0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.13 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.X86raOvOKM true 0.14/0.34 % Computer : n005.cluster.edu 0.14/0.34 % Model : x86_64 x86_64 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.34 % Memory : 8042.1875MB 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 0.14/0.34 % CPULimit : 1440 0.14/0.34 % WCLimit : 180 0.14/0.34 % DateTime : Mon Jul 3 04:38:45 EDT 2023 0.14/0.34 % CPUTime : 0.14/0.34 % Running portfolio for 1440 s 0.14/0.34 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p 0.14/0.34 % Number of cores: 8 0.14/0.34 % Python version: Python 3.6.8 0.14/0.35 % Running in HO mode 0.52/0.63 % Total configuration time : 828 0.52/0.63 % Estimated wc time : 1656 0.52/0.63 % Estimated cpu time (8 cpus) : 207.0 0.54/0.69 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s 0.54/0.74 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s 0.54/0.75 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s 0.54/0.76 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s 62.42/8.58 % Solved by lams/20_acsne_simpl.sh. 62.42/8.58 % done 922 iterations in 7.688s 62.42/8.58 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p' 62.42/8.58 % SZS output start Refutation 62.42/8.58 thf(a_type, type, a: $tType). 62.42/8.58 thf('#sk4_type', type, '#sk4': a). 62.42/8.58 thf('#sk30_type', type, '#sk30': a > a > $o). 62.42/8.58 thf('#sk343_type', type, '#sk343': (a > a > $o) > a). 62.42/8.58 thf('#sk3_type', type, '#sk3': a). 62.42/8.58 thf('#sk149_type', type, '#sk149': (a > a > $o) > a). 62.42/8.58 thf('#sk12_type', type, '#sk12': a). 62.42/8.58 thf('#sk21_type', type, '#sk21': a > a > $o). 62.42/8.58 thf('#form243_type', type, '#form243': (a > a > $o) > $o). 62.42/8.58 thf('#sk100_type', type, '#sk100': (a > a > $o) > a). 62.42/8.58 thf('#sk47_type', type, '#sk47': (a > a > $o) > a). 62.42/8.58 thf('#sk6_type', type, '#sk6': a). 62.42/8.58 thf('#sk301_type', type, '#sk301': (a > a > $o) > a). 62.42/8.58 thf('#sk122_type', type, '#sk122': (a > a > $o) > a). 62.42/8.58 thf('#sk2_type', type, '#sk2': a > a > $o). 62.42/8.58 thf('#sk434_type', type, '#sk434': (a > a > $o) > a). 62.42/8.58 thf('#sk334_type', type, '#sk334': (a > a > $o) > a). 62.42/8.58 thf('#sk8_type', type, '#sk8': a). 62.42/8.58 thf('#sk10_type', type, '#sk10': a). 62.42/8.58 thf('#sk7_type', type, '#sk7': a). 62.42/8.58 thf('#form91_type', type, '#form91': $o). 62.42/8.58 thf('#sk74_type', type, '#sk74': (a > a > $o) > a). 62.42/8.58 thf('#sk177_type', type, '#sk177': (a > a > $o) > a). 62.42/8.58 thf('#form9_type', type, '#form9': $o). 62.42/8.58 thf('#form360_type', type, '#form360': (a > a > $o) > $o). 62.42/8.58 thf('#form11_type', type, '#form11': $o). 62.42/8.58 thf('#sk5_type', type, '#sk5': a > a > $o). 62.42/8.58 thf('#sk1_type', type, '#sk1': a > a > $o). 62.42/8.58 thf('#sk113_type', type, '#sk113': (a > a > $o) > a). 62.42/8.58 thf('#sk224_type', type, '#sk224': (a > a > $o) > a). 62.42/8.58 thf('#sk206_type', type, '#sk206': (a > a > $o) > a). 62.42/8.58 thf('#form223_type', type, '#form223': (a > a > $o) > $o). 62.42/8.58 thf('#sk442_type', type, '#sk442': (a > a > $o) > a). 62.42/8.58 thf(cTHM250G_pme, conjecture, 62.42/8.58 (![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 62.42/8.58 ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx @ Xy ) ) ) | 62.42/8.58 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xy0 @ Xz ) ) ) & 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx @ Xy ) ) ) ) ) ))). 62.42/8.58 thf(zf_stmt_0, negated_conjecture, 62.42/8.58 (~( ![R:( a > a > $o ),S:( a > a > $o ),Xx:a,Xy:a]: 62.42/8.58 ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx0 @ Xy0 ) & ( Xp1 @ Xy0 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx @ Xy ) ) ) | 62.42/8.58 ( ~( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xy0 @ Xz ) ) ) & 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz0 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( S @ Xx1 @ Xy1 ) | ( R @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz0:a]: 62.42/8.58 ( ( ( Xp1 @ Xy1 @ Xz0 ) & ( Xp1 @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( S @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) | 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( R @ Xx1 @ Xy1 ) => ( Xp1 @ Xx1 @ Xy1 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx1:a,Xy1:a]: 62.42/8.58 ( ( ( R @ Xx1 @ Xy1 ) | ( S @ Xx1 @ Xy1 ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xy1 ) ) ) & 62.42/8.58 ( ![Xx1:a,Xy1:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xx1 @ Xy1 ) & ( Xp1 @ Xy1 @ Xz ) ) => 62.42/8.58 ( Xp1 @ Xx1 @ Xz ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) ) ) => 62.42/8.58 ( ![Xp1:( a > a > $o )]: 62.42/8.58 ( ( ( ![Xx0:a,Xy0:a,Xz:a]: 62.42/8.58 ( ( ( Xp1 @ Xy0 @ Xz ) & ( Xp1 @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xz ) ) ) & 62.42/8.58 ( ![Xx0:a,Xy0:a]: 62.42/8.58 ( ( ( S @ Xx0 @ Xy0 ) | ( R @ Xx0 @ Xy0 ) ) => 62.42/8.58 ( Xp1 @ Xx0 @ Xy0 ) ) ) ) => 62.42/8.58 ( Xp1 @ Xx @ Xy ) ) ) ) ) ) )), 62.42/8.58 inference('cnf.neg', [status(esa)], [cTHM250G_pme])). 62.42/8.58 thf(zip_derived_cl0, plain, 62.42/8.58 (~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((!!) @ (^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 (Y0 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3)))))) | 62.42/8.58 (((~) @ (((( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y10 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) & 62.42/8.58 (Y7 @ 62.42/8.58 Y9 @ Y10))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y10)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) | 62.42/8.58 (Y1 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y9))))))))))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y5 @ Y6)))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) | 62.42/8.58 (Y1 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y9))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y10 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) & 62.42/8.58 (Y7 @ 62.42/8.58 Y9 @ Y10))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y10)))))))))))))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y4 @ Y5)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) | 62.42/8.58 (Y0 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y9))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y10 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y7 @ 62.42/8.58 Y9 @ 62.42/8.58 Y10) & 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y8 @ Y10)))))))))))))) => 62.42/8.58 (Y7 @ 62.42/8.58 Y4 @ Y6))))))))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y4 @ Y5)))))) | 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y4 @ Y5)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) | 62.42/8.58 (Y1 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y4 @ Y5)))))))))))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 (Y0 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3))))))))))))))))))))))))), 62.42/8.58 inference('cnf', [status(esa)], [zf_stmt_0])). 62.42/8.58 thf(zip_derived_cl1, plain, 62.42/8.58 (~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ Y1 @ Y2)))))) | 62.42/8.58 (((~) @ (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) | 62.42/8.58 (Y0 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y4 @ Y5)))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) | 62.42/8.58 (Y0 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ Y9))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y3 @ Y4)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y9 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y6 @ 62.42/8.58 Y8 @ 62.42/8.58 Y9) & 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y7 @ Y9)))))))))))))) => 62.42/8.58 (Y6 @ 62.42/8.58 Y3 @ Y5))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y3 @ Y4)))))) | 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y3 @ Y4)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) | 62.42/8.58 (Y0 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y3 @ Y4)))))))))))))))) => 62.42/8.58 (((!!) @ (^[Y3 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y0 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y1 @ Y2)))))))))))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl0])). 