ ('#sk42' @ X2)) & 51.42/7.20 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) => 51.42/7.20 (X2 @ ('#sk56' @ X2)))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15'))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 51.42/7.20 thf(zip_derived_cl148, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (X2 @ ('#sk56' @ X2)) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 51.42/7.20 thf(zip_derived_cl148, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ (X2 @ ('#sk56' @ X2)) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 51.42/7.20 thf(zip_derived_cl158, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form254' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl160, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ('#form254' @ X2) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ~ (X2 @ ('#sk56' @ X2)))), 51.42/7.20 inference('renaming', [status(thm)], 51.42/7.20 [zip_derived_cl148, zip_derived_cl158])). 51.42/7.20 thf(zip_derived_cl82, plain, 51.42/7.20 (( (((((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 51.42/7.20 Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) & 51.42/7.20 (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl68])). 51.42/7.20 thf(zip_derived_cl93, plain, 51.42/7.20 (( (((!!) @ (^[Y0 : a]: 51.42/7.20 (((!!) @ (^[Y1 : a]: 51.42/7.20 ((((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) & 51.42/7.20 ('#sk43' @ Y0))) => 51.42/7.20 ('#sk43' @ Y1))))))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 51.42/7.20 thf(zip_derived_cl107, plain, 51.42/7.20 (![X2 : a]: 51.42/7.20 ( (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) & 51.42/7.20 ('#sk43' @ X2))) => 51.42/7.20 ('#sk43' @ Y0)))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl93])). 51.42/7.20 thf(zip_derived_cl124, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 ( ((((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk43' @ X2))) => 51.42/7.20 ('#sk43' @ X4))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl107])). 51.42/7.20 thf(zip_derived_cl138, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 (~ ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) & ('#sk43' @ X2))) 51.42/7.20 | ('#sk43' @ X4) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl124])). 51.42/7.20 thf(zip_derived_cl151, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 51.42/7.20 | ~ ('#sk43' @ X2) 51.42/7.20 | ('#form9') 51.42/7.20 | ('#sk43' @ X4))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl138])). 51.42/7.20 thf(zip_derived_cl167, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 (~ ('#sk1' @ X2 @ X4) 51.42/7.20 | ('#sk43' @ X4) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#sk43' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 51.42/7.20 thf(zip_derived_cl166, plain, 51.42/7.20 (![X2 : a, X4 : a]: 51.42/7.20 (~ ('#sk2' @ X2 @ X4) 51.42/7.20 | ('#sk43' @ X4) 51.42/7.20 | ('#form9') 51.42/7.20 | ~ ('#sk43' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl151])). 51.42/7.20 thf(zip_derived_cl147, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( (((X2 @ ('#sk42' @ X2)) & 51.42/7.20 ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ ('#sk56' @ X2)))))) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl136])). 51.42/7.20 thf(zip_derived_cl156, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( (X2 @ ('#sk42' @ X2)) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 51.42/7.20 thf(zip_derived_cl158, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form254' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl168, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ('#form254' @ (^[Y0 : a]: (X2 @ Y0))) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ ('#sk42' @ X2)))), 51.42/7.20 inference('renaming', [status(thm)], 51.42/7.20 [zip_derived_cl156, zip_derived_cl158])). 51.42/7.20 thf(zip_derived_cl176, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ('#form254' @ X2) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ ('#sk42' @ X2)))), 51.42/7.20 inference('ho_norm', [status(thm)], [zip_derived_cl168])). 51.42/7.20 thf(zip_derived_cl157, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ ('#sk56' @ X2)))) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl147])). 