62.42/8.58 thf(zip_derived_cl2, plain, 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((~) @ (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y3 @ Y4)))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ Y8))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y2 @ Y3)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y8 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y5 @ 62.42/8.58 Y7 @ 62.42/8.58 Y8) & 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y6 @ Y8)))))))))))))) => 62.42/8.58 (Y5 @ 62.42/8.58 Y2 @ Y4))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3)))))) | 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3)))))))))))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1))))))))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl1])). 62.42/8.58 thf(zip_derived_cl3, plain, 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((( 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y3) & 62.42/8.58 (Y1 @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y4)))))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 ((((('#sk2' @ 62.42/8.58 Y2 @ Y3) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ Y2 @ Y3))))))))))) => 62.42/8.58 (Y1 @ '#sk3' @ Y0)))))) | 62.42/8.58 (((~) @ (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y2 @ Y3)))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ Y7))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y1 @ Y2)))))))) => 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : 62.42/8.58 a > a > $o]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y7 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y4 @ 62.42/8.58 Y6 @ 62.42/8.58 Y7) & 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y5 @ Y7)))))))))))))) => 62.42/8.58 (Y4 @ 62.42/8.58 Y1 @ Y3))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : 62.42/8.58 a > a > $o]: 62.42/8.58 (((( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y1 @ Y2)))))) | 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : 62.42/8.58 a > a > $o]: 62.42/8.58 (((( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y1 @ Y2)))))))) => 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a > a > $o]: 62.42/8.58 (((((( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y1 @ 62.42/8.58 Y2)))))))))))))))) => 62.42/8.58 (((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y4)))))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 ((((('#sk2' @ 62.42/8.58 Y2 @ Y3) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ Y2 @ 62.42/8.58 Y3))))))))))) => 62.42/8.58 (Y1 @ '#sk3' @ Y0)))))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl2])). 62.42/8.58 thf(zip_derived_cl4, plain, 62.42/8.58 (~ (((((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) | 62.42/8.58 (((~) @ (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : 62.42/8.58 a > a > $o]: 62.42/8.58 (((( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y1 @ Y2)))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : 62.42/8.58 a > a > $o]: 62.42/8.58 (((( 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a > a > $o]: 62.42/8.58 (((((( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ 62.42/8.58 Y2))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))) => 62.42/8.58 (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y3 : a]: 62.42/8.58 (((((Y0 @ 62.42/8.58 Y2 @ Y3) & 62.42/8.58 (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ 62.42/8.58 Y1 @ Y2) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4'))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3])). 62.42/8.58 thf(zip_derived_cl6, plain, 62.42/8.58 ( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ Y1 @ 62.42/8.58 Y2)))))) & 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ 62.42/8.58 Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ Y2))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))) => 62.42/8.58 (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4'))))))))), 62.42/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 62.42/8.58 thf(zip_derived_cl8, plain, 62.42/8.58 ((~ (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ Y1 @ 62.42/8.58 Y2)))))) & 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ 62.42/8.58 Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ Y2))))))))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl6])). 62.42/8.58 thf(zip_derived_cl11, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))))) => 62.42/8.58 (Y3 @ Y1 @ Y2)))))) & 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ Y6))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y3 : a > a > $o]: 62.42/8.58 (((((((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))))))))) & 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y6 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y3 @ 62.42/8.58 Y5 @ 62.42/8.58 Y6) & 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y3 @ 62.42/8.58 Y4 @ Y6)))))))))))))) => 62.42/8.58 (Y3 @ Y0 @ Y2))))))))))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl8])). 62.42/8.58 thf(zip_derived_cl14, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) & 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ '#sk6' @ Y0)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ 62.42/8.58 Y5) & 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ '#sk6' @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl11])). 62.42/8.58 thf(zip_derived_cl17, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((((((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ 62.42/8.58 Y3) & 62.42/8.58 (Y1 @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y4)))))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 ((((('#sk1' @ 62.42/8.58 Y2 @ 62.42/8.58 Y3) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ Y2 @ 62.42/8.58 Y3))))))))))) => 62.42/8.58 (Y1 @ '#sk7' @ Y0)))))) & 62.42/8.58 (((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 ((((('#sk1' @ 62.42/8.58 Y2 @ 62.42/8.58 Y3) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ Y2 @ 62.42/8.58 Y3))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ 62.42/8.58 Y3) & 62.42/8.58 (Y1 @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y4)))))))))))))) => 62.42/8.58 (Y1 @ '#sk6' @ '#sk7')))))))) => 62.42/8.58 (((!!) @ (^[Y1 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 ((((('#sk2' @ 62.42/8.58 Y2 @ Y3) | 62.42/8.58 ('#sk1' @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ Y2 @ 62.42/8.58 Y3))))))))) & 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (((( 62.42/8.58 (Y1 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y1 @ 62.42/8.58 Y2 @ Y4)))))))))))))) => 62.42/8.58 (Y1 @ '#sk6' @ Y0))))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl14])). 62.42/8.58 thf(zip_derived_cl20, plain, 62.42/8.58 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ 62.42/8.58 Y1 @ 62.42/8.58 Y2) & 62.42/8.58 (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))) & 62.42/8.58 (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ 62.42/8.58 Y1 @ 62.42/8.58 Y2) & 62.42/8.58 (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk7')))))))) => 62.42/8.58 (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y2))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk8')))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl17])). 62.42/8.58 thf(zip_derived_cl24, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk8')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 62.42/8.58 thf(zip_derived_cl24, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk8')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 62.42/8.58 thf(zip_derived_cl30, plain, 62.42/8.58 (( ('#form9') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl32, plain, 62.42/8.58 ((~ ('#form9') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y2))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk8')))))))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl24, zip_derived_cl30])). 62.42/8.58 thf(zip_derived_cl23, plain, 62.42/8.58 (( (((((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))) & 62.42/8.58 (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk7')))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl20])). 62.42/8.58 thf(zip_derived_cl28, plain, 62.42/8.58 (( (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 62.42/8.58 thf(zip_derived_cl34, plain, 62.42/8.58 ((~ ('#form11') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl41, plain, 62.42/8.58 (( ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y2))) => 62.42/8.58 (Y0 @ Y1 @ 62.42/8.58 Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk8')))))) 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl32, zip_derived_cl34])). 62.42/8.58 thf(zip_derived_cl47, plain, 62.42/8.58 ((~ (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y1 @ Y2) & 62.42/8.58 ('#sk21' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))))) => 62.42/8.58 ('#sk21' @ '#sk6' @ '#sk8'))) 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl41])). 62.42/8.58 thf(zip_derived_cl62, plain, 62.42/8.58 ((~ ('#sk21' @ '#sk6' @ '#sk8') | ('#form11') | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 62.42/8.58 thf(zip_derived_cl28, plain, 62.42/8.58 (( (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 62.42/8.58 thf(zip_derived_cl34, plain, 62.42/8.58 ((~ ('#form11') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl39, plain, 62.42/8.58 (( ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl28, zip_derived_cl34])). 62.42/8.58 thf(zip_derived_cl30, plain, 62.42/8.58 (( ('#form9') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl43, plain, 62.42/8.58 ((~ ('#form9') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk7' @ '#sk8')))))) 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl39, zip_derived_cl30])). 62.42/8.58 thf(zip_derived_cl50, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))) => 62.42/8.58 (X2 @ '#sk7' @ '#sk8'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 62.42/8.58 thf(zip_derived_cl51, plain, 62.42/8.58 (( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))))) => 62.42/8.58 ('#sk21' @ '#sk7' @ '#sk8'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('triggered_bool_instantiation', [status(thm)], 62.42/8.58 [zip_derived_cl50])). 62.42/8.58 thf(zip_derived_cl278, plain, 62.42/8.58 ((~ (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))))) 62.42/8.58 | ('#sk21' @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl51])). 62.42/8.58 thf(zip_derived_cl279, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#sk21' @ '#sk7' @ '#sk8'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl278])). 62.42/8.58 thf(zip_derived_cl29, plain, 62.42/8.58 (( (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk7')))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl23])). 62.42/8.58 thf(zip_derived_cl34, plain, 62.42/8.58 ((~ ('#form11') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y2 @ 62.42/8.58 Y3) & (Y0 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk2' @ Y1 @ Y2) | 62.42/8.58 ('#sk1' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))))) => 62.42/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl40, plain, 62.42/8.58 (( ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))) 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk7')))))))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl29, zip_derived_cl34])). 62.42/8.58 thf(zip_derived_cl30, plain, 62.42/8.58 (( ('#form9') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))) | 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))) => 62.42/8.58 (((!!) @ (^[Y2 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (( 62.42/8.58 ('#sk1' @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) | 62.42/8.58 ('#sk2' @ 62.42/8.58 Y3 @ Y4))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y4))))))))) & 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((!!) @ ( 62.42/8.58 ^[Y4 : a]: 62.42/8.58 ( 62.42/8.58 ( 62.42/8.58 (!!) @ ( 62.42/8.58 ^[Y5 : a]: 62.42/8.58 (( 62.42/8.58 (( 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ 62.42/8.58 Y4) & 62.42/8.58 (Y2 @ 62.42/8.58 Y4 @ Y5))) => 62.42/8.58 (Y2 @ 62.42/8.58 Y3 @ Y5)))))))))))))) => 62.42/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl45, plain, 62.42/8.58 ((~ ('#form9') 62.42/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 62.42/8.58 (((((((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk1' @ Y1 @ Y2) | 62.42/8.58 ('#sk2' @ Y1 @ Y2))) => 62.42/8.58 (Y0 @ Y1 @ Y2))))))))) & 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((!!) @ (^[Y3 : a]: 62.42/8.58 (((((Y0 @ Y1 @ 62.42/8.58 Y2) & (Y0 @ 62.42/8.58 Y2 @ Y3))) => 62.42/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 62.42/8.58 (Y0 @ '#sk6' @ '#sk7')))))) 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('renaming', [status(thm)], [zip_derived_cl40, zip_derived_cl30])). 62.42/8.58 thf(zip_derived_cl56, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))) => 62.42/8.58 (X2 @ '#sk6' @ '#sk7'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 62.42/8.58 thf(zip_derived_cl70, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))) 62.42/8.58 | (X2 @ '#sk6' @ '#sk7') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])). 62.42/8.58 thf(zip_derived_cl83, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | (X2 @ '#sk6' @ '#sk7'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl70])). 62.42/8.58 thf(zip_derived_cl98, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 ((((('#sk1' @ ('#sk122' @ X2) @ Y0) | ('#sk2' @ 62.42/8.58 ('#sk122' @ X2) @ Y0))) => 62.42/8.58 (X2 @ ('#sk122' @ X2) @ Y0)))))) 62.42/8.58 | (X2 @ '#sk6' @ '#sk7') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl83])). 62.42/8.58 thf(zip_derived_cl108, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ ((((('#sk1' @ ('#sk122' @ X2) @ ('#sk177' @ X2)) | ('#sk2' @ 62.42/8.58 ('#sk122' @ X2) @ ('#sk177' @ X2)))) => 62.42/8.58 (X2 @ ('#sk122' @ X2) @ ('#sk177' @ X2)))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | (X2 @ '#sk6' @ '#sk7'))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl98])). 62.42/8.58 thf(zip_derived_cl121, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#form243' @ X2) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl280, plain, 62.42/8.58 ((~ ('#form243' @ '#sk21') 62.42/8.58 | ('#sk21' @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))))), 62.42/8.58 inference('renaming', [status(thm)], 62.42/8.58 [zip_derived_cl279, zip_derived_cl121])). 62.42/8.58 thf(zip_derived_cl50, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))) => 62.42/8.58 (X2 @ '#sk7' @ '#sk8'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl43])). 62.42/8.58 thf(zip_derived_cl68, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))) 62.42/8.58 | (X2 @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])). 62.42/8.58 thf(zip_derived_cl81, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | (X2 @ '#sk7' @ '#sk8'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl68])). 62.42/8.58 thf(zip_derived_cl96, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((((X2 @ ('#sk100' @ X2) @ Y0) & (X2 @ 62.42/8.58 Y0 @ Y1))) => 62.42/8.58 (X2 @ ('#sk100' @ X2) @ Y1))))))))) 62.42/8.58 | (X2 @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl81])). 62.42/8.58 thf(zip_derived_cl105, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((((X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) & (X2 @ 62.42/8.58 ('#sk149' @ X2) @ Y0))) => 62.42/8.58 (X2 @ ('#sk100' @ X2) @ Y0)))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | (X2 @ '#sk7' @ '#sk8'))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl96])). 62.42/8.58 thf(zip_derived_cl115, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((((X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) & (X2 @ 62.42/8.58 ('#sk149' @ X2) @ ('#sk206' @ X2)))) => 62.42/8.58 (X2 @ ('#sk100' @ X2) @ ('#sk206' @ X2)))) 62.42/8.58 | (X2 @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl105])). 