51.42/7.20 thf(zip_derived_cl158, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form254' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl169, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ('#form254' @ (^[Y0 : a]: (X2 @ Y0))) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ ('#sk56' @ X2)))))), 51.42/7.20 inference('renaming', [status(thm)], 51.42/7.20 [zip_derived_cl157, zip_derived_cl158])). 51.42/7.20 thf(zip_derived_cl177, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ('#form254' @ X2) 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ('#form9') 51.42/7.20 | ((('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) | ('#sk1' @ 51.42/7.20 ('#sk42' @ X2) @ ('#sk56' @ X2)))))), 51.42/7.20 inference('ho_norm', [status(thm)], [zip_derived_cl169])). 51.42/7.20 thf(zip_derived_cl178, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#sk2' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) 51.42/7.20 | ('#sk1' @ ('#sk42' @ X2) @ ('#sk56' @ X2)) 51.42/7.20 | ('#form9') 51.42/7.20 | (X2 @ '#sk15') 51.42/7.20 | ~ ('#form254' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl177])). 51.42/7.20 thf(zip_derived_cl158, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#form254' @ X2) 51.42/7.20 | ~ (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 (X2 @ Y0)))))))), 51.42/7.20 define([status(thm)])). 51.42/7.20 thf(zip_derived_cl159, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 (~ ((((('#sk1' @ '#sk10' @ ('#sk255' @ X2)) | ('#sk2' @ '#sk10' @ 51.42/7.20 ('#sk255' @ X2)))) => 51.42/7.20 (X2 @ ('#sk255' @ X2)))) 51.42/7.20 | ('#form254' @ X2))), 51.42/7.20 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl158])). 51.42/7.20 thf(zip_derived_cl170, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ((('#sk1' @ '#sk10' @ ('#sk255' @ X2)) | ('#sk2' @ '#sk10' @ 51.42/7.20 ('#sk255' @ X2)))) 51.42/7.20 | ('#form254' @ X2))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 51.42/7.20 thf(zip_derived_cl179, plain, 51.42/7.20 (![X2 : a > $o]: 51.42/7.20 ( ('#sk1' @ '#sk10' @ ('#sk255' @ X2)) 51.42/7.20 | ('#sk2' @ '#sk10' @ ('#sk255' @ X2)) 51.42/7.20 | ('#form254' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl170])). 51.42/7.20 thf(zip_derived_cl171, plain, 51.42/7.20 (![X2 : a > $o]: (~ (X2 @ ('#sk255' @ X2)) | ('#form254' @ X2))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 51.42/7.20 thf(zip_derived_cl94, plain, 51.42/7.20 (( (((!!) @ (^[Y0 : a]: 51.42/7.20 ((((('#sk1' @ '#sk10' @ Y0) | ('#sk2' @ '#sk10' @ Y0))) => 51.42/7.20 ('#sk43' @ Y0)))))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl82])). 51.42/7.20 thf(zip_derived_cl108, plain, 51.42/7.20 (![X2 : a]: 51.42/7.20 ( ((((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) => 51.42/7.20 ('#sk43' @ X2))) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 51.42/7.20 thf(zip_derived_cl125, plain, 51.42/7.20 (![X2 : a]: 51.42/7.20 (~ ((('#sk1' @ '#sk10' @ X2) | ('#sk2' @ '#sk10' @ X2))) 51.42/7.20 | ('#sk43' @ X2) 51.42/7.20 | ('#form9'))), 51.42/7.20 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])). 51.42/7.20 thf(zip_derived_cl139, plain, 51.42/7.20 (![X2 : a]: (~ ('#sk1' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 51.42/7.20 thf(zip_derived_cl140, plain, 51.42/7.20 (![X2 : a]: (~ ('#sk2' @ '#sk10' @ X2) | ('#form9') | ('#sk43' @ X2))), 51.42/7.20 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl125])). 51.42/7.20 thf(zip_derived_cl10229, plain, ($false), 51.42/7.20 inference('eprover', [status(thm)], 51.42/7.20 [zip_derived_cl49, zip_derived_cl50, zip_derived_cl270, 51.42/7.20 zip_derived_cl271, zip_derived_cl273, zip_derived_cl115, 51.42/7.20 zip_derived_cl135, zip_derived_cl119, zip_derived_cl47, 51.42/7.20 zip_derived_cl120, zip_derived_cl31, zip_derived_cl30, 51.42/7.20 zip_derived_cl145, zip_derived_cl130, zip_derived_cl131, 51.42/7.20 zip_derived_cl146, zip_derived_cl89, zip_derived_cl218, 51.42/7.20 zip_derived_cl221, zip_derived_cl222, zip_derived_cl216, 51.42/7.20 zip_derived_cl219, zip_derived_cl220, zip_derived_cl90, 51.42/7.20 zip_derived_cl341, zip_derived_cl121, zip_derived_cl343, 51.42/7.20 zip_derived_cl344, zip_derived_cl175, zip_derived_cl183, 51.42/7.20 zip_derived_cl160, zip_derived_cl167, zip_derived_cl166, 51.42/7.20 zip_derived_cl176, zip_derived_cl178, zip_derived_cl179, 51.42/7.20 zip_derived_cl171, zip_derived_cl139, zip_derived_cl140])). 51.42/7.20 51.42/7.20 % SZS output end Refutation 51.42/7.20 51.42/7.20 51.42/7.20 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s 51.42/7.20 % Terminating... 51.97/7.27 % Runner terminated. 51.97/7.28 % Zipperpin 1.5 exiting 51.97/7.29 EOF