62.42/8.58 thf(zip_derived_cl132, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (X2 @ ('#sk100' @ X2) @ ('#sk206' @ X2)) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | (X2 @ '#sk7' @ '#sk8'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])). 62.42/8.58 thf(zip_derived_cl149, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#form360' @ X2) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl281, plain, 62.42/8.58 ((~ ('#form360' @ '#sk21') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#sk21' @ '#sk7' @ '#sk8') 62.42/8.58 | ~ ('#form243' @ '#sk21'))), 62.42/8.58 inference('renaming', [status(thm)], 62.42/8.58 [zip_derived_cl280, zip_derived_cl149])). 62.42/8.58 thf(zip_derived_cl56, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))) => 62.42/8.58 (X2 @ '#sk6' @ '#sk7'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl45])). 62.42/8.58 thf(zip_derived_cl57, plain, 62.42/8.58 (( (((((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))))) => 62.42/8.58 ('#sk21' @ '#sk6' @ '#sk7'))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('triggered_bool_instantiation', [status(thm)], 62.42/8.58 [zip_derived_cl56])). 62.42/8.58 thf(zip_derived_cl294, plain, 62.42/8.58 ((~ (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))))) 62.42/8.58 | ('#sk21' @ '#sk6' @ '#sk7') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl57])). 62.42/8.58 thf(zip_derived_cl295, plain, 62.42/8.58 ((~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#sk21' @ '#sk6' @ '#sk7'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl294])). 62.42/8.58 thf(zip_derived_cl149, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#form360' @ X2) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl296, plain, 62.42/8.58 ((~ ('#form360' @ '#sk21') 62.42/8.58 | ('#sk21' @ '#sk6' @ '#sk7') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & 62.42/8.58 ('#sk21' @ Y1 @ Y2))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))))), 62.42/8.58 inference('renaming', [status(thm)], 62.42/8.58 [zip_derived_cl295, zip_derived_cl149])). 62.42/8.58 thf(zip_derived_cl121, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#form243' @ X2) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 62.42/8.58 Y1 @ Y2))) => 62.42/8.58 (X2 @ Y0 @ Y2)))))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl297, plain, 62.42/8.58 ((~ ('#form243' @ '#sk21') 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#sk21' @ '#sk6' @ '#sk7') 62.42/8.58 | ~ ('#form360' @ '#sk21'))), 62.42/8.58 inference('renaming', [status(thm)], 62.42/8.58 [zip_derived_cl296, zip_derived_cl121])). 62.42/8.58 thf(zip_derived_cl149, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#form360' @ X2) 62.42/8.58 | ~ (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 62.42/8.58 Y1))) => 62.42/8.58 (X2 @ Y0 @ Y1))))))))))), 62.42/8.58 define([status(thm)])). 62.42/8.58 thf(zip_derived_cl150, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ (((!!) @ (^[Y0 : a]: 62.42/8.58 ((((('#sk1' @ ('#sk122' @ X2) @ Y0) | ('#sk2' @ 62.42/8.58 ('#sk122' @ X2) @ Y0))) => 62.42/8.58 (X2 @ ('#sk122' @ X2) @ Y0)))))) 62.42/8.58 | ('#form360' @ X2))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl149])). 62.42/8.58 thf(zip_derived_cl163, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 (~ ((((('#sk1' @ ('#sk122' @ X2) @ ('#sk177' @ X2)) | ('#sk2' @ 62.42/8.58 ('#sk122' @ X2) @ ('#sk177' @ X2)))) => 62.42/8.58 (X2 @ ('#sk122' @ X2) @ ('#sk177' @ X2)))) 62.42/8.58 | ('#form360' @ X2))), 62.42/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl150])). 62.42/8.58 thf(zip_derived_cl173, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ((('#sk1' @ ('#sk122' @ X2) @ ('#sk177' @ X2)) | ('#sk2' @ 62.42/8.58 ('#sk122' @ X2) @ ('#sk177' @ X2)))) 62.42/8.58 | ('#form360' @ X2))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 62.42/8.58 thf(zip_derived_cl177, plain, 62.42/8.58 (![X2 : a > a > $o]: 62.42/8.58 ( ('#sk1' @ ('#sk122' @ X2) @ ('#sk177' @ X2)) 62.42/8.58 | ('#sk2' @ ('#sk122' @ X2) @ ('#sk177' @ X2)) 62.42/8.58 | ('#form360' @ X2))), 62.42/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl173])). 62.42/8.58 thf(zip_derived_cl61, plain, 62.42/8.58 (( (((((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) & 62.42/8.58 (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y1 @ Y2) & 62.42/8.58 ('#sk21' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl47])). 62.42/8.58 thf(zip_derived_cl72, plain, 62.42/8.58 (( (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 (((!!) @ (^[Y2 : a]: 62.42/8.58 ((((('#sk21' @ Y1 @ Y2) & 62.42/8.58 ('#sk21' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y2)))))))))))) 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 62.42/8.58 thf(zip_derived_cl85, plain, 62.42/8.58 (![X2 : a]: 62.42/8.58 ( (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk21' @ Y0 @ Y1) & ('#sk21' @ X2 @ 62.42/8.58 Y0))) => 62.42/8.58 ('#sk21' @ X2 @ Y1))))))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl72])). 62.42/8.58 thf(zip_derived_cl100, plain, 62.42/8.58 (![X2 : a, X4 : a]: 62.42/8.58 ( (((!!) @ (^[Y0 : a]: 62.42/8.58 ((((('#sk21' @ X4 @ Y0) & ('#sk21' @ X2 @ X4))) => 62.42/8.58 ('#sk21' @ X2 @ Y0)))))) 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl85])). 62.42/8.58 thf(zip_derived_cl110, plain, 62.42/8.58 (![X2 : a, X4 : a, X6 : a]: 62.42/8.58 ( ((((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) => ('#sk21' @ X2 @ 62.42/8.58 X6))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 62.42/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl100])). 62.42/8.58 thf(zip_derived_cl126, plain, 62.42/8.58 (![X2 : a, X4 : a, X6 : a]: 62.42/8.58 (~ ((('#sk21' @ X4 @ X6) & ('#sk21' @ X2 @ X4))) 62.42/8.58 | ('#sk21' @ X2 @ X6) 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl110])). 62.42/8.58 thf(zip_derived_cl139, plain, 62.42/8.58 (![X2 : a, X4 : a, X6 : a]: 62.42/8.58 (~ ('#sk21' @ X4 @ X6) 62.42/8.58 | ~ ('#sk21' @ X2 @ X4) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#sk21' @ X2 @ X6))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl126])). 62.42/8.58 thf(zip_derived_cl71, plain, 62.42/8.58 (( (((!!) @ (^[Y0 : a]: 62.42/8.58 (((!!) @ (^[Y1 : a]: 62.42/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 62.42/8.58 ('#sk21' @ Y0 @ Y1))))))))) 62.42/8.58 | ~ ('#form9') 62.42/8.58 | ('#form11'))), 62.42/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl61])). 62.42/8.58 thf(zip_derived_cl84, plain, 62.42/8.58 (![X2 : a]: 62.42/8.58 ( (((!!) @ (^[Y0 : a]: 62.42/8.58 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 62.42/8.58 ('#sk21' @ X2 @ Y0)))))) 62.42/8.58 | ('#form11') 62.42/8.58 | ~ ('#form9'))), 68.70/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl71])). 68.70/8.58 thf(zip_derived_cl99, plain, 68.70/8.58 (![X2 : a, X4 : a]: 68.70/8.58 ( ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk21' @ X2 @ X4))) 68.70/8.58 | ~ ('#form9') 68.70/8.58 | ('#form11'))), 68.70/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl84])). 68.70/8.58 thf(zip_derived_cl109, plain, 68.70/8.58 (![X2 : a, X4 : a]: 68.70/8.58 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) 68.70/8.58 | ('#sk21' @ X2 @ X4) 68.70/8.58 | ('#form11') 68.70/8.58 | ~ ('#form9'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl99])). 68.70/8.58 thf(zip_derived_cl125, plain, 68.70/8.58 (![X2 : a, X4 : a]: 68.70/8.58 (~ ('#sk1' @ X2 @ X4) 68.70/8.58 | ~ ('#form9') 68.70/8.58 | ('#form11') 68.70/8.58 | ('#sk21' @ X2 @ X4))), 68.70/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 68.70/8.58 thf(zip_derived_cl174, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (X2 @ ('#sk122' @ X2) @ ('#sk177' @ X2)) | ('#form360' @ X2))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl163])). 68.70/8.58 thf(zip_derived_cl124, plain, 68.70/8.58 (![X2 : a, X4 : a]: 68.70/8.58 (~ ('#sk2' @ X2 @ X4) 68.70/8.58 | ~ ('#form9') 68.70/8.58 | ('#form11') 68.70/8.58 | ('#sk21' @ X2 @ X4))), 68.70/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl109])). 68.70/8.58 thf(zip_derived_cl34, plain, 68.70/8.58 ((~ ('#form11') 68.70/8.58 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ Y2 @ 68.70/8.58 Y3) & (Y0 @ 68.70/8.58 Y1 @ Y2))) => 68.70/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk2' @ Y1 @ Y2) | 68.70/8.58 ('#sk1' @ Y1 @ Y2))) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.58 (Y0 @ '#sk3' @ '#sk4')))))))), 68.70/8.58 define([status(thm)])). 68.70/8.58 thf(zip_derived_cl35, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((((X2 @ Y1 @ Y2) & (X2 @ 68.70/8.58 Y0 @ Y1))) => 68.70/8.58 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))) => 68.70/8.58 (X2 @ '#sk3' @ '#sk4'))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 68.70/8.58 thf(zip_derived_cl36, plain, 68.70/8.58 (( (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))))) => 68.70/8.58 ('#sk5' @ '#sk3' @ '#sk4'))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('triggered_bool_instantiation', [status(thm)], 68.70/8.58 [zip_derived_cl35])). 68.70/8.58 thf(zip_derived_cl5, plain, 68.70/8.58 (~ (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ Y1 @ 68.70/8.58 Y2) & (Y0 @ 68.70/8.58 Y2 @ Y3))) => 68.70/8.58 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk2' @ Y1 @ Y2) | 68.70/8.58 ('#sk1' @ Y1 @ Y2))) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.58 (Y0 @ '#sk3' @ '#sk4'))))))), 68.70/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl4])). 68.70/8.58 thf(zip_derived_cl7, plain, 68.70/8.58 (~ (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y0 @ Y1) & 68.70/8.58 ('#sk5' @ Y1 @ Y2))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))))) => 68.70/8.58 ('#sk5' @ '#sk3' @ '#sk4')))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl5])). 68.70/8.58 thf(zip_derived_cl10, plain, (~ ('#sk5' @ '#sk3' @ '#sk4')), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 68.70/8.58 thf(zip_derived_cl209, plain, 68.70/8.58 (( (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))))) => 68.70/8.58 ($false))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('demod', [status(thm)], [zip_derived_cl36, zip_derived_cl10])). 68.70/8.58 thf(zip_derived_cl210, plain, 68.70/8.58 (( (((~) @ (((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ 68.70/8.58 Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))))))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('simplify boolean subterms', [status(thm)], [zip_derived_cl209])). 68.70/8.58 thf(zip_derived_cl211, plain, 68.70/8.58 ((~ (((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('simplify nested equalities', [status(thm)], 68.70/8.58 [zip_derived_cl210])). 68.70/8.58 thf(zip_derived_cl212, plain, 68.70/8.58 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y1))))))))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl211])). 68.70/8.58 thf(zip_derived_cl35, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((((X2 @ Y1 @ Y2) & (X2 @ 68.70/8.58 Y0 @ Y1))) => 68.70/8.58 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))) => 68.70/8.58 (X2 @ '#sk3' @ '#sk4'))) 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl34])). 68.70/8.58 thf(zip_derived_cl44, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((((X2 @ Y1 @ Y2) & (X2 @ 68.70/8.58 Y0 @ Y1))) => 68.70/8.58 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))) 68.70/8.58 | (X2 @ '#sk3' @ '#sk4') 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl35])). 68.70/8.58 thf(zip_derived_cl55, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((((X2 @ Y1 @ Y2) & (X2 @ 68.70/8.58 Y0 @ Y1))) => 68.70/8.58 (X2 @ Y0 @ Y2)))))))))))) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | (X2 @ '#sk3' @ '#sk4'))), 68.70/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl44])). 68.70/8.58 thf(zip_derived_cl69, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.58 ('#sk47' @ X2) @ Y0))) => 68.70/8.58 (X2 @ ('#sk47' @ X2) @ Y1))))))))) 68.70/8.58 | (X2 @ '#sk3' @ '#sk4') 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl55])). 68.70/8.58 thf(zip_derived_cl82, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((((X2 @ ('#sk74' @ X2) @ Y0) & (X2 @ 68.70/8.58 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 68.70/8.58 (X2 @ ('#sk47' @ X2) @ Y0)))))) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | (X2 @ '#sk3' @ '#sk4'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl69])). 68.70/8.58 thf(zip_derived_cl97, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((((X2 @ ('#sk74' @ X2) @ ('#sk113' @ X2)) & (X2 @ 68.70/8.58 ('#sk47' @ X2) @ ('#sk74' @ X2)))) => 68.70/8.58 (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)))) 68.70/8.58 | (X2 @ '#sk3' @ '#sk4') 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl82])). 68.70/8.58 thf(zip_derived_cl107, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (X2 @ ('#sk47' @ X2) @ ('#sk113' @ X2)) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | (X2 @ '#sk3' @ '#sk4'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl97])). 68.70/8.58 thf(zip_derived_cl118, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( ('#form223' @ X2) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))), 68.70/8.58 define([status(thm)])). 68.70/8.58 thf(zip_derived_cl213, plain, 68.70/8.58 ((~ ('#form223' @ '#sk5') 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk5' @ Y1 @ Y2) & 68.70/8.58 ('#sk5' @ Y0 @ Y1))) => 68.70/8.58 ('#sk5' @ Y0 @ Y2)))))))))))))), 68.70/8.58 inference('renaming', [status(thm)], 68.70/8.58 [zip_derived_cl212, zip_derived_cl118])). 68.70/8.58 thf(zip_derived_cl214, plain, 68.70/8.58 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 68.70/8.58 ('#sk47' @ '#sk5') @ Y0))) => 68.70/8.58 ('#sk5' @ ('#sk47' @ '#sk5') @ Y1))))))))) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ ('#form223' @ '#sk5'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl213])). 68.70/8.58 thf(zip_derived_cl215, plain, 68.70/8.58 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.58 ((((('#sk5' @ ('#sk74' @ '#sk5') @ Y0) & ('#sk5' @ 68.70/8.58 ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')))) => 68.70/8.58 ('#sk5' @ ('#sk47' @ '#sk5') @ Y0)))))) 68.70/8.58 | ~ ('#form223' @ '#sk5') 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl214])). 68.70/8.58 thf(zip_derived_cl216, plain, 68.70/8.58 ((~ ((((('#sk5' @ ('#sk74' @ '#sk5') @ ('#sk113' @ '#sk5')) & ('#sk5' @ 68.70/8.58 ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')))) => 68.70/8.58 ('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk113' @ '#sk5')))) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ ('#form223' @ '#sk5'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl215])). 68.70/8.58 thf(zip_derived_cl217, plain, 68.70/8.58 (( ((('#sk5' @ ('#sk74' @ '#sk5') @ ('#sk113' @ '#sk5')) & ('#sk5' @ 68.70/8.58 ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')))) 68.70/8.58 | ~ ('#form223' @ '#sk5') 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 68.70/8.58 thf(zip_derived_cl220, plain, 68.70/8.58 (( ('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk74' @ '#sk5')) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ ('#form223' @ '#sk5'))), 68.70/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 68.70/8.58 thf(zip_derived_cl218, plain, 68.70/8.58 ((~ ('#sk5' @ ('#sk47' @ '#sk5') @ ('#sk113' @ '#sk5')) 68.70/8.58 | ~ ('#form223' @ '#sk5') 68.70/8.58 | ~ ('#form11'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl216])). 68.70/8.58 thf(zip_derived_cl118, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( ('#form223' @ X2) 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 (X2 @ Y0 @ Y1))))))))))), 68.70/8.58 define([status(thm)])). 68.70/8.58 thf(zip_derived_cl119, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (((!!) @ (^[Y0 : a]: 68.70/8.58 ((((('#sk2' @ ('#sk224' @ X2) @ Y0) | ('#sk1' @ 68.70/8.58 ('#sk224' @ X2) @ Y0))) => 68.70/8.58 (X2 @ ('#sk224' @ X2) @ Y0)))))) 68.70/8.58 | ('#form223' @ X2))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl118])). 68.70/8.58 thf(zip_derived_cl135, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ ((((('#sk2' @ ('#sk224' @ X2) @ ('#sk301' @ X2)) | ('#sk1' @ 68.70/8.58 ('#sk224' @ X2) @ ('#sk301' @ X2)))) => 68.70/8.58 (X2 @ ('#sk224' @ X2) @ ('#sk301' @ X2)))) 68.70/8.58 | ('#form223' @ X2))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl119])). 68.70/8.58 thf(zip_derived_cl154, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( ((('#sk2' @ ('#sk224' @ X2) @ ('#sk301' @ X2)) | ('#sk1' @ 68.70/8.58 ('#sk224' @ X2) @ ('#sk301' @ X2)))) 68.70/8.58 | ('#form223' @ X2))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 68.70/8.58 thf(zip_derived_cl164, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 ( ('#sk2' @ ('#sk224' @ X2) @ ('#sk301' @ X2)) 68.70/8.58 | ('#sk1' @ ('#sk224' @ X2) @ ('#sk301' @ X2)) 68.70/8.58 | ('#form223' @ X2))), 68.70/8.58 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl154])). 68.70/8.58 thf(zip_derived_cl155, plain, 68.70/8.58 (![X2 : a > a > $o]: 68.70/8.58 (~ (X2 @ ('#sk224' @ X2) @ ('#sk301' @ X2)) | ('#form223' @ X2))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl135])). 68.70/8.58 thf(zip_derived_cl219, plain, 68.70/8.58 (( ('#sk5' @ ('#sk74' @ '#sk5') @ ('#sk113' @ '#sk5')) 68.70/8.58 | ~ ('#form11') 68.70/8.58 | ~ ('#form223' @ '#sk5'))), 68.70/8.58 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl217])). 68.70/8.58 thf(zip_derived_cl30, plain, 68.70/8.58 (( ('#form9') 68.70/8.58 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((((((!!) @ (^[Y2 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 (( 68.70/8.58 (!!) @ ( 68.70/8.58 ^[Y5 : a]: 68.70/8.58 (( 68.70/8.58 (( 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) & 68.70/8.58 (Y2 @ 68.70/8.58 Y4 @ Y5))) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y5)))))))))))) & 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 (( 68.70/8.58 ('#sk2' @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y4))))))))))) => 68.70/8.58 (Y2 @ Y0 @ Y1)))))) | 68.70/8.58 (((!!) @ (^[Y2 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 (( 68.70/8.58 (!!) @ ( 68.70/8.58 ^[Y5 : a]: 68.70/8.58 (( 68.70/8.58 (( 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) & 68.70/8.58 (Y2 @ 68.70/8.58 Y4 @ Y5))) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y5)))))))))))) & 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 (( 68.70/8.58 ('#sk1' @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y4))))))))))) => 68.70/8.58 (Y2 @ Y0 @ Y1)))))))) => 68.70/8.58 (((!!) @ (^[Y2 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 ( 68.70/8.58 ( 68.70/8.58 (( 68.70/8.58 ('#sk1' @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) | 68.70/8.58 ('#sk2' @ 68.70/8.58 Y3 @ Y4))) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y4))))))))) & 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 ( 68.70/8.58 ( 68.70/8.58 (!!) @ ( 68.70/8.58 ^[Y5 : a]: 68.70/8.58 (( 68.70/8.58 (( 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ 68.70/8.58 Y4) & 68.70/8.58 (Y2 @ 68.70/8.58 Y4 @ Y5))) => 68.70/8.58 (Y2 @ 68.70/8.58 Y3 @ Y5)))))))))))))) => 68.70/8.58 (Y2 @ Y0 @ Y1)))))))))))))))), 68.70/8.58 define([status(thm)])). 68.70/8.58 thf(zip_derived_cl31, plain, 68.70/8.58 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.58 (((((((!!) @ (^[Y1 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 ( 68.70/8.58 ( 68.70/8.58 (( 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ 68.70/8.58 Y3) & 68.70/8.58 (Y1 @ 68.70/8.58 Y3 @ Y4))) => 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ Y4)))))))))))) & 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 ((('#sk2' @ 68.70/8.58 Y2 @ Y3) => 68.70/8.58 (Y1 @ Y2 @ 68.70/8.58 Y3))))))))))) => 68.70/8.58 (Y1 @ '#sk10' @ Y0)))))) | 68.70/8.58 (((!!) @ (^[Y1 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 ( 68.70/8.58 ( 68.70/8.58 (( 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ 68.70/8.58 Y3) & 68.70/8.58 (Y1 @ 68.70/8.58 Y3 @ Y4))) => 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ Y4)))))))))))) & 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 ((('#sk1' @ 68.70/8.58 Y2 @ Y3) => 68.70/8.58 (Y1 @ Y2 @ 68.70/8.58 Y3))))))))))) => 68.70/8.58 (Y1 @ '#sk10' @ Y0)))))))) => 68.70/8.58 (((!!) @ (^[Y1 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 ((((('#sk1' @ 68.70/8.58 Y2 @ Y3) | 68.70/8.58 ('#sk2' @ 68.70/8.58 Y2 @ Y3))) => 68.70/8.58 (Y1 @ Y2 @ 68.70/8.58 Y3))))))))) & 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((!!) @ ( 68.70/8.58 ^[Y4 : a]: 68.70/8.58 (((( 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ 68.70/8.58 Y3) & 68.70/8.58 (Y1 @ 68.70/8.58 Y3 @ Y4))) => 68.70/8.58 (Y1 @ 68.70/8.58 Y2 @ Y4)))))))))))))) => 68.70/8.58 (Y1 @ '#sk10' @ Y0))))))))))) 68.70/8.58 | ('#form9'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl30])). 68.70/8.58 thf(zip_derived_cl42, plain, 68.70/8.58 ((~ (((((((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ 68.70/8.58 Y1 @ 68.70/8.58 Y2) & 68.70/8.58 (Y0 @ 68.70/8.58 Y2 @ Y3))) => 68.70/8.58 (Y0 @ Y1 @ 68.70/8.58 Y3)))))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((('#sk2' @ Y1 @ Y2) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.58 (Y0 @ '#sk10' @ '#sk12')))))) | 68.70/8.58 (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ 68.70/8.58 Y1 @ 68.70/8.58 Y2) & 68.70/8.58 (Y0 @ 68.70/8.58 Y2 @ Y3))) => 68.70/8.58 (Y0 @ Y1 @ 68.70/8.58 Y3)))))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((('#sk1' @ Y1 @ Y2) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.58 (Y0 @ '#sk10' @ '#sk12')))))))) => 68.70/8.58 (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk1' @ Y1 @ Y2) | 68.70/8.58 ('#sk2' @ Y1 @ Y2))) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ Y1 @ 68.70/8.58 Y2) & 68.70/8.58 (Y0 @ Y2 @ 68.70/8.58 Y3))) => 68.70/8.58 (Y0 @ Y1 @ 68.70/8.58 Y3)))))))))))))) => 68.70/8.58 (Y0 @ '#sk10' @ '#sk12')))))))) 68.70/8.58 | ('#form9'))), 68.70/8.58 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl31])). 68.70/8.58 thf(zip_derived_cl49, plain, 68.70/8.58 ((~ (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.58 (((((((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 ((((('#sk1' @ Y1 @ Y2) | 68.70/8.58 ('#sk2' @ Y1 @ Y2))) => 68.70/8.58 (Y0 @ Y1 @ Y2))))))))) & 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 (((!!) @ (^[Y2 : a]: 68.70/8.58 (((!!) @ (^[Y3 : a]: 68.70/8.58 (((((Y0 @ Y1 @ 68.70/8.58 Y2) & (Y0 @ 68.70/8.58 Y2 @ Y3))) => 68.70/8.58 (Y0 @ Y1 @ Y3)))))))))))))) => 68.70/8.58 (Y0 @ '#sk10' @ '#sk12')))))) 68.70/8.58 | ('#form9'))), 68.70/8.58 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 68.70/8.58 thf(zip_derived_cl67, plain, 68.70/8.58 ((~ (((((((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.58 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ 68.70/8.58 Y1))) => 68.70/8.58 ('#sk30' @ Y0 @ Y1))))))))) & 68.70/8.58 (((!!) @ (^[Y0 : a]: 68.70/8.58 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))))) => 68.70/8.59 ('#sk30' @ '#sk10' @ '#sk12'))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl49])). 68.70/8.59 thf(zip_derived_cl80, plain, 68.70/8.59 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 68.70/8.59 thf(zip_derived_cl79, plain, 68.70/8.59 (( (((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 68.70/8.59 ('#sk30' @ Y0 @ Y1))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 68.70/8.59 thf(zip_derived_cl94, plain, 68.70/8.59 (( (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk1' @ Y0 @ Y1) | ('#sk2' @ Y0 @ Y1))) => 68.70/8.59 ('#sk30' @ Y0 @ Y1))))))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 68.70/8.59 thf(zip_derived_cl103, plain, 68.70/8.59 (![X2 : a]: 68.70/8.59 ( (((!!) @ (^[Y0 : a]: 68.70/8.59 ((((('#sk1' @ X2 @ Y0) | ('#sk2' @ X2 @ Y0))) => 68.70/8.59 ('#sk30' @ X2 @ Y0)))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl94])). 68.70/8.59 thf(zip_derived_cl113, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 ( ((((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) => ('#sk30' @ X2 @ X4))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl103])). 68.70/8.59 thf(zip_derived_cl129, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 (~ ((('#sk1' @ X2 @ X4) | ('#sk2' @ X2 @ X4))) 68.70/8.59 | ('#sk30' @ X2 @ X4) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl113])). 68.70/8.59 thf(zip_derived_cl144, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 (~ ('#sk1' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 68.70/8.59 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl129])). 68.70/8.59 thf(zip_derived_cl48, plain, 68.70/8.59 (( (((((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk2' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))) | 68.70/8.59 (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl42])). 68.70/8.59 thf(zip_derived_cl63, plain, 68.70/8.59 (( (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk2' @ Y1 @ Y2) => (Y0 @ 68.70/8.59 Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))) 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl48])). 68.70/8.59 thf(zip_derived_cl73, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (((((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 68.70/8.59 (X2 @ '#sk10' @ '#sk12'))) 68.70/8.59 | ('#form9') 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ 68.70/8.59 Y1 @ Y2) & 68.70/8.59 (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ 68.70/8.59 Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 68.70/8.59 thf(zip_derived_cl86, plain, 68.70/8.59 ((~ ('#form91') 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))), 68.70/8.59 define([status(thm)])). 68.70/8.59 thf(zip_derived_cl87, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (((((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 68.70/8.59 (X2 @ '#sk10' @ '#sk12'))) 68.70/8.59 | ~ ('#form91'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl86])). 68.70/8.59 thf(zip_derived_cl102, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form91'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl87])). 68.70/8.59 thf(zip_derived_cl112, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))) 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))) 68.70/8.59 | ~ ('#form91') 68.70/8.59 | (X2 @ '#sk10' @ '#sk12'))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl102])). 68.70/8.59 thf(zip_derived_cl121, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( ('#form243' @ X2) 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))))), 68.70/8.59 define([status(thm)])). 68.70/8.59 thf(zip_derived_cl128, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ ('#form243' @ (^[Y0 : a,Y1 : a]: (X2 @ Y0 @ Y1))) 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form91') 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 68.70/8.59 inference('renaming', [status(thm)], 68.70/8.59 [zip_derived_cl112, zip_derived_cl121])). 68.70/8.59 thf(zip_derived_cl142, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ ('#form243' @ X2) 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form91') 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk1' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))), 68.70/8.59 inference('ho_norm', [status(thm)], [zip_derived_cl128])). 68.70/8.59 thf(zip_derived_cl143, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((!!) @ (^[Y0 : a]: 68.70/8.59 ((('#sk1' @ ('#sk343' @ X2) @ Y0) => (X2 @ 68.70/8.59 ('#sk343' @ X2) @ Y0)))))) 68.70/8.59 | ~ ('#form91') 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl142])). 68.70/8.59 thf(zip_derived_cl159, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ ((('#sk1' @ ('#sk343' @ X2) @ ('#sk442' @ X2)) => (X2 @ 68.70/8.59 ('#sk343' @ X2) @ ('#sk442' @ X2)))) 68.70/8.59 | ~ ('#form243' @ X2) 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form91'))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl143])). 68.70/8.59 thf(zip_derived_cl170, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (X2 @ ('#sk343' @ X2) @ ('#sk442' @ X2)) 68.70/8.59 | ~ ('#form91') 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 68.70/8.59 thf(zip_derived_cl9, plain, 68.70/8.59 ( (((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk5' @ Y0 @ Y1) & 68.70/8.59 ('#sk5' @ Y1 @ Y2))) => 68.70/8.59 ('#sk5' @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 68.70/8.59 ('#sk5' @ Y0 @ Y1)))))))))))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])). 68.70/8.59 thf(zip_derived_cl13, plain, 68.70/8.59 ( (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk2' @ Y0 @ Y1) | ('#sk1' @ Y0 @ Y1))) => 68.70/8.59 ('#sk5' @ Y0 @ Y1)))))))))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 68.70/8.59 thf(zip_derived_cl16, plain, 68.70/8.59 (![X2 : a]: 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 ((((('#sk2' @ X2 @ Y0) | ('#sk1' @ X2 @ Y0))) => 68.70/8.59 ('#sk5' @ X2 @ Y0))))))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl13])). 68.70/8.59 thf(zip_derived_cl19, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 ((((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) => ('#sk5' @ X2 @ X4)))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl16])). 68.70/8.59 thf(zip_derived_cl22, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 (~ ((('#sk2' @ X2 @ X4) | ('#sk1' @ X2 @ X4))) | ('#sk5' @ X2 @ X4))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl19])). 68.70/8.59 thf(zip_derived_cl27, plain, 68.70/8.59 (![X2 : a, X4 : a]: (~ ('#sk1' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 68.70/8.59 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 68.70/8.59 thf(zip_derived_cl26, plain, 68.70/8.59 (![X2 : a, X4 : a]: (~ ('#sk2' @ X2 @ X4) | ('#sk5' @ X2 @ X4))), 68.70/8.59 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl22])). 68.70/8.59 thf(zip_derived_cl12, plain, 68.70/8.59 ( (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk5' @ Y0 @ Y1) & ('#sk5' @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 ('#sk5' @ Y0 @ Y2))))))))))))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl9])). 68.70/8.59 thf(zip_derived_cl15, plain, 68.70/8.59 (![X2 : a]: 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk5' @ X2 @ Y0) & ('#sk5' @ Y0 @ Y1))) => 68.70/8.59 ('#sk5' @ X2 @ Y1)))))))))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl12])). 68.70/8.59 thf(zip_derived_cl18, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ Y0))) => 68.70/8.59 ('#sk5' @ X2 @ Y0))))))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl15])). 68.70/8.59 thf(zip_derived_cl21, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 ((((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) => ('#sk5' @ X2 @ X6)))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl18])). 68.70/8.59 thf(zip_derived_cl25, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 (~ ((('#sk5' @ X2 @ X4) & ('#sk5' @ X4 @ X6))) | ('#sk5' @ X2 @ X6))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])). 68.70/8.59 thf(zip_derived_cl33, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 (~ ('#sk5' @ X2 @ X4) | ~ ('#sk5' @ X4 @ X6) | ('#sk5' @ X2 @ X6))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl25])). 68.70/8.59 thf(zip_derived_cl169, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( ('#sk1' @ ('#sk343' @ X2) @ ('#sk442' @ X2)) 68.70/8.59 | ~ ('#form91') 68.70/8.59 | (X2 @ '#sk10' @ '#sk12') 68.70/8.59 | ~ ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl159])). 68.70/8.59 thf(zip_derived_cl73, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (((((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => (X2 @ Y0 @ Y1))))))))))) => 68.70/8.59 (X2 @ '#sk10' @ '#sk12'))) 68.70/8.59 | ('#form9') 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ 68.70/8.59 Y1 @ Y2) & 68.70/8.59 (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ 68.70/8.59 Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl63])). 68.70/8.59 thf(zip_derived_cl74, plain, 68.70/8.59 (( (((((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 68.70/8.59 Y1))))))))))) => 68.70/8.59 ('#sk30' @ '#sk10' @ '#sk12'))) 68.70/8.59 | ('#form9') 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))), 68.70/8.59 inference('triggered_bool_instantiation', [status(thm)], 68.70/8.59 [zip_derived_cl73])). 68.70/8.59 thf(zip_derived_cl86, plain, 68.70/8.59 ((~ ('#form91') 68.70/8.59 | (((!!) @ (^[Y0 : a > a > $o]: 68.70/8.59 (((((((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((!!) @ (^[Y3 : a]: 68.70/8.59 (((((Y0 @ Y1 @ 68.70/8.59 Y2) & (Y0 @ 68.70/8.59 Y2 @ Y3))) => 68.70/8.59 (Y0 @ Y1 @ Y3)))))))))))) & 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((('#sk1' @ Y1 @ Y2) => 68.70/8.59 (Y0 @ Y1 @ Y2))))))))))) => 68.70/8.59 (Y0 @ '#sk10' @ '#sk12')))))))), 68.70/8.59 define([status(thm)])). 68.70/8.59 thf(zip_derived_cl261, plain, 68.70/8.59 (( ('#form91') 68.70/8.59 | ('#form9') 68.70/8.59 | (((((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 68.70/8.59 Y1))))))))))) => 68.70/8.59 ('#sk30' @ '#sk10' @ '#sk12'))))), 68.70/8.59 inference('renaming', [status(thm)], [zip_derived_cl74, zip_derived_cl86])). 68.70/8.59 thf(zip_derived_cl262, plain, 68.70/8.59 ((~ (((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))) 68.70/8.59 | ('#sk30' @ '#sk10' @ '#sk12') 68.70/8.59 | ('#form9') 68.70/8.59 | ('#form91'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl261])). 68.70/8.59 thf(zip_derived_cl80, plain, 68.70/8.59 ((~ ('#sk30' @ '#sk10' @ '#sk12') | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl67])). 68.70/8.59 thf(zip_derived_cl263, plain, 68.70/8.59 (( ('#form91') 68.70/8.59 | ('#form9') 68.70/8.59 | ~ (((((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) & 68.70/8.59 (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ 68.70/8.59 Y1))))))))))))), 68.70/8.59 inference('clc', [status(thm)], [zip_derived_cl262, zip_derived_cl80])). 68.70/8.59 thf(zip_derived_cl264, plain, 68.70/8.59 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))) 68.70/8.59 | ('#form9') 68.70/8.59 | ('#form91'))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl263])). 68.70/8.59 thf(zip_derived_cl121, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( ('#form243' @ X2) 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))))), 68.70/8.59 define([status(thm)])). 68.70/8.59 thf(zip_derived_cl265, plain, 68.70/8.59 ((~ ('#form243' @ '#sk30') 68.70/8.59 | ('#form91') 68.70/8.59 | ('#form9') 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((('#sk2' @ Y0 @ Y1) => ('#sk30' @ Y0 @ Y1))))))))))), 68.70/8.59 inference('renaming', [status(thm)], 68.70/8.59 [zip_derived_cl264, zip_derived_cl121])). 68.70/8.59 thf(zip_derived_cl266, plain, 68.70/8.59 ((~ (((!!) @ (^[Y0 : a]: 68.70/8.59 ((('#sk2' @ ('#sk334' @ '#sk30') @ Y0) => ('#sk30' @ 68.70/8.59 ('#sk334' @ '#sk30') @ Y0)))))) 68.70/8.59 | ('#form9') 68.70/8.59 | ('#form91') 68.70/8.59 | ~ ('#form243' @ '#sk30'))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl265])). 68.70/8.59 thf(zip_derived_cl267, plain, 68.70/8.59 ((~ ((('#sk2' @ ('#sk334' @ '#sk30') @ ('#sk434' @ '#sk30')) => 68.70/8.59 ('#sk30' @ ('#sk334' @ '#sk30') @ ('#sk434' @ '#sk30')))) 68.70/8.59 | ~ ('#form243' @ '#sk30') 68.70/8.59 | ('#form91') 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl266])). 68.70/8.59 thf(zip_derived_cl269, plain, 68.70/8.59 ((~ ('#sk30' @ ('#sk334' @ '#sk30') @ ('#sk434' @ '#sk30')) 68.70/8.59 | ('#form9') 68.70/8.59 | ('#form91') 68.70/8.59 | ~ ('#form243' @ '#sk30'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl267])). 68.70/8.59 thf(zip_derived_cl268, plain, 68.70/8.59 (( ('#sk2' @ ('#sk334' @ '#sk30') @ ('#sk434' @ '#sk30')) 68.70/8.59 | ('#form9') 68.70/8.59 | ('#form91') 68.70/8.59 | ~ ('#form243' @ '#sk30'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl267])). 68.70/8.59 thf(zip_derived_cl145, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 (~ ('#sk2' @ X2 @ X4) | ('#form9') | ('#sk30' @ X2 @ X4))), 68.70/8.59 inference('lazy_cnf_or', [status(thm)], [zip_derived_cl129])). 68.70/8.59 thf(zip_derived_cl121, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( ('#form243' @ X2) 68.70/8.59 | ~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 (((((X2 @ Y0 @ Y1) & (X2 @ 68.70/8.59 Y1 @ Y2))) => 68.70/8.59 (X2 @ Y0 @ Y2)))))))))))))), 68.70/8.59 define([status(thm)])). 68.70/8.59 thf(zip_derived_cl122, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((((X2 @ ('#sk100' @ X2) @ Y0) & (X2 @ 68.70/8.59 Y0 @ Y1))) => 68.70/8.59 (X2 @ ('#sk100' @ X2) @ Y1))))))))) 68.70/8.59 | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl121])). 68.70/8.59 thf(zip_derived_cl138, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((!!) @ (^[Y0 : a]: 68.70/8.59 (((((X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) & (X2 @ 68.70/8.59 ('#sk149' @ X2) @ Y0))) => 68.70/8.59 (X2 @ ('#sk100' @ X2) @ Y0)))))) 68.70/8.59 | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl122])). 68.70/8.59 thf(zip_derived_cl157, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (((((X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) & (X2 @ 68.70/8.59 ('#sk149' @ X2) @ ('#sk206' @ X2)))) => 68.70/8.59 (X2 @ ('#sk100' @ X2) @ ('#sk206' @ X2)))) 68.70/8.59 | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl138])). 68.70/8.59 thf(zip_derived_cl165, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (((X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) & (X2 @ 68.70/8.59 ('#sk149' @ X2) @ ('#sk206' @ X2)))) 68.70/8.59 | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])). 68.70/8.59 thf(zip_derived_cl175, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (X2 @ ('#sk100' @ X2) @ ('#sk149' @ X2)) | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl165])). 68.70/8.59 thf(zip_derived_cl166, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 (~ (X2 @ ('#sk100' @ X2) @ ('#sk206' @ X2)) | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl157])). 68.70/8.59 thf(zip_derived_cl176, plain, 68.70/8.59 (![X2 : a > a > $o]: 68.70/8.59 ( (X2 @ ('#sk149' @ X2) @ ('#sk206' @ X2)) | ('#form243' @ X2))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl165])). 68.70/8.59 thf(zip_derived_cl95, plain, 68.70/8.59 (( (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 (((!!) @ (^[Y2 : a]: 68.70/8.59 ((((('#sk30' @ Y0 @ Y1) & 68.70/8.59 ('#sk30' @ Y1 @ Y2))) => 68.70/8.59 ('#sk30' @ Y0 @ Y2)))))))))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl79])). 68.70/8.59 thf(zip_derived_cl104, plain, 68.70/8.59 (![X2 : a]: 68.70/8.59 ( (((!!) @ (^[Y0 : a]: 68.70/8.59 (((!!) @ (^[Y1 : a]: 68.70/8.59 ((((('#sk30' @ X2 @ Y0) & ('#sk30' @ Y0 @ 68.70/8.59 Y1))) => 68.70/8.59 ('#sk30' @ X2 @ Y1))))))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl95])). 68.70/8.59 thf(zip_derived_cl114, plain, 68.70/8.59 (![X2 : a, X4 : a]: 68.70/8.59 ( (((!!) @ (^[Y0 : a]: 68.70/8.59 ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ Y0))) => 68.70/8.59 ('#sk30' @ X2 @ Y0)))))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl104])). 68.70/8.59 thf(zip_derived_cl130, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 ( ((((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) => ('#sk30' @ X2 @ 68.70/8.59 X6))) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl114])). 68.70/8.59 thf(zip_derived_cl146, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 (~ ((('#sk30' @ X2 @ X4) & ('#sk30' @ X4 @ X6))) 68.70/8.59 | ('#sk30' @ X2 @ X6) 68.70/8.59 | ('#form9'))), 68.70/8.59 inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl130])). 68.70/8.59 thf(zip_derived_cl160, plain, 68.70/8.59 (![X2 : a, X4 : a, X6 : a]: 68.70/8.59 (~ ('#sk30' @ X2 @ X4) 68.70/8.59 | ~ ('#sk30' @ X4 @ X6) 68.70/8.59 | ('#form9') 68.70/8.59 | ('#sk30' @ X2 @ X6))), 68.70/8.59 inference('lazy_cnf_and', [status(thm)], [zip_derived_cl146])). 68.70/8.59 thf(zip_derived_cl8737, plain, ($false), 68.70/8.59 inference('eprover', [status(thm)], 68.70/8.59 [zip_derived_cl62, zip_derived_cl281, zip_derived_cl297, 68.70/8.59 zip_derived_cl177, zip_derived_cl139, zip_derived_cl125, 68.70/8.59 zip_derived_cl174, zip_derived_cl124, zip_derived_cl220, 68.70/8.59 zip_derived_cl218, zip_derived_cl164, zip_derived_cl155, 68.70/8.59 zip_derived_cl219, zip_derived_cl80, zip_derived_cl144, 68.70/8.59 zip_derived_cl170, zip_derived_cl27, zip_derived_cl26, 68.70/8.59 zip_derived_cl33, zip_derived_cl169, zip_derived_cl269, 68.70/8.59 zip_derived_cl268, zip_derived_cl145, zip_derived_cl175, 68.70/8.59 zip_derived_cl166, zip_derived_cl176, zip_derived_cl160])). 68.70/8.59 68.70/8.59 % SZS output end Refutation 68.70/8.59 68.70/8.59 68.70/8.59 % Terminating... 69.07/8.66 % Runner terminated. 69.07/8.68 % Zipperpin 1.5 exiting 69.07/8.68 EOF